Via a reader, interested in this issue:
Jessica Blanchard:
When Seattle elementaryschoolers open their math textbooks this fall, they'll all be on the same page  literally.In an attempt to boost stagnant test scores, elementary teachers will start using the same math textbooks and materials and covering lessons at the same time as their colleagues at other Seattle elementary schools, the School Board decided Wednesday.
"It's clear to me that the math adoption is long overdue, and Seattle desperately needs a consistent and balanced approach," board member Brita ButlerWall said.
Lessons will now be taught using the conceptual "Everyday Math" books, which help students discover algorithms on their own and explore multiple ways to solve problems, and the more traditional "Singapore Math" books, which help hone students' basic computation skills through repetition and problem solving. Teachers will follow the district's guidelines for the order the lessons would be taught.
Click to view MMSD Accounting Details.  A number of questions have been raised over the past few years regarding the Madison School District's math curriculum:
The Task force includes David Griffeath, who, according to this document, provided by a reader, has been a paid math consultant for the Madison School District. 
Related: Take the Math Homework Survey  via Joanne
Gov. Chris Gregoire on Tuesday delayed until 2013 a requirement that students pass the math and science portions of a high stakes exam in order to graduate from high school.She also liberally applied her veto pen to four large sections of the bill overhauling the Washington Assessment of Student Learning exam.
Gregoire said she would have preferred to delay the math and science WASL graduation requirement only until 2012.
She eliminated the sections of the WASLoverhaul bill that would have established endofcourse exams, regional appeals, a special exemption for students learning English as a second language and the clause declaring an emergency.
According to an independent survey commissioned by Microsoft Corp., 77 percent of teachers and 73 percent of parents claim math and science are the most difficult homework subjects for students, yet only 36 percent of parents feel capable to help their children. While parents and teachers struggle to find the time or knowledge to provide their kids with adequate assistance in math and science, students can grow frustrated by the lack of resources and the amount time it may take to find relevant guidance in these difficult subjects. To address these issues, Microsoft has developed a lowcost, comprehensive resource for middle school, high school and entrylevel college students.Related, maybe? Karen Arenson:Today Microsoft releases Microsoft® Math 3.0, a new software solution designed to help students complete their math and science homework more quickly and easily while teaching important fundamental concepts. Microsoft Math 3.0 features an extensive collection of capabilities to help students tackle complicated problems in prealgebra, algebra, trigonometry, calculus, physics and chemistry, and puts them all in one convenient place on the home PC. Similar to a hired tutor, Microsoft Math 3.0 is designed to help deepen students' overall understanding of these subjects by invoking a fullfeatured graphing calculator and stepbystep instructions on how to solve difficult problems.
Only onequarter of high school students who take a full set of collegepreparatory courses — four years of English and three each of mathematics, science and social studies — are well prepared for college, according to a new study of last year’s high school graduates released today by ACT, the Iowa testing organization.ACT Report: Rigor at Risk: 350K PDFThe report analyzed approximately 1.2 million students who took the ACT college admissions test and graduated from high school last June. The study predicted whether the students had a good chance of scoring C or better in introductory college courses, based on their test scores and the success rates of past test takers.
The study concluded that only 26 percent were ready for collegelevel work in all four core areas, while 19 percent were not adequately prepared in any of them.
Late last month, over 400 high school math teachers and education professors gathered in Brooklyn for a threeday conference, titled “Creating Balance in an Unjust World: Math Education and Social Justice.” Prominently displayed on the official program’s first page was a passage from Paulo Freire, the Brazilian Marxist educator and icon of the teachingforsocialjustice movement: “There is no such thing as a neutral education process. Education either functions as an instrument which is used to . . . bring about conformity or it becomes the practice of freedom, the means by which men and women deal critically and creatively with reality and discover how to participate in the transformation of our world.”The conference’s organizers left nothing to the imagination about their leftist agenda. At many of the conference’s 28 workshops, math teachers proudly demonstrated how they used classroom projects to train students in seeing social problems from a radical anticapitalist perspective. At a plenary session, Professor Marilyn Frankenstein of the University of Massachusetts’ math education department proclaimed that elementary school teachers should not use traditional math lessons, in which students calculate, say, the cost of food. Rather, the teachers should make clear that in a truly “just society,” food would “be as free as breathing the air.”
New York City’s Department of Education insists that the radical math conference was perfectly appropriate. In fact, as I recently learned, the whole affair got rolling with the assistance of the DOE, which gave a financial grant to the conference’s principal organizer, Jonathan Osler. Osler is a math teacher at El Puente Academy, a small “socialjustice” high school in Brooklyn. In 2005, he and two math teachers from other schools applied for the DOE’s Zone Teacher Inquiry Grants Program. Their application proposed “the creation of a system to bring together NYC math teachers to share ideas, curriculum, resources, and experiences integrating issues of social justice into math classes.” Some of the social justice issues that math classes could explore: “Checkcashing locations ripping off poor people. H&R Block and Jackson Hewitt ripping off poor people. Foreclosure agencies ripping off poor people. Issues of joblessness, homelessness, incarceration, lack of funding for education, excessive funding for war. . . . The list goes on and on.”
Via a reader's email; Solomon Friedberg:
Mathematics is crucial in the modern world. It is the foundation of modern science and engineering, and the prerequisite to any number of careers. Children’s formal learning of mathematics occurs throughout elementary school, and their success or failure at this level will have an impact on the entire rest of their lives.Thus it is vital that elementary teachers be wellprepared to teach mathematics.
You would think that all elementary teachers know elementary math. After all, they are college graduates. Unfortunately, you’d be wrong. For example, mathematics educator Liping Ma, a senior scholar at the Carnegie Foundation for the Advancement of Teaching, reports that only 43 percent of a group of “above average” U.S. elementary teachers chosen for their interest in math could carry out a simple calculation involving division of fractions.
Moreover, teaching elementary school math requires more than simply knowing how to do elementary school math. Teachers must be able to present mathematics as a coherent body of knowledge rather than a bunch of arbitrary rules, to recognize and address a range of misconceptions, to encourage mathematical thinking and develop student selfconfidence. They need to know elementary math well enough to teach it in all its subtlety.
In Ma’s study, only 4 percent of U.S. teachers were able to write a story problem that corresponded to the division of fractions problem. If that’s the case, how can they teach this subject well?
This is not the fault of current teachers. The present system in Massachusetts allows prospective teachers with inadequate knowledge of mathematics to pass the general curriculum requirement for teacher licensure. Passing is determined by the cumulative score on an exam in which mathematics is only one of five subject areas.Solomon Friedberg is a professor of mathematics at Boston College, and a member of the Commonwealth’s MathScience Partnership Steering Committee. He is teaching a course in mathematics for elementary teachers at BC. Clusty search.Moreover, the curricula of teacherpreparation programs reflects this testing, and frequently includes very little mathematics. The present situation ignores a great deal of research linking teacher knowledge and student achievement in mathematics, and it ignores the reality of what is necessary if our children are to succeed in their schools and careers.
Proposed remedies are before the Board of Education. The board recently mandated a separate math subtest of the general curriculum test beginning in 2008, and this month it will vote on additional math course requirements. These changes are long overdue, and adopting them is simple common sense. Teachers must know math if they are to communicate it to our children.
The new regulations are accompanied by guidelines for the scope and depth of knowledge required in math. These guidelines are consistent with an emerging consensus of mathematicians and mathematics educators concerning math knowledge related to the elementary curriculum. (Full disclosure: I provided feedback on a draft of these guidelines.) Programs preparing teachers will be required to offer multisemester sequences in math for elementary teachers. Such courses can be rich intellectual experiences, developing the kind of knowledge that we know makes a difference and enabling the next generation of elementary teachers to enter classrooms genuinely prepared.
In today’s quantitative society, the ability to teach math is just as necessary as the ability to teach reading for prospective elementary school teachers, and we should design our license requirements with this in mind.
There are many reasons parents might be interested in their children's math program(s), including this discussion of math scores. Math Forum audio / video.KitchenTableMath and Text Savvy aren’t happy with the Education Department’s advice to parents on teaching children math:
Try to be aware of how your child is being taught math, and don’t teach strategies and shortcuts that conflict with the approach the teacher is using.
From Diana Kasbaum, Mathematics Consultant & School Improvement Consultant, Title I and School Support Team, WI Department of Public Instruction
This is a reminder that the WI Mathematics Council's Annual Conference (May 24) is fast approaching and will provide valuable opportunities to schools and districts using Title I funding for mathematics. As noted below, the Wednesday preconference focus is 'Meeting the Needs of Diverse Learners' and will focus on ELL, Special Education and Gifted & Talented. The information will be valuable to those who work with Title I students. There are also keynote and sectional presentations about interventions, struggling learners, special education and Title I at the conference on Thursday and Friday. Additional information can also be found at: http://wismath.org/GL.html. If you have further questions about Title I mathematics, please feel free to contact me: Diana.Kasbaum@dpi.state.wi.us.
The Madison School District's Math Task Force was introduced to the School Board last night. Watch the video or listen to the mp3 audio.
Background Links:
UPDATE: A reader emailed this:
I noticed that there were 10 student books in the 6th grade pile for CMP. That was surprising since there are only 8 in publication. Then I looked at the teacher editions and noticed there were 10 as well. There are two copies of both How Likely is It? and Covering and Surrounding.The statement, "A quick look at the size of the Connected Math textbooks compared to the equivalent Singapore Math course materials illustrates the publisher and author interests in selling these large volumes irrespective of curriculum quality and rigor (not to mention the much larger potential for errors or the lost trees....)" is following the picture in one of the discussions. Taking a look at the Singapore Math website It appears that in addition to the 2 textbooks pictured and student workbooks pictured, there are Intensive Practice books, Extra Practice Books, and Challenging Word Problems books, as well as other resources. Also, the white book on the bottom of the pile appears to be an answer key. There are also teacher guides for 6A and 6B that are not in the picture.
I'm not suggesting the statement above is false, I would just like to point out that the picture being used is not an accurate comparison. I hope you find this information valuable.
According to Arlene Silveira, the superintendent named the following members of a math task force:
Merle Price (cochair): an adjunct faculty member in education policy at Cal State University, Northridge. A former high school principal and deputy superintendendt for Los Angeles Unifed School District.Jim Lewis (cochair): professor of mathematics at University of Nebraska, Lincoln. Was department for 15 years and has numerous NSF grants, including funding to improve mathematics education.
Neither cochair has been directly involved in NCTMbased curricula implementation, in the interest of impartiality.
Other members:
Norman Webb, mathematics educator and evaluator
Martha Alibali, cognitive scientist
David Griffeath, mathematician
Eric Knuth, math education researcher
Mitchell Nathan, cognitive scientist
Ken Zeichner, university teacher education expert
A K12 teacher and a parent are still to be named.
Arlene added:
No MMSD employee is on the task force, in the interest of impartiality. Lisa Wachtel and Brian S. will serve as point people for the task force if information or data is needed for the district.The Board will be responsible for setting the direction of the task force and making decisions on "branch points" in the process. The community will be involved.
If one could make a case against the perpetrators of reform math—complete with arrests and jail time—showing that such programs are a form of child abuse, the math wars would cease in a matter of days. As it is, however, reasoned arguments from those who oppose the reform programs haven’t seemed to carry much weight, as the programs seem to proliferate in school after school across the U.S. And in a recent Education Week column, Mr. T.C. O’Brien seems quite content to skewer those who criticize the reform programs, resorting at times to borderline namecalling, and laying blame in large part on mathematicians. It seems that mathematicians’ call for math to be in math textbooks and that such math be is an artifact of purism and backwards thinking.More on GarelickOrdinarily I would ignore such a diatribe. But I believe there have been too few rebuttals to this type of editorial which Education Week seems only too happy to publish. Take for example this statement: “The National Mathematics Advisory Panel, established by the Bush administration in April of last year, has been meeting to discuss the improvement of achievement in mathematics in the schools. A good portion of its members have no experience in mathematics, no experience teaching children, or both.”
Shirley Dang
CONTRA COSTA TIMES
Amid the whir of an overhead projector, Concord High School biology teacher Ellen Fasman sketched out the long, chubby legs of an Xshaped chromosome with her erasable marker.
"What do you remember from seventh grade about mitosis?" she asked the class.
Her question on cell division met with blank stares. From underneath his baseball cap in the back of the room, sophomore Vincent Thomas muttered in confusion.
"Wait, I don't get this," Thomas said. "We learned this in seventh grade?"
Even in her college prep biology class, students come less and less prepared each year, Fasman said.
"They're every bit as bright as they've ever been," said Fasman, who has taught for 16 years. However, they increasingly come hampered by smaller vocabularies, lacking knowledge of basic cell biology and unable to deal with fractions, she said.
"Their math skills are rather poor," Fasman said. "When we do the metric system at the beginning of the year, it's a killer for them. When we get into genetics, sometimes it's hard for them, understanding ratios."
American students  particularly those in California  come up short in math and science.
Experts say the trend toward early algebra is driven by more rigorous teaching and a commitment to providing greater access to a course that provides a crucial foundation for further study in math and science. Algebra, they say, opens doors. That can be especially important at schools such as Gunston Middle, where about half of the students are economically disadvantaged."We work to identify and support students so that they can move ahead as they are successful, and we sometimes make moves midyear," Allen said. "Many kids move ahead in elementary school, but many of our students make the leap in sixth or seventh grade."
Some skeptics worry that kids are being rushed and the math curriculum is being watered down.
Via a reader looking at this issue: Stephanie Banchero, Darnell Little and Diane Rado:
Illinois elementary school pupils passed the newly revamped state achievement exams at record rates last year, but critics suggest it was more the result of changes to the tests than real progress by pupils.Kevin Carey criticized Wisconsin's "Statistical Manipulation of No Child Left Behind Standards". The Fordham Foundation and Amy Hetzner have also taken a look at this issue.
State and local educators attribute the improvement to smarter pupils and teachers' laserlike focus on the state learning standards—the detailed list of what pupils should know at each grade level. They also say that the more childfriendly exams, which included color and better graphics, helped pupils.But testing experts and critics suggest that the unprecedented growth is more likely the result of changes to the exams.
Most notably, the state dramatically lowered the passing bar on the 8thgrade math test. As a result—after hovering at about 50 percent for five years—the pass rate shot up to 78 percent last year.
While the number of test questions remained generally the same, the number that counted on pupil scores dropped significantly.
The writing of textbooks and making them freely available on the web is an idea whose time has arrived. Most college mathematics textbooks attempt to be all things to all people and, as a result, are much too big and expensive. This perhaps made some sense when these books were rather expensive to produce and distributebut this time has passed.A few years ago when I first posted a list of mathematics textbooks freely available on line, there existed only a handful of such books. Now there are many. The list here has grown and grown and is perhaps in serious need of some kind of organization into topics. There are also now many other sites at which there are links to online mathematics books and lecture notes. This site is far from comprehensive and I have considered abandoning it. Many people, however, still seem to find it useful, and so I shall continue to maintain it for a while.
Milwakee JournalSentinel Editorial:
Too many grads of the Milwaukee Public Schools wind up in remedial classes in math when they pursue college. Key educational leaders in the city have come up with a proven plan to reverse this alarming trend  a plan Gov. Jim Doyle has proposed to finance with $15 million in state money as part of his $80 million financial package to help Milwaukee over two years.The "Math Coach" model mentioned by the JS is also under discussion in Madison.Raising math achievement in the state's sole big city is all the more reason to support that package. Math proficiency among workers can attract good jobs to Milwaukee. And the better the city does economically, the better the state does.
I believe that the school board voted to move forward on the superintendent's recommendation to form a math task force. The board asked the administration to:
Initiate and complete a comprehensive, independent and neutral review and assessment of the District's K12 math curriculum.
· The review and assessment shall be undertaken by a task force whose members are appointed by the Superintendent and approved by the BOE. Members of the task force shall have math and math education expertise and represent a variety of perspectives regarding math education.More details of the superintendent's plans are here.· The task force shall prepare and present to the BOE a preliminary outline of the review and assessment to be undertaken by the task force. The outline shall, at a minimum, include: (1) analysis of math achievement data for MMSD K12 students, including analysis of all math subtests scores disaggregated by student characteristics and schools; (2) analysis of performance expectations for MMSD K12 students; (3) an overview of math curricula, including MMSD's math curriculum; (4) a discussion of how to improve MMSD student achievement; and (5) recommendations on measures to evaluate the effectiveness of MMSD's math curriculum. The task force is to present the preliminary outline and a timeline to the BOE for comment and approval.
· The task force is to prepare a written draft of the review and assessment, consistent with the approved preliminary outline. The draft is to be presented to the BOE for review and comment.
· The task force is to prepare the final report on the review and assessment.
From a reader involved in these issues, by Kerry Hill: Demystifying math: UWMadison scholars maintain focus on effective teaching, learning
Tuesday, January 30, 2007  By Kerry HillNew generation of Math Ed
Many people still see mathematics as a difficult subject that only a select group of students with special abilities can master. Learning math, they believe, consists of memorizing facts and mastering the application of complicated concepts and procedures.
“That’s simply not true,” says Thomas Carpenter, who has plenty of research to justify his succinct rebuttal.
A pioneering cohort of education researchers at UWMadison – led by Carpenter, Thomas Romberg, and Elizabeth Fennema, all emeriti professors in the Department of Curriculum and Instruction – have shown, for instance, that children of all abilities enter school with an informal base of mathematical knowledge that enables them to learn more substantive material than traditionally taught.
For more than 30 years, these researchers have put the learning of mathematics under the microscope in search of ways to improve teaching and student understanding. They’ve found, for instance, that math instruction can be strengthened by tapping into children’s informal knowledge, by teaching them to use the same practices as mathematicians, and by engaging them in realworld problemsolving instead of rote drills on abstract skills.By making math more accessible to students of all ages and abilities, they hope that more people will recognize mathematics as they do – as a language for thought.
Having established a solid foundation, the trailblazing cohort led by Carpenter, Romberg, and Fennema in recent years has been passing the torch at UWMadison to a new generation of scholars.
“The Mathematics Education area is in good hands,” says Eric Knuth, associate professor in the Department of Curriculum and Instruction, who leads a group that includes three assistant professors – Amy Ellis, Victoria Hand, and Edd Taylor. Adapting a phrase used by Sir Isaac Newton, Knuth adds, “We are continuing on the shoulders of giants.”
Like those giants, all four are engaged in research aimed at adding to the body of knowledge of how diverse populations of students learn and understand mathematics. Likewise, they are dedicated to equipping current and future teachers with the best practices, based on the latest knowledge, for supporting all students in their development of mathematical understanding and reasoning.
The path of giants
Tom Romberg describes mathematics as “a human activity involving the ability to represent quantitative and spatial relationships in a broad range of situations, express those relations using the language of mathematics, and use various techniques to carry out numerical procedures.” While humans have used mathematics for centuries to help make sense of the world, he explains, research on the teaching and learning of math is a relatively young discipline.
Romberg is widely recognized for playing an instrumental role in creating the mathematics education research community. Since the late 1960s, he has held numerous leadership posts, including the chairmanships of the Research Committee for the National Council of Teachers of Mathematics (NCTM), the Special Interest Group in Mathematics Education for the American Educational Research Association, and the North American branch of the International Group for the Psychology of Mathematics Education.
In the 1990s, he chaired the NCTM committee that produced the mathematics curriculum and assessment standards, marking the start of the standards movement in education. He notes, “These documents have had considerable impact throughout the world.”
While the accomplishments to date have been substantial, Romberg and his colleagues acknowledge that plenty of work remains. “While all instructional programs have a goal of teaching mathematics so that students ‘understand,’ there has been little evidence that the goal has been reached,” he says.
With evident pride, Romberg and Tom Carpenter describe the contributions of mathematics education research at UWMadison.
“As a consequence of our program of research for over 30 years, we have developed a workable conception of how to characterize ‘student understanding’ and some ‘powerful practices’ that lead to such understanding,” Romberg explains. “The impact of these conceptions is reflected in our most recent work on teaching early algebra, the development of a middleschool curriculum (Mathematics in Context), and the creation of a classroom assessment system.”
“We have been instrumental in bringing together research on the development of students’ mathematical thinking and the research on classroom interactions and classroom processes,” adds Carpenter, whose credits include serving as editor of NCTM’s Journal for Research in Mathematics Education, the leading journal in the field. He also has been honored for his research publications by the NCTM and the American Educational Research Association.
“This has been a major development in research during the last 15 years,” he says, “and our faculty members have played major roles both in articulating the need and conceptual framework for the integration and in the specific research that was at the forefront of the changes.”
Carpenter also points to his collaboration with Fennema – who is especially known for her research on gender differences in learning mathematics – and others in the development of Cognitively Guided Instruction, a highly regarded professional development program. CGI prepares elementary school teachers to recognize and build on their students’ informal mathematical knowledge by providing a framework that teachers can use in making their own instructional decisions.
“I would consider the remarkable accomplishments of teachers I have worked with in CGI as one of the most significant and satisfying aspects of my career,” says Carpenter. “Elizabeth and I clearly cannot take credit for all they have accomplished, but my relations with them and whatever I contributed to them has been exceptionally rewarding.”
In her CGI research of children in grades 13, Fennema noted gender differences in the strategies boys and girls used to solve problems, although not in the results. Girls tended to use more concrete strategies like modeling and counting, while boys used more abstract strategies. Fennema says this study revealed that gender differences emerged earlier and were more complex than previously recognized.
Both Romberg and Carpenter have directed the National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA), a decadelong (19952004), federally funded initiative based at the Wisconsin Center for Education Research (WCER). NCISLA involved researchers at six institutions collaborating with K12 teachers to advance effective reform of mathematics and science.
The researchers found, for example, that children are capable of learning more complex ideas at earlier ages than traditionally thought, that teachers need more substantive professional development about student thinking and subject matter, and that standardized tests do not adequately assess students’ longterm growth of knowledge nor depth of understanding.
Carpenter, Romberg, and other NCISLA staff summarized the center’s work in Understanding Mathematics and Science Matters (Mahwah, N.J.: Lawrence Erlbaum, 2005), and created a multimedia product, Powerful Practices in Mathematics and Science (Madison, Wis.: NCISLA, 2004) for use by practitioners.
Beyond the research findings and publications, the Mathematics Education program can measure its enduring influence in terms of people. “One of our most significant contributions has been the outstanding graduates of our program who have made important contributions to mathematics education,” Carpenter notes.
Since 1980, UWMadison has conferred 84 Ph.D.’s in mathematics education and has graduates on the faculties of many universities, including major state universities in California, Georgia, Texas, Illinois, Colorado, Arizona, Missouri, Delaware, Indiana, Pennsylvania, and Minnesota.
New faces, same focus
Effective mathematics instruction, explains Eric Knuth, involves three key components: understanding how children learn, preparing teachers who can tap into and build upon that knowledge, and having a curriculum that supports these efforts. Like the pioneers who preceded them, Knuth and his mathematics education colleagues are engaged in all three parts.
Like Carpenter and others, Knuth and Amy Ellis – who joined the faculty in 1999 and 2004, respectively – are interested in promoting the development of algebraic reasoning. Math researchers describe algebra – which introduces students to the use of symbolic representations – as the gatekeeper between the concrete calculations of arithmetic and higher levels of mathematics.
“A lack of success in algebra means losing opportunities for advanced studies,” Knuth explains. Ellis notes that algebra – which involves “the study of structures and systems generalized beyond specific computations and relations” – plays a vital role in access to college and careers in the sciences and engineering, which are associated with higher earning power.
They regard the development of algebraic reasoning as far too important to wait until eighth or ninth grade, when many students first encounter algebra. The seeds of algebraic reasoning need to be planted and nurtured in the elementary and middle school grades, they say.
“We want students to move beyond solving one problem,” Ellis says.
In studies funded by the National Science Foundation (NSF), Knuth and Ellis are looking at the development of key practices used by mathematicians and scientists –generalization, modeling, and proof/justification – that are often not emphasized by traditional instruction.
Algebra marks the first time that students are encouraged to generalize patterns, relations, and functions, says Ellis, adding “it’s fairly common for them to struggle with this.”
Ellis, whose work on generalization is funded by a threeyear NSF Research on Learning and Education (RoLE) grant, describes generalization as “a sophisticated mathematical activity that involves extending the range of reasoning beyond one specific problem.”
She has found that the development of the abilities to make generalizations and to construct arguments to justify mathematical claims seem to go hand in hand. She also has seen that grounding abstract lessons in measurable situations enhances students’ abilities to generalize.
In a fiveyear, longitudinal study funded by an NSF Career grant, Knuth has been examining how middle school students acquire and develop their understanding of what constitutes evidence and justification and how such understandings can be refined and extended. Traditionally, students first encounter – and struggle with – justification and proofs in high school geometry.
Knuth and Ellis also have been working with Charles Kalish, professor of educational psychology, to study relationships between student reasoning inside and outside of math. Understanding how children develop their reasoning abilities, especially those related to mathematics, can lead to instructional practices that support and foster their development.
Knuth and other UWMadison researchers have looked at such essential concepts as how elementary and middle school students understand the equal sign (=). They’ve found that, instead of recognizing that this symbol indicates a relationship – that one side is equivalent to the other – many children interpret it as something like “find the total,” “the answer comes next,” or “do something.”
NCISLA’s Powerful Practices video provides an example: Asked to fill in the blank on 8 + 4 = __ + 5, a fourthgrade class reaches a quick consensus that the correct answer is 12 (the sum of 8 and 4, ignoring the 5). Instead of correcting them, the teacher poses a series of number sentences that prompt the students to reevaluate their understanding of the equal sign and, ultimately, recognize that the correct answer to the original question is 7.
“We need to provide these kinds of experiences for kids much earlier,” Knuth says.
Edd Taylor and Vicki Hand – who joined the faculty in 2004 and 2005, respectively – address how issues of diversity and equity affect the teaching and learning of mathematics – an area where Elizabeth Fennema and other UWMadison faculty have made significant contributions. Both Taylor and Hand are involved with Diversity in Mathematics Education (DiME), the National Science Foundation Center for Learning and Teaching based at UWMadison and led by Tom Carpenter.
DiME – a consortium consisting of UWMadison, the University of California at Los Angeles, and the University of California at Berkeley, and school districts in Madison, Los Angeles, and Berkeley – is engaged in preparing a new generation of mathematics education scholars, creating professional development programs for teachers, and facilitating research on equity issues in mathematics education. More information about this project is available online at www.wcer.wisc.edu/dime/.
To the casual observer, the teaching and learning of mathematics might not seem like something that’s affected by ethnic and cultural diversity. Yet, Hand notes, “The notion that mathematics education is culturefree is problematic.”
The broader cultural and social context in which mathematics education takes place influences teachers’ perceptions of what productive and unproductive learning look like – for instance, what “counts” as a justification for students’ mathematical ideas. Hand says misalignments can occur when these cultural differences aren’t taken into account.
Hand has examined structural issues, such as the impact of tracking on opportunities for learning and students’ trajectories for higher education. She has noted that, for a variety of reasons, students of color more often end up in lowtracked classes. Often, these classrooms are less rigorous and put students on a trajectory that doesn’t prepare them for college, she explains. This perpetuates the achievement gap, and feeds the stereotypical view that students of color cannot do math. DiME researchers have found that tracking, even when eliminated as policy, might continue in practice.
Hand also considers broader issues – for example, how the inequitable distribution of highquality teachers across urban and suburban schools affects students’ opportunities to learn – as she investigates the interplay of structure and student backgrounds.
In his research, Taylor looks beyond the conventional methods used by the mathematics education community at the informal ways children think about math and solve problems outside of school. For instance, he has studied the mathematical development of children who spend money at corner stores in lowincome neighborhoods.
Taylor explains that students might solve problems more easily if linked to their everyday practices. For example, a traditional problem – e.g., 160 – 100 = __ – can be presented in a way that draws upon their understanding of money: “If you have $160 and I take away $100, how much do you have left?”
Making teachers more aware of cultural understanding and experiences outside of the classroom can help them create classroom environments that tap into how their students reason through mathematics, he explains. He plans to extend his investigation of math reasoning outside of school to religious organizations and such practices as tithing.
“We want teachers to honor more ways of doing math,” he says. “That’s just good mathematics.”
Influencing practice
“The research has to impact more than just the academic community,” says Knuth.
He and his colleagues underscored the importance of working directly with classroom teachers and connecting their research to the preparation of new teachers. The bridge between research and classroom instruction includes curriculum development and effective teacher education and professional development.
“The kind of research we do has us engaged in the local schools,” explains Ellis. In addition to advancing the research, this benefits the school community and helps teachers address current needs.
Knuth and Ellis design and run the preparation program for secondary mathematics teachers. As the program director, Knuth arranges field placements for preservice teachers, oversees the teaching assistants who teach methods courses and/or provide field placement supervision, and communicates with cooperating teachers. Taylor directs the preparation program for elementary mathematics teachers.
All four teach also undergraduate courses. Knuth has a class on teaching mathematics with technology. Hand, Taylor, and Ellis have taught various methods courses. Ellis helps run a seminar for preservice teachers in their final year, and Hand has cotaught a geometry content course within the Mathematics Department for preservice teachers.
“We all work with graduate students, as well,” Ellis adds. “There is a core sequence of four graduate courses that our mathed students take, and we all four teach these courses.”
And, all four work with inservice teachers.
Knuth has directed several professional development programs for secondary school mathematics teachers, ranging from a threeyear program designed to help high school teachers learn to teach with technology to multiyear programs designed to help middleschool teachers foster students’ mathematical reasoning.
He and Ellis ran a professional development program for preservice teachers and their cooperating teachers that was geared toward promoting the mentoring relationship. The program was funded by a small grant from the Calculus Consortium for Higher Education.
Through DiME, Hand and Taylor have been involved in creating professional development programs for local school districts to make teachers aware of the learning opportunities that they create. Hand conducts professional development for Madison teachers on equity in mathematics instruction.
Hand and UWMadison graduate students work with math teachers in the Madison Metropolitan School District in a group designed as a venue for sharing knowledge. She says that efforts by teachers to improve mathematics education for all students in the district have made significant progress over the last three years in narrowing the achievement gap.
The Mathematics Education group also has collaborated with the Mathematics Department to improve the preparation of middle school teachers in both content and teaching diverse populations.
“Teachers need to be given more respect for work they do in their field,” Hand says. “It’s not just about knowing mathematics, but about knowing how to teach mathematics to diverse learners.”
“The research influences how we teach the teachers,” Ellis says. “The teacher’s role is critical in shaping student reasoning.”
“In the end,” Knuth says, “we want all students to learn to meaningfully engage in mathematical practices and to develop increasingly more sophisticated ways of engaging in those practices.”
Mathematics education seems to be very subject to passing trends  surprisingly more so than many other subjects. The most notorious are, of course, the rise of New Math in the 60s and 70s, and the corresponding backlash against it in the late 70s and 80s. It turns out that mathematics education, at least in the US, is now subject to a new trend, and it doesn't appear to be a good one.To be fair the current driving trend in mathematics education is largely an extension of an existing trend in education generally. The idea is that we need to cater more to the students to better engage them in the material. There is a focus on making things fun, on discovery, on group work, and on making things "relevant to the student". These are often noble goals, and it is something that, in the past, education schemes have often lacked. There is definitely such a thing as "too much of a good thing" with regard to these aims, and as far as I can tell that point was passed some time ago in the case of mathematics.
was recently trying to list the 10 most encouraging initiatives by black people in 2006 and I thought I’d share one with you. It’s the Baltimore Algebra Project, a group of African American innercity teens who’ve evolved from tutors to activists in an effort to force change in the failing Baltimore City School system. The Algebra Project, many of you may know, was created by the brilliant softspoken civil rights activist and organizer Robert Moses, who left the U.S. to live in Africa, in the 1960s. When Moses returned to the U.S., he became convinced that the abysmal performance of African American students in math and science are a major barrier to full citizenship and empowerment. He created a program designed to help African American students excel in math in science. There are Algebra Projects in several U.S. cities. The Baltimore Algebra Project began as a tutoring program, but the young people in the project – students at many of the city’s struggling schools – have become increasingly more activist over the past 3 years. Finally, frustrated at continuing inequities in the school system, the Project announced the launch of “Freedom Fall” [fascinating  more at Clusty] this past September. They marched on the headquarters of the school board, and in a stroke of courage and brilliance created an alternative school board, called the Freedom Board.
Watch an excellent explanation of current math instruction and alternatives to it. I've never before seen such clear demonstrations of current math education. It really helps make the current math controversies much more concrete. Go to You Tube.
It's also different from American math in that fewer topics are taught in an academic year, giving the instructor the opportunity to teach the concept until it is mastered. "There's a tendency in the United States to teach a topic, then it's never seen or heard from again," said Jeffery Thomas, president of SingaporeMath.com Inc., the official distributor of the math books based in Oregon City, Ore.The American Institute for Research, one of the largest behavioral and social science research organizations in the world, says Singapore Math is better than American math because Singapore's textbooks provide a more thorough understanding of concepts, while traditional American math books barely go beyond formulas and definitions. Before someone in Singapore can become a teacher, she must demonstrate math skills superior to her American counterparts, according to the AIR, which is based in Washington, D.C. Additionally, Singapore offers an alternative math framework for lowperforming students, but at a slower pace and with greater repetition.
The Madison School Board's 2006/2007 Goals for Superintendent Art Rainwater included the "Initiatiation and completion of a comprehensive, independent and neutral review and assessment of the District's K12 math curriculum". Watch the discussion [Video] and read a memo [240K PDF] from the Superintendent regarding his plans for this goal. Much more here and here.
Barbara Lehman kindly emailed the Board's conclusion Monday evening:
It was moved by Lawrie Kobza and seconded by Ruth Robarts to approve the revised plan for implementation of the Superintendent’s 200607 goal to initiate and complete a comprehensive, independent, and neutral review and assessment of the District’s K12 math curriculum as presented at this meeting, including extension for completion of the evaluation to the 200708 school year. The Board of Education shall receive a report in 200607 with analysis of math achievement data for MMSD K12 students, including analysis of all math subtest scores disaggregated by student characteristics and schools in addition to reports in subsequent years. Student representative advisory vote * aye. Motion carried 61 with Lucy Mathiak voting no.
W. Stephen Wilson [75K PDF]:
Professors are constantly asked if their students are better or worse today than in the past. This paper answers that question for one group of students.Wilson is a Professor of Mathematics at Johns Hopkins University.For my fall 2006 Calculus I for the Biological and Social Sciences course I administered the same final exam used for the course in the fall of 1989. The SAT mathematics (SATM) scores of the two classes were nearly identical and the classes were approximately the same percentage of the Arts and Sciences freshmen. The 2006 class had significantly lower exam scores.
This is not a traditional research study in mathematics education. The value of this study is probably in the rarity of the data, which compares one generation to another.
....
Nineteen eightynine is, in mathematics education, indelibly tied to the National Council of Teachers of Mathematics’ publication, Curriculum and Evaluation Standards for School Mathematics (1989), which downplayed pencil and paper computations and strongly suggested that calculators play an important role in K12 mathematics education. My 2006 students would have been about two years old at the time of this very influential publication, and it could easily have affected the mathematical education many of them received. Certainly, one possibility is that mathematics preparation is down across the country, thus limiting the pool of well prepared college applicants.
Ted Widerski, via email:
I would like to thank the many of you that have supported our efforts to bring together our many promising young mathematicians for a day of comaraderie and competition. Many of you have offered kind words, your help, or your $$. All are greatly appreciated!As a result of your support, we will be holding a Middle School Mathfest on February 21st and Elementary (East & West) Mathfests on March 2nd and 12th.
We are currently planning the events, but the schedule will include a talk from a math professor, learning about a challenging math topic, and individual and team contests.
At the elementary level, the school will be asked to choose a team consisting of a total of eight 4th and 5th graders. For middle schools, the TAG department collaborated with learning coordinators to select students.
For the math competition, we’d love to have a celebrity team join us. Perhaps, TV personalities, UW athletes, the mayor, etc. If anyone would like to take on such a cause and has some connections, it would be great!
We would like to run a firstclass event for these firstclass students. Additional funds could be used. If any group or individual wishes to contribute, please contact Ted Widerski, TAG Resource Teacher at twiderski@madison.k12.wi.us or at 6635221.
What is 256 times 98? Can you do the multiplication without using a calculator? Two thirds of Massachusetts fourthgraders could not when they were asked this question on the statewide MCAS assessment test last year.Much more, here.
Math education reformers have a prescription for raising the mathematical knowledge of schoolchildren. Do not teach the standard algorithms of arithmetic, such as long addition and multiplication, they say. Let the children find their own methods for adding and multiplying twodigit numbers! For larger numbers, let them use calculators! One determined reformer puts it decisively: "It's time to acknowledge that continuing to teach these skills (i.e., pencilandpaper computational algorithms) to our students is not only unnecessary, but counterproductive and downright dangerous."Mathematicians are perplexed, and the proverbial man on the street, when hearing the argument, appears to be perplexed as well: improve mathematical literacy by downgrading computational skills?
Yes, precisely, say the reformers. The old ways of teaching mathematics have failed. Too many children are scared of mathematics for life. Let's teach them mathematical thinking, not routine skills. Understanding is the key, not computations.
Mathematicians are not convinced. By all means liven up the textbooks, make the subject engaging, include interesting problems, but don't give up on basic skills! Conceptual understanding can and must coexist with computational facility  we do not need to choose between them!
Ted Widerski:
The Talented and Gifted Division of MMSD is busy organizing ‘MathFests’ for strong math students in grades 4 – 8. These events are planned to provide an opportunity for students to interact with other students across the city who share a passion for challenging mathematics. Many of these students study math either online, with a tutor, by traveling to another school, or in a class with significantly older students.These events will be hosted by Cuna Mutual Insurance and American Family Insurance. Students will have an opportunity to learn math in several ways: a lecture by a math professor, group learning of a new concept, and individual and small group math contests. Over 300 students from 38 schools will be invited to participate.
The funding for this project is challenging as there are no significant MMSD funds available. A plea for funding in the last several weeks has resulted in gifts totaling about $1000. Those gifts will guarantee that the middle school Mathfest will be held on Wednesday, February 21st.
In order to hold the Elementary MathFests on each side of Madison would require additional donations. Gifts totaling $1600 would provide the necessary support to provide 200 students with a very special experience. If anyone or any group would like to contribute, it would be most appreciated. Please contact me: Ted Widerski, TAG Resource Teacher at: twiderski@madison.k12.wi.us
Thank you for supporting this math event.
EVERY YEAR, as many California high school seniors struggle with basic algebra, which is required for graduation, Times readers complain, "Who needs it? How many students will ever use it?" Well, I use it every day; I'm using it now, even though I haven't worked an algebraic equation since my son was in the seventh grade several years ago.Mathematics and science are unnatural practices. As physics professor Alan Cromer has brutally and elegantly written, "the human mind wasn't designed to study physics," and of course mathematics is the language of physics. "Design" here does not indicate an intelligent designer, which would suggest a creator with a math phobia. Rather it indicates evolutionary processes by which the human brain and mind have come to be what they are.
During the approximately 2 million years that it took for our Homo forebears to progress from habilis to sapiens, they had little use for mathematical reasoning abilities. Their sapientia seems to have been more suited in a good Darwinian sense to the immediate demands of their survival, such as eating, mating and avoiding premature death. Whether for good or ill, as time may tell, our situations have changed much in the last few thousand years, and so have demands on our poor, lagging minds. I don't mean only the obvious and oftrepeated claim that technical jobs require greater skills. That is clear enough in auto mechanics and computer programming. I mean the need to think abstractly, systematically and rationally in various ways.
But one of the secrets of KIPP's success in attracting the brightest young teachers and raising achievement for lowincome children throughout the country is its insistence on letting good teachers decide how they are going to teach. KIPP principals, such as Johnson, have the power to hire promising young people such as Suben and let them follow their best instincts, as long as the results  quality of student work, level of student classroom responses, improvement in standardized test scores  justify the teacher's confidence in her approach.Johnson and Schaeffler were variously startled, amused and intrigued by Suben's determination to do math her way. They say they are also very pleased with the results, which justify both the hiring of Suben and the KIPP insistence on lively engagement of every child in class.
The Madison United for Academic Excellence (MUAE) meeting of 12December2006 offered a Question and Answer session with Madison Director of Teaching and Learning, Lisa Wachtel, and Brian Sniff, District K12 Math Coordinator.
A list of questions was prepared and given to the speakers in advance so they could address the specific concerns of parents.
The video
of the meeting is 130MB, and 1 hour and 30 minutes long. Click on the image at left to watch the video.
The video contains chapter headings which allow quick navigation to sections of the meeting. The video will play immediately, while the file continues to download.
The topics covered during remarks and the question and answer sessions were accompanied by a PowerPoint presentation (here in PDF format), highlights of which are
Gov. Chris Gregoire urged lawmakers Monday to plow nearly $200 million into Washington's classrooms to help students who are struggling with math and science.The governor's sweeping proposal includes smaller middle school and high school math and science classes, recruiting hundreds of new math and science teachers, offering master teachers up to $10,000 in annual pay bonuses and expanding tutoring and other help for struggling students. She also wants to beef up local districts' curriculum to "worldclass" standards and then design achievement tests accordingly.
Janet Mertz recently mentioned (along with UW Placement's James Wollack recently) this paper by Richard Hill & Thomas Parker [750K PDF]:
The latest, December 2006 issue of the American Mathematical Monthly, an official publication of the Mathematical Association of America, contains an 18page article entitled "A study of CorePlus students attending Michigan State University" by Richard Hill and Thomas Parker, professors at MSU who teach preservice high school math teachers.CorePlus is used in some Madison High Schools. Much more on math here.They state that, "as the implementation progressed, from 1996 to 1999, CorePlus students placed into, and enrolled in, increasingly lower level courses; this downward trend is statistically robust (p<.0005). The percentages of students who (eventually) passed a technical calculus course show a statistically significant (p<.005) decline averaging 27 percent a year; this trend is accompanied by an obvious and statistically significant increase in percentages of students who placed into lowlevel and remedial algebra courses.
The grades the CorePlus students earned in their university mathematics courses are also below average, except for a small group of top students. ACT scores suggest the existence but not the severity of these trends."
For many college students, high school math is but a distant memory of derivative functions and playing games on graphing calculators.When a professor mentions that certain math skills are necessary for his class, it sends the lecture hall into a frenzy of questions and worry. It seems that math, more than any other subject, is lost in the student’s transition from high school to college.
With a $69,000 grant, University of WisconsinOshkosh geology professor Jennifer Wenner intends to figure out why.
“There are a couple of hypotheses,” Wenner said. “From my own experience, some people get it in their head that they can’t do math, and they get this block about it.”
As controversies rage about the best way to teach math and whether students should be allowed to use calculators — incidentally, the State Education Department on Dec. 1 declared that calculators will now be considered teaching materials, like textbooks, and schools must provide them to students — the real question is why children in this country are not better at learning math. Is it the curriculum? Is it the equipment? Is it the tests? And, haven’t we heard all this before?More on math here.In 1957, the Russians sent up Sputnik, stealing a march in the space race, and the United States decided that something had to be done, in a hurry, about math and science instruction in this country. Thus were born National Science Foundation grants to teachers of math and science so that they might get master’s degrees in their subjects rather than in education. A generation of teachers excitedly brought their advanced knowledge back to their classrooms.
Also in the early ’60s, the socalled New Math was influencing curricula across the country. The result was an emphasis on concepts to the detriment of the basics. Naturally, there was an eventual backlash when parents could no longer understand their children’s homework.
By the ’70s, teachers in middle and high schools were noticing that students were getting weaker on their recall of times tables and other basics. This could not then be blamed on calculators because there were no calculators yet in general use.
Connected Math textbooks for one year and the equivalent Singapore Math version.
Brandon Lorenz:
A recent meeting at Central Middle School attracted about 50 people to discuss concerns with the district's Connected Mathematics Project, a new constructivist approach that was introduced in sixth, seventh and eighth grades this year.More on Connected Math and the recent Math Forum.Another meeting for parents is scheduled for Dec. 13 at Horning Middle School.
Such new math programs rely on more handson activities and problemsolving skills than traditional programs.
Speaking with Zaborowski, Lynn Kucek said she was worried the math program would make it more difficult for her daughter, who does well in other subjects, to get into college.
It says the typical state math curriculum runs a mile wide and an inch deep, resulting in students being introduced to too many concepts but mastering too few, and urges educators to slim down those lessons.Math Forum audio / videoSome scholars say the American approach to math instruction has allowed students to fall behind those in Singapore, Japan and a dozen other nations. In most states, they say, the math curriculum has swelled into a thick catalogue of skills that students are supposed to master to attain "proficiency" under the federal No Child Left Behind mandate.
Wisconsin students continue to fare far better on the state's standardized tests than they do on those given by the federal government, according to a new analysis that raises questions about what it means to be "proficient."More on the Fordham Foundation's report and EdTrust. Finally, WISTAX offers a free report on testing.About 70% to 85% of Wisconsin students were considered proficient or better on the state's reading and math tests for the 2005'06 school year. Yet only 33% to 40% of the state's fourth and eighthgraders scored at least proficient on the most recent National Assessment of Educational Progress in those subjects, according to the study by the Wisconsin Taxpayers Alliance.
The state was one of 16 in the country that had a proficiency gap of 45 to 55 percentage points, the Taxpayers Alliance found. Several states, such as Oklahoma and Mississippi, had even larger differences between the percentage of students considered proficient by their states as opposed to the federal government.
"It just creates confusion," said Dale Knapp, research director for the Taxpayers Alliance. "We want a sense of what our students know, where they sort of stand. And we're really getting two different answers that are very different answers."
The blame doesn't necessarily fall on the Wisconsin Knowledge and Concepts Examinations, said Tony Evers, deputy superintendent of the state Department of Public Instruction, which administers the tests annually.
"Math is the same in Madison as it is in Missouri as it is in Mumbai."  Michael Petrilli,
Thomas B. Fordham Foundation, a group that has raised the idea of national standards"What that ought to be is a big signal to the folks in Wisconsin that they really need to evaluate the rigor of their standards and their assessment."  Daria Hall, Education Trust
NYT Letters to the Editor regarding "As Math Scores Lag, a New Push for the Basics":
s a middle school tutor, I’m always amazed at the pride many schools feel because their middle school curriculum includes topics in prealgebra/algebra. This sounds like good news until it becomes clear that it’s not prealgebra that students find problematic: it’s basic arithmetic.Enabling students to have rote facts at their fingertips endows them with great selfconfidence and permits them to take risks with subsequent higherthinking math skills. This selfconfidence eliminates that “fear” of math that prevails in our culture.
When I was an elementary school student in the 1950s, what was drilled daily in the classroom was reinforced nightly with numerous homework problems.
This is a technique that not only allows students to master the math basics, it also instills a sense of selfesteem gained through accuracy, precision and academic discipline.
E. S. Goldberg
Miami, Nov. 14, 2006
I was an educator in New York City for 31 years, and in my educational lifetime as dean of a Manhattan high school, a teacher in several junior and senior high schools and in summer and afternoon school tutorial programs, and a night adultschool teacher, I was involved in many new teaching programs.
Education is not an activity to promote politically correct reforms. Education is a process by which students are taught fundamentals in a structured environment with the least amount of distractions and political or doctorateminded invasions.
The outrageous proposals to substitute the basics will always be with us, and the smart thing to do is not to waste the good taxpayer’s patience or money.
John A. Manicone
Port St. Lucie, Fla., Nov. 14, 2006
As a high school teacher of many years and a mother, I, too, am greatly concerned with curriculum revision that tends toward the dogmatic acceptance of one educational model over other models.As most teachers know, there is not one path to mastery. What works well in one arena does not necessarily translate to another arena. Children who memorize multiplication tables have an easier time on standardized tests and in life than those who only know how to creatively group together dried kidney beans to figure out the process and answer.
Realistically, both models have a place in the classroom. But ultimately, at the end of the day, the person needs to know the answer.
Perhaps the problem lies with the commercialization of educational models and the proliferation of highpriced consultants. When incomes are determined by reinvention, then reinvention reigns over best practices. The question should not be what are the most interesting or creative models but what are the most effective strategies for teaching a particular subject.
Elizabeth Napp
Mount Kisco, N.Y., Nov. 14, 2006To the Editor:
Isn’t there a very simple and obvious answer here? If the kids in Japan, Taiwan and elsewhere do so much better in math than our kids do, why not just use their textbooks and curriculum rather than reinvent the wheel?
Certainly, this would be a faster and more economical approach to this problem than reinventing curriculum and textbooks yet again.
Diana d’Ambra
Maplewood, N.J., Nov. 14, 2006•
To the Editor:
No pun intended, the common denominator in predicting either the success or failure of any math curriculum — and I have been involved in a countless number of them during the past 45 years as a math educator — is the balance in it between theory and rote learning.
It didn’t harm me any to wait till I learned collegelevel and in some instances postgraduatelevel mathematics to learn of the theoretical underpinnings of some algorithms. Frankly, frequently a greater level of mathematical maturity is needed to fully understand and appreciate such.
And let’s not forget the need for teachers who understand the nature of mathematics!
Milton L. Meller
Brooklyn, Nov. 14, 2006
•To the Editor:
Thank you for publishing your article on the country’s lagging math scores.
I wrote a letter to the superintendent of my suburban Seattle school district when I was a junior in high school being poorly prepared for the SAT. I pointed out precisely the same problems with “reform math” that your article outlined.
I am now a sophomore in college and still paying the price for the poorly developed methods of “Integrated Mathematics.” You can be sure I will be forwarding a copy of this article to the superintendent, as well as updating her on my progress in remedial algebra. I’ll get the basics this time around; unfortunately, my parents are now paying $40,000 for them.
Alison Bailey
Portland, Ore., Nov. 14, 2006•
To the Editor:
Raising the bar won’t help, unless the children are developmentally ready for the concepts being taught.
As a fifthgrade teacher in California, I am forced to teach concepts that I learned in junior high school (prime factorization, plane geometry, integers), in addition to some concepts I learned in high school, like the volume of a pyramid or copying a triangle with a compass. If that weren’t bad enough, I find that I spend much time trying to bring them up to snuff on doing all basic operations in decimals and fractions.
All of this would be great to use as enrichment, since the upper fourth of the class usually grasps the material. However, the rest of the class truly struggles. I would advise against using California’s math standards, unless they are thoughtfully pruned.
Carol Tensen
Burbank, Calif., Nov. 14, 2006•
To the Editor:
One reads every day that American students are lagging in mathematics and sciences. Has anyone paid any attention to their English lately? We’re a country where the majority of people speak only one language, and that one they speak badly. Arts? Literature? History? Government? American students are lagging, period!
Mary C. Stephenson
Austin, Tex., Nov. 15, 2006
Well, I teach high school kids, and I've sat through about five hundred IEP meetings. I have sat through meetings for kids in middle school and then meetings for the same kids in high school. And there's one thing I can tell you.Alison Kepner has more.In five years, their goals had not changed one bit. In middle school, they were only expected to do 70% of their homework at 70% accuracy, and in high school, they were still only expected to do 70% of their homework with 70% accuracy. And for those of you who are reaching for your calculators because of the New New Math, that means that they only had to get 49% of their math work correct. Ever. Now if one were to bring this up before an IEP meeting, one will get looked at in much the same way that people avert their eyes at the sight of road kill.
This does not equate to proficiency in a onesizefitsall world.
But they strongly believe that their math textbooks should include actual math.The Madison School District uses Connected Math in middle school. Many links and notes on math, including the recent Math Forum audio/video.Donald's "Connected Mathematics" book at Harbour Pointe Middle School in Mukilteo asks him to arrange a list of 20 cities in order of their populations, all in the tens of millions.
Yes, he concedes, he must recognize differences among numbers, but it's a pretty lowlevel task for a bright sixthgrader, about as challenging as alphabetizing words.
But check out the next activity: Locate the cities on a map.
"That's not math," Donald protests. "That's geography."
The ChaconTaylor children and their parents, Hugh Taylor and Monique ChaconTaylor, are among Snohomish County families raising questions about the effectiveness of widely used math textbooks that encourage discovery and writing about math, but deemphasize basics such as multiplication and long division.
They've joined other Washington parents in an organization called Where's the Math? that's calling on the state Office of Superintendent of Public Instruction (OSPI) to rewrite its K12 math standards, select more effective textbooks and reexamine the math content of the Washington Assessment of Student Learning (WASL)
The calls for rethinking the state's math education come amid signs that the present system is failing large numbers of students. Just 51 percent of 10thgraders and 59 percent of fourthgraders passed the math section of the WASL in the spring. About 29,000 juniors haven't passed the WASL math test, which they must do to graduate in spring 2008..
According to the agenda for the Board of Education meeting on November 20, 2006:
It is recommended that the Board approve the 200607 goals for the Superintendent that require the Superintendent to:
a. Initiate and complete a comprehensive, independent and neutral review and assessment of the District's K12 math curriculum.
 The review and assessment shall be undertaken by a task force whose members are appointed by the Superintendent and approved by the BOE. Members of the task force shall have math and math education expertise and represent a variety of perspectives regarding math education.
 The task force shall prepare and present to the BOE a preliminary outline of the review and assessment to be undertaken by the task force. The outline shall, at a minimum, include:
 analysis of math achievement data for MMSD K12 students, including analysis of all math subtests scores disaggregated by student characteristics and schools;
 analysis of performance expectations for MMSD K12 students;
 an overview of math curricula, including MMSD's math curriculum;
 a discussion of how to improve MMSD student achievement; and
 recommendations on measures to evaluate the effectiveness of MMSD's math curriculum. The task force is to present the preliminary outline and a timeline to the BOE for comment and approval.
 The task force is to prepare a written draft of the review and
assessment, consistent with the approved preliminary outline. The draft is to be presented to the BOE for review and comment. The task force is to prepare the final report on the review and assessment.
b. Develop in collaboration with the Board and external advisors, a plan for the District to communicate to the community why parents or guardians should send their children to MMSD schools. Specific tasks includec. Provide information to the Board in a clear, accurate, complete yet concise, and timely manner. The Board will evaluate progress on this goal through the use of a rating sheet for Board members to give periodic feedback on the information they receive from the administration. Information provided to the Board shall be rated for timeliness, accuracy, organization and presentation.
 determining what parents and guardians consider important in selecting schools;
 determining whether and how MMSD schools provide what parents and guardians consider important in selecting schools;
 using the information gained from parents and guardians, developing a vision of what MMSD should be in the future; and
 developing a communications plan to promote MMSD schools and why parents or guardians should send their children to them. Timeframe to develop: 6 months.
d. Implement the Administrative Intern Professional Development Program. Program participants should be selected by the 4th quarter of this year. Special attention will be given to the recruitment of people of color and other historically underrepresented groups in administrative positions in all employment categories of the District. (principals, building services, etc.) A report on the program shall be provided to the BOE at least annually.
SEATTLE — For the second time in a generation, education officials are rethinking the teaching of math in American schools.
The changes are being driven by students’ lagging performance on international tests and mathematicians’ warnings that more than a decade of socalled reform math — critics call it fuzzy math — has crippled students with its deemphasizing of basic drills and memorization in favor of allowing children to find their own ways to solve problems.
At the same time, parental unease has prompted ever more families to pay for tutoring, even for young children. Shalimar Backman, who put pressure on officials here by starting a parents group called Where’s the Math?, remembers the moment she became concerned.
“When my oldest child, an Aplus stellar student, was in sixth grade, I realized he had no idea, no idea at all, how to do long division,” Ms. Backman said, “so I went to school and talked to the teacher, who said, ‘We don’t teach long division; it stifles their creativity.’ ”
As Math Scores Lag, a New Push for the Basics
And parents shouldn't only be concerned about math instruction. They should be looking hard at the reading and writing parts of their kids' educations, too. Are they learning grammar? Can they spell? Punctuate? Understand what they are reading? Most of the Ivy League English majors whose writing I grade have trouble in these areas, which suggests to me that most everyone their age does. I tend to assume that the students I see are among the most linguistically competent students of their generationbut there are still a lot of issues with things such as runon sentences, comma splices, murky phrasing, limited vocabulary, dangling modifiers, spelling, and so on. That's the legacy of a pedagogical attitude toward literacy that mirrors the one the mother above encountered when she inquired why her son wasn't being taught basic math skills. When I taught high school English in a boarding school a couple of years ago, I found that a great many students there had abysmal language skills. Some bordered on functional illiteracy. When I asked whether the school taught grammar at any point, the head of school told me that teaching grammar thwarted students' creativity and stifled their interest in reading. The utter inadequacy of that outlook really hits home when you realize that it amounts to lying to parents and kids about their kids' abilities, and that it involves sending kids off to college without the skills they will need to succeed there.Tamar Lewin:
For the second time in a generation, education officials are rethinking the teaching of math in American schools.Notes and links here. More comments. Joanne has more on "word problems".The changes are being driven by students’ lagging performance on international tests and mathematicians’ warnings that more than a decade of socalled reform math — critics call it fuzzy math — has crippled students with its deemphasizing of basic drills and memorization in favor of allowing children to find their own ways to solve problems.
At the same time, parental unease has prompted ever more families to pay for tutoring, even for young children. Shalimar Backman, who put pressure on officials here by starting a parents group called Where’s the Math?, remembers the moment she became concerned.
“When my oldest child, an Aplus stellar student, was in sixth grade, I realized he had no idea, no idea at all, how to do long division,” Ms. Backman said, “so I went to school and talked to the teacher, who said, ‘We don’t teach long division; it stifles their creativity.
Grassroots groups in many cities are agitating for a return to basics. Many point to California’s standards as a good model: the state adopted reform math in the early 1990s but largely rejected it near the end of the decade, a turnaround that led to rising math achievement.
“The Seattle level of concern about math may be unusual, but there’s now an enormous amount of discomfort about fuzzy math on the East Coast, in Maine, Massachusetts and Pennsylvania, and now New Jersey is starting to make noise,” said R. James Milgram, a math professor at Stanford University. “There’s increasing understanding that the math situation in the United States is a complete disaster.”
Problem: Find the slope and yintercept of the equation 10 = x – 2.5.Notes and links on math curriculum. Audio / Video from the recent math forum.Solution: The equation 10 = x – 2.5 is a specific case of the equation y = x – 2.5, which has a slope of 1 and a yintercept of –2.5.
This problem comes from a 7th grade math quiz that accompanies a widely used textbook series for grades 6 to 8 called Connected Mathematics Program or CMP.[1] The solution appears in the CMP Teacher’s Guide and is supported by a discussion of sample student work.
Richard Askey, a mathematician at the University of Wisconsin at Madison, reported, “I was told about this problem by a parent whose child took this quiz. The marking was exactly as in the text.”[2] Students instructed and graded in this way learn incorrect mathematics, and teachers who know better may be undermined by their less informed peers, armed with the “solution.” This example is far from the only failing of CMP. Among other shortcomings, there is no instruction on division of fractions in the entire three year CMP series, and the other parts of fraction arithmetic are treated poorly.[3]
Is CMP just an anomaly? Unfortunately not. CMP is only one of more than a dozen defective K12 math programs funded by the National Science Foundation. More specifically, the NSF programs were created and distributed through grants from the Education and Human Resources (EHR) Division within the NSF. In contrast to the NSF’s admirable and important role in supporting fundamental scientific research, the EHR has caused, and continues to cause, damage to K12 mathematics education.
Connected Math is widely used within the Madison School District resulting in no small amount of supplementing by teachers, students and parents.
A nation full of students who enjoy mathematics and feel confident in the subject is not necessarily a nation that scores high on international math tests, a report being released this week concludes.
The report from the Brookings Institution suggests, in fact, that the socalled “happiness factor” in math may be inversely related to achievement. In countries where students express high levels of math confidence and enjoyment, it says, students tend to score below average on international math exams in 4th and 8th grades, and vice versa.
Students in the United States are among the world’s happiest, though their average scores are higher than those for most countries that rate strongly on the “happiness” scale.
By Debra Viadero, in Education Week, published October 18, 2006
“I’m not trying to say we should go out and destroy kids’ confidence,” said Tom Loveless, the author of the annual report and the director of the Brown Center on Education Policy at the Washington think tank. “What’s clear from these findings is happiness is not everything. Our national obsession with student happiness over academic content may, in fact, be hurting our children when considered in an international context.”
Other scholars, though, saw less cause for concern in the findings for American students.
“We’re scoring above the international average with kids who like math,” said David C. Berliner, an education professor at Arizona State University in Tempe. “That suggests we’re producing enough highlevel math students to meet the needs of our economy.”
Mr. Loveless based his conclusions on 2003 results from the Trends in International Mathematics and Science Study, or TIMSS, which tested 4th graders from 25 countries and 8th graders from 46 countries. He compared the test scores with students’ responses to questions gauging their confidence in and enjoyment of math, and teachers’ ratings of the extent to which they made math lessons relevant to real life—strands that Mr. Loveless calls the “happiness factor.”
Sad in Singapore?
Of the 10 countries where 8th graders scored highest on average for confidence in their mathematical abilities, only two—Israel and the United States—scored above average for achievement. More than 40 percent of students in Egypt, Ghana, Israel, and Jordan said that they usually do well in math; students in all of the countries but Israel fell below the international average. The United States, where 22 percent of 8th graders expressed the same level of confidence, ranked ninth.
The bottom 10 countries in selfconfidence, on the other hand, include some of the world’s highestachieving nations in 8th grade mathematics—Singapore, Chinese Taipei, Hong Kong, Japan, and South Korea.
Even the least confident 8th graders in Singapore, on average, outscored the most confident American students on an international math test.
That pattern was the same, according to Mr. Loveless, among 4th graders and for questions gauging students’ enjoyment of math. Mr. Loveless could find no relationship, though, between math achievement and the degree of relevance in students’ math lessons.
Yet, within countries, the data showed the opposite pattern occurred: The happiest, most confident students were those with the highest test scores.
Mr. Loveless said that paradox may be due partly to differences in how cultures define success. It could also be explained, he said, by what researchers have dubbed the “frogpond effect.” In other words, students may measure their own abilities against those of their peers.
“A lot of American kids think they’re good in math, and they may be good in the United States,” said Mr. Loveless. “But if they went to another country, their perceptions may change.”
The 29page report also examines claims that the federal No Child Left Behind Act is prompting states to exaggerate the gains their students are making on state reading tests.
For that part of his study, Mr. Loveless compared five to seven years of data from state tests with states’ 4th and 8th grade scores on the National Assessment of Educational Progress, a federal program that periodically tests representative samples of students within states and nationwide. While the statetest scores are higher on average than the NAEP scores, the analysis showed, the gains they report vary by grade level and are not steep enough for states to meet federal targets by 2014, as the law requires.
“There’s no clear evidence,” Mr. Loveless concluded, “that states before or after NCLB did anything different.”
Video  Audio  School Board members that ask questions are essential to public confidence in and strong oversight of our $332m+ district. Monday evening's Superintendent review discussion with respect to the district's controversial math curriculum was interesting in this respect. Watch the video or listen to the mp3 audio file. The math related discussion starts about 24 minute into the video and ends at about the one hour mark. 
Children who are turned off by math often say they don't enjoy it, they aren't good at it and they see little point in it. Who knew that could be a formula for success?
The nations with the best scores have the least happy, least confident math students, says a study by the Brookings Institution's Brown Center on Education Policy.Countries reporting higher levels of enjoyment and confidence among math students don't do as well in the subject, the study suggests. The results for the United States hover around the middle of the pack, both in terms of enjoyment and in test scores.
In essence, happiness is overrated, says study author Tom Loveless."We might want to focus on the math that kids are learning and just be a little less obsessed with the fact that they have to enjoy every minute of it," said Loveless, who directs the Brown center and serves on a presidential advisory panel on math.
"The implication is not Let's go make kids unhappy,'" he said. "It's Let's give kids better signals as to how they're performing, relative to the rest of the world.'"
Other countries do better than the United States because they seem to expect more from students, he said. That could also explain why high performers in other nations express less confidence and enjoyment in math.
Here's a math problem for you: Count the excuses people are trotting out for why schoolkids in New York City and State did poorly in the latest round of math scores. The results showed just 57% of the city's and 66% of the state's students performing at grade level  and a steady decline in achievement as kids got older.Everyday Math is used in the Madison School District. Much more on Math curriculum and politics here. Via Joanne.
It's about family income, said an article in The New York Times. "The share of students at grade level in affluent districts was more than twice as big as in impoverished urban districts."It's about unfair funding levels, said state education Secretary Richard Mills.
It's about class size, said activist Leonie Haimson.
Wrong again, claimed other observers. The real culprit was a new test.
If, like me, you're running out of fingers  and patience  there's a reason. Nobody spinning the test scores is zeroing in on the single biggest reason math achievement in New York City and state lags and will continue to lag: Our schools use a fartoofuzzy curriculum that fails to give kids rigorous instruction in the basics.
In New York City, the program required in the vast majority of schools is called Everyday Mathematics. Chancellor Joel Klein swears by it. If you ask administrators to explain it, they'll use just enough jargon to make it sound decent.
But the truth is, Everyday Math systematically downplays addition, subtraction, multiplication and division, which everyone knows are the foundations for all higher math. Instead of learning those basic four operations like the backs of their hands, students are asked to choose from an array of alternative methods, such as an ancient Egyptian method for multiplication. Long division is especially frowned upon.
Carson is CoFounder and Executive Director of NYC Hold:
The performance of American students in mathematics is mediocre at best. In many cases, mathematics instruction is not serving our children's best interests. In order to help all students achieve success in school mathematics courses, have access to adequate preparation for the broadest options in high school math and science courses, and the opportunity to advance into mathematics based college courses and careers, it is important to examine the direction of recent attempts at mathematics education reform.More on Everyday math.
New York State Education Department:
The Mathematical Education of Teachers [268K PDF] recommends that the mathematical education of teachers be viewed as a partnership between mathematics faculty and mathematics education faculty and further recommends that there needs to be more collaboration between mathematics faculty and school mathematics teachers. We will report on The Mathematics Semester at the University of NebraskaLincoln, a partnership that resulted from Math Matters, a NSFCCLI grant.Also: Math in the Middle Institute Partnership [PDF]
Jean Johnson, Ana Maria Arumi and Amber Ott [350K PDF]:
It's probably natural for leaders of organizations to be upbeat about their institutions, and the nation's school children might not be wellserved by superintendents and principals who see public schools as places of disappointment, failure and ineptitude. Even so, the positive, almost buoyant outlook of school leaders nationwide captured in this fourth installment of Reality Check 2006 may come as something of a surprise to reformers and critics, including regulators enforcing No Child Left Behind. In many respects, local school leaders seem to operate on a very different wavelength from many of those aiming to reform public schools. The two groups have different assumptions about how much change today's public schools really need. Even when they see the same problems, they often seem to strive for different solutions.Via Brett.To most public school superintendents  and principals to a lesser extent  local schools are already in pretty good shape. In fact, more than half of the nation's superintendents consider local schools to be "excellent." Most superintendents (77 percent) and principals (79 percent) say low academic standards are not a serious problem where they work. Superintendents are substantially less likely than classroom teachers to believe that too many students get passed through the system without learning. While 62 percent of teachers say this is a "very" or "somewhat serious" problem in local schools, just 27 percent of superintendents say the same.
Some highlights:
 93% of superintendents, and 80% of principals, think public schools offer a better education than in the past, and most (86% and 82%) think the material is harder.
 Despite the call from the business community for a great focus on science/math, 59% of superintendents and 66% say that the statement “kids are not taught enough science and math” is not a serious problem in their schools.
 77% of superintendents and 79% of principals say that the statement “academic standards are too low, and kids are not expected to learn enough” is not a serious problem in their schools.
 51% of superintendents say that local schools are excellent; 43% say they are good.
 Only 27% of superintendents, compared with 62% of teachers, say it’s a serious problem that too many students get passed through the system without learning.
 76% of superintendents and 59% of principals, compared with 33% of high school teachers, say that students graduating from middle school have the reading, writing, and math skills needed to succeed in high school.
More than 15 years after its publication of influential national standards in mathematics, a leading professional organization has unveiled new, more focused guidelines that describe the crucial skills and content students should master in that subject in elementary and middle school.Much more here and here.The National Council of Teachers of Mathematics last week released “Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics,” a document that supporters hope will encourage the polyglot factions of state and local school officials, textbook publishers, and teachers to set clearer, more common goals for math learning.
While the report is being published by the NCTM, it was reviewed by numerous math experts from across the country, some of whom have strongly disagreed with the organization’s past positions on essential skills. The new document reflects an attempt to overcome those conflicts and focus on a number of crucial, agreedupon concepts.
“I would hope that this has a large impact, because I believe it gets it right,” said R. James Milgram, a Stanford University mathematics professor and a critic of the math organization’s previously issued national standards. He was one of 14 individuals who provided an outside, formal review of the document. “I would like to hope that this represents a new era of cooperation,” he added. “I hope that what this represents is an end to the math wars.”
Typical of many math textbooks in the U.S., this one is thick, multicolored,and full of games,puzzles,and activities,to help teachers pass the time, but rarely challenge students. Singapore Math’s textbook is thin, and contains only mathematics — no games. Students are given briefexplanations, then confronted with problems which become more complex as the unit progresses.
It was another body blow to education. In December of 2004, media outlets across the country were abuzz with news ofthe justreleased results of the latest Trends in International Mathematics and Science Study (TIMSS) tests. Once again despite highly publicized efforts to reform American math education (some might say because of the reform efforts) over the past two decades, the United States did little better than average (see Figure 1). Headquartered at the International Study Center at Boston College and taken by tens of thousands of students in more than three dozen countries, TIMSS has become a respected standard of international academic achievement. And in three consecutive TIMSS test rounds (in 1995, 1999,and 2003), 4th and 8thgrade students in the former British trading colony of Singapore beat all contenders, including math powerhouses Japan and Taiwan. United States 8th graders did not even make the top ten in the 2003 round; they ranked 16th. Worse, scores for American students were, as one Department of Education study put it,"among the lowest of all industrialized countries."
The countries that outperform the United States in math and science education have some things in common. They set national priorities for what public school children should learn and when. They also spend a lot of energy ensuring that every school has a highquality curriculum that is harnessed to clearly articulated national goals. This country, by contrast, has a wildly uneven system of standards and tests that varies from place to place. We are also notoriously susceptible to educational fads.Much more, here.One of the most infamous fads took root in the late 1980’s, when many schools moved away from traditional mathematics instruction, which required drills and problem solving. The new system, sometimes derided as “fuzzy math,’’ allowed children to wander through problems in a random way without ever learning basic multiplication or division. As a result, mastery of highlevel math and science was unlikely. The new math curriculum was a mile wide and an inch deep, as the saying goes, touching on dozens of topics each year.
Despite North Carolina students' steady improvement in reading and math, their performance on state endofgrade tests has been far better than on the National Assessment of Educational Progress. In fact, North Carolina stands out because of the wide gap between results on the state and national tests.More on "how states inflate their progress under No Child Left Behind".In 2005, about 84 percent of North Carolina eighthgraders earned proficient or better scores on state math tests; 32 percent were proficient or advanced on the national math test. Only West Virginia showed a sharper difference.
"When you see the huge disparity that you do between proficiency levels [on state and national tests], at least part of it is about rigor," said Ross Weiner, policy director for the Education Trust, a Washington group that advocates for poor and minority students. "North Carolina has a bigger difference than most other states. That raises questions about expectations and whether North Carolina's standards are high enough to demonstrate that students are learning what they need to know."
In a major shift from its influential recommendations 17 years ago, the National Council of Teachers of Mathematics yesterday issued a report urging that math teaching in kindergarten through eighth grade focus on a few basic skills.Lewin's article references a 2005 document: "10 myths of NCTM (Fuzzy) Math".If the report, “Curriculum Focal Points,” has anywhere near the impact of the council’s 1989 report, it could signal a profound change in the teaching of math in American schools. It could also help end the math curriculum struggles that for the last two decades have set progressive educators and their liberal supporters against conservatives and many mathematicians.
At a time when most states call for dozens of math topics to be addressed in each grade, the new report sets forth just three basic skills for each level. In fourth grade, for example, the report recommends that the curriculum should center on the “quick recall” of multiplication and division, the area of twodimensional shapes and an understanding of decimals. It stopped short of a call for memorization of basic math facts.
The 1989 report is widely seen as an important factor nudging the nation away from rote learning and toward a constructivist approach playing down memorization in favor of having children find their own approaches to problems, and write about their reasoning.
“It was incredibly influential,” said Chester E. Finn Jr., a Department of Education official in the Reagan administration. “More than half the states explicitly acknowledged it in devising their own standards. This report is a major turnaround.”
NCTM source materials and related links here.
Critics of "Fuzzy" Methods Cheer Educators' Findings; Drills Without Calculators. Taking Cues from Singapore.
The nation's math teachers, on the front lines of a 17year curriculum war, are getting some new marching orders: Make sure students learn the basics.Links:In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.
The council's advice is striking because in 1989 it touched off the socalled math wars by promoting openended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.
Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.
Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests. There, children focus intensely on a relative handful of topics, such as multiplication, division and algebra, then practice by solving increasingly difficult word and other problems. That contrasts sharply with the U.S. approach, which the report noted has long been described as "a mile wide and an inch deep."
If school systems adopt the math council's new approach, their classes might resemble those at Garfield Elementary School in Revere, Mass., just north of Boston. Threequarters of Garfield's students receive free and reduced lunches, and many are the children of recent immigrants from such countries as Brazil, Cambodia and El Salvador.
Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country's official program and now used in about 300 school systems in the U.S. Many school systems and parents regard Singapore Math as an antidote for "reform math" programs that arose from the math council's earlier recommendations.
The Singapore Math curriculum differs sharply from reform math programs, which often ask students to "discover" on their own the way to perform multiplication and division and other operations, and have come to be known as "constructivist" math.
I am in a class in which the teacher is, shall we say, an adherent of the National Council of Teachers of Mathematics (NCTM) and its standards. In fact, the NCTM standards and our understanding of same make up a portion of the syllabus. Our first assignment is a comparison of those standards with the math standards for the state in which we reside for a particular “content standard”, grade level, and “process standard. The content standard describes what students are supposed to learn. The process standard describes how they are supposed to learn it. I got assigned Geometry/11th grade/representation. "What is 'representation'?" I hear you asking. Expressing things in different ways, I think. You can use a graph to express a function, or a table of values, or a formula, for example. Which one is best to analyze the problem at hand, I think is what they’re getting at but they go on and on in the standards, bringing in all sorts of ways to show things which might be good things to mention as an aside, but to devote so much class time to it supplants the basics that they are supposed to be learning. (And which educationists think is mundane, and mind numbing.)Joanne has more. John Dewey background.
I have a friend that teaches at MATCshe tells me that she is shocked at the lack of math and writing ability of the Madison high school students coming to MATC's two year technical programs. MATC is very important to Wisconsin's future. What is happening at the high school level that these students are not prepared properly? Anyone have any thoughts?
Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of threedimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.Nadejda Lobastova has more. Poincaré ConjectureUnlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.
“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that selfpromotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”
Running some searches recently, I came across this April, 2004 article by Lee Sensenbrenner on Connected Math. The words remain timely more than two years later:
A seventhgrader at a Madison middle school is posed with the following situation: A gas station sells soda in three sizes. A 20ounce cup costs 80 cents, a 32ounce cup is 90 cents and a 64ouncer goes for $1.25.Many links and articles on math can be found here. The recent Math Forum is also worth checking out, along with a discussion of the District's math performance.
The first question, which appeared in similar form on a recent exam, is as traditional as any mathematical story problem: What size offers the most soda for the money?But the second question carries the spirit of the Connected Math Program, which has developed strong undercurrents of controversy  both here and nationally  and plays prominently in one of the Madison School Board races Tuesday.
This question asks: If the gas station were to offer an 84ounce Mega Swig, what would you expect to pay for it?
There's really no concrete answer. A student, for instance, could argue that the 84ouncer would cost what the 20ounce and 64ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some perounce price slightly less than what was given for the 64ounce drink.
For the people fighting an impassioned battle over Connected Math, the differences between question number one and question number two are not subtle or inconsequential.On one side, those who support Connected Math say that engaging students by presenting problems as reallife scenarios  often with no absolute solution or single path to arrive at an answer  fosters innovation and forces students to explain and defend their reasoning as they discover mathematical concepts.
The other side says the approach trades the clear, fundamental concepts of math, distilled through thousands of years of logical reasoning, for verbiage and vagary that may help students learn to debate but will not give them the foundation they need for more advanced mathematical study.
Teaching mathematics has been my profession in New York City public schools since 1969, first at I.S. 201 in District 5, then at J.H.S. 17 in District 2, and since 1983, at Stuyvesant High School. I'm also the father of a 10yearold daughter who attends District 2 schools and a member of an organization, Nychold (nychold.com), dedicated to bringing sanity to math education.I'm a firm believer in public education, the great equalizer. Sadly, over the past 10 years, I've witnessed how badly things can go wrong. I am referring specifically to the constructivist math curricula that abound in our city public schools in general and more specifically in District 2, where I live, teach, and raise my daughter.
Constructivist curricula, such as TERC and CMP, forsake algorithms, postulates, and theorems (the foundation of math) as well as teachercentered learning. Instead, they have students working among themselves in groups, loosely guided by the teacher in a drawn out attempt to "discover" math truths.
In my Upper East Side neighborhood, an incredible number of intelligent young students from the fourth grade and up are seeing private math tutors. Many of these are not the type of children who would normally struggle in arithmetic or elementary algebra. As a result of the way they're taught elementary math, they find themselves unable to do real math. When they're taught math in a more traditional way by their tutors, they invariably find themselves relieved and highly critical of the way they've been taught mathematics.
At Stuyvesant, we have a disproportionate number of freshmen from District 2 taking our introductory algebra course. Most Stuyvesant students have already completed that course before they enter our school. The ratio of District 2 students to nonDistrict 2 students in those classes is close to twice that same ratio in the freshman class as a whole.
The issue of curriculum quality and rigor continues to generate attention. PI:
The good news is that the high school class of 2006 posted the biggest nationwide average score increase on the ACT college entrance exam in 20 years and recorded the highest scores of any class since 1991.Alan Borsuk has more:The bad news is that only 21 percent of the students got a passing grade in all four subject areas, including algebra and social science.
"The ACT findings clearly point to the need for high schools to require a rigorous, fouryear core curriculum and to offer Advanced Placement classes so that our graduates are prepared to compete and succeed in both college and the work force," Education Secretary Margaret Spellings said in Washington, D.C.
Wisconsin high school graduates are better prepared to succeed in college than students nationwide  but that means only that more than 70% of state students are at risk of having trouble in one or more freshmanlevel subjects while the national figure is almost 80%, according to ACT, the college testing company.The message still isn't getting across," Ferguson said in a telephone news conference. If students want to go to college and do well, they have to take high school seriously and take challenging courses, he said.
ACT results showed that students who took at least four years of English and three years each of math, science and social studies in high school did substantially better on the tests (22.9 in Wisconsin, 22.0 nationwide) than those who took lighter loads in those core areas (21.0 and 19.7, respectively).
Elizabeth Burmaster, Wisconsin's superintendent of public instruction, said she believes that if schools in Wisconsin stay focused on efforts such as early childhood education and small class sizes in the early grades, combined with strong academic programs in middle school and high school, achievement will go up and racial and ethnic gaps will close.
Individual state data is available here.
Burmaster's statement, along with the ACT information will increase the attention paid to curriculum issues, such as the ongoing questions over the Madison School District's math program (See UW Math professor Dick Askey's statement on the MMSD's interpration and reporting of math scores). Will we stick with the "same service" approach? This very important issue will be on voters minds in November (referendum) and again in April, 2007 when 3 board seats are up for election. See also the West High School Math Faculty letter and a recent open letter to the Madison School District Board and Administration from 35 of the 37 UW Math Department faculty members. Vaishali Honawar has more.
The Madison School District issued a press release on the recent ACT scores (68% of Wisconsin high school graduates took the ACT  I don't know what the MMSD's percentage is):
Madison students who took the 2006 ACT college entrance exam continued to outperform their state and national peers by a wide margin, and the scores of Madison's AfricanAmerican test takers increased significantly. Madison students' composite score of 24.2 (scale of 1 to 36) was higher for the 12th straight year than the composite scores of Wisconsin students and those across the nation (see table below). District students outscored their state peers by 9% (24.2 vs. 22.2,) and their national peers by 15% (24.2 vs. 21.1).The Madison School District recently published this summary of student performance vs other similar sized and nearby districtions (AP, ACT and WKCE) here. Madison's individual high schools scored as follows: East 22.9, LaFollette 22.1, Memorial 25.1 and West 25.5. I don't have the % of students who took the ACT.Compared to the previous year, the average ACT composite score among the district's AfricanAmerican students increased 6% — 18.8 vs. 17.7 last year. The gap between district AfricanAmerican and white student ACT scores decreased this year. The relative difference this year was 24% (18.8 vs. 24.8) compared to 30% last year.
Scores also increased this year for the district's Asian students (22.1 to 23.0) and Hispanic students (21.5 to 21.8).
222 students took the ACT in 20052006.Waunakee High School:Our composite score was 23.6 compared to the state at 22.2
87% of test takers proved college ready in English Composition (vs. 77%)
66% of test takers proved college ready in College Algebra (vs. 52%)
77% of test takers proved college ready in Social Science (vs. 61%)
45% of test takers proved college ready in Biology (vs. 35%)
37% of test takers proved college ready in all four areas (vs. 28%)
(#) as compared to the state %
Score HS Mean (Core/NonCore)McFarland High School's 2006 Composite average was 23.7. 110 students were tested.
Composite 23.3 (24.3/21.5)English 22.5 (23.9/19.5)
Mathematics 23.2 (24.2/21.8)
Reading 23.3 (24.1/21.5)
Science 23.7 (24.4/22.7)
UPDATE: A few emails regarding these results:
In the Waunakee information I sent to Jim Z, our mean for the Class of 2006 comes first, followed by the core/noncore in parentheses. So, our mean composite score for our 157 seniors who sat for the ACT was 23.3, the mean composite for those completing the ACT suggested core was 24.3, the mean composite for those who did not complete the core was 21.5.
With ACT profile reports, the student information is selfreported. It's reasonably accurate, but some students don't fill in information about course patterns and demographics if it is not required.
Please let me know if there are any other questions.
It appears that Jim Z's chart comparing scores uses Waunakee's "Core score" as opposed to the average composite that the other schools (at
least McFaland) gave to Jim Z.. If Jim Z. wishes to report average "Core" for McFarland it is 24.5. Our noncore is 22.2 with our average composite 23.7.
Probably everyone is familiar with the ACT definition of core, but it's 4 years of English, and three years each of math, science, and social studies. ACT is refining their position on what course patterns best position a student for undergraduate success, however.
he board that sets policy for the National Assessment of Educational Progress has revised the blueprint for the 12th grade mathematics version of the influential exam, in an attempt to make the test better reflect the skills that students need for college and highly skilled jobs.The changes, approved Aug. 4, are expected to make the math test more challenging in some areas, through the addition of morecomplex algebraic concepts, trigonometry, and a stronger emphasis on mathematical reasoning and problemsolving, officials associated with the board say. Those revisions could also shape individual states’ math standards, which are often influenced by the content of the NAEP frameworks.
The National Assessment Governing Board, the independent entity that directs NAEP, unanimously agreed to make the changes at its quarterly meeting here. The board has spent about two years on the project.
“What we’re doing here is not unique to NAEP. It is what society is demanding,” said Sharif M. Shakrani, a professor of psychometric testing at Michigan State University in East Lansing, who consulted on changes to the framework. “We need to judge what students know and where they are weak.”
When results are broken down by race, just 10 percent of black and Latino sophomores in Colorado schools are proficient in math; 90 percent are not.
Those scores are "scary," said Jenna Fleur Lin, a math teacher who tutors high school students in the Cherry Creek School District and runs a free weeklong math and science camp at an innercity Denver church.
"What it means is you have a huge population that's not going to function properly," Lin said.
Moloney said one problem is that, unlike elementary and middle school students, high schoolers have the freedom to choose many of their own courses.
"Are minority youngsters being channelled into challenging programs or are you being (steered) to diminished programs?" he said.
Lin said she believes many students don't have a solid foundation in math in elementary school.
They are just learning to do calculations but they don't understand how to
A college math student might grapple with this topic in an advanced elective. Ryan was stretching his elementaryschool mind at MathPath, perhaps the nation's toughest summer camp for numerical prodigies.Another example of the "Brave New World" referenced in Marc Eisen's recent words. Neal Gleason comments.Math camps are multiplying in part because families are seeking an edge in competitive college admissions and worry about the quality of U.S. math instruction. Last summer, parents paid $280 million to send 120,000 children to academic summer camps, with math among the most popular subjects, according to Eduventures, a Boston research firm, which estimates enrollment is climbing 10% a year. Sylvan Learning Centers, the big tutoring company, says participation in summer math programs, including day camp, jumped 23% last year  twice the rate of other subjects.
The American Mathematical Society counts two dozen "challenging summer math programs"  twice as many as seven years ago. Most focus on highschool students. MathPath caters only to middleschool kids, age 10 to 14. It is also smaller  and more selective  than some better known programs.
About 80,000 kids in second through eighth grade, for example, take part in the annual "talent search" run by Johns Hopkins University's Center for Talented Youth. Through the search, about 70% qualify for summer camps across the country and some 10,000 enroll in a given year.
Links: MathPath, Johns Hopkins Center for Talented Youth.
Neal Gleason in a letter to the Isthmus Editor:
I have long admired Marc Eisen's thoughtful prose. But his recent struggle to come to grips with a mutliethnic world vvers from xenophobia to hysteria ("Brave New World", 6/23/06). His "unsettling" contact with "stylish" Chinese and "turbaned Sikhs" at a summer program for gifted children precipitated first worry (are my kids prepared to compete?), And then a villain (incompetent public schools).Although he proclaims himself "a fan" of Madison public schools, he launches a fusillade of complaints: doubting that academic excellence is high on the list of school district pirorities and lamentin tis "dubious maht and reading pedagogy." The accuracy of these concerns is hard to assess, because he offers no evidence.
His main target is heterogeneous (mixedability) classes. He speculates that Madison schools, having failed to improve the skills of black and Hispanic kids, are now jeopardizing the education of academically promising kids (read: his kids) for the sake of politically correct equality. The edict from school district headquarters: "Embrace heterogeneous classrooms. Reject tracking of brighter kids. Suppress dissent in the ranks." Whew, that is one serious rant for a fan of public schools.
Eisen correctly observes that "being multilingual" will be a powerful advantage in the business world; familiarity and ease with other cultures will be a plus." Mare than 20 years ago, my kids began to taste this new world in the diverse classrooms of MidvaleLincoln Elementary, and continued on through West High with its 50plus nationalitities and a mix of heterogeneous and advanced classes.Background:They did just fine in college and grad school, emerged biand trilingual with well worn passorts, and started interesting careers at high tech internationl companies. How will Eisen's kids acquire modern cultural skills if they are cloistered in honors classes, sheltered from daily contact with kids of varied ability?
Neal Gleason
Pittsburgh has hired a private company to write a coherent curriculum for city schools, reports the PostGazette.Interesting. Perhaps an RFP looking for different ideas might be useful. Public and private organizations could respond. One only has to look at the "Cathedral and the Bazaar" to see the power of a community vs a top down approach. Leadership, particularly that which embraces the community is critical  as Lucy Mathiak recently pointed out:Because course content is uneven and out of sync with state standards, the Pittsburgh Public School district is paying New Yorkbased Kaplan K12 Learning Services $8.4 million to write standardized curricula for grades six through 12.
. . . Teachers in other districts have complained that Kaplan's detailed curriculum turned them into automatons and deprived them of time to cover material in adequate detail or help students with individual needs.
. . . Pittsburgh school officials cite an urgent need to bring coherence and rigor to what's taught and tested in the district's classrooms.
Later, she added: "I think one of the fundamental questions facing our district is whether we treat parents as resources or problems. Any parent who is concerned about safety, discipline or academic issues needs to feel confident that their concerns are going to be heard. We have to court the parents. The future of our schools depends on their confidence that we are working as partners with them."Here's a parent's perspective on curriculum and school climate. Another. A vast majority of the UW Math Department's perspective (35 of the 37 signed this letter). Marc Eisen offers still another perspective.
Only 11 states met the union’s criteria for strong standards and tests that “align” with them, it says, and 20 states “have much work to do”—beefing up their standards, matching up tests with standards, or showing what they have done online.Full PDF study can be found here. The report noted that only 1 to 25% of Wisconsin's state tests aligned to "strong content standards".“The systems in those states aren’t smart enough yet to bear the weight of the accountability functions they are asked to serve,” said Antonia Cortese, the AFT’s executive vice president. As one example of such a function, she cited the “in need of improvement” label applied to schools if they don’t meet measures of adequate yearly progress, or AYP. The label triggers a series of consequences for the schools.
In their study, the AFT researchers looked for standards to be clear, explicit by grade level, and rooted in the knowledge and skills for the particular subject, as well as accessible on the Web. Similarly, documentation of the relationship between the standards and the tests had to be available online.
The researchers contend that such “transparency” helps teachers do their jobs and builds trust in the system among educators and the public.
The union, which from 1995 to 2001 published an annual report evaluating states’ academic standards, found significant progress on that front. The standards that relate to NCLB testing are more specific and more often set out by grade levels—a help to teachers and testmakers—than the acrosstheboard standards examined five years ago, the report says. The progress is particularly noteworthy because of the pressure on state education departments to respond quickly to the sweeping federal law’s mandates, which include annual tests in reading and mathematics in grades 38 and once in high school and, starting next year, three tests of science spread across grade levels.
There is an interesting post and series of comments about homework at The Daily Grind.I agree that homework needs to be assigned every class period. But, like every teacher, I've struggled with how to best hold students accountable for not just completing it, but understanding it. In our freshmen math courses (Algebra 1, Numeracy), we give students full credit on an assignment if it is completed and turned in on time (we don't assess it for correctness at all). We also don't accept late work, unless students have an excused absence. The purpose of this is to build the ethic of doing homework and turning it in  as many students seem to come to high school with out having done much  if any  homework in the past. We are pretty successful at getting students to turn in their work by the end of freshman year. Getting them to really think about it, try hard on questions they don't understand, and seek help when they have difficulties is another thing altogether.
The national education reform effort has long suffered from magical thinking about what it takes to improve children’s chances of learning. Instead of homing in on teacher training and high standards, things that distinguish effective schools from poor ones, many reformers have embraced the view that the public schools are irreparably broken and that students of all kinds need to be given vouchers to attend private or religious schools at public expense.This belief, though widespread, has not held up to careful scrutiny. A growing body of work has shown that the quality of education offered to students varies widely within all school categories. The public, private, charter and religious realms all contain schools that range from good to not so good to downright horrendous.
What the emerging data show most of all is that public, private, charter and religious schools all suffer from the wide fluctuations in quality and effectiveness. Instead of arguing about the alleged superiority of one category over another, the country should stay focused on the overarching problem: on average, American schoolchildren are performing at mediocre levels in reading, math and science — wherever they attend school.
L.A. Unified plans to spend millions to train, recruit and keep math and science teachers, who are a hot commodity nationwide.Recognizing the critical need to boost math and science test scores, the Los Angeles Unified School District has taken several steps — including offering bonuses — to attract and keep teachers in those fields at the district's neediest schools.
Let's look at the recent "Nation's Report Card," published annually by the U.S. Department of Education's National Center for Education Statistics.Nationally, in reading, only 13 percent of black fourth graders, and 11 percent of black eighth graders score as proficient. Twentynine percent achieve a score of "basic," defined as a partial knowledge and skills needed to be proficient in the grade. Fiftynine percent score below basic, lacking necessary knowledge and skills. It's the same story for black eighth graders, with 40 percent scoring basic and 49 percent below basic.
In math, it's roughly the same story. For black fourth graders, 12 percent score proficient, 47 percent score basic and 40 percent below basic. For black eighth graders, 8 percent score proficient, while 33 percent score basic and 59 percent score below basic; however, 1 percent of black fourth graders and eighth graders achieved an advanced score in math.
Teachers and politicians respond to this tragic state of affairs by saying more money is needed. The Washington, D.C., school budget is about the nation's highest with about $15,000 per pupil. Its student/teacher ratio, at 15.2 to 1, is lower than the nation's average. Despite this, black academic achievement in D.C. is the lowest in the nation. Reading scores for D.C.'s fourthgrade black students are: 7 percent proficient, 21 percent basic and 71 percent below basic. For eighthgraders, it's 6 percent proficient, 33 percent basic and 58 percent below basic.
Participation in a rigorous secondary school program of study may qualify a postsecondary student to receive an ACG, if otherwise eligible. The Secretary recognizes at least one rigorous secondary school program of study for each state annually. States may submit proposals for recognition or may elect to accept rigorous secondary school programs of study prerecognized by the Secretary. The following are recognized rigorous secondary school programs of study for each state for the 200607 award year.Wisconsin [PDF]:
He created Reasoning Mind because he had a dismal opinion of American education, from kindergarten through high school.Reasoning Mind website.This Webbased math program "does not merely incorporate technology into teaching. It is based in technology and capitalizes on the power of technology to deliver information and content," Dr. Alexander R. "Alex" Khachatryan said.
The results from a pilot program during the 200506 school year were impressive. Atrisk students at a Houston school and advanced math students at a school in College Station were introduced to Reasoning Mind.
"At the innercity school, the test group's average improvement from the pretest to the posttest was 67 percent, while the control group improved 6 percent," Dr. Khachatryan said.
"The test group students also demonstrated extraordinary results – a 20 percent higher passing rate – on the Texas Assessment of Knowledge and Skills test, despite the fact that only three out of 48 problems directly checked students' knowledge of the two math units covered by RM in the pilot," he said.
The average incoming level for our freshmen is around 5th grade. Our mission is to get them to a 4year college. This requires not just development of their academic skills, but it also requires a shift in their thinking and selfperception. Our students come in with comparable literacy levels; however, in our society, it seems much clearer to people that being able to read and write is an essential skill. There are plenty of welleducated people who happily admit that they can't do math, but none that laugh about their inability to read a book.
Dan Greene, a San Jose, CA high school math teacher maintains a blog whose purpose is to "help generate and share ideas for teaching high school math concepts to students whose skills are below grade level.".
This report takes an incisive look at what U.S. education leaders can learn from China's success in math and science education. From a comparative perspective, it evaluates complementary strengths and weaknesses in the two education systems. The report also outlines areas of potential collaboration so that both the U.S. and China can build and sustain excellence in math and science.35 Page report: 267K PDF File.
Nicholas Kristof follows up Marc Eisen's recent words on a world of competition for our children:
But the investments in China's modernization that are most impressive of all are in human capital. The blunt fact is that many young Chinese in cities like Shanghai or Beijing get a better elementary and high school education than Americans do. That's a reality that should embarrass us and stir us to seek lessons from China.On this trip I brought with me a specialist on American thirdgrade education — my thirdgrade daughter. Together we sat in on thirdgrade classes in urban Shanghai and in a rural village near the Great Wall. In math, science and foreign languages, the Chinese students were far ahead.
My daughter was mortified when I showed a group of Shanghai teachers some of the homework she had brought along. Their verdict: firstgrade level at a Shanghai school.
Granted, China's education system has lots of problems. Universities are mostly awful, and in rural areas it's normally impossible to hold even a primitive conversation in English with an English teacher. But kids in the good schools in Chinese cities are leaving our children in the dust.
Last month, the Asia Society published an excellent report, "Math and Science Education in a Global Age: What the U.S. Can Learn from China." It notes that China educates 20 percent of the world's students with 2 percent of the world's education resources. And the report finds many potential lessons in China's rigorous math and science programs.Yet, there isn't any magic to it. One reason Chinese students learn more math and science than Americans is that they work harder at it. They spend twice as many hours studying, in school and out, as Americans.
Chinese students, for example, must do several hours of homework each day during their summer vacation, which lasts just two months. In contrast, American students have to spend each September relearning what they forgot over the summer.
China's government has developed a solid national curriculum, so that nearly all high school students study advanced biology and calculus. In contrast, only 13 percent of American high school pupils study calculus, and fewer than 18 percent take advanced biology.
Yet if the Chinese government takes math and science seriously, children and parents do so even more. At Cao Guangbiao elementary school in Shanghai, I asked a thirdgrade girl, Li Shuyan, her daily schedule. She gets up at 6:30 a.m. and spends the rest of the day studying or practicing her two musical instruments.
So if she gets her work done and has time in the evening, does she watch TV or hang out with friends? "No," she said, "then I review my work and do extra exercises."
A classmate, Jiang Xiuyuan, said that during summer vacation, his father allows him to watch television each evening — for 10 minutes.
The Chinese students get even more driven in high school, as they prepare for the national college entrance exams. Yang Luyi, a tenth grader at the firstrate Shanghai High School, said that even on weekends he avoided going to movies. "Going to the cinema is timeconsuming," he noted, "so when all the other students are working so diligently, how can you do something so irrelevant?"
And romance?
Li Yafeng, a tenthgrade girl at the same school, giggled at my question. "I never planned to have a boyfriend in high school," she said, "because it's a waste of time."
Now, I don't want such a pressured childhood for my children. But if Chinese go overboard in one direction, we Americans go overboard in the other. U.S. children average 900 hours a year in class and 1,023 hours in front of a television.
I don't think we could replicate the Chinese students' drive even if we wanted to. But there are lessons we can learn — like the need to shorten summer vacations and to put far more emphasis on math and science. A central challenge for this century will be how to regulate genetic tinkering with the human species; educated Chinese are probably better equipped to make those kinds of decisions than educated Americans.
During the Qing Dynasty that ended in 1912, China was slow to learn lessons from abroad and adjust its curriculum, and it paid the price in its inability to compete with Western powers. These days, the tables are turned, and now we need to learn from China.
Marc Eisen:
Most of us have had those eerie moments when the distant winds of globalization suddenly blow across our desks here in comfortable Madison. For parents, it can lead to an unsettling question: Will my kids have the skills, temperament and knowledge to prosper in an exceedingly competitive world?I’m not so sure.
I’m a fan of Madison’s public schools, but I have my doubts if such preparation is high on the list of school district priorities. (I have no reason to think things are any better in the suburban schools.) Like a lot of parents, I want my kids pushed, prodded, inspired and challenged in school. Too often  in the name of equity, or progressive education, or union protectionism, or just plain cheapness  that isn’t happening.
Brave New World: Are our kids ready to compete in the new global economy? Maybe not
Last summer I saw the future, and it was unsettling.My daughter, then 14, found herself a racial minority in a class of gifted kids in a threeweek program at Northwestern University. Of the 16 or so kids, a dozen were Asian or Asian American.
The class wasn't computer science or engineering or chemistry  classes increasingly populated by international students at the college level  but a “soft” class, nonfiction writing.
When several hundred parents and students met that afternoon for the introductory remarks, I spotted more turbaned Sikhs in the auditorium than black people. I can't say if there were any Hispanics at all.
Earlier, I had met my daughter's roommate and her mom  both thin, stylish and surgically connected to their cell phones and iPods. I casually assumed that the kid was a suburban princess, Chinese American division. Later, my daughter told me that her roommate was from Hong Kong, the daughter of a banker, and had at the age of 14 already taken enrichment classes in Europe and Canada. Oh, and she had been born in Australia.
Welcome to the 21st century.
In the coming decades, you can be sure the faces of power and influence won't be monochromatic white and solely American. Being multilingual will be a powerful advantage in the business world, familiarity and ease with other cultures will be a plus, and, above all, talent and drive will be the passwords of success in the global economy.
Thomas Friedman's The World Is Flat, his chronicle of the rapid economic and social changes wrought by the mercurylike spread of new technology, serves as an essential primer for understanding this new world.
In a nutshell, we shouldn't bet on American hegemony in technology and economic growth in the 21st century. In a rampedup, knowledgebased, digitalized economy, there are no borders. The builtin advantage the U.S. enjoyed after World War II  our industrial based was untouched, while the rest of the developed world's was in ruins  has finally run its course. Today, many tech jobs can just as easily be performed in Bangalore and Beijing as in Fitchburg.
Whether America's youth, raised in the lap of luxury with an overpowering sense of entitlement, will prosper in this meritocratic environment is an interesting question. And what of America's underprivileged youth, struggling in school and conspicuously short of family assets: How well will they fare in the new global marketplace?
My own aha! moment came a year ago at about the same time I dropped my youngest daughter off at Northwestern. Out of the blue I received an email from a young man in India, offering his services to proofread the paper. Technically, it was no problem to ship him copy, and because of the 12hour time difference he could work while the rest of us slept and played  if we wanted to go down the outsourcing road.
Most of us have had those eerie moments when the distant winds of globalization suddenly blow across our desks here in comfortable Madison. For parents, it can lead to an unsettling question: Will my kids have the skills, temperament and knowledge to prosper in an exceedingly competitive world?
I'm not so sure.
I'm a fan of Madison's public schools, but I have my doubts if such preparation is high on the list of school district priorities. (I have no reason to think things are any better in the suburban schools.) Like a lot of parents, I want my kids pushed, prodded, inspired and challenged in school. Too often  in the name of equity, or progressive education, or union protectionism, or just plain cheapness  that isn't happening.
Instead, what we see in Madison is just the opposite: Advanced classes are choked off; onesizefitsall classes (“heterogeneous class groupings”) are mandated for more and more students; the talentedandgifted staff is slashed; outside groups promoting educational excellence are treated coolly if not with hostility; and arts programs are demeaned and orphaned. This is not Tom Friedman's recipe for student success in the 21st century.
Sure, many factors can be blamed for this declining state of affairs, notably the howlingly bad way in which K12 education is financed in Wisconsin. But much of the problem also derives from the district's own efforts to deal with “the achievement gap.”
That gap is the euphemism used for the uncomfortable fact that, as a group, white students perform better academically than do black and Hispanic students. More to the point, mandating heterogeneous class grouping becomes a convenient cover for reducing the number of advanced classes that fail the PC test: too white and unrepresentative of the district's minority demographics.
The problem is that heterogeneous classes are based on the questionable assumption that kids with a wide range of skills  from highschoolers reading at a fourthgrade level to future National Merit students  can be successfully taught in the same sophomore classroom.
“It can be done effectively, but the research so far suggests that it usually doesn't work,” says Paula OlszewskiKubilius, head of Northwestern's Center for Talent Development, which runs an enrichment program for Evanston's schools.
I have to ask: After failing to improve the skills of so many black and Hispanic kids, is the Madison district now prepared to jeopardize the education of its most academically promising kids as well?
Please don't let me be misunderstood. Madison schools are making progress in reducing the achievement gap. The district does offer alternatives for its brightest students, including collegelevel Advanced Placement classes. There are scores of educators dedicated to improving both groups of students. But it's also clear which way the wind blows from the district headquarters: Embrace heterogeneous classrooms. Reject tracking of brighter kids. Suppress dissent in the ranks.
The district's wrongheaded approach does the most damage in the elementaryschool years. That's where the schools embrace dubious math and reading pedagogy and shun innovative programs, like those operated by the Wisconsin Center for Academically Talented Youth, a nonprofit group that works tirelessly to promote gifted education. (Credit school board president Johnny Winston Jr. for cracking the door open to WCATY.)
In a perfect world, Madison would learn from Evanston's schools and their relationship with WCATY's peer, the Center for Talent Development. Faced with predominantly white faces in its advanced high school classes, this racially mixed district didn't dump those classes but hired OlszewskiKubilius' group to run an afterschool and weekend math and science enrichment program for promising minority students in grades 36.
In other words, raise their performance so they qualify for those advanced classes once they get to high school. Now there's an idea that Tom Friedman would like!
MARC EISEN IS EDITOR OF ISTHMUS.Email: EISEN at ISTHMUS.COM
A reader deep into math issues emailed these two reviews of curriculum currently used within the Madison School District:
The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. This means that
 standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions
 precise definitions are never given
 repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials, no discussion of things as basic as the standard exponent rules
 throughout the booklets, topics are introduced, usually in a single problem and almost always indirectly  topics which, in traditional texts are basic and will have an entire chapter devoted to them  and then are dropped, never to be mentioned again. (Examples will be given throughout the detailed analysis which follows.)
 in the booklets on probability and data analysis a huge amount of time is spent learning rather esoteric methods for representing data, such as stem and leaf plots, and very little attention is paid to topics like the use and misuse of statistics. Statistics, in and of itself, is not that important in terms of mathematical development. The main reason it is in the curriculum is to provide students with the means to understand common uses of statistics and to be able to understand when statistical arguments are being used correctly.
In a recent issue of the NCTM Dialogues, Prof. R. Askey comments on a particular and remarkably inept misunderstanding in CorePlus, of some basic methods in probability Prof. R. Askey's comments on a problem with Core Plus.
Recently, Core Plus has begun to appear in the Minnesota High Schools, with the usual results, including servere questions from parents and the withdrawal of a significant number of students from the school system. This has also prompted a number of independent analyses of the program by other professional mathematicians. Here are the comments of Larry Gray, a Professor of Mathematics at the University of Minnesota. A Sample List of Mathematical Errors in the Core Plus program.
R. James Milgram 15MB ebook pdf:
It has long been felt that the mathematical preparation of preservice teachers throughout the country has been far too variable, and often too skimpy to support the kind of outcomes that the United States currently needs. Too few of our K  12 graduates are able to work in technical areas or obtain college degrees in technical sub jects. This impacts society in many and increasingly harmful ways, and it is our failure in K  8 mathematics instruction that is at the heart of the problem.This is especially true when we compare outcomes in the United States with outcomes in countries that do a better job of teaching mathematics, countries such as Poland, Hungary, Bulgaria, Romania, Singapore, China, and Japan, to name a few.
It has also been increasingly recognized that if we are to improve our performance in K  8 mathematics instruction, preservice teachers should take focused, carefully designed courses directly from the mathematics departments, and not, as is often the case, just a single math methods course taught in the Education School. A focused two year sequence in the basic mathematics teachers have to know is the minimal mathematics sequence that preservice teachers need in order to to successfully teach students in K  8.
Are Mathematicians Smarter Than Math Teachers?June 6, 2006 04:45 PM
Maybe. But math teachers know things that are (1) useful for teaching math and (2) difficult for nonteaching mathematicians to grasp, according to Deborah Loewenberg Ball, a University of Michigan researcher who spoke recently to a gathering of AFT leaders and staff.
Here's an example of a task* at which math teachers outperform mathematicians.
Three students were asked to multiply 35 by 25. The answer is 875. Each came up with the wrong answer, but for different reasons. (Click on the links to see if you can figure out the thinking behind the errors.)
Ball reports that math teachers were much better than mathematicians at identifying where students went wrongan important fact to know to help put students back on track.
In "Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide?" a 2005 article in American Educator, Bell and coauthors Heather C. Hill and Hyman Bass conclude that there is a body of knowledge math teachers need to be effective. They created test questions that captured this body of knowledge, tested teachers, and used the results to accurately predict which teachers' students would learn more.
Ball told AFT leaders that the finding that there is a body of knowledge teachers need to have to teach math can be extended to other subjects. As the drumbeat for "content knowledge" becomes louder and louder, this research answers the questions "Which content?" "Which knowledge?"
*Ball notes that this type of thinking, error analysis, is not only a teacher thing but an important area of mathematics
Posted by John on June 6, 2006 04:45 PM  Permalink
Comments
Understanding the source of error is very important. A math teacher needs to have extensive experience analyzing mistakes. This requires a strong, strong handle on arithmetic.
But I would be careful before dismissing the math professors. They don't teach, that is true. They don't know error analysis, and some other things math teachers need.
But when they get outraged, there is usually a reason. Such as not teaching standard algorithms at all. Avoiding fractions. Not teaching long division. Placing so much emphasis on concept that skill is overlooked (each year I get incoming freshmen from a progressive district who have a real solid understanding of what multiplication is, the variety of meanings it might have, etc, but who have difficulty with facts, eg, 7 x 8.)
Pedagogy and content are both important. Some of the education people and the 'modern' curricula privilege pedagogy over content. Back to basics folks tend to emphasize content and ignore pedagogy. Good math teachers, experienced math teachers, we know that we need to pay attention to both and defend our work from either extreme.
Madison Metropolitan School District Superintendent Art Rainwater replied via email to our "Open letter about Math Coordinator position at MMSD":
On Wed, 31 May 2006, Art Rainwater wrote:My reply:Dear Steffen and others;
Thank you for sharing your concens.
The District has always employed outstanding curriuclum leaders in our Teaching and Learning Department. Mary Ramberg has been a leader in Teaching and Learning as have Lisa Wachtel in Science and Mary Watson Peterrson in Literacy and Language Arts.
Please rest assured that I. even more than you, am committed to employing the best possible math corrdinator. The minimum requirements posted are exactly what they say. They are minimum requirements and failure to meet the requirements eliminates the person from consideration immedately without even a further paper screen. Our district has a hiring process that has served us vrey well over the years and this is only the first part of that process.
The breadth and depth of knowledge of mathematics is obviously one of two key components in determining who will be the final pick for this position. However, equally important in the decision is the breadth and depth of pedogogical knowledge. Both of these will be given equal weight and I will not employ anyone who does not have both.
Art Rainwater
Dear Art,Thanks for your prompt reply.
What caused all of us to write/sign this letter is that the posted job ad does precisely NOT require what we consider two MINIMUM requirements for this position, namely (and I repeat):
I do hope that the school board and the district administration will RESTRICT its search to ONLY candidates meeting these two MINIMUM requirements.
 subject knowledge equivalent to a strong bachelor's degree in mathematics, and
 teaching experience at the highest level in the high school curriculum.
Thanks for your attention!
Steffen
OPEN LETTER:
Dear Members of the School Board, dear Superintendent Rainwater,
We are writing to strongly urge that the new Coordinator of Mathematics have the depth of knowledge of mathematics that we believe is essential for the position. While we are obviously concerned about the preparation of students entering the University, our concerns are much broader than that. The new Coordinator must have a high level of understanding of both mathematical content and pedagogy to independently navigate through the controversies that surround the established standards and published curricula. These "navigational skills" are essential if we are to achieve a program for the Madison school system that meets the needs and aspirations of all the students in the system.
The posted criteria do not give us confidence that the new coordinator will have the required depth of knowledge. Specifically, we recommend adding the following to the list of knowledge and experience that the new Coordinator should have:
The posted criteria call for a Master's degree, but there is no requirement specific to the subject area. Knowledge at the level of a Bachelor's degree seems to us to be a minimum requirement.
The posted criteria call for teaching experience in mathematics, but do not specify the level. Experience at the highest level seems essential if the individual is to have the necessary overview of the entire curriculum.
Respectfully,
Alejandro Adem
Sigurd Angenent
Richard Askey
Eric Bach
Lev Borisov
Richard Brualdi
Andrei Caldararu
David Camacho
Serguei Denissov
Mikhail Feldman
Simon Hellerstein
Shi Jin
Alexander Kiselev
James Kuelbs
Steffen Lempp
Shirin Malekpour
Eugenia Malitsky
Gloria MariBeffa
Gabi Meyer
Paul Milewski
Julie Mitchell
YongGeun Oh
Marshall Osborn
Seymour Parter
Paul Rabinowitz
Diane Rivard
Joel Robbin
JeanPierre Rosay
James Rossmanith
Hans Schneider
Andreas Seeger
Timo Seppalainen
Dietrich Uhlenbrock
Stephen Wainger
Tonghai Yang
Department of Mathematics
University of WisconsinMadison
"Finding Common Ground in the U.S. Math Wars", Science Magazine, May 19, 2006 describes the 18month effort initiated by Richard Schaar, mathematician and former president of Texas Instruments, to bridge the gap between professional mathematicians, and math educators. Leaving many issues still to be addressed, the following is their initial statements:
All students must have a solid grounding in mathematics to function effectively in today's world. The need to improve the learning of traditionally underserved groups of students is widely recognized; efforts to do so must continue. Students in the top quartile are underserved in different ways; attention to improving the quality of their learning opportunities is equally important. Expectations for all groups of students must be raised. By the time they leave high school, a majority of students should have studied calculus.
For further elaboration, see Common Ground
Last month, NCTM (National Coucil of Teachers of Mathematics) endorsed a short list of skills, by grade, that every grade and middle school student must master. These "Curriculum Focal Points" are an attempt to correct the "milewide, inchdeep" curricula in most schools, which leave most student incapable and illprepared for further work in mathematics, science and engineering disciplines. The Focal Points document has not be published at this time.
After a number of parents and teachers objected, the school board of Olympia, Washington, has ignored an administrative recommendation to adopt a constructivist math program for their middle schoolers:Connected Math and the Madison School District was discussed at a recent math forum (audio / video).
UW Emeritus Math Professor Dick Askey wrote a followup article on test scores and the local math curriculum.
The MMSD is currently looking for a "Coordinator of Mathematics".
Clusty Connected Math Search.
Education Secretary Spellings recently announced the formation of a presidentially appointed panel that was formed to address math teaching. According to the charter of this panel, one of its purposes is “to foster greater knowledge of and improved performance in mathematics among American students.” The panel is charged with producing a report in two years, which must contain recommendations pertaining to how math instruction can be improved in the U.S. In particular, the report must address the skills necessary for students to acquire competence in algebra and to prepare them for higher levels of mathematics.The workings of the panel are not the type of thing that makes the front page of newspapers, the top story on TV news, or what is talked about in the local cafes. To hear about this you need to drop in to the blogs (like Edspresso), or the various list serves on the internet devoted to math education. There you will notice some discomfort among those who think that the way math is currently taught and the present crop of math texts being used in the U.S. is just fine. They have openly expressed dismay at the inclusion on the panel of people who have been vocal critics of reform math, stating "This panel is filled with hacks, toadies and stooges. Can you say ‘show trial’, children? Have you ever seen the old reels of the Communist Party Congresses in Moscow?” Allegations of preconceived conclusions then follow.
Madison Metropolitan School District:
Lead K12 mathematics programming; develop and promote documents defining the mathematics program and expectations; organize and promote professional development opportunities; seek and implement researchbased best practices in mathematics education; serve on various district and Teaching & Learning committees and task forces; create, recommend and administer budget for mathematics curriculum coordination; coordinate Evaluation of Learning Materials in mathematics; serve as District liaison with state, private, professional, city, and local mathematics groups and organizations; seek and develop relationships with institutions of higher education to coordinate inservice and preservice mathematics education; collaborate with other District departments to ensure all students have the opportunity to learn standardsbased mathematics; develop and promote standardsbased assessment tools and practices; analyze District mathematics student achievement data and use the data to inform action plans; supervise and evaluate instructional resource teacher staff and program assistant; author grant applications; coordinate mathematics grants; support District Improvement Plans, decisions and initiatives; demonstrate evidence of cultural competence.Additional MMSD jobs can be found here.
The Bush administration has named a former president of the University of Texas at Austin to lead a national panel to weigh in on the math wars playing out across the country. The politically fraught battle pits a more freeform approach to teaching math against the traditional method that emphasizes rules and formulas to solve number problems.More on the National Math Panel.In traditional math, children learn multiplication tables and specific techniques for calculating 25 x 25, for example. In socalled constructivist math, the process by which students explore the question can be more important than getting the right answer, and the early use of calculators is welcomed.
According to a 2005 study by ACT, the college entrance exam organization, only 40 percent of high school seniors were ready to take the most basic collegelevel algebra course.
I believe in the power of numbers. I don't know when my belief in numbers began. Perhaps when I was a child. My high school dropout, bookkeeper dad came home each week to tell us that he had played the numbers  my neighborhood’s equivalent of lotto but lots more complex.Dad would convert every thought and dream to a number with help from his trusty dream book. You had a dream about mice? Consult the book. "That's a 12, 17 or 21. What was the mouse doing  climbing out of a garbage can? Well climbing is a 21, 34, or 42 and garbage is a 17, 39, or 32. So, let's play 12 and 21 (the reverse of each other), 17 (it appeared twice), and 34, the year your mom was born."
This is to briefly summarize from my point of view what went on at the MSRI workshop on equity in math education last week. (Vicki was also there and may wish to give her side of the story so you get a more complete picture. It was a very broad workshop, 13 hours a day for 3 days. The web site is down right now, but you can view a cached version here.)
The charge of the workshop was to brainstorm solutions to the underrepresentation of (racial and ethnic) minorities in mathematics and mathematics courses which frequently serve as gatekeepers to other areas.
The participants were thus rather heterogeneous, policymakers, mathematics educators, mathematicians and teachers, including several groups of young people from various projects who serve as mentors and tutors in mathematics.
The talks and presentations were thus rather mixed, from talks by a law professor about constitutional issues on education to examples of math games played by young tutors and an actual 9th grade math class right with 22 students from a nearby high school right in front of all participants.
There were also some chilling descriptions of the abominable conditions at some schools serving mostly black and native American students.
The usual disagreements between research mathematicians and math educators were not brought to the surface much, but were brought up in many personal conversations during breaks and meals. However, there was general agreement that the underrepresentation of minorities is a serious national problem, and that more resources and better teachers are crucial to its solution.
However, no firm solutions or consensus emerged.
The two things I took away from the workshop are:
It wasn't quite a Miss America pageant, but it had a gusto of its own. To the beat of rock music, more than 200 middle schoolers in Tshirts adorned with pi symbols or jokes about binary numbers jogged into a Crystal City hotel conference hall yesterday, waving and holding up signs identifying their home states.Madison area middle schools that participated included Hamilton (Madison), Jefferson (Madison), Eagle (Fitchburg), Badger Ridge (Verona) and Madison Country Day School (Waunakee). Mathcounts website.The 57 teams  from every state, plus the District, the U.S. territories and military or State Department schools around the world  had spent the day vying for the MathCounts national championship, and they were about to find out which fourmember team had won.
Google constantly leaves numerical puns and riddles for those who care to look in the right places. When it filed the regulatory documents for its stockmarket listing in 2004, it said that it planned to raise $2,718,281,828, which is $e billion to the nearest dollar. A year later, it filed again to sell another batch of shares—precisely 14,159,265, which represents the first eight digits after the decimal in the number pi (3.14159265).The mathematics comes from the founders, Sergey Brin and Larry Page. The Russianborn Mr Brin is the son of a professor of statistics and probability and a mother who works at NASA; Mr Page is the son of two computerscience teachers. The breakthrough that made their search engine so popular was the realisation that the chaos of the internet had an implicit mathematical order. By counting, weighting and calculating the link structures between web pages, Messrs Page and Brin were able to return search results more relevant than those of any other search engine.
New math textbooks for Seattle middle and highschool students are on hold.Concerned that it may cost too much and not produce results, School Board members have delayed a decision to allow more time to study the issue.
At stake is whether the district adopts a single style of teaching math that focuses more on understanding concepts than honing computation skills  a prospect that has sparked debate among parents, teachers and administrators.
Recently Utah schools have been given an F for technology use in the classroom (or lack thereof). This is one area I hope Utah continues to fail in. Technology has been touted as a fabulous tool for teaching math and other subjects, but it’s not. Technology teaches technology; you still have to learn math separately if you want to know math too.I agree. The basics come first  technology, which changes frequently and may not always be appropriate (see Powerpoint, and here.)
To visit the Exhibit Hall at an NCTM conference is an infuriating activity for me, but I can't avoid it. I am charged with checking out the competition.Via Joanne.
“A small cadre of math specialists is helping teachers with instruction and curriculum.”While it sounds promising that “math specialists” will be helping teachers with instruction and curriculum, the converse may be likely to occur.
In the following excerpt from "Why Johnny Can’t Calculate" (Los Angeles Times, September 26, 2005link here), CSUNorthridge mathematics professor David Klein and high school teacher Jennifer Marple have detailed how the “experts” responsible for professional development for LAUSD often fail to deliver.
The district requires math teachers to attend inservice meetings to learn more math and better ways to teach it. No one would quarrel with those goals, but the quality of professional development programs is often so poor that they are likely to cause more harm than good.
Rick Burke remembers looking at his elementaryschool daughter's math homework and wondering where the math was.Sarah Natividad adds:Like many Seattle schools, his daughter's school was teaching "reform" math, a style that encourages students to discover math principles and derive formulas themselves. Burke, an engineer, worried that his daughter wasn't learning basic math skills.
"It was a lot of drawing pictures and playing games," he said. "Her whole firstgrade year was pretty much a lateral move."
So for the past few years, Burke and his wife have been tutoring their three children after school  and this fall, they plan to switch them to North Beach Elementary, which uses a more traditional approach to math.
The biggest problem is that the teachers currently in service never learned enough math to begin with, and so can’t be expected to teach what they don’t already know. We only think our teachers know math because they know just as little math as we do. If you want to know how scarily ignorant of math our teachers are, I suggest reading Liping Ma’s Knowing and Teaching Elementary Mathematics for a start.DEd Reckoning touches on math as well.I’ve written about this on my own blog, and I’m not just talking out of my butt here. I’ve taught math to these potential teachers. They lack the prerequisite skills to pass a college algebra class. You can tell who in the class is in the Elementary Education program; they’re the ones sitting in the back row, getting a D on every exam because they have to use a calculator to do three times two (and they think this is normal). So when Bob Brandt of Bellevue says "How do you know three times two equals six? Any idiot knows that," I would counter that an exceptional idiot must be teaching his kids math. We’ve raised an entire generation of teachers who don’t even know enough about math to know that they are ignorant of it.
Some parents say the Madison School District's spending cuts, combined with its attempts to close the achievement gap, have reduced opportunities for higherachieving students.Check out Part I and Part II of Cullen's series.
Jeff Henriques, a parent of two highachieving students, said one of the potential consequences he sees is "bright flight"  families pulling students with higher abilities out of the district and going elsewhere because their needs aren't being met.One of the larger examples of this conflict is surfacing in the district's move toward creating "heterogeneous" classes that include students of all achievement levels, eliminating classes that group students of similar achievement levels together.
Advocates of heterogeneous classes say students achieving at lower levels benefit from being in classes with their higherachieving peers. But some parents of higherachieving students are concerned their children won't be fully challenged in such classes  at a time when the amount of resources going to talented and gifted, or TAG, programs is also diminishing.
Watch Professor Gamoran's presentation, along with others related to the homogeneous / heterogeneous grouping debate here. Links and commentary and discussion on West's English 10. Jason Shepherd took a look at these issues in his "Fate of the Schools" article.
Working in conjunction with the Schools of Hope project led by the United Way of Dane County, the district has made progress in thirdgrade reading scores at the lowest achievement levels. But racial and income gaps persist among thirdgraders reading at proficient and advanced levels.The first part of Cullen's series is here.Other initiatives are taking place in the middle and high schools. There, the district has eliminated "deadend classes" that have less rigorous expectations to eliminate the chance that students will be put on a path of lower achievement because they are perceived as not being able to succeed in higherlevel classes.
In the past, high school students were able to take classes such as general or consumer math. Now, all students are required to take algebra and geometry  or two credits of integrated mathematics, combining algebra, statistics and probability, geometry and trigonometry  in order to graduate.
One of the district's more controversial efforts has been a move toward "heterogeneous" classes that include students of all achievement levels, eliminating classes that group students of similar achievement levels together.
Advocates of heterogeneous classes say students who are achieving at lower levels benefit from being in classes with their higherachieving peers. But others say the needs of higherachieving students aren't met in such classes.
And in addition to what schools are already doing, Superintendent Art Rainwater said he would like to put learning coaches for math and reading in each of the district's elementary schools to improve teachers' ability to teach all students effectively.
Five years ago we moved to Madison. A big factor in this decision was the expectation that we could rely on Madison public schools to educate our children. Our eldest went through West High School. To our delight the rigorous academic environment at West High transformed him into a better student, and he got accepted at several good public universities.
Now we are finding this promise betrayed for our younger children. Our elementary school appears to be sliding into disarray. Teachers and children are threatened, bullied, assaulted, and cursed at. Curricula are dumbed down to accommodate students who are unprepared for real school work. Cuts in special education are leaving the special needs kids adrift, and adding to the already impossible burdens of classroom teachers. To our disappointment we are forced to pull one child out of public school, simply to ensure her an orderly and safe learning environment.
Unless the School Board addresses these challenges forcefully and without obfuscation, I am afraid a historic mistake will be made. Madison schools will slip into a vicious cycle of middle class flight and steady decline. The very livability of our city might be at stake, not to mention our property values.
To me the necessary step is clear. The bottom five to ten percent of students, and especially all the aggressive kids, must be removed from regular classes. They should be concentrated in separate schools where they can receive the extra attention and intensive instruction they need, with an option to join regular classes if they are ready.
Meanwhile regular schools should be populated by children who can actually remain in their seats and do school work. Money can be saved by increasing class size. Achievement of underprivileged kids would improve when harmful distractions are removed and teachers can focus on teaching instead of constant discplinary management.
I have boiled things down to three theses, which I imagine most Madisonians would agree with:
I sincerely hope we can maintain a viable city and its great schools. In the case of Madison these two are inextricably tied together.
Timo Seppalainen
An overwhelming majority of Ashland students who were given the choice between traditional math and the Core Plus curriculum decided to take algebra I courses next school year, according to a report given Monday by Ashland High School Principal Steve Gromala.In a report to the Ashland School Board, it was noted that 83 percent of students signed up for algebra I, which was offered for the first time in several years after parents and board members demanded an alternative to the Core Plus curriculum.
A total of 170 students, including 115 incoming freshmen and 55 of next year’s sophomores, enrolled in the newly offered algebra I course for the 200607 school year. By comparison, 34 students enrolled in Core Plus 1.
The addition of algebra I next school year is the first step toward offering a dualtrack math curriculum that will allow incoming freshmen to choose between algebra classes and Core Plus. Additional classes such as geometry, algebra II and precalculus will be added in future years as students advance.
"I want to ensure you that we will not need any additional staff next year," Gromala told the board. "For future years, we'll have to wait and see."The 55 sophomores who chose to take algebra I next year will have to start over in the traditional curriculum and must take a minimum of three years of algebra to meet graduation requirements, Gromala noted.
To ensure that students had equal opportunity to choose either algebra or Core Plus, Gromala said the new algebra class was offered during each of the school's eight daily sections.
Board member Jeanne Thompson, a longtime proponent of implementing a dual math curriculum, thanked Gromala and Curriculum Director Barb O'Brien for setting up the new schedule.
"It's been a long road, but the parents' wishes are being met," Thompson said. "That's very important."
Now that enrollment numbers have been determined, the school's math department is trying to decide which textbook to purchase for next year's students.
Math teachers have already reviewed 14 different algebra books using a list of criteria and have narrowed their selection to two choices: Glencoe/McGraw Hill 2005 and McDougal Littell 2007.
"They're in unanimous agreement that either of these textbooks would be appropriate," O'Brien said.
However, because of the public's interest in the new math curriculum, O'Brien wanted to give community members an opportunity to review the two texts before the board approves a set of books at its April meeting.
As a result, over the next month, community members can stop by the school district's administrative offices, review each of the textbooks and fill out comment cards.
The Ashland School District's central office is located at 2000 Beaser Avenue, and Curriculum Director Barb O'Brien can be contacted at 6827080, ext. 4.
Institute of Educational Sciences:
The new TIMSS 1999 Video Study report on eighthgrade science teaching examines how students in 5 countries, including the United States, experience science as it is actually taught.
Richard O. Hill and Thomas H. Parker: Department of Mathematics  Michigan State University [Complete Study: PDF]:
One measure of the effectiveness of a high school mathematics program is the success students have in subsequent university mathematics courses. As part of a largescale study of Michigan students, we analyzed the records of students arriving at Michigan State University from four high schools which adopted the CorePlus Mathematics program. Those students placed into, and enrolled in, increasingly lower level courses as the implementation progressed; the downward trend is statistically very robust (p < .0005). The grades these students earned in their university mathematics courses were also below average (p < .01). ACT scores suggested the existence but not the severity of these trends.Over the past two decades there has been a growing awareness of the inadequacy of the mathematical skills of American high school graduates. That was the assessment of the 1983 report A Nation at Risk [9]. Many subsequent studies point to the same conclusion. The most recent National Assessment of Educational Progress (NAEP) Report [2] concluded that only 17 percent of US twelfth graders were proficient at mathematics (1). International comparisons also indicate a relatively low level of mathematics achievement by US high schoolstudents. The Third International Mathematics and Science Study (TIMSS) assessed the ‘Mathematics Literacy’ of endof secondary students in 22 countries and found that US students statistically outperformed only two countries, Cyprus and South Africa [13]. Related studies suggest that the mathematics courses taken by American high school students are often at a lower level than those taken by their international peers, and that US high schools are offering a wide assortment of courses which lack the focus and coherence found in many foreign curricula [14]. This situation has been of particular concern on college and university campuses, where large numbers of students require remedial courses to bring their mathematical knowledge and skills up to what is required for collegelevel mathematics and science courses.
Despite nearly 30 years of improvements in U.S. children's overall quality of life, their basic academic skills have barely budged, according to research led by a Duke University sociologist.2006 Child WellBeing Results.
The "educational flatline," as measured by scores on math and reading exams, defies researchers' expectations, because other qualityoflife measures, such as safety and family income, have improved steadily since 1975.More recently, even areas that had worsened in the 1970s and 1980s, such as rates of teen suicide, have improved dramatically, so researchers had expected that education improvements would soon follow. They didn't.
The Educational Flatline, Causes and Results:The Education Flatline: Causes and Solutions
Thousands of schools across the nation are responding to the reading and math testing requirements laid out in No Child Left Behind, President Bush's signature education law, by reducing class time spent on other subjects and, for some lowproficiency students, eliminating it.Schools from Vermont to California are increasing — in some cases tripling — the class time that lowproficiency students spend on reading and math, mainly because the federal law, signed in 2002, requires annual exams only in those subjects and punishes schools that fall short of rising benchmarks.
The changes appear to principally affect schools and students who test below grade level.
Shepherd has written the definitive piece for the April 4, 2006 election. Pick up the current Isthmus and have a look or view the article online here. I've placed two charts from the article below (click continue reading..... if you don't see them).Unless you have a kid in the Madison schools, many of the issues discussed by the four Madison school board candidates in our weekly TakeHome Test may not strike a familiar chord.
That's why we asked our schools reporter Jason Shepard to provide an overview in this week's Isthmus of the trends buffeting the 24,000student district. The cover story is: The Fate of the Schools: Will the Madison district sink or swim? April 4th elections could prove pivotal.
As you'll read, the growing number of poor students, decreased state funding and nasty board infighting provide a sobering context for the election.
Espen Andersen, Associate Professor, Norwegian School of Management and Associate Editor, Ubiquity:
[The following article was written for Aftenposten, a large Norwegian newspaper. The article encourages students to choose math as a major subject in high school  not just in preparation for higher education but because having math up to maximum high school level is important in all walks of life. Note: This translation is slightly changed to have meaning outside a Norwegian context.]
Why you should choose math in high schoolA recurring problem in most rich societies is that students in general do not take enough math  despite high availability of relatively wellpaid jobs in fields that demand math, such as engineering, statistics, teaching and technology. Students see math as hard, boring and irrelevant, and do not respond (at least not sufficiently) to motivational factors such as easier admission to higher education or interesting and important work.
Linda Borg writing in the Providence Journal:
Michael Lauro, the district's new math coordinator, will discuss plans for a curriculum called FASTT Math.PROVIDENCE  Osiris Harrell, an outspoken critic of the school district's math curriculum, has invited parents and school officials to a meeting March 22 to discuss the effectiveness of the math program.
The forum will be held from 6 to 8 p.m. at the Federal Hill House, 9 Cortland St., Providence.
Michael Lauro, the district's new math coordinator, will discuss plans for a fresh approach to math called FASTT Math. The district is considering trying it on a limited basis next year.
Harrell has met with Lauro to discuss his concerns about the current math program and to agree on how to work together, according to school spokeswoman Maria Tocco.
Harrell, in a recent interview with The Providence Journal, said he was distressed by the district's approach to math instruction, a program called Math Investigations that teaches students how to think about problemsolving rather that drilling them in the basics. The district adopted it in 2003 at the urging of thenSupt. Diana Lam.
Harrell, who is forming a parents' watchdog group called Project Future 2000 and Beyond, has been circulating a petition that asks the district to prove that its current math curriculum works. When Harrell gets 800 signatures, he said he will present the petition to Mayor David N. Cicilline and Schools Supt. Donnie Evans.After Harrell's comments were published in The Journal, he said that a number of parents contacted him to share their frustration with Math Investigations, which encourages students to come up with their own solutions to basic math problems.
By contrast, FASTT Math is a return to the skillanddrill approach familiar to many of today's parents. After taking an online test to determine their skill levels, students spend 10 minutes answering basic math problems. The problems get harder as the student progresses.
"The theory is that students need to be able to recall these facts within so many seconds so they can free up their minds for higherorder math skills," said Debbie Hodin, director of direct marketing for Tom Snyder Productions, the company that makes the software.
A number of school districts, including Hillsborough, Fla., Evans' former employer, have adopted the program, which is designed for students who are struggling with basic math, especially those who are performing at least one grade level below their peers.
FASTT Math was developed by Ted Hasselbring, a professor of special education technology at the University of Kentucky, and Laura Goin, the CEO of Designs for Learning.
In his State of the Union address in January, President Bush stressed the importance of improving math education. He proposed to "train 70,000 high school teachers to lead advanced placement courses in math and science, bring 30,000 math and science professionals to teach in classrooms, and give early help to students who struggle with math."Jonathan Farley is a professor in the Department of Mathematics and Computer Science at the University of the West Indies, Jamaica, and a CISAC science fellow.But where will these teachers come from? And will the training of teachers be sufficient to increase the number of students choosing math and science careers? And why does all this matter?
Because mathematics is the foundation of the natural sciences. It is no coincidence that Isaac Newton, the man who formulated the law of gravitational attraction that revolutionized our understanding of the universe, was also the man who popularized the calculus. And the natural sciences, however pure, are what give us airplanes, cable TV and the Internet.
In the 2003 Program for International Student Assessment, a test that measures math literacy, American 15yearolds performed worse than their peers in 23 countries, as well as those in Hong Kong. It's not hard to see why. According to the National Council of Teachers of Mathematics, 40 percent of the nation's middle school math teachers do not have the equivalent of an undergraduate minor in math. The average starting salary of a teacher is only $30,000, whereas the average starting salary for a recent college graduate in computer science or engineering is $50,000.
California Department of Education (pdf):
Additional standards and frameworks are posted here.
A highquality mathematics program is essential for all students and provides every student with the opportunity to choose among the full range of future career paths. Mathematics, when taught well, is a subject of beauty and elegance, exciting in its logic and coherence. It trains the mind to be analytic—providing the foundation for intelligent and precise thinking.To compete successfully in the worldwide economy, today’s students must have a high degree of comprehension in mathematics. For too long schools have suffered from the notion that success in mathematics is the province of a talented few. Instead, a new expectation is needed: all students will attain California’s mathematics academic content standards, and many will be inspired to achieve far beyond the minimum standards.
The content standards identify what all students in California public schools should know and be able to do in mathematics at each grade level. The standards emphasize computational and procedural skills, conceptual understanding, and problem solving. The standards are organized by grade level and are presented in five strands up to grade seven: number sense, algebra and functions, measurement and geometry; statistics, data analysis, and probability; and mathematical reasoning. The mathematics studied in grades eight through twelve falls naturally under the discipline headings of algebra, geometry, etc.
Wisconsin State Journal Editorial:
The United States is falling behind China and India in producing scientists and mathematicians, raising serious questions about America's economic future.There's been a great deal of discussion on these issues here.While the national scene is troubling, Wisconsin enjoys some bright spots.
State students consistently score above the national average on the ACT college admissions test, especially in math and science. An increasing number 69 percent of 2005 graduates took the test.
To compete in the global knowledgebased economy, Wisconsin must continue its commitment to math and science education and encourage more students to take related courses.
Susan Lochen, Madison West High School (cosigned by other West math teachers: Janice Cis, Keith Knowles, Carol Michalski, Jackie Hubbard, Daniel Boyland, Artie L. Orlik, Stephen Lang, Stephen Land, Tim Goldsworthy):
Moreover, parents of future West High students should take notice: As you read this, our department is under pressure from the administration and the math coordinator's office to phase out our "accelerated" course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a onesizefitsall curriculum.I'd forgotten (unfortunately) about this letter. School Board Seat 1 candidate Maya's post below included a link to these words. The current school board majority has not addressed these critical questions....It seems the administration and our school board have redefined "success" as merely producing "fewer failures." Astonishingly, excellence in student achievement is visited by some school district administrators with apathy at best, and with contempt at worst. But, while raising low achievers is a laudable goal, it is woefully shortsighted and, ironically, racist in the most insidious way. Somehow, limiting opportunities for excellence has become the definition of providing equity! Could there be a greater insult to the minority community?
Madison School Board Seat 1 Candidate Maya Cole:
From his book, Innumeracy, Mathematical Illiteracy And Its Consequences, John Allen Paulos defines innumeracy as, "...an inability to deal comfortably with the fundamental notions of number and chance, [it] plagues far too many otherwise knowledgeable citizens."Paulos goes on to state that, "[i]n an increasingly complex world full of senseless coincidence, what's required in many situations in not more factswe're inundated alreadybut a better command of known facts, and for this a course in probability is invaluable...Probability, like logic, is not just for mathematicians anymore. It permeates our lives."
Finally, Paulos concludes, "I'm distressed by a society which depends so completely on mathematics and science and yet seems so indifferent to the innumeracy and illiteracy of so many of its citizens; with a military that spends more than one quarter of a trillion dollars each year on ever smarter weapons for ever more poorly educated soldiers; and with the media which invariably become obsessed with this hostage on an airliner, or that baby who has fallen into a well, and seems insufficiently passionate when it comes to addressing problems such as urban crime, environmental deterioration, or poverty."
So where do we start?
Math curriculum.
That's right, we start with math. The complicated and controversial topic of many school districts; but one that I hope, can be dicussed at every school board forum in the next few weeks.
A very lively discussion of the math curriculum in the Madison Metropolitan School District ensued recently at a forum held with University math professors, the school of Education, the general public and the MMSD administration. (You can watch the video below.)
Carrick Mollenkamp and Charles Fleming:
As a result, banks are hiring an increasing number of recruits who understand derivatives. Inside banks, they are known as "quantitative analysts," or "quants" for short. They are able to marry stochastic calculus  the study of the impact of random variation over time  with the realities of financial trading.Derivatives are financial contracts, often exotic, whose values are derived from the performance of an underlying asset to which they are linked. Companies use them to help mitigate risk. For example, a company that stands to lose money on fixedrate loans if rates rise can mitigate that risk by buying derivatives that increase in value as rates rise. Increasingly, investors are also using derivatives to make big bets on, say, the direction that interest rates will move. That carries the possibility of large returns, but also the possibility of large losses.
The 75 or so students who take Ms. El Karoui's "Probability and Finance" course each year are avidly sought by recruiters. Three years ago, Joanna Cohen, a specialist in quant recruitment at Huxley Associates in London traveled to Paris to meet Ms. El Karoui to ensure her search firm was in the loop when students hit the job market. Today, Ms. Cohen says she carefully checks résumés with Ms. El Karoui's name to make sure applicants aren't overstating their interaction with the professor.
Isthmus:
The Memorandum to Local Media represented one attempt to at least look at the issues rather than simply compare and contrast personalities.
Columnist Richard Cohen isn't the first to advise young people not to bother about learning math. In 2003, WOAI in San Antonio asked a selection of adults  a radio DJ, a school board president, a councilman and a former judge  to take Texas' new TAKS test, a graduation requirement. The school board president got an A in English and a B in math. Everyone else flunked the math. DJ Jamie Martin tells students not to worry."Kids did you hear me? You don't need to learn math like me. You can still be successful and do bad on math."
Despite the grammatical error, she scored a B in English.
More than half of San Antonio's 11th graders failed on their first try.Educators say they saw the same kind of failure rates and complaints when they introduced the TAAS test. By the time it was retired, those teachers say, the TAAS test was considered too easy.
Adults who've been away from the classroom for years are bound to be rusty on their "vertices and vortexes," not to mention "the little numbers." If they needed to pass the test to get ahead, they'd study and learn. San Antonio students can do that too. They're more likely to be successful if they can do the math. Not everybody can grow up to work in the innumerate media.
"And that's what's so exciting about the program for the kids," said Luke Felker, Madison Country Day School, "is that through some solid work at the beginning, they begin to realize that they can do a lot of this in their heads."Felker says the program also focuses more on depth, than it does covering a variety of math lessons, making it easier for the kids to retain what they learn.
Retired UW professor Richard Askey says the Singapore program is highly successful, but it isn't the only way to properly teach math.
"It's possible to do it in other ways," said Askey. "Japanese elementary schools are not exactly the same as the Singapore, and they're done carefully."
Askey says US schools haven't been teaching math 'carefully.'
At a meeting on February 22 (audio / video), representatives of the Madison Metropolitan School District presented some data [820K pdf  html (click the slide to advance to the next screen)] which they claimed showed that their middle school math series, Connected Mathematics Project, was responsible for some dramatic gains in student learning. There was data on the percent of students passing algebra by the end of ninth grade and data from the state eighth grade math test for eight years. Let us look at the test data in a bit more detail.
All that was presented was data from MMSD and there was a very sharp rise in the percent of students scoring at the advanced and proficient level in the last three years. To see if something was responsible for this other than an actual rise in scores consider not only the the Madison data but the corresponding data for the State of Wisconsin.
The numbers will be the percent of students who scored advanced or proficient by the criteria used that year. The numbers for Madison are slightly different than those presented since the total number of students who took the test was used to find the percent in the MMSD presented data, and what is given here is the percent of all students who reached these two levels. Since this is a comparative study, either way could have been used. I think it is unlikely that those not tested would have had the same overall results that those tested had, which is why I did not figure out the State results using this modification. When we get to scores by racial groups, the data presented by MMSD did not use the correction they did with all students ( All 8th grade students in both cases)
MMSD  Wisconsin  
Oct 97  40  30 
Feb 99  45  42 
Feb 00  47  42 
Feb 01  44  39 
Feb 02  48  44 
Nov 02  72  73 
Nov 03  60  65 
Nov 04  71  72 
This is not a picture of a program which is remarkably successful. We went from a district which was above the State average to one with scores at best at the State average. The State Test was changed from a nationally normed test to one written just for Wisconsin, and the different levels were set without a national norm. That is what caused the dramatic rise from February 2002 to November 2002. It was not that all of the Middle Schools were now using Connected Mathematics Project, which was the reason given at the meeting for these increases.
It is worth looking at a breakdown by racial groups to see if there is something going on there. The formats will be the same as above.
Hispanics  
MMSD  Wisconsin  
Oct 97  19  11 
Feb 99  25  17 
Feb 00  29  18 
Feb 01  21  15 
Feb 02  25  17 
Nov 02  48  46 
Nov 03  37  38 
Nov 04  50  49 
Black (Not of Hispanic Origin)  
MMSD  Wisconsin  
Oct 97  8  5 
Feb 99  10  7 
Feb 00  11  7 
Feb 01  8  6 
Feb 02  13  7 
Nov 02  44  30 
Nov 03  29  24 
Nov 04  39  29 
Asian  
MMSD  Wisconsin  
Oct 97  25  22 
Feb 99  36  31 
Feb 00  35  33 
Feb 01  36  29 
Feb 02  41  31 
Nov 02  65  68 
Nov 03  55  53 
Nov 04  73  77 
White  
MMSD  Wisconsin  
Oct 97  54  35 
Feb 99  59  48 
Feb 00  60  47 
Feb 01  58  48 
Feb 02  62  51 
Nov 02  86  81 
Nov 03  78  73 
Nov 04  88  81 
I see nothing in the demography by race which supports the claim that Connected Mathematics Project has been responsible for remarkable gains. I do see a lack of knowledge in how to read, understand and present data which should concern everyone in Madison who cares about public education. The School Board is owed an explanation for this misleading presentation. I wonder about the presentations to the School Board. Have they been as misleading as those given at this public meeting?
Richard AskeyMs. Cornelius (an anonymous AP History high school teacher):
All of my grades are based on percentages. I'm not one of these teachers who wants to convert someone's scores in my head, so I just weight grades differently. But all grades are based on 100 possible points. I can tell at a glance how a student is doing this way.But this habit often makes it interesting when students are trying to figure out their grades on quizzes. I usually have a rather simple number of questions in terms of being able to calculate grades easily: 5, 10, 12, 20, 25, or 33 items. As I watched several of my AP students struggle with figuring out their grades, I had to suppress a groan of frustration. It was a 20 item quiz therefore each question would be worth 5 points, right? Young Frederick wanted to pull out his calculator to figure out what his score would be if he missed 7.
"No calculator. You can do this," I urged.
He couldn't begin to figure out how to determine his grade without a calculator. He is 16 years old and taking precalculus and other collegetrack classes (I never took a course beyond algebra 2, much to my chagrin). He doesn't immediately know that 7x5=35, and then subtract 35 from 100, nor can he figure out that 13x5=65. As a matter of fact, he stumbled over the 10035 part and insisted the answer was 75.
It is obvious that his only problem is NOT that he didn't do his reading for my AP US history class carefully enough last night. His problem begins with a basic innumeracy. Of course, many would say that he is a victim of a larger educational trend which I pray to God is finally being placed on the pyre of idiotic educational theories: that rote memorization is bad, bad, baddety bad bad.
Video and audio from Wednesday's Math Forum are now available [watch the 80 minute video] [mp3 audio file 1, file 2]. This rare event included the following participants:
The conversation, including audience questions was lively.
 Dick Askey (UW Math Professor)
 Faye Hilgart, Madison Metropolitan School District
 Steffen Lempp (MMSD Parent and UW Math Professor)
 Linda McQuillen, Madison Metropolitan School District
 Gabriele Meyer (MMSD Parent and a UW Math Department Lecturer)
 Dr. Terry Millar of the Wisconsin Center for Education Research
The discussion continues with these notes and links from the audience and participants:
West High School Math Teachers:
Moreover, parents of future West High students should take notice: As you read this, our department is under pressure from the administration and the math coordinator's office to phase out our "accelerated" course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a onesizefitsall curriculum.
It seems the administration and our school board have redefined "success" as merely producing "fewer failures." Astonishingly, excellence in student achievement is visited by some school district administrators with apathy at best, and with contempt at worst. But, while raising low achievers is a laudable goal, it is woefully shortsighted and, ironically, racist in the most insidious way. Somehow, limiting opportunities for excellence has become the definition of providing equity! Could there be a greater insult to the minority community?
Learning from Teaching: Exploring the Relationship between Reform Curriculum and Equity, Jo Boaler, Stanford University [110K pdf]:Some researches have expressed doubts about the potential of reformoriented curricula to promote equity. This article considers this important issue and argues that investigations into equitable teaching must pay attention to the particular practices of teaching and learning that are enacted in the classrooms. Data are presented from two studies which middle school and high school using reformoriented mathematics curricula achived a reduction in linquistic, ethnic, and class inequalities in their schools. The teaching and learnign practices that these teachers employed were central to the attainment of equality, suggesting that it is critical that relational analyses of equity go beyond the curriculum to include the teacher and training.
The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning Kenneth R. Koedinger, Human–Computer Interaction Institute Carnegie Mellon University; Mitchell J. Nathan, School of Education, University of Colorado [677K PDF]:This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problemsolving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students’ strategies and errors as th ebasis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external represen tations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.
Dick Askey:Madison and Wisconsin Math Data, 8th Grade
NAEP 2005 data for US, Wisconsin, Minnesota, and Texas
4th gradeUS WI MN TX
All students 237 241 246 242
White 246 247 251 254
AfricanAmerican 220 210 219 228
Hispanic 225 224 223 235
8th grade
All students 278 285 290 281
White 288 291 296 295
AfricanAmerican 254 246 251 264
Hispanic 261 265 263 271
Terry Millar:
Wisconsin Center for Education Research:Attached is the powerpoint presentation [820K pdf  html (click the slide to advance to the next screen)] that Linda, Faye, and I used.I also have cc'd UWMadison Curriculum and Instruction Professor Victoria Hand who spoke from the audience Wednesday evening. You might contact her about contacts in the School of Education with expertise on the science of testing, or for research in math education. Dr. Norman Webb is one such person, and therefore I have copied him also. As I said that evening, Connected Math will be releasing a report sometime in March that has a lot of information about implementation of Connected Math nationwide. Their url is
I found the forum interesting  thanks for arranging it.
Gisele Sutherland:
Madison ParentLast night was a display of statistics that 3 of the 4 professors shot holes in quickly. I really don't care what the statistics show  I'm NOT happy with the math curriculum. And, as a taxpayer, I should have a say, and I do, but I am not heard  as evidenced last night, where I felt I was dismissed when I went to speak to one of the MMSD panelists.We have to reinforce fractions and teach percentages, decimals, etc at home because the basic building blocks are not being addressed in the classroom. Ridiculous. As parents, we should not have to do the job ourselves  support the job done at school, YES. But, do the job ourselves, NO. And, my sense is the teachers agree with us  two or three with whom I have spoken at Thoreau would love direction to switch to Singapore. It's logical, sequential, and textbook based, as opposed to all these loose sheets that come home, which do not seem to build on anything.
Steffen Lempp:
Madison Parent and UW Math Professor:www.singaporemath.com
Larry Winkler:
Madison ParentGood meeting last night.But, whenever data or statistics or testing was mentioned, the conversation was redirected.
There seems to be little understanding of testing, what each test means, what each kind of test tests; characteristics of norm referenced tests (NRT), of criterion referenced tests with their cut scores, achievement tests, predictive tests, how test items are chosen, the specific characteristics of WKCE, NAEP, TIMSS, PISA, ACT, SAT, GRE, LSAT, MCAT, etc.
Statistics is not understood, and how it is reflected in the testing, and testing wars. Classics such as Huff's How to Lie With Statistics, and more currently, Best's two books "Damn Lies and Statistics", and "More Damn Lies and Statistics". Seems to me these books are the bibles of the advocates.
Prof Askey mentioned the NAEP as the key indicator of student success, but the National Academy of Science, as cited approvingly by NCES, "NAEP's current achievement level setting procedures remain fundamentally flawed. The judgment tasks are difficult and confusing; raters’ judgments of different item types are internally inconsistent; appropriate validity evidence for the cut scores is lacking; and the process has produced unreasonable results."
What I am seeing is purposeful misrepresentation in the schooling wars, each side conveniently hiding flaws and inconsistency in their reasoning and data. All smoke and little light.
I would like to suggest a forum to discuss the "science" of testing to help remove the smoke.
Thanks

Larry Winkler
Gabriele Meyer:
Madison Parent and UW Math LecturerGood evening, I am Gabriele Meyer and I am a lecturer in the Math dept at
UW Madison. Through my son, Walter, I first encountered Connected Math.
Here is what I found:on a practical level:
 the material covered in Connected Math is insufficient in depth and structure and even in scope, e.g. it doesn't explicitly cover double fractions and even though it is excessively wordy, it doesn't cover multistep word problems.
 The way material is covered does not stress the connections within math, i.e. the mathematical structures and rules, which to a large extent are the beauty of the field
 there are way too few exercises to firm up the concept in the learner.
 It takes a very good teacher to achieve a good outcome given these flaws. In particular, the teacher would have to supplement with other material and modify lesson plans. This is inefficient and prone to great inequities in teaching performance.
on a philosophical level:
Math was discovered over thousands of years and represents the distillate of the efforts of its many practitioners. The next step can only be comprehended if the previous one has been understood. The investigative/discovery method, while very enjoyable, makes the student to reinvent the wheel, without the benefit of the rules already discovered. 12 years of math education are simply too short to have students discover their way to calculus, a path that took humanity from prehistory to the 16 hundreds.What can be done?
On a general note, any teaching philosophy elevated to the level of dogma is bad. Good teachers usually use a mix of techniques. We should not completely discard the investigative approach, but we should look at what others, also in other countries, do better.
For uniform Math instruction at the Middle school level, I personally, would use Singapore Math. It worked for our son, with Discovery/Connected Math as a backup and supplement. This ensures that the benchmarks (arithmetic with whole numbers and fractions, some geometry) are met and the kids can go on to geometry and algebra in high school.
If there are to be different Math class styles in middle school, then the choice of which class to attend should be left to the parents/children with the understanding that in some classes more homework is required to keep up.
Also, it should be clear that certain types of math are terminal in the sense that they do not prepare for the next level. For example, to a very large extent Discovery type math throughout high school does not prepare for the rigors of Calculus, as is needed for the sciences and engineering. It costs time and money to make up for this in college.
I think it is especially important that *Public Schools* provide a solid math curriculum for the sake of economically and socially disadvantaged youths. They can't get it anywhere else.
Thank you.
Mike and Kristin Jenkins:
Chapel Hill, NCWe feel your pain, and have left Madison to live in an area that "gets it". Our 6th grade son is now enrolled in a racially diverse public school program and studying among other things the quadratic equation and Shakespeare. In addition to this our property taxes are about half what they were in Madison. A short description of the program is below. UW is just as good (probably better) as UNC and I expect this could be put together in Wisconsin. We would move back in a minute if a "LEAP like" program was available in Wisconsin. Wisconsin spends lots of money on challenged folks who need help...gifted kids need help too...as your dropout rates indicate. I have no doubt in my mind that my son would not have made it through public school in Wisconsin.Tar Heel Education: Something For The Gifted
In the schools of the college town of Chapel Hill, North Carolina, kids who score above the 97th percentile in reading and math are invited to participate in a program that is designed to meet their needs:
Carol Horne, gifted program curriculum coordinator for Chapel HillCarrboro City Schools, explained in a presentation Tuesday night at Smith Middle School the logistics of LEAP. [ Learning Environment for Advanced Programming]
The program is geared toward kids who have “demonstrated extraordinary levels of intellectual potential and academic achievement found in the top 1 percent of the national population in reading and math,” according to Horne’s presentation.
Previously offered only to fourth and fifthgraders, the program now is available at Smith to all eligible district students in sixth and seventhgrades. And by the 200607 school year, eighthgraders will get their chance to prove their skills.
Ed Holub, whose child participates in the program, said he is pleased with the program and emphasized its necessity.
“It’s hard to operate with a wide range of students in the class,” he said. “It fulfills the district’s mission of meeting each child’s potential in every classroom.”
Holub said it is almost impossible for teachers to instruct each student at his or her own proficiency level in a class, and that LEAP provides an efficient way of teaching the most talented kids.
Tuesday’s information session focused on availability and which children qualify for the program. Horne explained that a committee decides entrance based on aptitude or achievement — students take the Naglieri NonVerbal Aptitude Test as one indicator.
Only those who score in the 97th percentile or higher on both the reading and math portions of the test are eligible for the program.
Horne said many parents who have children who qualified for the program might choose not to leave their individual school, adding that each system school had a “thriving, excellent gifted program.”
One concern about LEAP is that students might be isolated from the rest of the school population, which might prove detrimental.
But Valerie Reinhardt, principal at Smith, said no such problem exists.
Students in the program have homeroom and four core sections with their LEAP classmates but attend three electives that allow them to follow an avenue of learning of their choice, she added.
“Above all, they are Smith students, not LEAP students,” she said.
Boyd Blackburn, a math and social studies teacher in the program, agreed.
“In the middle school, they aren’t isolated,” he said. “It’s a good mix. I would not describe them as isolated, and I don’t think they feel isolated either.”
So far, Reinhardt said the installation of the program into middle school has progressed smoothly.
“There’s a lot of healthy learning,” she said. “There were a couple of bumps in the beginning, but the kids and parents are pleased.”
Holub admitted how satisfied he was with the program so far.
“I think the district did an outstanding job of recruiting teachers and putting together a curriculum,” he said. “They are very committed to making the entire LEAP program a success.”
It is a most unfortunate fact that in many American schools bright and highlymotivated children are often "pickedon" by students who think that school is not a place to work and learn but a place to play and waste time.It is even more unfortunate that in many cases, the schools permit this to continue.
The books are distributed by an Oregonbased company known as SingaporeMath.com, which counts a private school in Madison as the first of its growing number of clients.More on the Connected Math / Singapore Math textbook photos.The biggest difference between math instruction in Singapore  a citystate with a population of about 4.4 million  and the United States is a simple premise: Less is more.
Students in Singapore are introduced to roughly half the number of new math topics a year as students in the United States are. Experts and policy analysts say Singapore's emphasis on depth over breadth is a formula for success.
The thicker the textbooks and the greater the volume of math topics introduced a year, the less likely American students and teachers are to achieve similar results, says Alan Ginsburg, director of the policy and program studies service at the U.S. Department of Education.
With scientific expertise sweeping the globe, the next generation of American scientists and engineers are going to face unprecedented competition, and college is too late to begin preparing them for it, according to the National Science Board.The board released its “Science and Engineering Indicators, 2006″[pdf] report Thursday. The report, which focused on elementary and secondary education, cast a foreboding tone. According to the report, while the scores of American students on national math assessments have risen slightly in recent years, the same cannot be said for science. According to the 2003 Trends in International Mathematics Science Study , fourth and eighth graders in the United States performed better in math and science than the international average of industrial nations, but improvement since 1995 was modest for eighth graders, and fourth graders took a slight step backward.
Even a fourth grade student who is getting his or her first exposure to science might already be left in the starting blocks, according to Jo Ann Vasquez, a National Science Board member and the lead author of the report. “[Kids] have to get science by third grade,” she said, “or that wonderment disappears.”
This is from a recent article in the Los Angeles Times. I was alerted to it by the Daily Howler blog http://www.dailyhowler.com/. I mention this because that site has had some great education coverage lately and will soon be launching an alleducation companion blog.
http://www.latimes.com/news/education/lamedropout30jan30,0,3211437.story?coll=lanewslearning
THE VANISHING CLASS
A Formula for Failure in L.A. Schools
Because they can't pass algebra, thousands of students are denied diplomas. Many try again and again  but still get Fs.
By Duke Helfand
Times Staff Writer
January 30, 2006
Each morning, when Gabriela Ocampo looked up at the chalkboard in her ninthgrade algebra class, her spirits sank.
There she saw a mysterious language of polynomials and slope intercepts that looked about as familiar as hieroglyphics.
She knew she would face another day of confusion, another day of pretending to follow along. She could hardly do long division, let alone solve for x.
"I felt like, 'Oh, my God, what am I going to do?' " she recalled.
Gabriela failed that first semester of freshman algebra. She failed again and again — six times in six semesters. And because students in Los Angeles Unified schools must pass algebra to graduate, her hopes for a diploma grew dimmer with each F.
Midway through 12th grade, Gabriela gathered her textbooks, dropped them at the campus book room and, without telling a soul, vanished from Birmingham High School.
Her story might be just a footnote to the Class of 2005 except that hundreds of her classmates, along with thousands of others across the district, also failed algebra.
Of all the obstacles to graduation, algebra was the most daunting.
The course that traditionally distinguished the collegebound from others has denied vast numbers of students a high school diploma.
"It triggers dropouts more than any single subject," said Los Angeles schools Supt. Roy Romer. "I think it is a cumulative failure of our ability to teach math adequately in the public school system."
When the Los Angeles Board of Education approved tougher graduation requirements that went into effect in 2003, the intention was to give kids a better education and groom more graduates for college and highlevel jobs. For the first time, students had to pass a year of algebra and a year of geometry or an equivalent class to earn diplomas.
The policy was born of a worthy goal but has proved disastrous for students unprepared to meet the new demands.
In the fall of 2004, 48,000 ninthgraders took beginning algebra; 44% flunked, nearly twice the failure rate as in English. Seventeen percent finished with Ds.
In all, the district that semester handed out Ds and Fs to 29,000 beginning algebra students — enough to fill eight high schools the size of Birmingham.
Among those who repeated the class in the spring, nearly threequarters flunked again.
The school district could have seen this coming if officials had looked at the huge numbers of high school students failing basic math.
Lawmakers in Sacramento didn't ask questions either. After Los Angeles Unified changed its policy, legislators turned algebra into a statewide graduation requirement, effective in 2004.
Now the Los Angeles school board has raised the bar again. By the time today's secondgraders graduate from high school in 2016, most will have to meet the University of California's entry requirements, which will mean passing a third year of advanced math, such as algebra II, and four years of English.
Former board President Jose Huizar introduced this latest round of requirements, which the board approved in a 61 vote last June.
Huizar said he was motivated by personal experience: He was a marginal student growing up in Boyle Heights but excelled in high school once a counselor placed him in a demanding curriculum that propelled him to college and a law degree.
"I think there are thousands of kids like me, but we're losing them because we don't give them that opportunity," said Huizar, who left the school board after he was elected to the Los Angeles City Council last fall. "Yes, there will be dropouts. But I'm looking at the glass half full."
Discouragement, Frustration
Birmingham High in Van Nuys, where Gabriela Ocampo struggled to grasp algebra, has a failure rate that's about average for the district. Nearly half the ninthgrade class flunked beginning algebra last year.
In the spring semester alone, more freshmen failed than passed. The tally: 367 Fs and 355 passes, nearly onethird of them Ds.
All those failures and near failures have left a wake of discouraged students and exasperated teachers.
Fifteenyearold Abraham Lemus, the son of Salvadoran immigrants, finally scraped by with a D after his mother hired a tutor. But he recalls how he failed the first time he took the course. "I was starting to get suicide thoughts in my head, just because of math," he said.
Shane Sauby, who worked as an attorney and stockbroker before becoming a teacher, volunteered to teach the students confronting firstyear algebra for a second, third or fourth time. He thought he could reach them.
But, Sauby said, many of his students ignored homework, rarely studied for tests and often skipped class.
"I would look at them and say, 'What is your thinking? If you are coming here, why aren't you doing the work or paying attention or making an effort?' " he said. Many would just stare back.
Sauby, who now teaches in another district, failed as many as 90% of his students.
Like other schools in the nation's secondlargest district, Birmingham High deals with failing students by shuttling them back into algebra, often with the same teachers.
Last fall, the school scheduled 17 classes of up to 40 students each for those repeating firstsemester algebra.
Educational psychologists say reenrolling such students in algebra decreases their chances of graduating.
"Repeated failure makes kids think they can't do the work. And when they can't do the work, they say, 'I'm out of here,' " said Andrew Porter, director of the Learning Sciences Institute at Vanderbilt University in Nashville.
The strategy has also failed to provide students with what they need most: a review of basic math.
Teachers complain that they have no time for remediation, that the rapid pace mandated by the district leaves behind students like Tina Norwood, 15, who is failing beginning algebra for the third time.
Tina, who says math has mystified her since she first saw fractions in elementary school, spends class time writing in her journal, chatting with friends or snapping pictures of herself with her cellphone.
Her teacher wasn't surprised when Tina bombed a recent test that asked her, among other things, to graph the equations 4x + y = 9 and 2x  3y =  6. She left most of the answers blank, writing a desperate message at the top of the page: "Still don't get it, not gonna get it, guess i'm seeing this next year!"
Teachers wage a daily struggle in classes filled with students like Tina.
Her teacher, George Seidel, devoted a class this fall to reviewing equations with a single variable, such as x  1 = 36. It's the type of lesson students were supposed to have mastered in fourth grade.
Only seven of 39 students brought their textbooks. Several had no paper or pencils. One sat for the entire period with his backpack on his shoulders, tapping his desk with a finger.
Another doodled an eagle in red ink in his notebook. Others gossiped as Seidel, a secondyear teacher, jotted problems on the front board.
"Settle down," Seidel told the fifthperiod students a few minutes after the bell rang. "It doesn't work if you guys are trying to talk while I'm trying to talk."
Seidel once brokered multimilliondollar business deals but left a 25year law career, hoping to find a more fulfilling job and satisfy an old desire to teach. Nothing, however, prepared him for period five.
"I got through a year of Vietnam," he said, "so I tell myself every day I can get through 53 minutes of fifth period…. I don't know if I am making a difference with a single kid."
Seidel did not appear to make a difference with Gabriela Ocampo. She failed his class in the fall of 2004 — her sixth and final semester of Fs in algebra.
But Gabriela didn't give Seidel much of a chance; she skipped 62 of 93 days that semester.
After dropping out, Gabriela found a $7anhour job at a Subway sandwich shop in Encino. She needed little math because the cash register calculated change. But she discovered the cost of not earning a diploma.
"I don't want to be there no more," she said, her eyes watering from raw onions, shortly before she quit to enroll in a training program to become a medical assistant.
Could passing algebra have changed Gabriela's future? Most educators would say yes.
Algebra, they insist, can mean the difference between menial work and highlevel careers. High school students can't get into most fouryear colleges without it. And the U.S. Department of Education says success in algebra II and other higherlevel math is strongly associated with college completion.
Apprenticeship programs for electricians, plumbers and refrigerator technicians require algebra, which is useful in calculating needed amounts of piping and electrical wiring.
"If you want to work in the real world, if you want to wire buildings and plumb buildings, that's when it requires algebra," said Don Davis, executive director of the Electrical Training Institute, which runs apprenticeship programs for union electricians in Los Angeles.
Algebra, with its idiom of equations and variables, is more abstract than the math that comes before it. It uses symbols, usually letters, to represent numbers and sets of symbols to express mathematical relationships.
Educators say algebra offers a practical benefit: Analytical skills and formulas enable people to make sense of the world. Algebra can help a worker calculate income taxes, a baseball fan determine a pitcher's earnedrun average and a driver determine a car's gas mileage.
"It's the language of generalization. It's a very powerful problemsolving tool," said Zalman Usiskin, director of the University of Chicago School Mathematics Project.
Rationale for Algebra
Although experts widely agree that algebra sharpens young minds, some object to making it a graduation requirement.
"If you want to believe you're for standards, you're going to make kids take algebra. It has that ring of authenticity," said Robert Balfanz, an associate research scientist with the Center for Social Organization of Schools at Johns Hopkins University in Baltimore. "But you're not really thinking through the implications. There may be no good reason why algebra is essential for all high school students."
Compulsory algebra is a relatively new idea in the faddish realm of education reform.
Until recently, high schools offered a range of programs. Students seen as academically able were placed in collegeprep classes. Others were funneled into vocational courses in which they learned such skills as auto mechanics and office technology.
It was an imperfect system in which some bright students, particularly minorities, could find themselves trapped in classes that steered them away from higher education.
Then, about a decade ago, the pendulum began to swing as the state decided to raise academic standards for high school graduation.
The concept of algebra for all also was meant to elevate the level of U.S. high school students, whose math performance has long trailed that of peers in other industrialized countries where algebra is introduced at earlier grade levels.
Eager to close this competitive chasm, education and business leaders in California sought to reengineer the state's approach to math. They produced new math standards they believed would foster a "rising tide of excellence."
This meant teaching algebra earlier, as soon as eighth grade for some students, even if instructors questioned whether younger students could handle abstract concepts.
"We didn't regard any of this as extreme," Stanford University mathematician James Milgram said recently, defending the 1997 math standards he helped write. "We need competent people in this country. We're on our way to [becoming] a secondrate economic power."
Legislators joined the charge in 1999, creating a high school exit exam with algebra questions, which takes effect this spring. They then enacted the law requiring algebra for graduation, starting with the Class of 2004, to prepare students for the exam.
To its staunchest advocate in the Legislature, algebra stood for higher expectations and new opportunities.
"We have a problem with a high dropout rate. You don't address it by making it easier to get through and have the meaning of the diploma diluted," said state Sen. Chuck Poochigian (RFresno), who wrote the algebra graduation law. "It should be a call to action … not to lower standards but to find ways to inspire. Our future depends on it."
'I Give Up'
Whether requiring all students to pass algebra is a good idea or not, two things are clear: Schools have not been equipped to teach it, and students have not been equipped to learn it.
Secondary schools have had to rapidly expand algebra classes despite a shortage of credentialed math teachers.
The Center for the Future of Teaching & Learning in Santa Cruz found that more than 40% of eighthgrade algebra teachers in California lack a math credential or are teaching outside their field of expertise; more than 20% of high school math teachers are similarly unprepared.
Recruitment programs and summer math institutes for teachers have been scaled back or eliminated because of budget cuts.
"It's a real collision of circumstance, and students are now having … to bear the brunt of public policy gone awry," said Margaret Gaston, executive director of the Santa Cruz research center.
High school math instructors, meanwhile, face crowded classes of 40 or more students — some of whom do not know their multiplication tables or how to add fractions or convert percentages into decimals.
Birmingham teacher Steve Kofahl said many students don't understand that X can be an abstract variable in an equation and not just a letter of the alphabet.
Birmingham math coach Kathy De Soto said she was surprised to find something else: students who still count on their fingers.
High school teachers blame middle schools for churning out illprepared students. The middle schools blame the elementary schools, where teachers are expected to have a command of all subjects but sometimes are shaky in math themselves.
At Cal State Northridge, the largest supplier of new teachers to Los Angeles Unified, 35% of future elementary school instructors earned Ds or Fs in their first collegelevel math class last year.
Some of these students had already taken remedial classes that reviewed high school algebra and geometry.
"I give up. I'm not good at math," said sophomore Alexa Ganz, 19, who received a D in math last semester even after taking two remedial courses. "I think I've been more confused this semester than helped."
Ganz, who wants to teach third grade, thinks the required math courses are overkill. "I guarantee I won't need to know all this," she said, perhaps not realizing that if she were to teach in a public school, she could be bumped as a newcomer to upper grade levels that demand greater math knowledge.
Administrators in L.A. Unified say they are trying to reverse the alarming failure rates of high school students by changing the way math is taught, starting in elementary schools.
The new approach stresses conceptual lessons rather than rote memorization, a change that some instructors think is wrong. New math coaches also are training teachers and coordinating lesson plans at many schools.
The simplest algebraic concepts are now taught — or are supposed to be taught — beginning in kindergarten.
These changes appear to be paying off, at least in elementary grades. L.A. Unified's elementarylevel math scores have risen sharply over the last five years, although middle schools and high schools have yet to show significant progress.
Searching for a solution in its secondary schools, L.A. Unified is investing millions of dollars in new computer programs that teach prealgebra, algebra and other skills.
Officials are considering other costly changes, including reducing the size of algebra classes to 25, launching algebra readiness classes for lagging eighthgraders and creating summer programs for students needing a kickstart before middle school or high school.
Some schools have taken matters into their own hands.
Cleveland High, four miles from Birmingham, places ninth and 10thgraders who get a D or F in algebra into semesterlong classes that focus on sixth and seventhgrade material and prealgebra. Students then return to standard algebra classes.
Eighteen percent of Cleveland's 10thgraders were proficient in algebra on state tests last spring, compared with 8% at Birmingham and 3% districtwide.
But Cleveland's strategy comes with risk. The state can lower the academic rankings of schools that remove ninth graders from firstyear algebra. Consistently low rankings can invite district audits and penalties, including removal of teachers and administrators.
Birmingham High, wary of these consequences, is attacking the algebra crisis the way many other schools do: providing students with extra help after school and on weekends. The school launched a round of Saturday classes last fall for 600 students who were failing beginning algebra. Only 100 showed up, even though administrators called each student's home.
The Saturday sessions start anew in February with a twist: separate algebra classes for parents who want to help their children.
But even as it tries to solve its algebra puzzle, Birmingham — along with the district's 50 other traditional high schools — will soon face the even more rigid graduation requirements passed by the school board.
The chairman of Birmingham's math department, Rick Prizant, said he believes the collegeprep agenda is a noble but misguided policy dictated by district officials out of touch with the realities of the classroom. Where others see opportunity, he sees catastrophe.
"They're being very unrealistic in what they are asking…. We're spinning our wheels here," said Prizant, who doubles as the school's athletic director. "I think you're going to see more dropouts. It's frightening to me."
*

Times staff writer Mitchell Landsberg contributed to this report.
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(BEGIN TEXT OF INFOBOX)
Go figure
Most Los Angeles ninthgraders find algebra difficult. A sample question from the algebra standards test:
A 120footlong rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope?
A) 20 feet
B) 40 feet
C) 60 feet
D) 80 feet
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Correct answer: C
More algebra problems inside
Source: California Department of Education

Algebra test
A majority of ninthgraders in Los Angeles fail algebra or pass with a D grade.
Algebra grades of LAUSD freshmen in fall 2004:
C and above 39%
D 17%
F 44%
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Sources: Los Angeles Unified School District, California Department of Education
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About This Series
Students drastically limit their prospects by dropping out of high school. To understand why so many do, Times journalists spent eight months studying Birmingham High School in Van Nuys. This series began Sunday. The remaining parts:
Friday: Fast friends — 11 started; three finished.
Saturday: The dropout industry.
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On the Web
An interactive algebra quiz, a photo gallery, a discussion forum and other multimedia features, as well as Sunday's article, are available at latimes.com/dropouts.
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On TV
"Class of 2005," a segment of the news magazine "California Connected" produced in partnership with The Times, will air at 8:30 p.m. Friday on KCET in Los Angeles and at varying times that night on other PBS stations. For a complete broadcast schedule, go to www.californiaconnected.org.

Copyright 2206 Los Angeles Times
Joanne Jacobs rounds up a number of links:
Mathphobe Richard Cohen advises a girl who's flunked algebra six times that the subject is useless in later life since "most of math can now be done by a computer or a calculator," while "no computer can write a column or even a thankyou note  or reason even a little bit."
Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence. I can cite Shelly, whose last name will not be mentioned, who aced algebra but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. She was off by a whole continent.if that's the kind of reasoning taught by writing, I'll take algebra.
The first Toolbox provided the most powerful argument by far for getting more high school students into challenging courses, my favorite reporting topic. Using data from a study of 8,700 young Americans, it showed that students whose high schools had given them an intense academic experience  such as a heavy load of English courses or advanced math or Advanced Placement  were more likely to graduate from college. It has been frequently cited by high school principals, college admissions directors and anyone else who cared about giving more choices in life to more students, particularly those from lowincome and minority families.The new Toolbox is 193 pages [pdf] of dense statistics, obscure footnotes and a number of insightful and surprising assessments of the intricacies of getting a college degree in America. It confirms the lessons of the old Toolbox using a study of 8,900 students who were in 12th grade in 1992, 10 years after the first group. But it goes much further, prying open the American higher education system and revealing the choices that are most likely to get the least promising students a bachelor's degree.
Toward the end of the report, Adelman offers seven tips. I call them the "College Completion Cliff Notes." They are vintage Adelman, very ungovernmentreportlike, so I will finish by just quoting them in full:"1. Just because you say you will continue your education after high school and earn a college credential doesn't make it happen. Wishing doesn't do it; preparation does! So . . .
"2. Take the challenging course work in high school, and don't let anyone scare you away from it. Funny thing about it, but you learn what you study, so if you take up these challenges, your test scores will inevitably be better (if you are worried about that). If you cannot find the challenge in the school's offerings, point out where it is available online, and see if you can get it that way. There are very respectable Web sites offering full courses in precalculus, introductory physics, humanities, music theory, and computer programming, for example.
"3. Read like crazy! Expand your language space! Language is power! You will have a lot less trouble in understanding math problems, biology textbooks, or historical documents you locate on the Web. Chances are you won't be wasting precious credit hours on remedial courses in higher education.
"4. If you don't see it now, you will see it in higher education: The world has gone quantitative: business (obviously), geography, criminal justice, history, allied health fields  a full range of disciplines and job tasks tells you why math requirements are not just some abstract school exercise. So come out of high school with more than Algebra 2, making sure to include math in your senior year course work, and when you enter higher education, put at least one collegelevel math course under your belt in the first year  no matter what your eventual major.
"5. When you start to think seriously about postsecondary options, log on to college and community college Web sites and look not so much for what they tell you of how wonderful life is at Old Siwash, but what they show you of the kinds of assignments and examination questions given in major gateway courses you will probably take. If you do not see these indications of what to expect, push! Ask the schools for it! These assignments and questions are better than SAT or ACT preparation manuals in terms of what you need to complete degrees.
"6. See if your nearest community college has a dualenrollment agreement with your school system, allowing you to take significant general education or introductory occupational courses for credit while you are still in high school. Use a summer term or part of your senior year to take advantage, and aim to enter higher education with at least six credits earned this way  preferably more.
"7. You are ultimately responsible for success in education. You are the principal actor. The power is yours. Seize the day  or lose it!"
Would you rather have $1,000 for sure or a 90 percent chance of $5,000? A guaranteed $1,000 or a 75 percent chance of $4,000?In economic theory, questions like these have no right or wrong answers. Even if a gamble is mathematically more valuable  a 75 percent chance of $4,000 has an expected value of $3,000, for instance  someone may still prefer a sure thing.
People have different tastes for risk, just as they have different tastes for ice cream or paint colors. The same is true for waiting: Would you rather have $400 now or $100 every year for 10 years? How about $3,400 this month or $3,800 next month? Different people will answer differently.
Stanford's Keith Devlin, via Joanne Jacobs:
. . . professional mathematicians, scientists and engineers, want the schools  the pipeline that keeps those professions supplied with new personnel  to ensure student mastery of numerical, algebraic and computational skills. "We don't want to spend our time having to reteach the incoming students how to add fractions!" is a common refrain heard in university science and engineering departments.
Basic skills are not all they want, but they don't want them left out or deemphasized.Ranged against them (again, broadly speaking) is the mathematics education community, which argues that a focus on procedural skills is misplaced, and that the primary aim of school mathematics education should be to produce conceptual understanding. "If students understand the concepts, they can pick up any skills they need easily enough, as and when they need them."
As a professional mathematician, I often have to learn a new part of my subject. Every time I have to go through the same process: Start by learning the rules, then practice using the rules, and keep practicing until understanding develops. Practically every professional mathematician, scientist, or engineer I have spoken to has said more or less the same. Understanding follows experience.
There's been no shortage of discusion regarding math curriculum. Rafael Gomez's latest event, this Wednesday's Math Forum should prove quite interesting. The event will be at the Doyle Administration Building (McDaniels Auditorium) [Map] from 7:00 to 8:00p.m. Participants include:
The problems with CMP go far beyond failing to reach parents. One big problem is that the edifice of mathematics is so huge. Think of how long it took mathematicians to discover all of it. When one tries to use the discovery paradigm as the sole model for math lessons, all of the time available is spent in discovery process of basic concepts. There isn't time for more than a cursory look at any topic. There isn't any work on hard problems related to basic concepts. There isn't time to master computational aspects of basic concepts. Everyone learns 1/2 + 1/4, but no one learns how to find the least common denominator of 1/14 and 1/35. The people who promote a constructivist approach to math set up a false dichotomy between traditional math which teaches one to memorize formulas and tables of computations, and discovery math which teaches one to really understand how math works. I actually had a TAG resource teacher say this to me very patronizingly. "We don't teach math anymore the way that YOU learned it. Now children really understand math when they learn it." Excuse me, but traditional math was never like that. Tradtional math presents concepts AND teaches understanding of concepts. One learns formulas AND why they work. One also does large numbers of progressively more difficult computations to become skilled at them. The problem with traditional math is that large numbers of students don't understand the concepts as presented and try to get by with memorizing and manipulating formulas which they don't understand. They also don't master the computational aspects and try to make up for this deficit by using calculators inappropriately.
When I was TAing calculus in grad school, a typical scenario would be the student who never understood the algebra lesson about what a logarithm is and tried to memorize the associated list of formulas to get by. Now here we are in logs again. The student doesn't understand the algebra of logs, misplacing minus signs willynilly, so is destined to fail at calculus. In addition he doesn't really have a good handle on the multiplication tables, so every example has to be presented sooo slowly for him to follow. Why does this happen? Well it may be that some kids don't have enough mathematical talent/interest to master the material, but I don't believe it. In countries like Singapore and my husband's native country of Finland, everyone learns this math and learns it pretty well. I don't believe the gene pool is so radically different there. I think it has to do with expectations and foundations. If you live in a culture where everyone knows math and expects everyone else to know it, people will learn it. Math is built like a brick wall, bottom up. You have to learn the foundations properly and well to get along well further on. At each step, mastery requires doing lots of problems until they are like second nature. Learning some fuzzy understanding of the basic concept doesn't cut it here. You have to do lots of problems. You have to work hard. You can't do trigonometry if basic calculation is slow and difficult. It's no different than athletic training. You don't go out and run a marathon without practice and sweat. The problem needs to be fixed at the elementary level and also in our society with its dysfunctional attitude toward math. I think the people who promote curricula like CMP see this as a way to reach the kids with low math skills. These kids can at least get some kind of tenuous connection to math this way. But it is absolutely hopeless as a preparation for rigorous collegeprep math. Of course the way to cure that is, guess what, put discovery math into the collegeprep courses since with CMP as a background the kids will never be able to master real math. At West the Algebra text has been replaced with Discovery Algebra, and soon, I believe, Geometry will follow. Check it out at www.keypress.com. Maybe I'm wrong. Maybe this math is the way to go for the nonmathematical kids. But then they should have an alternative curriculum for kids who really like math and expect to need it in their careers. This CMP stuff(along with Everyday Math) just makes kids who like math scream in agony. It's torture. If you have a kid who's managing fine in CMP, it's likely the teacher is heavily supplementing with outside resources. But of course they can't let the brightest kids go. It would be (gasp!) tracking, and in any case the lesson structure requires that the bright kids be there to facilitate success in the group and help others along. I recommend you save your $30,000. Do not invest more money in this curriculum. It's just throwing good money after bad.I know that the people who create and implement these curricula have good intentions. They want the kids to learn. I know they don't intend to pull the schools down. There's some kind of mass delusion that has infected the education researchers, and we have to deal with the consequences.
Full disclosure. We are a family of math nerds. My husband is a math prof at UW and I have a master's degree in math. I run a math olympiad group at my children's elementary school and assist in the classroom whenever the teachers can use my assistance. We do Singapore Math at home to fill in the gaps in school instruction and do math for fun at the dinner table. I just made the painful decision to move my soontobemiddleschooler daughter to private school next year, in part (but only a small part) to avoid CMP.
Science and math have zoomed to the top of the nation's education agenda. Yet Amanda Cook, a parent of two schoolage girls, can't quite see the urgency."In Maine, there aren't many jobs that scream out 'math and science,'" said Cook, who lives in Etna, in the central part of the state. Yes, both topics are important, but "most parents are saying you're better off going to school for something there's a big need for."
Nationwide, a new poll shows, many parents are content with the science and math education their children get  a starkly different view than that held by national leaders.
Dissatisfaction with math curriculum in Alpine School District might seem like a local issue. It isn't.Alpine's math wars made the area ground zero for the explosion of charter, home and private schools in Utah, and the discord continues to drive legislation regarding school choice.
Eagle Mountain resident Doug Cannon, father of seven, became concerned about Alpine's math curriculum soon after the district adopted the "Investigations" math program in its elementary schools in 2001.
The textbook series is meant to improve students' understanding of math through discovery of math concepts. As originally implemented, it downplayed rote learning and memorization of traditional algorithms such as times tables.
What struck me was that the reasons why Johnny can't do algebra in L.A. today are remarkably similar to why Johnny Patrello couldn't do algebra almost four decades ago in Yonkers, N.Y.Via JoanneJohnny and I were brought together by Mrs. Elizabeth Bukanz, the algebra teacher. Mrs. Bukanz wore her sandy hair in a frizzy French twist and her glasses on a chain. But she was gentle and smiling, and she had passion — at least for what she called "the beauty of algebra." I, too, loved its perfect logic and tidy solutions, so unlike my messy teenage life.
But Johnny was deaf to algebra's siren song. He was flunking, and Mrs. Bukanz hoped that if I used my study halls to tutor him, he might score at least 65% on the New York State Regents exam. Passing the exam allowed even failing students to move on to high school, which started in 10th grade; otherwise, Johnny would be left behind.
As the Los Angeles Times' Monday installment of "The Vanishing Class" series described, 35% of future elementary school instructors who studied at Cal State Northridge, the largest supplier of new teachers to the Los Angeles Unified School District, got Ds or Fs in their first collegelevel math class last year.Los Angeles schools Supt. Roy Romer has cited the "cumulative failure of our ability to teach math adequately in the public school system."
William Schmidt, a professor at Michigan State University and executive director of its Third International Math and Science Study Research Center, was asked by The Times whether other countries have as much trouble finding adequately trained math teachers as the United States.
Some Washington area high school students are pushing so far ahead in math courses that Advanced Placement, the widely accepted pinnacle of precollegiate study, no longer goes far enough.More than 500 students in the Montgomery and Fairfax school systems, the region's two largest, are taking multivariable calculus, a course traditionally taken by math majors in their second year of college  at least in the old days. That means the students have a full year of collegelevel calculus under their belt before they leave high school.
Reed Schneider emails on recent posts regarding a School Board's role in curriculum policy:
I agree that the school board should be responsible for the district's curriculum. In fact, it is the most important thing they are charged with. 10 or more years ago, before widespread internet availability, the noneduestab person on a board would have the excuse that it would be impossible for them to know which curricula works. All decisions would be deferred to the socalled experts. That excuse doesn't work any more. Any board member can now go to www.nrrf.org and discover opinion and independent research showing programs like Reading Recovery and balanced Literacy have serious flaws. They can go to www.mathematicallycorrect.com and discover that math programs recommended by the NCTM like Everyday Math fail our children.Even if the board becomes involved, it will take board members willing to do this. Just because they become involved with curriculum will not automatically mean they will critically evaluate administrators recommendations. Far too often they simply rubber stamp what the curriculum specialist puts in front of them.
The parents and tax payers are the only ones with the power to change this. A good question at a board candidate's forum would be: "What is your opinion of reading or math programs based on constructivist theory?" If they don't understand the question, can't answer, hem and haw, or embrace it, don't vote for them. It's really that simple.
Reader Troy Dassler emailed this photo, taken a few hours ago, at Leopold's Math Night event.
Expanding on its efforts to increase the reading skills of elementary school students, the Schools of Hope project led by the United Way of Dane County also is focusing on helping middle school students develop the math skills needed to be successful in high school, college, employment and daily life.Rafael Gomez is organizing a Forum on Math Curriculum Wednesday evening, February 22, 2006 at McDaniels Auditorium. Look for more information soon.Since the Madison School Board adopted the goal that all students would complete algebra by the end of ninth grade and geometry by the end of 10th grade, the option of taking less rigorous classes, such as general or consumer math, has disappeared.
All high school students are now required to take algebra and geometry  or two credits of integrated mathematics, combining algebra, statistics and probability, geometry and trigonometry  in order to graduate.
"These are really gatekeeping courses and skills," said Mary Ramberg, the district's director of teaching and learning. She added that without them, students "will have a lot of options closed."
Neal Goldman is a math entrepreneur. He works on Wall Street, where numbers rule. But he's focusing his analytic tools on a different realm altogether: the world of words.Goldman's startup, Inform Technologies LLC, is a robotic librarian. Every day it combs through thousands of press articles and blog posts in English. It reads them and groups them with related pieces. Inform doesn't do this work alphabetically or by keywords. It uses algorithms to analyze each article by its language and context. It then sends customized news feeds to its users, who also exist in Inform's system as  you guessed it  math.
At least 2,500 ninthgraders in Prince George's County will abruptly move this week from a standard oneyear algebra course into a twoyear program, shielding the struggling students from a state graduation test this spring that officials said they were likely to fail.The highly unusual shift comes midway through the school year in one of Washington's largest suburban school systems and in some respects runs counter to a regional trend of pushing students to take higherlevel mathematics as early as possible.
This small event says a lot about global competition. Traveling around Asia for most of the past month, I have been struck by the relentless focus on education. It makes sense. Many of these countries have no natural resources, other than their people; making them smarter is the only path for development. China, as always, appears to be moving fastest.But one thing puzzles me about these oftmade comparisons. I talked to Tharman Shanmugaratnam to understand it better. He's the minister of Education of Singapore, the country that is No. 1 in the global science and math rankings for schoolchildren. I asked the minister how to explain the fact that even though Singapore's students do so brilliantly on these tests, when you look at these same students 10 or 20 years later, few of them are worldbeaters anymore. Singapore has few truly topranked scientists, entrepreneurs, inventors, business executives or academics.
Beautiful Minds: An Innovative Math Program Helps Change the Face of Gifted and Talented Education
By John O'Neil (from NEA Today, January, 2006)
"Friendly fractions" are the day's topic, but Alison Foley's 20 fourthgraders can't dig into that concept until they've tallied and graphed their favorite desserts. Votes for ice cream, brownies, cake, and cookies—even a lone vote for cannoli—go up on the board.
"What about ice cream cake?" one student asks. "If we were doing a Venn diagram, we could put that in the intersection," Courtney offers. Soon, desks and chairs are pulled aside and Foley's kids use yarn and their bodies to make a human pie chart illustrating their data, then go on to calculate what fractions result when you add various categories together.
Foley's math curriculum—which presents concepts several years above grade level—isn't the only thing unusual about her classroom at Smith School in West Hartford, Connecticut. Smith is one of 10 schools in Connecticut and Kentucky piloting an innovative project, Mentoring Mathematical Minds (Project M3), aimed at identifying children in grades 3–5 capable of handling advanced mathematics. Developed at the University of Connecticut, the program is designed to expand the population of students typically served by gifted and talented programs. Sure enough, look around Foley's classroom—which draws students from Section 8 housing as well as milliondollar homes—and you'll see students as diverse as their favorite desserts, with Black students elbow to elbow with Hispanic, AsianAmerican, and White pupils.
National figures on gifted education programs suggest such diversity is unusual. Data collected by the Education Department's Office of Civil Rights show that White and Asian students are typically overrepresented among programs for the gifted, while other minorities tend to be underrepresented.
The University of Connecticut project is part of a movement to broaden the scope of gifted and talented programs, which in some communities are fighting for survival. Some advocates for gifted programs say the federal socalled No Child Left Behind law (NCLB), which mandates that schools raise all students' performance to minimally acceptable standards, has school officials focused on average or underachieving learners.
"Teachers who used to teach AP are now teaching remedial reading instead," notes Jane Clarenbach, director of public education and affiliate relations for the National Association for Gifted Children. More bad news: President Bush has proposed eliminating federal Jacob Javits grants, which support research on gifted education (including programs like Project M3).
While research consistently shows the advantages of offering gifted students content tailored to their needs, many buy into the notion that it's not necessary—they say gifted kids will do just fine, even without special curricula. Indeed, with NCLB pressures mounting and district budgets tight, some see gifted programs as offering extra resources to kids who already have all the advantages.
But Clarenbach and others argue that forcing gifted students to march in lockstep with their peers holds them back. Nineyearold Courtney would probably agree. She spent part of last year in Smith School's regular thirdgrade math class, and part of the year receiving Project M3's enriched curriculum. Looking back at her gradelevel math work, Courtney recalls, "I'd just zip through it in five minutes and have to wait half an hour for everyone to finish. It gave me headaches when I had to do the same things over and over again, honestly."
Clarenbach points out that the issue can be further complicated because the gifted population itself is diverse. For example, some gifted students excel in a single content area but are weak in others; some even have learning disabilities. Still, that doesn't mean areas of strength should be ignored. Project M3 Director Kathy Gavin, who works at the Neag Center for Gifted Education and Talent Development at the University of Connecticut, cites the example of one student who was almost held back in second grade because of reading difficulties, but who it was thought could benefit from the M3 program. The student was placed in it and "has excelled," she says.
Broadening the Pool
Without a special math program like Project M3, the talents of children like Courtney, a vivacious AfricanAmerican who has already mapped out her life's goals, might go unchallenged. Kathy Gavin says she's met an urban principal who told her flatout, "I don't have any gifted kids in my school." But Project M3 helps find them. Kids are selected based on multiple criteria, including a special assessment of nonverbal math ability, which measures such things as spatial sense and reasoning, and standardized tests when available. Teacher recommendations and prior grades also factor in. Opening up the selection process (gifted programs in the past often selected students based on IQ scores alone) has allowed students with less obvious talents to benefit, says Gavin. Once they're in, kids take four units of about six weeks each, with content pitched several years beyond gradelevel standard: the fourthgraders in Foley's class, for example, studied a unit on algebra in which they solved for variables. The lessons focus on conceptual understanding, with lots of time for reflection and discussion.
Early results show that the program has promise. Students taking the M3 curriculum at the 10 schools where the program is being piloted have posted "significant gains" on standardized math tests compared with control groups, with lowerincome students recording the highest gains, says Gavin. Alison Foley's fourthgraders were among those who showed gains, and, to her relief, her kids also swept through their districtlevel tests. She had worried about the results, because the M3 curriculum was such a departure from the standard (and tested) math curriculum in the district.
Foley sees other benefits too—especially for girls who traditionally have been underrepresented in advanced math programs. In regular math classes, boys tend to be more assertive, blurting out answers, while girls hang back. In the M3 classrooms, students often work in pairs and discuss solutions, Foley says, and that helps girls rehearse their answers and support their thinking.
Students like Mariam are benefiting. When the class began, says Foley, "Mariam was overshadowed by the other kids, especially the boys." But as the year went on her confidence grew. In a recent algebra unit, she argued her point against the entire class—and she was right, says Foley. "That was a huge step for her, and now she has become, in a subtle way, a leader."
Courtney, who pronounces Project M3 "just awesome," appreciates being in a class with kids who share her passion for numbers. "The difference between this class and the others is that the kids in the other math classes do it for the rewards, because they're going to get gum or chocolate or something," she says. "And when they come out of math, they look so unhappy! But when we come out of math, we have smiles on our faces because we love it."
Scouting For Talent
Look around your classroom. Could bored Brittany, loquacious Lakisha, or rambunctious Robert benefit from gifted education services? Here's how to find out:
* Know the signs. Gifted students often demonstrate advanced performance in one or more disciplines and abstract or complex thinking. They may also have an increased ability to make connections and see relationships. Varying your assignments can bring out the best in some students: For example, try letting kids show what they know through skits, poems, or dioramas.
* Pretest. Find out what students know before you teach a new topic. Both formal assessments (quizzes or interest inventories) and informal (observations or class discussion) can help you identify students who require enrichment activities or an accelerated pace.
* Watch for clues. Sometimes actions speak louder than words. A kid who seems bored or disinterested (even acting up) may, in fact, need more challenging work. Talk with the child, a parent, or his or her former teacher to track the behavior pattern and address the issue.
* Allow for differences. All students have academic strengths and weaknesses. A gifted student who excels in science may struggle in writing. Try to make sure students are working at the appropriate level of challenge in each subject area to ensure their growth.
Link to article for those who want photo and charts:
http://www.nea.org/neatoday/0601/gifted.html
Interesting interview with Burt Rutan on his approach to space travel (low cost, efficient) vs. the traditional NASA approach (very expensive).I found it interesting to listen to Rutan's young engineer's discuss the challenges and opportunities in their work. Two related articles worth reading:
One place where such heroic work is taking place is the Watts Learning Center (WLC) charter school, one of the most improved charter schools in California.Links:From 2000 to 2005, the WLC rose from a low testscore ranking to a level near the state’s proficiency target score of 800. The K5 charter school was able to defy low expectations and accomplish this feat with a student population nearly all African American and low income. In an example of what the President called “the soft bigotry of low expectations,” these two factors are too often considered indicators of educational failure. WLC charter school proved defied that expectation.
Gene Fisher, founder and president of WLC, says that the school’s mission is to create a culture of learning and high expectations for students, parents, faculty and staff. He points out that, "The job of our teachers includes an emphasis on a proven curriculum while also reinforcing these high expectations – a belief that students can and will succeed."
The school uses the structured phonicsbased Open Court reading program. WLC chose Open Court before the Los Angeles Unified School District adopted the same program. Open Court emphasizes continuous review and practice of already learned material. Sandra Fisher, the school’s executive director, says that it is important that the curriculum be structured because so many students lack structure in their lives.
A year ago the Jefferson PTO planned to have a mathematics night, with a discussion of their math program. I was asked if I would appear and said yes. The Madison Metropolitan School District was asked and they refused to send anyone, saying that they did not want to do this school by school. but district wide. When Mary Ramberg was asked when this would be done, she said they had no plans to do this.
Here is part of the report from 1882 from the State Superintendent about textbooks. At this time changes in textbooks had to be approved by the State Superintendent. The following should be done:
Why is the MMSD afraid to have a general discussion of their mathematics program?
Earlier this semester, 60 MMSD students  including 29 from West HS  were named 2006 National Merit Semifinalists. In a 10/12/05 press release, MMSD Superintendent Art Rainwater said, "I am proud of the many staff members who taught and guided these students all the way from elementary school, and of this district's overall guidance and focus that has led to these successes."
A closer examination of the facts, however, reveals that only 12 (41%) of West High School's 29 National Merit Semifinalists attended the Madison public schools continuously from first grade on (meaning that 59% received some portion of their K8 schooling in either private schools or nonMMSD public schools). Here's the raw data:
NMSF #1: Wingra K5th; HamiltonNMSF #2: FranklinRandall K5th; Wright for 6th; Hamilton 7th8th
NMSF #3: MidvaleLincoln, K5th; Cherokee
NMSF #4: Denver public schools (magnet Montessori school) K6th; Hamilton 7th8th
NMSF #5: New Orleans parochial school K8th; New Orleans public high school through 11th
NMSF #6: Libertyville, IL, public schools ("extremely rigorous") through first semester 10th
NMSF #7: FranklinRandall, K5th; Hamilton
NMSF #8: Van Hise, K5th; Hamilton
NMSF #9: Van Hise, K5th; Hamilton
NMSF #10: Starkville, MS, public schools K8th
NMSF #11: Japanese school for K; Glenn Stephens 1st4th; Van Hise for 5th; Hamilton
NMSF #12: FranklinRandall, K5th; Hamilton
NMSF #13: Madison Central Montessori through 3rd; Shorewood 3rd5th; Hamilton
NMSF #14: LincolnMidvale through 4th; Eagle 5th8th
NMSF #15: Eagle K8th
NMSF #16: MMSD through 9th; home schooled beginning in 10th
NMSF #17: Leopold though 4th; Eagle 5th8th
NMSF #18: Lapham K2nd; Randall 3rd5th; Hamilton
NMSF #19: California private school through 5th; Hamilton
NMSF #20: Midvale and Van Hise; Hamilton
NMSF #21: Seattle public schools (TAG pullout program) through 7th; Hamilton for 8th
NMSF #22: Unknown private school K1st; Eagle 2nd8th
NMSF #23: LincolnMidvale K5th; Cherokee
NMSF #24: Madison Central Montessori through 4th; Eagle 5th8th
NMSF #25: Shorewood K5th; Hamilton
NMSF #26: Queen of Peace through 5th; Hamilton
NMSF #27: West Middleton through 4th; Eagle 5th8th
NMSF #28: Montessori preK through 2nd; Shorewood 4th5th; Eagle 5th8th
NMSF #29: Shorewood K5th; Hamilton
Descriptive data like these are certainly interesting, though they often raise more questions than they answer. And of course, they don't prove anything. Nevertheless, with 45% of the West HS National Merit Semifinalist sample attending nonMMSD schools for over half of their K8 years, it is recommended that the District temper its sense of pride in and ownership of these very accomplished students.
Many thanks to each of these fine young people for speaking with us on the telephone. Congratulations and good luck to each and every one of them!
EDUSAT, sent into space last year, is India’s first educational satellite. It will allow American instructors to lead classes in remote classrooms, thousands of miles away, via Web cast.“Any Indian village could set up a receiving station and receive a signal, and schools would need only a computer and a simple Web camera to view the lessons,” Sanjay Limaye, senior scientist at the UWMadison Space Science and Engineering Center, said in a release.
The targets of the satellite are rural Indian communities, which are plagued by a lack of educational infrastructure and a lack of good teachers.
Gov. Jim Doyle supports the push to increase the math and science proficiency of high school students, which is primarily coming from business leaders.Additional links and background on math and science curriculum.They say a lack of these skills among those entering the labor pool is putting Wisconsin at risk of losing jobs because there won't be enough qualified workers to fill positions ranging from manufacturing jobs to computer specialists, from engineers to mathematical, life and physical scientists and engineering and science technicians.
Art Rainwater, superintendent of the Madison School District, supports increasing the state requirements. Madison high schools require two years of each subject, but in recent years the district has strengthened its math requirement so that all students must now take algebra and geometry to graduate, Rainwater said.
If the state does not increase its math and science requirements, the district will likely consider raising them, he said.
But School Board President Carol Carstensen said she isn't certain requiring more courses is the way to best prepare all students to succeed after high school.
And just increasing the requirements (emphasis added) won't make the classes more rigorous, said Lake Mills chemistry teacher Julie Cunningham, who recently won the prestigious Milken Family Foundation National Educator Award.
American Institutes for Research:
U.S. students consistently performed below average, ranking 8th or 9th out of twelve at all three grade levels. These findings suggest that U.S. reform proposals to strengthen mathematics instruction in the upper grades should be expanded to include improving U.S. mathematics instruction beginning in the primary grades.“The conventional wisdom is that U.S. students perform above average in grades 4 and 8, and then decline sharply in high school,” says Steven Leinwand, principal research analyst at AIR and one of the report’s authors. “But this study proves the conventional wisdom is dead wrong.”
Previous studies compared U.S. performance with substantially more countries, whose characteristics vary widely. A total of 24 countries participated in TIMSSgrade 4, 45 countries in TIMSSgrade 8, and 40 countries in PISA.
The nation’s 4th graders may not stack up quite so well against their peers around the globe as previously thought, but also may not post as big a dropoff in achievement when they get to high school, a new analysis of internationaltest comparisons concludes.
The study, conducted by the Washingtonbased American Institutes for Research and sponsored by the U.S. Department of Education and the Urban Institute, looked at two internationalassessment comparisons, covering grades 4 and 8 and 15yearolds. It found that, when compared only with those countries that participate in both studies for all three student groups, the United States ranked in the middle or bottom of each.
By Kathleen Kennedy Manzo
From Education Week, November 22, 2005
“There has been a broad perception that the United States does reasonably well in 4th grade mathematics internationally, about average in 8th grade, and then [its performance] falls off a cliff in high school. But that is based upon a comparison of apples and oranges,” said Steve Leinwand, the AIR’s lead author of the report.
For More Info
The report, “Reassessing U.S. International Mathematics Performance: New Findings from the 2003 TIMSS and PISA,” as well as an executive summary, is available from the American Institutes for Research. Requires Adobe Acrobat Reader
Until now, comparisons have been made among all the countries participating in each of the studies. The United States has scored above the international average on the Trends in International Mathematics and Science Study, or TIMSS, for 4th and 8th graders, but at the bottom among industrialized countries on the Program for International Student Assessment, or PISA, which tests math literacy and problemsolving.
Twentyfour countries participated in the 4th grade TIMSS, and 40 were involved in the 8th grade comparison. Those lists don’t necessarily match up closely with the nations involved in the PISA exam either, Mr. Leinwand said.
The new study compares the United States with 11 other developed countries that participated in all three student groups: Australia, Belgium, Hong Kong, Hungary, Italy, Japan, Latvia, the Netherlands, New Zealand, Norway, and the Russian Federation.
“What’s most important is that there is a fairly consistent pattern of mediocrity” among U.S. students, Mr. Leinwand said.
The latest ranking puts the United States eighth on the grade 4 comparison and ninth for both groups of older students. Students in seven other countries performed statistically better than American 4th graders, five outscored U.S. 8th graders, and six were better than this nation’s high school students.
Computational Skills Questioned
The AIR study also challenges the common notion that American students do well on basic computational skills. The nations in the study that did well on the easy questions also tended to do well on the more difficult ones. But the United States was below average in those areas as well.
The United States, for example, was below average on both low and highdifficulty test items, and the performance of American students at all three grade levels was particularly weak on measurement questions and geometry skills. The students, however, showed strong abilities in data and statistics.
To improve the nation’s standing internationally, American schools need to focus more intently on building students’ foundational math skills in the early grades, the report recommends, and beef up instruction in geometry for middle school students. U.S. schools should also consider ways to narrow the lingering achievement gap between boys and girls, a trend evident in only one other country, Italy.
Although the new rankings suggest greater problems with U.S. math proficiency than had been reported previously, the performance of American students is still about average internationally, according to Gerald W. Bracey, an Alexandria, Va.based researcher. Mr. Bracey also suggested that the substance of the PISA test—which includes broad questions gauging students’ analytical, quantitative, and analogical skills—may not yield adequate information about high school math achievement.
“What I object most to is the use of the word ‘mediocre.’ ‘Average’ is a statistic; ‘mediocre’ is a judgment,” said Mr. Bracey, who has challenged the notion that American students perform poorly on international comparisons. “When they run the final heat in the 100meter dash in the Olympics, the guys who finish fourth or fifth are called average. Nobody is going to call them mediocre. How well you do depends on how stiff the competition is.”
AfricanAmerican rates increased from 27.5 percent to 49.7 percent in the four years and from 29.8 percent to 50 percent for Hispanic students. Among white students algebra completion rates had improved from 68.9 percent to 82.6 percent, the report said.Related: this week's Isthmus article on Middle School Curriculum.
LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician.This sort of thing is happening in Madison as well. Much more here.So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.
Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problemsolving formulas that constructivist math denigrates as mindless memorization.
"My whole experience in math the last few years has been a struggle against the program," Jim said recently. "Whatever I've achieved, I've achieved in spite of it. Kids do not do better learning math themselves. There's a reason we go to school, which is that there's someone smarter than us with something to teach us."
In Maryland, the current class of 9th graders will be the first to have to pass an algebra test to graduate from high school. That's putting pressure on some parents to brush up on their math skills so that they can help their children. Baltimore County's school system has recognized this potential problem and is now offering classes to bring parents up to speed on algebra.The school system is offering its algebra awareness class for parents in a threesession format. Each session is two hours long.
The idea came from discussions of the new algebra requirement at ParentTeacher Association meetings last year.
What's the price of leaving high school unprepared? Ask Chelsea Stephanoff, a Wayne State University student who is spending nearly $600 this semester for a class that won't count toward graduation.Via Joanne.Why? Her math skills were poor enough that even after four years of high school math, she was placed in a remedial class.
"Math is not my strong point at all. I'm horrible at it. I have a hard time focusing on it," said Stephanoff, a fourthyear student from Shelby Township who wants to be an elementary school teacher.
Last spring a longtime parent at West HS was asked to write a description  content area by content area  of the curriculum changes that have occurred at West HS in recent years that have affected the academic opportunities of West's "high end" students. Below you will find what she wrote. It includes changes that have actually occurred; changes that may and probably will occur; and important questions about what else may happen in the future.
This summary was then forwarded to two other longtime West parents for their comments. Excerpts from those comments may be found just after the original description. Next, the description of each content area was sent to the appropriate department head at West, for their comment with the goal being to produce a brief, descriptive document that everyone would agree was factually accurate, for educational and advocacy purposes. Unfortunately, none of the department heads responded.
Here is the original description:
1. English
a. A few students gifted in English used to be permitted to begin taking upperlevel English courses beginning 2nd semester of 9th grade, based upon their English teacher's recommendation, outstanding performance during their 1st semester at West, and the availability of open slots in appropriate courses that fit the student's schedule. (Note: this option involves no monetary cost.)
b. The two sections of integrated 9thgrade English/Social Studies were eliminated as of the 20032004 academic year. The primary purpose of these experimental courses  very similar in philosophy to the SLCs  was to provide an opportunity for one English and one social studies teacher to pair together to partially integrate their curricula and get to know the same group of students, along with the students having the same set of classmates for both classes. "TAG" students were among the ones who selfselected into these courses, creating cluster grouping within mainstreamed classrooms.
c. 10thgrade English core curriculum will likely be introduced in 20062007. This change will prevent highly motivated and capable students from having the opportunity to take appropriately challenging courses in English until 11th grade (currently, students get to start choosing from among the English electives in 10th grade). Ultimately, the effect will be a reduction in the number and variety of upperlevel English courses West is able to offer.
2. Social Studies
a. 9thgrade Integrated English/Social Studies course was eliminated (see above).
b. The British version of 10thgrade European History was eliminated as an option a couple of years ago when the teacher of this course officially retired. (Note: this teacher still teaches some sections of 10thgrade European History at West.) As with Integrated English/Social Studies, "TAG" students were among the ones who selfselected into this variant of 10thgrade social studies, creating high ability cluster grouping within a mainstreamed classroom.
c. West's Social Studies Department decided this year that underclassmen will no longer be permitted to take 12thgrade elective courses prior to 12thgrade, not even on a spaceavailable basis that would involve no monetary cost. No other department has this restriction. Might they follow suit?
3. Science
a. 9thgrade Accelerated Biology is restricted to one section despite there being approximately four classrooms worth of students who desire each year to take on the extra challenge this class entails (i.e., over 100 students choose to take the optional test for admission into Accelerated Biology each year, some years, many more than that). Budget constraints will likely lead to the elimination of even this one section in the near future unless West is willing to assign all of the students in this class to the same SLC (or have one section per SLC).
b. Will the implementation of a 10thgrade Core include science as well? If so, will everyone take the same Chemistry course in 10th grade, eliminating the variety of science options currently available to 10thgrade students? (Note: at the March 2005 West PTSO meeting, West HS Science Department Chair Mike Lipp stated  in response to a parent question  that they would not eliminate the regular Chemistry class because the lack of math content/rigor in Chem Comm ("Chemistry in the Community") would leave West graduates unprepared for chemistry at the UW and other universities.)
4. Math
a. West used to have a course called "Precalculus." It covered Algebra 2/Trigonometry Accelerated and Algebra 3 Accelerated in one year. It was eliminated last year (200304). The math staff were needed, instead, for "Algebra I Extended." In addition, it was a controversial course, in that there was disagreement as to how many students could really handle and benefit from it. All of West's remaining "accelerated" math courses are really honors classes, that is, they are not accelerated in pace, as exists at many high schools of excellence in the US. (Important note: the "new" class that will be called "Precalculus" next year is simply Algebra 3 Accelerated with a new name, not the old Precalculus.)
b. With old Precalculus gone, will West now end up having too few students to justify continuing to offer Calculus II starting in 20062007? (Note: in order to take Calculus II in high school, a student must take geometry before 9th grade or take a year of math over a summer.) If so, West could end up the only MMSD high school not offering Calculus II.
c. In the future, will most students at West be mainstreamed into "Core Plus" starting in 9th grade? (Note: this would fit well with the plan to have an SLCbased core curriculum in 9th and 10th grade; that is, to have all students take Core Plus from the beginning would make possible a 9th and 10th grade core curriculum in math.) If so, will none of these students be able to take Calculus in high school?
Here are excerpts from the comments of Person #1:
The institutional history corresponds well with my experience and my children's experiences at West.
One other point that is not made is that it used to be easier to take an Independent Study course for credit if you were a high achieving student. ... Also, the school people will point to the option of going to UW as a way of providing for high end kids. [Although this works well for some], I think it is a bad option since the calendars [and daily schedules] do not in any way correspond with one another  on a daily basis, the UW offers courses on a MW, TR, or MWF schedule, while West offers their courses on a MTWRF schedule. The transportation time and the differences in the class start times means that, essentially, taking a single course at UW makes a massive hole in a student's schedule.
Here are excerpts from the comments of Person #2:
As for science, 10th grade students either take Chemistry acclerated or Chem Com. In 11th grade, there are two physics offerings, Advanced Math Physics or General Physics. In 12th grade, the advanced topics courses in these two areas  as well as in biology  are fairly subjective, dependent on teacher interest. By contrast, Memorial students have AP Chem, Physics and Bio, as well as a 9th grade earth science class; additionally, the sequence is taught in the more accepted order, chem, physics and finally, biology. Many Memorial students graduate with 2545 AP credits; very few West students take any other than calculus, foreign language and/or statistics1015 credits. This can make a huge difference in college, either for placement and/or early graduation with its attendant reduction in cost.
Fundamentally, the problem lies with the SLC program. Its primary purpose, despite the social rhetoric, is to homogenize the student body across all variables, including academics. Most of the features that made West a haven for TAG students are eliminated. Taking courses out of the normal sequence will be very difficult and the clustering of students, unless it happens de facto as the result of changes in the middle school curriculum, will disappear. It was this menu of options and flexibility that offset West's weak to nonexistent AP program. I would also be very concerned whether a student will be able to participate in UW's Youth Options program; coordinating the university and high school schedules is difficult under the current arrangement with West's variety of courses and times. Youth Options has been a tremendous opportunity for gifted students to expand beyond the typical constraints of the high school curricula. (Note: the State now limits the number of college credits for which a District must pay to 18 per student. Also, the Youth Options Program may well face threat of extinction again in the near future.)
Several writers have mentioned the positive news that the Madison Board of Education has reviewed Superintendent Art Rainwater for the first time since 2002. I agree that it is a step in the right direction.
In my view, the first responsibility of the Board and Administration, including the Superintendent is curriculum: Is the Madison School District using the most effective methods to prepare our children for the future?
There seems to be some question about this:
Many organizations live on the fumes of their past. Is this the case with the Madison School District?
Superintendent Rainwater visited with the Capital Times on the day the Board released the report on the his evaluation. Matt Pommer briefly summarized the discussion and closes by mentioning that state budget controls prevent new programs from being developed. This statement reflects the "same service mantra". The District could certainly change expensive programs like Reading Recovery and invest in a different approach. The District could also strongly adopt virtual learning tools. WeyauwegaFremont School Board President Steve Loehrke has spoken and written extensively on these questions. The District could also change the way in which it delivers information (there's a little movement on this).
Finally, Jason Shepherd's recent Isthmus article on the Superintendent's review process is well worth reading:
But the evaluation marks the first step toward charting Rainwater's leadership of the city's schools. Leaders of public institutions are best governed by public bodies that set forth clear expectations. The board's new goals for the superintendent in the coming year are due by Nov 1.I've not seen much, if any discussion of curriculum issues at the Board level, or the Performance and Achievement subcommittee, which has not met since 1/31/2005. I seem to remember (but can't find the quote) that Board President Carol Carstensen said at a District event, that "we leave the curriculum up to the staff". I could not disagree more with this approach.
I think it's time for a serious Board curriculum discussion. Madison is fortunate to have some fabulous resources just down the street at a world class University. Let's work with them, before they move on.
A year's worth of Connected Math textbooks and teacher guides are on the left while the equivalent Singapore Math texts are on the right.
Friedman's latest ,where he demonstrates how other countries are "eating our kid's lunch in math" is well worth reading, as are these www.schoolinfosystem.org math posts. UW Math Professor Dick Askey has much more to say on K12 math curriculum.
A few observations from a layperson who couldn't be farther from a math expert's perspective on this (in other words, I'm not a math expert):
Tom Friedman writes "...math and science are the keys to innovation and power in today's world, and American parents had better understand that the people who are eating their kids' lunch in math are not resting on their laurels." His opinion piece in the New York Times writes more about HeyMath! and its use in Singapore and worldwide.
HeyMath! is
an Elearning system that supports the work of teachers in teaching and assessment, whilst helping students build a strong foundation in Math and become independent learners.
International Business Machines Corp., worried the United States is losing its competitive edge, will financially back employees who want to leave the company to become math and science teachers.The new program, being announced Friday in concert with city and state education officials, reflects tech industry fears that U.S. students are falling behind peers from Bangalore to Beijing in the sciences.
Up to 100 IBM employees will be eligible for the program in its trial phase. Eventually, Big Blue hopes many more of its tech savvy employees  and those in other companies  will follow suit.
Several AFT American Educator articles on Teaching Mathematics:
A professional mathematician shares his insights about effective instructional practice, how children learn, the importance of a coherent, systematic curriculum—and mathematics—after taking up the challenge of teaching in an Israeli elementary school.
There is general agreement that teachers’ knowledge of the mathematical content to be taught is the cornerstone of effective mathematics instruction. But the actual extent and nature of the mathematical knowledge teachers need remains a matter of controversy. A new program of research into what it means to know mathematics for teaching—and how that knowledge relates to student achievement—may help provide some answers.
I periodically here of requests for math tutors. The University of Wisconsin Math Department maintains a helpful list of tutors here.
"There's still a big disparity between the percentage of women in science, engineering and technology versus the percentage of men," Milgram said. "I think there has been a tendency to define certain things as masculine and feminine. Science and technology are defined as masculine."Milgram will be joined on the panel by Ellen Spertus, a computer science professor at Mills College and parttime software engineer at Google; Margaret Torn, a geological scientist at Lawrence Berkeley Lab; Neveia Chappell, product marketing engineer for Agilent Technologies; and Violet Votin, a recent graduate of Stanford University in cell biology.
Catherine Johnson sends a link to her Kitchen Table Math Wiki. Quite useful. (What's a wiki?)
UW Math Professor Dick Askey kindly took the time to visit with a group of schoolinfosystem.org writers and friends recently. Dick discussed a variety of test results, books, articles and links with respect to K12 math curriculum. Here are a few of them:
Most college curricula offer no rescue. In the modern American university, nobody takes responsibility for what is taught. Faculty members avoid prescribing any subject matter in particular. The participatory democracy of curriculum making somehow always manages to end at the same point: Anything must be declared to be as good as anything else, lest the balance of departmental enrollments (and faculty positions) be disturbed. The arguments are not, of course, so crudely put. We academicians are too skilled at spinning high reasons for low acts. Letting students ignore the events and ideas that have shaped them and their world is called freedom of choice. Amnesia becomes liberation. The notion that freedom can proceed only out of requirements is too deep for us, especially at budget time, and as enrollments fall.
If American education is ever to be made democratic, so that, as deTocqueville said, democracy may be educated, nothing will be more crucial than a common, sequential study of history throughout the elementary and secondary years. Only history, and particularly the history of Western civilization, can begin to help us find who we are and what choices we may have before us. But history is also, in Clifton Fadiman’s words, a generative subject, upon which the coherence and usefulness of many other subjects depend. It is essential to a serviceable view of art, architecture, drama, and literature, of the evolution of the natural sciences and social sciences. These are high claims for the uses of history, but they are justified by the aesthetic and intellectual experiences of countless Westerners, stretching back through time from Churchill to Thucydides. And such claims must be kept uppermost in mind, for otherwise it would prove impossible to decide what is most worth teaching out of the enormous mass of historical data facing us.
Check out your middle schooler's math skills with an online Saxon Math placement test.
Saxon Math offers excellent math programs from all grade levels. Some parents ask the teachers not to assign math homework to their child and use daily Saxon Math lessons instead.
Virginia will drop a basic skills test for wouldbe teachers which measures highschoollevel reading, writing and math performance. Instead, the state will develop its own test of collegelevel reading and writing skills. Only math teachers will be tested on math knowledge.
Here are "advanced math" test prep questions for Praxis I, which is being abandoned. Thirtyfive years out of high school, I can do these problems in my head. It's hard to believe there are people smart enough to teach who can't pass a basic math test. How are they going to average students' grades?
In a comparison of a 1973 algebra textbook and a 1998 "contemporary mathematics" textbook, Williamson Evers and Paul Clopton found a dramatic change in topics. In the 1973 book, for example, the index for the letter "F" included factors, factoring, fallacies, finite decimal, finite set, formulas, fractions and functions. In the 1998 book, the index listed families (in poverty data), fast food nutrition data, fat in fast food, feasibility study, feeding tours, ferris wheel, fish, fishing, flags, flight, floor plan, flower beds, food, football, Ford Mustang, franchises and fundraising carnival.......
It seems terribly oldfashioned to point out that the countries that regularly beat our students in international tests of mathematics do not use the subject to steer students into political action. They teach them instead that mathematics is a universal language that is as relevant and meaningful in Tokyo as it is in Paris, Nairobi and Chicago. The students who learn this universal language well will be the builders and shapers of technology in the 21st century. The students in American classes who fall prey to the political designs of their teachers and professors will not.
A reader forwarded this article: Jay Mathews, writing in the Washington Post:
So when I found a new attack on the National Council of Teachers of Mathematics (NCTM), the nation's leading association for math teachers, by a group of smart advocates, I saw a chance to bring some clarity to what we call the Math Wars. For several years, loosely allied groups of activist teachers and parents with math backgrounds have argued that we are teaching math all wrong. We should make sure that children know their math facts  can multiply quickly in their heads and do long division without calculators, among other things  or algebra is going to kill them, they say. They blame the NCTM, based in Reston, Va., for encouraging loose teaching that leaves students to try to discover principles themselves and relies too much on calculators.
10 Myths (Maybe) About Learning MathBy Jay Mathews
I love debates, as frequent readers of this column know. I learn the most when I am listening to two wellinformed advocates of opposite positions going at each other.
I have held several debates here, although not all of them have worked because the debaters lose focus. One will make a telling point, and the other, instead of responding, will slide off into a digression.
So when I found a new attack on the National Council of Teachers of Mathematics (NCTM), the nation's leading association for math teachers, by a group of smart advocates, I saw a chance to bring some clarity to what we call the Math Wars. For several years, loosely allied groups of activist teachers and parents with math backgrounds have argued that we are teaching math all wrong. We should make sure that children know their math facts  can multiply quickly in their heads and do long division without calculators, among other things  or algebra is going to kill them, they say. They blame the NCTM, based in Reston, Va., for encouraging loose teaching that leaves students to try to discover principles themselves and relies too much on calculators.
The NCTM people, on the other hand, said this was a gross misstatement of what they were doing.
The advocates call their new assault "Ten Myths About Math Education and Why You Shouldn't Believe Them." I took the myths, and their explanation of each, and asked the NCTM to respond to each one. Here is the result. There are some quotes that are not attributed, but are found in sources cited on the myth Web page, and some technical language, but I think this provides a good quick review of what this raging argument is all about.
Feel free to send your comments to one of the people who came up with the list of 10, Elizabeth Carson at nycmathforum@yahoo.com or to the NCTM at president@nctm.org. The NCTM Web site is http://www.nctm.org/about/position_statements/, and the names of the dissident group are on the myth Web page.
Myth #1  Only what students discover for themselves is truly learned.
Advocates: Students learn in a variety of ways. Basing most learning on student discovery is timeconsuming, does not insure that students end up learning the right concepts, and can delay or prevent progression to the next level. Successful programs use discovery for only a few very carefully selected topics, never all topics.
NCTM: NCTM has never advocated discovery learning as an exclusive or even primary method of instruction. In fact, we agree that students do learn in a variety of ways, and effective learning depends on a variety of strategies at appropriate times. The goal is not just to know math facts and procedures but also to be able to think, reason and apply mathematics. Students must build their skills on a strong foundation of understanding.
Myth #2  Children develop a deeper understanding of mathematics and a greater sense of ownership when they are expected to invent and use their own methods for performing the basic arithmetical operations, rather than being taught the standard arithmetic algorithms and their rationale, and given practice in using them.
Advocates: Children who do not master the standard algorithms begin to have problems as early as algebra I.
The snubbing or outright omission of the long division algorithm by NCTM based curricula can be singularly responsible for the mathematical demise of its students. Long division is a preskill that all students must master to automaticity for algebra (polynomial long division), precalculus (finding roots and asymptotes), and calculus (e.g., integration of rational functions and Laplace transforms.) Its demand for estimation and computation skills during the procedure develops number sense and facility with the decimal system of notation as no other single arithmetic operation affords.
NCTM: NCTM has never advocated abandoning the use of standard algorithms. The notion that NCTM omits long division is nonsense. NCTM believes strongly that all students must become proficient with computation (adding, subtracting, multiplying, and dividing), using efficient and accurate methods.
Regardless of the particular method used, students must be able to explain their method, understand that other methods may exist, and see the usefulness of algorithms that are efficient and accurate. This is a foundational skill for algebra and higher math.
MYTH #3  There are two separate and distinct ways to teach mathematics. The NCTM backed approach deepens conceptual understanding through a problem solving approach. The other teaches only arithmetic skills through drill and kill. Children don't need to spend long hours practicing and reviewing basic arithmetical operations. It's the concept that's important.
Advocates: "The starting point for the development of children's creativity and skills should be established concepts and algorithms. ..... Success in mathematics needs to be grounded in welllearned algorithms as well as understanding of the concepts."
What is taught in math is the most critical component of teaching math. How math is taught is important as well, but is dictated by the "what." Much of understanding comes from mastery of basic skills  an approach backed by most professors of mathematics. It succeeds through systematically empowering children with the preskills they need to succeed in all areas of mathematics. The myth of conceptual understanding versus skills is essentially a false choice  a bogus dichotomy. The NCTM standards suggested "less emphasis" on topics needed for higher math, such as many basic skills of arithmetic and algebra.
"That students will only remember what they have extensively practiced  and that they will only remember for the long term that which they have practiced in a sustained way over many years  are realities that can't be bypassed."
NCTM: Math teaching does not fall into two extremes. There are several ways to teach effectively. Even a single teacher isn't likely to use the same method every day. Good teachers blend the best methods to help students develop a solid understanding of mathematics and proficiency with mathematical procedures.
It's worth noting that standard algorithms are not standard throughout the world. What is most important is that an algorithm works and that the student understands the math underlying why it works.
Every day teachers make decisions that shape the nature of the instructional tasks selected for students to learn, the questions asked, how long teachers wait for a response, how and how much encouragement is provided, the quality and level of practice needed  in short, all the elements that together become the opportunities students have to learn. There is no onesizefitsall model.
Myth #4  The math programs based on NCTM standards are better for children with learning disabilities than other approaches.
Advocates: "Educators must resist the temptation to adopt the latest math movement, reform, or fad when databased support is lacking. ....."
Largescale data from California and foreign countries show that children with learning disabilities do much better in more structured learning environments.
NCTM: Most of the math programs published in this country claim to be based on the NCTM Standards. More important than the materials we use is how we teach. Students, all students, are entitled to instruction that involves important mathematics and challenges them to think.
Myth #5  Urban teachers like using math programs based on NCTM standards.
Advocates: Mere mention of [TERC, a program emphasizing handson teaching of math that this group doesn't believe demands enough paper and pencil work] was enough to bring a collective groan from more than 100 Boston Teacher Union representatives. ..... "
NCTM: Curricular improvement is hard, takes a lot of work, and demands support  for the teacher, for students, and for parents. It should be noted that Boston students using the TERCdeveloped curriculum seem to be thriving. The percentage of failing students on the Massachusetts state assessment decreased from 46 to 30 percent and students scoring at the Proficient and Advanced categories increased from 14 to 22 percent between 20002004 (Boston Globe, December 14, 2004).
Myth #6  "Calculator use has been shown to enhance cognitive gains in areas that include number sense, conceptual development, and visualization. Such gains can empower and motivate all teachers and students to engage in richer problemsolving activities." (NCTM Position Statement)
Advocates: Children in almost all of the highest scoring countries in the Third International Mathematics and Science Survey (TIMMS) do not use calculators as part of mathematics instruction before grade 6.
A study of calculator usage among calculus students at Johns Hopkins University found a strong correlation between calculator usage in earlier grades and poorer performance in calculus.
NCTM: The TIMSS 1999 study of videotaped lessons of eighthgrade mathematics teachers revealed that U.S. classrooms used calculators significantly less often than the Netherlands (a higher achieving country) and not significantly differently from four of the five other higherachieving countries in the analysis. When calculators are used well in the classroom, they can enhance students' understanding without limiting skill development. Technology (calculator or computer) should never be a replacement for basic understanding and development of proficiency, including skills like the basic multiplication facts.
Myth #7 The reason other countries do better on international math tests like TIMSS and PISA is that those countries select test takers only from a group of the top performers.
Advocates: On NPR's "Talk of the Nation" program on education in the United States (Feb. 15, 2005), Grover Whitehurst, director of the Institute of Education Sciences at the Department of Education, stated that test takers are selected randomly in all countries and not selected from the top performers.
NCTM: This is a myth. We know that students from other countries are doing better than many U.S. students, but certainly not all U.S. students. One reason U.S. students have not done well is that the way we have taught math just doesn't work well for enough of our students, and we have the responsibility to teach them all.
Myth #8  Math concepts are best understood and mastered when presented "in context"; in that way, the underlying math concept will follow automatically.
Advocates: Applications are important and story problems make good motivators, but understanding should come from building the math for universal application. When story problems take center stage, the math it leads to is often not practiced or applied widely enough for students to learn how to apply the concept to other problems.
"[S]olutions of problems ..... need to be rounded off with a mathematical discussion of the underlying mathematics. If new tools are fashioned to solve a problem, then these tools have to be put in the proper mathematical perspective. ..... Otherwise the curriculum lacks mathematical cohesion.
NCTM: For generations, mathematics was taught as an isolated topic with its own categories of word problems. It didn't work. Adults groan when they hear "If a train leaves Boston at 2 o'clock traveling at 80 mph, and at the same time a train leaves New York ..... " Whatever problems and contexts are used, they need to engage students and be relevant to today's demanding and rapidly changing world.
An effective program lets students see where math is used and helps students learn by providing them a chance to struggle with challenging problems. The teacher's most important job in this setting is to guide student work through carefully designed questions and to help students make explicit connections between the problems they solve and the mathematics they are learning.
Myth #9  NCTM math reform reflects the programs and practices in higher performing nations.
Advocates: A recent study commissioned by the U.S. Department of Education, comparing Singapore's math program and texts with U.S. math texts, found that Singapore's approach is distinctly different from NCTM math "reforms."
Also, a paper that reviews videotaped math classes in Japan shows that there is teacherguided instruction (including a wide variety of hints and helps from teachers while students are working on or presenting solutions).
NCTM: The study commissioned by the U.S. Department of Education comparing Singapore's mathematics program and texts with U.S. math texts also found that the U.S. program "gives greater emphasis than Singapore's to developing important 21stcentury mathematical skills such as representation, reasoning, making connections, and communication. The U.S. frameworks and textbooks also place greater emphasis on applied mathematics, including statistics and probability."
NCTM's standards call for doing more challenging mathematics problems, as do programs in Singapore, Japan and elsewhere, but they also recognize the needs of 21stcentury learners.
Myth #10  Research shows NCTM programs are effective.
Advocates: There is no conclusive evidence of the efficacy of any math instructional program.
Increases in test scores may reflect increased tutoring, enrollment in learning centers, or teachers who supplement with texts and other materials of their own choosing. Also, much of the "research" touted by some of the NSF programs has been conducted by the same companies selling the programs. State exams are increasingly being revised to address state math standards that reflect NCTM guidelines rather than the content recommended by mathematicians.
NCTM: True, there is no compelling evidence that any curriculum is effective in every setting, nor are there data to show exactly what causes improvement in student learning when many factors are involved. There is evidence that some of the more recently developed curricula are effective in some settings. However, the effectiveness with which a program, any program, is implemented is critical to its success, as are teacher quality, ongoing professional development, continuing administrative support, and the commitment of resources. Again, the issue of effectiveness is more likely to be attributable to instruction than to any specific curriculum.
Contrary to what is stated in some of these myths, there is no such thing as an "NCTM program." NCTM does not endorse or make recommendations for any programs, curricula, textbooks, or instructional materials. NCTM supports local communities using Principles and Standards for School Mathematics as a focal point in the dialogue to create a curriculum that meets their needs.
UW's Dick Askey emailed links to two of his papers on Elementary Math Curriculum:
While there was a need to do something to improve school mathematics education, NCTM did not face up to the most critical problem, the lack of firm content knowledge of far too many teachers. There were other lacks in their program. NCTM did not look seriously at mathematics education in other countries. Mathematicians were not involved in the development of the Standards. The NCTM authors of their Standards had the strange notion that it is possible to teach conceptual understanding without developing technical skill at the same time. Instances of all of these failures and what came from them will be given below.
Elementary school mathematics, it turns out, is not so elementary. This means that teaching it well requires much deeper mathematical knowledge than almost everyone has thought. There will be no math reform unless we provide teachers with the training, textbooks, time, and support needed to develop this knowledge.
So it was a surprise to see the photograph in the weekly paper, The Quincy Sun. There, on Page 7, was the Quincy High math club, and 17 of 18 members were Asian. Mathematically, it made no sense. Quincy High is 22 percent Asian; why is the math club 94.4 percent Asian?Evelyn Ryan, the math department head, says that before the influx of Asian families began, there was one calculus class of 10 students; now there are two calculus classes totaling 40 students, 75 percent of them Asian.
I wanted to ask math club members why Asian students are so good in math. As I was to learn, it wasn't such a simple question.
Most Asians at Quincy High have been in America only a few years, from China, Vietnam and Thailand. Most know little English when they arrive and are placed in E.S.L. classes (English as a second language.) "When I was a freshman, half year in U.S., English is a big problem," said Chaoran Xie, a junior now. "I just know, 'Hello how are you?' History is a big problem. You don't openly express yourself because you don't know what to say and stuff. In history it's a simple idea, but you don't have the basic English."
Joanne Jacobs:
From the Huffington Post: Mike Piscal, founder of the very successful View Park Prep charter school in the lowincome, minority Crenshaw District of LA names names in analyzing why 3,950 ninth graders at South LA's four major high schools turn into 1,600 graduates, 900 college freshmen and 258 college graduates. More here.This is related: Shanghai Jiaotong University won the recent ACM International Collegiate Programming Contest. The US hasn't won since 1997. The University of Illinois finished 17th, CalTech,Duke and MIT finished 29th while UWMadison earned an honorable mention.
Several westside PTO's hosted a candidate forum Wednesday evening. The candidates discussed a wide variety of questions, including referendums, the budget process, strings, local education media coverage and differences with their opponents. Listen to the entire event (34.6MB mp3 audio file), or click on the links below to review specific questions & answers.
Opening Statements Video  Q1: Referendums: Where do you stand? All four candidates Video 
Q2: Do you agree with the proposed cuts? All four candidates Video  Q3: What can you do to protect TAG, arts and other programs due to the continuous funding changes? Bill Clingan & Carol Carstensen Video 
Q4: How would you respond to a parent who said that they were leaving the Madison Schools because their child would have better AP, arts or sports opportunities in another district? (Larry Winkler & Lawrie Kobza) Video  Q5: For the incumbents: What specific initiatives have you taken to raise math scores particularily with low income & minority students? (Bill Clingan & Carol Carstensen) Video 
Q6: For the challengers: What are the substantive differences between you and your opponent? (Lawrie Kobza & Larry Winkler) Video  Q7: Will you promise to evaluate the Superintendent annually, as his contract calls for? (Bill Clingan) Video 
Q8: You said you would vote for a 3 year operating referendum at the recent MAFAAC Forum, now you say you won't. Why have you changed your mind? (Lawrie Kobza) Video  Q9: Does the Administration's budget document reflect School Board priorities? (Carol Carstensen) Video 
Q10: Do you think we should be fund raising from corporations, and asking them for money? (Larry Winkler) Video  Q11: Do you feel the media covers school issues and how do you feel about the fact that there are no media representatives here tonight? (Bill Clingan) Video 
Q12: Comment on the proposed reduction in Program Support Teachers? (Carol Carstensen) Video  Q13: How important do you think nocut freshman sports are? (Lawrie Kobza) Video 
Q14: How do you propose to address growth in extended parts of the Madison School District? (Larry Winkler) Video  Q15: Strings is part of the Board approved standards. Why is the Administration proposing to eliminate it? What are your views on this issue? (All 4 candidates) Video 
Candidate Closing Statements (All 4 candidates) Video 
Surely, the quote of the day:
''What's going to happen when they go into a store? Are they going to say, 'Do you happen to have 25 Cheerios so I can break it down?' " said Jacqueline Azulay of Roslindale, who sees her two daughters going to great lengths to break large numbers into manageable pieces. ''I think they need to teach basic math."Vanessa Parks dives into the math wars with many interesting quotes.
New Yorker writer and author (Blink & Tipping Point) Malcolm Gladwell spoke recently at the UW. He had two comments on education:
From University Communications
Workshop focuses on using algebra to teach arithmetic
(Posted: 2/21/2005)
Helping gradeschoolers make the difficult transition from arithmetic to algebra is the goal of a oneday workshop on Tuesday, March 1.
"Thinking Mathematically: Teaching Elementary Students to Use Algebraic Reasoning to Support the Learning of Arithmetic," sponsored by the Office of Education Outreach, will be held at the Pyle Center, 702 Langdon St.
The aim of the workshop is to increase teachers' understanding of how the fundamental principles imbedded in arithmetic can provide a foundation for learning arithmetic with understanding as well as learning algebra.
The session, which runs from 8 a.m.4 p.m., will be led by Annie Keith, a teacher in the Madison Metropolitan School District and a member of the Cognitively Guided Instruction research project at the Wisconsin Center for Education Research (WCER), and Linda Levi, associate researcher at WCER.
Participants will learn about research that demonstrates how the principles of algebra apply to the learning of arithmetic. Keith and Levi also will discuss how to teach arithmetic so that the concepts and skills that students learn in elementary school are better aligned with the concepts and skills that they need in order to learn algebra.
Ensuring the individual applicability of the program, participants will be asked to pose certain problems to their students before the workshop and bring to the workshop information about how their students solved the problems.
Cost for the session is $135 and participants will be awarded 0.6 continuing education units for attendance. This workshop addresses Wisconsin Teacher Standards 1, 2, 3, 4 and 8.
For more information, contact Julie Seaborg, Office of Education Outreach, at (608) 2635140 or visit the Office of Education Outreach's Web page.
Barry Garelick on our "National crisis in mathematics education". Fat Link on Barry Garelick.
New York Times, December 12, 2004
The Last Time You Used Algebra Was...
By DONALD G. McNEIL Jr.
It's been a long time since most of us have used algebra in our daily lives  unless, perhaps, you're helping your child with homework or work in a field that uses lots of mathematics. However, learning algebra is still important. The concepts I learned in mathematics have helped me with learning other concepts in different fields  math teaches you a way of thinking.
"...kids don't study poetry just because they're going to grow up to be poets. It's about a habit of mind. Your mind doesn't think abstractly unless it's asked to  and it needs to be asked to from a relatively young age. The rigor and logic that goes into math is a good way for your brain to be trained," said Miss Collins, the author's daughter's math teacher.
The Last Time You Used Algebra Was...
PARIS, Dec. 6  High school students in Hong Kong, Finland and South Korea do best in mathematics among those in 40 surveyed countries while students in the United States finished in the bottom half, according to a new international comparison of mathematical skills shown by 15yearolds.
The United States was also cited as having the poorest outcomes per dollar spent on education. It ranked 28th of 40 countries in math and 18th in reading.
U.S. Students Fare Badly in International Survey of Math Skills
June Kronholz summarizes the OECD's Program for International Student Assessment, which finds that:
The percentage of topachieving math students in the nation is about half that of other industrialized countries, and the gap between scores of whites and minority groups  who will make up an increasing share of the labor force in coming decades  is enormous.Here's the report.
Melania Alvarez, former MMSD School Board candidate, spoke on Monday, November 30, 2004 before members of the School Board. Her comments raised concerns about the lack of evaluation of the math curriculum currently being used in the MMSD. Ms. Alvarez's comments are based upon her own review of the math curriculum and upon her conversations with concerned parents in the District.
Following are video clips of her comments and questions of her by School board members.
The Madison School Board Performance & Achievement Committee met monday night, to discuss "ResearchBase Underlying MMSD Mathematics Curriculum & Instruction" Here are some video clips from the meeting:
On Evaluating Curricular Effectiveness: Judging the Quality of K12 Mathematics Evaluations (2004)
Curricula play a vital role in educational practice. They provide a crucial link between standards and accountability measures. They shape and are shaped by the professionals who teach with them. Typically, they also determine the content of the subjects being taught. Furthermore, because decisions about curricula are typically made at the local level in the United States, a wide variety of curricula are available for any given subject area.
Under the auspices of the National Research Council, this committees charge was to evaluate the quality of the evaluations of the 13 mathematics curriculum materials supported by the National Science Foundation (NSF) (an estimated $93 million) and 6 of the commercially generated mathematics curriculum materials (listing in Chapter 2). Posted by at 03:37 PM  Comments (0)  TrackBack Subscribe to this site via RSS/Atom: Newsletter signup  Send us your ideas
Reminder: The Madison School Board Performance & Achievement Committee will meet monday night, 11.29 @ 7:00p.m. to discuss "ResearchBase Underlying MMSD Mathematics Curriculum & Instruction" Room 103 Doyle Administration building [Map].
This announcement was posted on the MMSD Web site:
Monday November 29th, 2004
7:00pm  Performance & Achievement, Doyle Admin Building, Rm 103
* ResearchBase Underlying MMSD Mathematics Curriculum & Instruction
If you have questions or concerns about the math curriculum, I'd guess that you might want to attend this meeting.
Ms. Dempsey circled all those numbers on her own chart, which was being projected onto the blackboard. Now, she said, everyone in the class should color in all the multiples of two on his or her page. The students uncapped their yellow markers and set about filling in the appropriate boxes, noting the patterns they formed."Wonderful," Ms. Dempsey said, looking over one child's completed worksheet. "Just awesome."
At one particular desk, though, Jimmy was solving a different problem. He had just transferred to Claremont from a nearby Catholic school, and during the lesson he had whispered to an educator who happened to be visiting the room, "I know all my facts," by which he meant his multiplication tables.
So that educator, Ferzeen Bhana, the math coordinator for Ossining's elementary schools, gave him a problem to try: 23 times 16. Within a minute, Jimmy delivered 368, the correct answer. Ms. Bhana asked him how he had gotten it. Jimmy offered her a shy, yearning face and said nothing.
That brief moment, one moment in one school in one middleincome town, described the divide of the math wars in America. It was evident to Ms. Bhana that Jimmy had learned multiplication the oldfashioned way, with drills, algorithms and concepts like placevalue. The rest of the students were using a curriculum called Investigations, one of the new constructivist models, which teaches reasoning out a solution.
Interesting thread on discovery learning, with notes from Alan Siegel's study of videotaped Japanese Math lessons:
Discovery learning is fashionable in math reform circles, writes Seebach. The Japanese are supposed to be the models. But the Japanese teach traditionally  with "beautifully designed and superbly executed" lessons.The videotape shows, Siegel says, that "a master teacher can present every step of a solution without divulging the answer, and can, by so doing, help students learn to think deeply. In such circumstances, the notion that students might have discovered the ideas on their own becomes an enticing mix of illusion intertwined with threads of truth."
Two articles of interest appear in the issue of Isthmus dated June 15, 2004.
A small article on page 6 says "Several Madison elementary schools, including Thoreau and Glenn Stephens, will begin teaching Singapore Math next year. The change comes amid concerns that the district's preferred math program, TERC Investigations, which stresses selfguided problem solving, does not teach students enough basic math skills."
A lengthier article reviews the "difficult transiton at East High." As "faculty vent deep discontent," the article headline asks "is new princiapl to blame?" One source doubts, says the article, that "Tillman's contract will be renewed" beyond next year."
Ed Blume
Jay Matthews writes that Mathcounts lets smart middle schoolers compete to solve complex math problems.
NPR's All Things Considered: Experts Say Best Instructors Spot Where Students Go Wrong:
Research shows that teachers with degrees in the subjects they teach are more successful. That's the reason behind teachercertification requirements in the federal No Child Left Behind education law.But as Robert Frederick reports, not all mathematicians are successful math teachers. Most could use some help in becoming calculating sleuths. Education experts note that most advanced math programs are geared toward theoretical as opposed to practical instruction.
It's not enough to know math, says Judith Ramaley of the National Science Foundation. Teachers "also need to understand how the minds of young people work, and how to diagnose the kinds of tangles kids get into," she says.
A group of West High math teachers recently wrote a letter to the Editor of the Isthmus criticizing the direction of the MMSD's math program.
"As you read this, our department is under pressure from the administration and the math coordinator's office to phase out our "accelerated" course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a onesizefitsall curriculum." more