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

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Teacher Ms. Cornelius:

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.
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.

Alison Kepner has more.

Lynn Thompson:

But they strongly believe that their math textbooks should include actual math.
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..

The Madison School District uses Connected Math in middle school. Many links and notes on math, including the recent Math Forum audio/video.

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

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 so-called “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

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Ben Feller:

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.

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 high-quality 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.
Editorial, New York Times, September 18, 2006

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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.
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.
Article by Tamar Lewin, New York Times, September 13, 2006

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“Show me how, Now“.

“John Dewey”:

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.

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 seventh-grader at a Madison middle school is posed with the following situation: A gas station sells soda in three sizes. A 20-ounce cup costs 80 cents, a 32-ounce cup is 90 cents and a 64-ouncer goes for $1.25.
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 84-ounce Mega Swig, what would you expect to pay for it?
There’s really no concrete answer. A student, for instance, could argue that the 84-ouncer would cost what the 20-ounce and 64-ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some per-ounce price slightly less than what was given for the 64-ounce 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 real-life 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.

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.

I’m told that the MMSD’s math curriculum will be getting some attention this fall. We’ll see (35 of 37 UW Math Faculty Open Letter on Math).

My largest concern with Connected Math – having read some of the books is that we’re training the students to be consumers, not creative types (figure out the phone bill, count the cheerios, buy a soda, etc.). TeacherL made a great point recently: We can choose to be consumers or we can choose to be citizens. I know which one I think will provide the stronger future for our country.”

Sean Cavanagh:

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 more-complex algebraic concepts, trigonometry, and a stronger emphasis on mathematical reasoning and problem-solving, 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.”

Dan Greene:

The average incoming level for our freshmen is around 5th grade. Our mission is to get them to a 4-year college. This requires not just development of their academic skills, but it also requires a shift in their thinking and self-perception. 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 well-educated people who happily admit that they can’t do math, but none that laugh about their inability to read a book.

The Asia Society:

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.

The Asia Society has an extensive set of teacher and student resources.

A reader deep into math issues emailed these two reviews of curriculum currently used within the Madison School District:

• Connected Math (Middle School); R. James Milgram:
  

  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.

• Core Plus (some high schools); R. James Milgram and Kim Mackey:
  

  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 e-book pdf:

It has long been felt that the mathematical preparation of pre-service 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, pre-service 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 pre-service 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 non-teaching 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 wrong–an 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 co-authors 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.

“Finding Common Ground in the U.S. Math Wars”, Science Magazine, May 19, 2006 describes the 18-month 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:

Fundamental Premises
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.

• Basic skills with numbers continue to be vitally important for a variety of everyday uses. They also provide crucial foundation for the higher-level mathematics essential for success in the workplace which must now also be part of a basic education. Although there may have been a time when being to able to perform extensive paper-and-pencil computations mechanically was sufficient to function in the workplace, this is no longer true. Consequently, today’s students need proficiency with computational procedures. Proficiency, as we use the term, includes both computational fluency and understanding of the underlying mathematical ideas and principles.
• Mathematics requires careful reasoning about precisely defined objects and concepts. Mathematics is communicated by means of a powerful language whose vocabulary must be learned. The ability to reason about and justify mathematical statements is fundamental, as is the ability to use terms and notation with appropriate degrees of precision. By precision, we mean the use of terms and symbols, consistent with mathematical definitions, in ways appropriate for students at particular grade levels. We do not mean formality for formality’s sake.
• Students must be able to formulate and solve problems. Mathematical problem solving includes being able to (a) develop a clear understanding of the problem that is being posed; (b) translate the problem from everyday language into a precise mathematical question; (c) choose and use appropriate methods to answer the question; (d) interpret and evaluate the solution in terms of the original problem, and (e) understand that not all questions admit mathematical solutions and recognize problems that cannot be solved mathematically.

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 “mile-wide, inch-deep” curricula in most schools, which leave most student incapable and ill-prepared for further work in mathematics, science and engineering disciplines. The Focal Points document has not be published at this time.

But, to place these “improvements” into perspective, no one expects these initiative to make improvements by themselves. Further, UC-Berkeley Math Prof Hung-Hsi Wu says “Better mathematics education won’t take place in the next 10 years, I think it will take 30 years.”

Education Wonks:

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.

Barry Garelick:

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 pre-conceived conclusions then follow.

Madison Metropolitan School District:

Lead K-12 mathematics programming; develop and promote documents defining the mathematics program and expectations; organize and promote professional development opportunities; seek and implement research-based 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 standards-based mathematics; develop and promote standards-based 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.

Diane Jean Schemo:

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 free-form approach to teaching math against the traditional method that emphasizes rules and formulas to solve number problems.
In traditional math, children learn multiplication tables and specific techniques for calculating 25 x 25, for example. In so-called 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 college-level algebra course.

More on the National Math Panel.

Martha Stark:

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.”

Tara Bahrampour:

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 T-shirts 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.
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 four-member team had won.

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 Economist:

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 Russian-born 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 computer-science 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.

Jessica Blanchard:

New math textbooks for Seattle middle- and high-school 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.

MathandText:

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.

Jo Anne Cobasko:

“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, 2005–link here), CSU-Northridge 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 in-service 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.

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 large-scale study of Michigan students, we analyzed the records of students arriving at Michigan State University from four high schools which adopted the Core-Plus 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 end-of -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 college-level mathematics and science courses.

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 school
A recurring problem in most rich societies is that students in general do not take enough math – despite high availability of relatively well-paid 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.

Jonathan David Farley:

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.”
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 15-year-olds 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.

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.

California Department of Education (pdf):

A high-quality 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.

Additional standards and frameworks are posted here.

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.
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 knowledge-based economy, Wisconsin must continue its commitment to math and science education and encourage more students to take related courses.

There’s been a great deal of discussion on these issues here.

Susan Lochen, Madison West High School (co-signed 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 one-size-fits-all curriculum.
It seems the administration and our school board have re-defined “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 short-sighted 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?

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….

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 facts—we’re inundated already—but 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 fixed-rate 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.

Joanne Jacobs:

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.

Ms. 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 pre-calculus and other college-track classes (I never took a course beyond algebra 2, much to my chagrin). He doesn’t immediately know that 7×5=35, and then subtract 35 from 100, nor can he figure out that 13×5=65. As a matter of fact, he stumbled over the 100-35 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:

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 conversation, including audience questions was lively.

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Jamaal Abdul-Alim:

The books are distributed by an Oregon-based company known as SingaporeMath.com, which counts a private school in Madison as the first of its growing number of clients.
The biggest difference between math instruction in Singapore – a city-state 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.

More on the Connected Math / Singapore Math textbook photos.

Madison Country Day School was the first US school to purchase Singapore Math textbooks, in 1997, according to this article.

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 thank-you 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.

Virginia Postrel:

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 de-emphasized.
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.

Celeste Roberts:

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.

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• Ben Feller:
  

  Science and math have zoomed to the top of the nation’s education agenda. Yet Amanda Cook, a parent of two school-age 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.

• Celia R. Baker:
  

  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.

Karin Klein:

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.
Johnny 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.

Via Joanne