June 03, 2007
Schools streamline how math is taught: Same textbooks, same lessons, at the same time
Via a reader, interested in this issue:
Jessica Blanchard:
When Seattle elementary-schoolers 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 Butler-Wall 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.
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MMSD Paid Math Consultant on Math Task Force
 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
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May 24, 2007
Washington Delays Math, Science Graduation Requirements
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 WASL-overhaul bill that would have established end-of-course exams, regional appeals, a special exemption for students learning English as a second language and the clause declaring an emergency.
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May 15, 2007
Microsoft Unveils Math 3.0 and Latest ACT Report: Rigor at Risk....
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 low-cost, comprehensive resource for middle school, high school and entry-level 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 pre-algebra, 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 full-featured graphing calculator and step-by-step instructions on how to solve difficult problems.
Only one-quarter of high school students who take a full set of college-preparatory 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 college-level work in all four core areas, while 19 percent were not adequately prepared in any of them.
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May 14, 2007
Radical Math in the NYC Department of Education
Late last month, over 400 high school math teachers and education professors gathered in Brooklyn for a three-day 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 teaching-for-social-justice 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 “social-justice” 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: “Check-cashing 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.”
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April 24, 2007
Teachers Must be Up for Count
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 well-prepared 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 self-confidence. 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 Math-Science Partnership Steering Committee. He is teaching a course in mathematics for elementary teachers at BC. Clusty search.Moreover, the curricula of teacher-preparation 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.
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April 22, 2007
Parents & Math
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.
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April 21, 2007
Math conference: Meeting the Needs of Diverse Learners
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 2-4) is fast approaching and will provide valuable opportunities to schools and districts using Title I funding for mathematics. As noted below, the Wednesday pre-conference 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.
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April 17, 2007
MMSD Math Review Task Force Introduction and Discussion
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:
- Madison School Board Discusses Independent Math Review: Audio / Video.
- Math Forum Audio / Video
- UW Math Professor Dick Askey on the MMSD's math scores; related: State test scores adjusted to match last year
- Isthmus Take Home Test on Curriculum
- Connected Math in Olympia, WA
- Lee Sensenbrenner on Connected Math
- The Politics of K-12 Math and Academic Rigor
- New Math Curriculum Draws Complaints
6th Grade Textbooks: Connected (left) and Singapore Math.
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.
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Math task force named
According to Arlene Silveira, the superintendent named the following members of a math task force:
Merle Price (co-chair): 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 (co-chair): 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 co-chair has been directly involved in NCTM-based 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 K-12 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.
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March 16, 2007
On Math Reform
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 name-calling, 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.”
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March 12, 2007
Science, math deficit holds back state
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 X-shaped 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.
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Growing Trend Toward Eighth Grade Algebra
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 mid-year," 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.
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March 07, 2007
Why Illinois Test Scores Went Up?: Changing the Test or Academic Improvements?
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' laser-like focus on the state learning standards—the detailed list of what pupils should know at each grade level. They also say that the more child-friendly 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 8th-grade 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.
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February 26, 2007
Online Mathematics Textbooks
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 distribute--but 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 on-line 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.
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February 22, 2007
Closing the Math Gap
Milwakee Journal-Sentinel 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 J-S 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.
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February 06, 2007
Outline of math task force
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 K-12 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 K-12 students, including analysis of all math sub-tests scores disaggregated by student characteristics and schools; (2) analysis of performance expectations for MMSD K-12 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.
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February 01, 2007
"No Need to Worry About Math Education"
From a reader involved in these issues, by Kerry Hill: Demystifying math: UW-Madison 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 UW-Madison – 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 real-world problem-solving 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 trail-blazing cohort led by Carpenter, Romberg, and Fennema in recent years has been passing the torch at UW-Madison 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 UW-Madison.
“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 middle-school 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 1-3, 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 decade-long (1995-2004), federally funded initiative based at the Wisconsin Center for Education Research (WCER). NCISLA involved researchers at six institutions collaborating with K-12 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’ long-term 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, UW-Madison 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 three-year 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 five-year, 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 UW-Madison 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 fourth-grade 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 re-evaluate 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 UW-Madison 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 UW-Madison and led by Tom Carpenter.
DiME – a consortium consisting of UW-Madison, 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 culture-free 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 low-tracked 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 high-quality 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 low-income 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 pre-service 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 pre-service teachers in their final year, and Hand has co-taught a geometry content course within the Mathematics Department for pre-service teachers.
“We all work with graduate students, as well,” Ellis adds. “There is a core sequence of four graduate courses that our math-ed students take, and we all four teach these courses.”
And, all four work with in-service teachers.
Knuth has directed several professional development programs for secondary school mathematics teachers, ranging from a three-year program designed to help high school teachers learn to teach with technology to multi-year programs designed to help middle-school teachers foster students’ mathematical reasoning.
He and Ellis ran a professional development program for pre-service 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 UW-Madison 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.”
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January 28, 2007
The Declining Quality of Mathematics Education in the US
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.
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January 26, 2007
The Baltimore Algebra Project
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 inner-city 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 soft-spoken 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.
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January 25, 2007
Math Education: An Inconvenient Truth
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.
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Singapore Math is a plus for South River students
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 low-performing students, but at a slower pace and with greater repetition.
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Madison School Board Discusses an Independent Math Curriculum Review
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 K-12 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 2006-07 goal to initiate and complete a comprehensive, independent, and neutral review and assessment of the District’s K-12 math curriculum as presented at this meeting, including extension for completion of the evaluation to the 2007-08 school year. The Board of Education shall receive a report in 2006-07 with analysis of math achievement data for MMSD K-12 students, including analysis of all math sub-test scores disaggregated by student characteristics and schools in addition to reports in subsequent years. Student representative advisory vote * aye. Motion carried 6-1 with Lucy Mathiak voting no.
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January 24, 2007
1989-2006 Math Comparison: Are Students Better Now?
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 eighty-nine 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 K-12 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.
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January 19, 2007
Middle and Elementary School Mathfests
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 first-class event for these first-class 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 663-5221.
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January 16, 2007
Reduced Math Rigor
What is 256 times 98? Can you do the multiplication without using a calculator? Two thirds of Massachusetts fourth-graders 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 two-digit 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., pencil-and-paper 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!
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January 12, 2007
Financially Support Madison Schools' Math Festival
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.
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January 06, 2007
Why You Should Learn Algebra
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 oft-repeated 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.
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December 19, 2006
25 Year Old KIPP Teacher's Math Program
But one of the secrets of KIPP's success in attracting the brightest young teachers and raising achievement for low-income 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.
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December 14, 2006
Madison United for Academic Excellence, 12-December-2006 Presentation
The Madison United for Academic Excellence (MUAE) meeting of 12-December-2006 offered a Question and Answer session with Madison Director of Teaching and Learning, Lisa Wachtel, and Brian Sniff, District K-12 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
- Changing demographics in the school district
- Listing of Superintendent's Goals for comprehensive review, as set by the Board of Education
- K-5 Math Standards, Resources, and role of Teaching and Learning
- Professional development for K-5 teachers
- 5th Grade Math Assessment Pilot project for advanced students
- Middle school math, 6th to 8th grade
- Math certification of middle school math teachers, with an extended discussion of the statistic that only 5% of middle school math teachers are math certified, comparing Wisconsin to bordering states
- WKCE tests and testing in general
- Discussion by audience of recent studies and trends in math preparation for college
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December 13, 2006
Washington Governor Wants More Math
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 "world-class" standards and then design achievement tests accordingly.
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December 12, 2006
A Study of Core-Plus Students Attending Michigan State University
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 18-page article entitled "A study of Core-Plus students attending Michigan State University" by Richard Hill and Thomas Parker, professors at MSU who teach pre-service high school math teachers.Core-Plus is used in some Madison High Schools. Much more on math here.They state that, "as the implementation progressed, from 1996 to 1999, Core-Plus 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 low-level and remedial algebra courses.
The grades the Core-Plus 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."
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Don't like math? UW-O asks 'why not?'
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 Wisconsin-Oshkosh 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.”
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Math failures - haven’t we heard this before?
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 so-called 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.
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December 07, 2006
New Math Curriculum Draws Complaints
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 hands-on activities and problem-solving 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.
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December 05, 2006
Do Math Topics Lead to Better Instruction?
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.
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November 24, 2006
Wisconsin Math, reading proficiency are much higher on state exams than on federal
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 eighth-graders 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
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November 20, 2006
NYT Letters: The New New Math: Back to Basics
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 pre-algebra/algebra. This sounds like good news until it becomes clear that it’s not pre-algebra that students find problematic: it’s basic arithmetic.Enabling students to have rote facts at their fingertips endows them with great self-confidence and permits them to take risks with subsequent higher-thinking math skills. This self-confidence 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 self-esteem 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 adult-school 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 doctorate-minded 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 high-priced 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 college-level and in some instances postgraduate-level 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 fifth-grade 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
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November 19, 2006
On Math Rigor
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 one-size-fits-all world.
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November 17, 2006
"Too Little Math in Math?"
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 low-level task for a bright sixth-grader, 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 Chacon-Taylor children and their parents, Hugh Taylor and Monique Chacon-Taylor, are among Snohomish County families raising questions about the effectiveness of widely used math textbooks that encourage discovery and writing about math, but de-emphasize 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 K-12 math standards, select more effective textbooks and re-examine 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 10th-graders and 59 percent of fourth-graders 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..
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Board proposes goals for superintendent
According to the agenda for the Board of Education meeting on November 20, 2006:
It is recommended that the Board approve the 2006-07 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 K-12 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 K-12 students, including analysis of all math sub-tests scores disaggregated by student characteristics and schools;
- analysis of performance expectations for MMSD K-12 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 include
c. 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 feed-back on the information they receive from the administration. Information provided to the Board shall be rated for timeliness, accuracy, organization and presentation.
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 under-represented 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.
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November 14, 2006
National Council of Teachers of Math Changes Course on Teaching Math Fundamentals
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 so-called reform math — critics call it fuzzy math — has crippled students with its de-emphasizing 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 A-plus 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
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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 generation--but there are still a lot of issues with things such as run-on 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 so-called reform math — critics call it fuzzy math — has crippled students with its de-emphasizing 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 A-plus 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.
Grass-roots 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.”