COMET • Vol. 2, No. 05 – 12 February 2001


(1) Knowing and Learning Mathematics for Teaching

Source: Gail Burrill, Director, Mathematical Sciences Education Board (MSEB)

In March 1999, the MSEB hosted a workshop for teacher educators, professional developers, mathematicians, and mathematics education researchers to consider what mathematical knowledge K-8 teachers need and how they might learn it. The Mathematics Teacher Preparation Content Workshop activities centered on the actual work of teaching, using videos of classrooms, student work, student curriculum materials, and written case studies. Deborah Ball chaired the program steering committee. Other members included Richard Askey, Hyman Bass, Genevieve Knight, Mark Saul, Deborah Schifter, and Olga Garcia Torres.

Copies of the proceedings, Knowing and Learning Mathematics for Teaching, can be ordered through the National Academy Press (NAP) by calling (800) 624-6242 or by visiting NAP’s Web site at The volume includes activities from the workshop, deliberations of working groups focused around particular questions of teacher development, papers presented by plenary session speakers, and tasks posed to the participants before and during the workshop.

(2) “Math Illiteracy Spells Trouble” by Valerie Strauss

Source: Washington Post – 6 February 2001

Florida’s Supreme Court chief justice votes to stop a presidential vote recount and quotes a mathematician to support his position, but the mathematician says his comments were misunderstood.

President Bush advances an education plan calling for an annual test to determine a school’s progress, though many mathematicians say it is not a statistically valid method of assessment.

Today’s headlines reveal new dimensions of a problem that mathematicians deplore: “innumeracy,” or math illiteracy, among many Americans who cannot tell millions from billions, average from median or percent from percentile.

The problem, while not preventing the country from soaring in science and technology, has important economic, social and personal consequences, mathematicians and others say. Money is wasted, bad policy is made, health and physical risks are taken based on faulty information.

“There are cashiers who are flummoxed by discounts and sales taxes…nurses who have difficulty determining appropriate dosages, and quality control managers who don’t understand simple statistical concepts,” said Temple University mathematician John Allen Paulos.

“Surely demagogues yearn for people who can’t recognize economic trade-offs, who lack a visceral feel for the difference between a million dollars for some cultural program, a billion dollars for some aircraft, or a trillion dollars in tax cuts.”

The problem is not new. In 1981, David Stockton, budget director for President Ronald Reagan, laid bare the issue, saying, “None of us really understands what’s going on with all these numbers”…

Douglas Hofstadter, director of the Center for Research on Concepts and Cognition at Indiana University and author of the prize-winning book “Godel, Escher, Bach: An Eternal Golden Braid,” says an increased understanding of math would improve society.

People would be safer, for example, if they could better calculate risk. “If you confuse something that is a thousand times larger than what it is, you are going to make some very bad decisions,” said Hofstadter, who coined the word “innumeracy.”

Hofstadter teaches kids about big numbers with packages of pasta, rice and sugar. They first guess that each bag has the same number of items but learn through calculations there are about 150 pieces of pasta, 1 million kernels of rice and 100 million or more sugar grains. “You don’t need to use fancy words like logarithms,” he said. “You just say number of digits or zeroes. You don’t have to scare anybody away.”

Recent news offers more evidence of innumeracy.

Take the case of Charles T. Wells, chief justice of Florida’s Supreme Court, who, during the recount drama, quoted Paulos as saying “the margin of error in this election is far greater than the margin of victory, no matter who wins.” He interpreted that to support his position against a recount. Paulos, author of “Innumeracy” and other books, said his comments were meant to support a recount. Yet, Paulos and others also believe that the Democrats used bad math when they sought a limited recount. After the election, Democratic lawyers asked for recounts in only a few counties, even though the entire state should have been involved for a statistically sound result.

In the end, the courts decided for legal, not mathematical, reasons that a full recount of undervotes was the only fair approach. But time had run out.

“Had the judiciary simply concentrated on the fundamental problem of counting from the beginning, rather than the narrow legal issues the parties raised, the controversy might have been resolved differently,” said Lee Kraftchick, assistant Dade County attorney and a mathematician.

In another example, Bush’s education plan calls for annual high-stakes tests to determine a school’s academic progress and the flow of some federal dollars. Depending on a single test, however, may well be a statistical error.

“The exclusive reliance on test scores to evaluate schools is as flawed as the exclusive reliance on a blood pressure test to make a ‘high stakes’ decision on heart surgery,” said Douglas Reeves, head of the nonprofit Center for Performance Assessment.

The error is not in the test itself, he said, but in the interpretation and use of a single set of test results to praise or condemn a school. “The greatest absurdity,” he said, “is when we compare this year’s third grade to last year’s third grade” — two different groups.

And the smaller the school district or class, the less valid the comparison. Even comparisons of fall and spring data are flawed in schools with mobility rates as high as the 70 percent common in urban areas.

David Murray, who heads the nonprofit Statistical Assessment Service, said one test may be better than none in this context, but more than one would be more fair. “Do a battery of tests, in a close cluster. Give people a chance to show, ‘I can get to right, get to left.’ Take the average. But that costs a little more, in time and resources. Whether anyone will spend those resources is another question.”

(3) The NewsHour with Jim Lehrer — President Bush’s Testing Proposals

A segment on standardized testing, accountability issues, and other education topics is scheduled for Thursday, 15 February 2001, on PBS’s NewsHour program. Check the “station finder” link at the above web site for local broadcast information.


  • Bill Evers–Hoover Institution, HOLD, Bush education advisor
  • Lisa Keegan–Arizona State Superintendent of Schools
  • Alfie Kohn–Author of The Schools Our Children Deserve, Punished by Rewards, and other books
  • Monty Neill–Executive Director, FairTest (

(4) “The Testing Obsession” by Howard Gardner

Source: Los Angeles Times – 31 December 2000 (now archived)

With California leading the way, the nation is going through a frenzy of testing its public school students. Never before have so many students been given so many formal standardized tests. The college-bound student can expect to take the PSAT, the SAT and an assortment of achievement and advanced placement tests; college-bound or not, students also take state-mandated tests, as well as nationally normed instruments like the Iowa Test of Basic Skills or the Stanford 9. The stakes for students, faculty, administrators and even politicians have never been higher. Admission to college, cost of student housing, jobs and promotions for those in the teaching profession, and election to office — all hinge on whether the all-important scores have gone up, or up enough. But few have even posed the central question: What is the relation between test scores and a quality education?

The testing frenzy is a response to a perceived problem. Over the last 20 years, Americans have become convinced that U.S. public schools are not doing a good enough job and, in particular, are failing their most disadvantaged students. Whether schools are absolutely worse off than in 1950 is not the issue; nor is there evidence that disadvantaged students were ever well-served. Yet, most observers would agree that today’s schools do not adequately prepare students for the knowledge economy that all developed nations compete in. So a predictable sequence has unfolded: 1) Create or resurrect instruments by which student performance can be assessed. 2) Attach high stakes to these performances. 3) Reward high test scores and punish those deemed responsible for their absence.

It is by no means easy to tell whether this strategy is working. The good news is, there are early reports of performance improvements in nearly every region. This is not surprising. Once a high-stakes test-measuring instrument has been revealed, the minds of everyone — students, teachers, parents, and the media — are wonderfully concentrated. Indeed, this phenomenon recently occurred in California, where most schools reported improvement on the Stanford 9 and on the Academic Performance Index that is derived from it.

But don’t start dancing in the streets yet. The experience of the last decade offers numerous cautionary notes. First, improvement based on sheer familiarity with a test is a onetime occurrence. Then, too, results are typically restricted to a particular test, or even to a particular version of a test. This happened in Chicago, when new versions of the same test resulted in system-wide regressions in scores. Finally, and most important, improvements on specific tests are often not reflected on more generic instruments. This was observed when the vaunted improvement on the Texas Assessment of Academic Skills was not matched by comparable improvements on the National Assessment of Educational Progress, a federal exam. Similarly, irrespective of local improvements in mathematics scores, international comparisons in mathematics and science consistently paint a bleak picture of the competence of American schoolchildren.

So what to do? It has been quipped that the best solution for indifferent test scores is to test even more, as if taking the temperature of a sick person repeatedly would in itself improve their health. A testing frenzy feeds on itself. But test scores in themselves should not be the goal of schooling; nor should practicing for the test be a primary activity for students. Rather, improved test scores should be an index of a good education. If an effective education is taking place, then one should be able to administer a wide variety of tests from one year to the next and encounter consistently good performance. But no jurisdiction would dare to carry out such an experiment, because, deep down, policymakers know that higher scores are more likely to be the result of “teaching to version X of test Y” than the dividend of generally strong preparation.

But, a randomly chosen politician might respond, “We spend huge amounts of federal, state and local tax dollars on public education, and that amount has increased in recent years. Unless we don’t care whether or not that money is wasted, it is essential that we hold schools — teachers, students, and perhaps parents — accountable for student learning.”

There is nothing wrong in calling for accountability. The crucial question concerns its manner. In this country, we have made the mistake of equating academic accountability with testing – -typically, the short-answer, machine-scored test. But many other forms of accountability exist.

In earlier times in the United States, teams of informed “inspectors” visited schools and evaluated them. This procedure is still followed in some independent private schools. U.S. colleges and universities, the envy of the world, do not depend on standardized testing of students; visiting committees evaluate specific departments or the school as a whole, and the subsequent careers of graduates are scrutinized by observers.

The Coalition of Essential Schools, a network of 1,000 high schools in the United States, spurns standardized instruments; instead, it advocates that students exhibit their work in front of knowledgeable teachers and experts, with graduation contingent on a certain number of successful exhibitions. Certification of teachers — for example, by the National Board for Professional Teaching Standards — rates of graduation, acceptance at four-year colleges, student involvement in community service, science fairs or debating clubs are other possible indices of accountability. Perhaps most important, a school should never be held accountable by a single metric; the best indices of accountability are pluralistic and suited to the context of a particular school in a particular community.

The goal of quality education requires an entirely different approach. We must begin with a vision of what it means to be an educated person; the means of assessment should follow from, rather than dictate, the ways in which we educate students. The educated person is one who can think well in terms of the major disciplines, in particular, who displays historical, scientific, mathematical and artistic understanding. Understanding is not the same as knowing lots of facts and figures. Rather, understanding in a discipline entails knowing how to make sense of a phenomenon that is unfamiliar but that can nonetheless be illuminated if one knows how to make sense of documents (history), conduct a controlled experiment (science), analyze a situation quantitatively (mathematics) or qualitatively (literature and the arts).

Should one adopt such a vision, the means of assessment should be performance-based. That is, students are given an unfamiliar example (an item from today’s news, data from a new experiment, a recently completed work of art) and are then required to make sense of it. Their score might be determined in part by their ability to indicate the steps that they would take, were they initially stymied. As Socrates taught us thousands of years ago, part of being educated is knowing what you don’t know and how to bootstrap yourself to understanding.

The United States is too vast to be satisfied with a single education vision. Indeed, California alone is too large. We could never come up with a collective education vision that would satisfy Jesse Helms, Jesse Jackson and Jesse Ventura. Our test-crazed society attempts to deal with this problem by ducking altogether the question of vision. This is a mistake.

We should develop perhaps a half-dozen educational pathways, each aligned to a particular vision of the educated human being. The pathway of “disciplinary understanding” described above would be one. As with current standardized tests, the results of assessments would be made public. But instead of the focus falling on numbers, whose meanings are obscure even to psychometricians, the focus would fall on actual knowledge that is cherished and the ways that knowledge has been exhibited by flesh and blood students. In France, questions on the baccalaureate examination — and they are not multiple choice – -are published on the front page of the newspaper, and the public argues about them. This represents a more sensible state of affairs than the current numbing tables of numbers in our newspapers.

The limits of the current testing frenzy should sooner or later become clear, and the focus will eventually shift to the kinds of minds that we value and the best ways to fashion them. There will certainly be a place for testing — or, better, assessment — and families will gravitate toward the pathways that reflect their value system. The idea of a handful of pathways represents a meaningful midpoint between a single system, which involves too many compromises, and a plethora of charter or voucher choices that would be impossible to sustain and monitor.

The biggest cost of a system geared single-mindedly to test scores is that we virtually never hear any public discussion of what it means to use your mind well, to understand, to appreciate, to create knowledge, to be an educated human being. And so students can properly draw the conclusion that we do not care about these values.

Winston Churchill once remarked that the American people can always be counted on to do the right thing — after they have exhausted every other alternative. It is time for those who do care to make known their concerns and visions — and perhaps meet the challenge set by Churchill.

(5) “Japan Wants Its Students to Learn — for the Joy of It” by Mark Magnier (Makiko Inoue in The Times’ Tokyo Bureau contributed to this report)

Source: Los Angeles Times – 9 February 2001

…Japan’s perceived delight deficit was highlighted by the release of a comparative international education survey. Although eighth-graders here ranked comfortably near the top, as usual, for their ability to solve math and science problems, parents and educators were startled to see just how much the students hated these subjects.

“Everyone was really quite taken aback,” said Katsuhiko Maeda, senior curriculum specialist with the Education Ministry, “especially because our students are so good at math and science.”

The survey issued in December by the Amsterdam-based International Assn. for the Evaluation of Educational Achievement ranked Japan’s students No. 36 out of the 37 nations surveyed for their interest in math–just above Moldova–and No. 22 out of 23 for their interest in science.

Fun and enjoyment are not commonly associated with education in a nation famous for its “entrance exam hell,” rote learning and bullying. It’s not uncommon for Japanese junior high students to attend regular classes and special cram schools from 8 in the morning until 10:30 or 11 at night…

Although students everywhere like to complain about school, Japanese parents and educators fear that such widespread erosion of enjoyment will lead to a sharp drop in standards. And for traditionalists, that spells disaster, given this nation’s reputation for world-class products and its heavy reliance on applied science and engineering.

In response, the Education Ministry is touting a revised curriculum due out by next year that will encourage flexibility, “education of the heart” and ikiruchikara, or “zest for living.” The plan calls for more electives, a five-day school week–down from six–and at least three hours a week of flexible time.

Behind the debate over how to make fractions fun and experiments exciting is a broad-based fear that Japan is not producing the type of graduates required in the 21st century.

Japan’s rigorous conformity and centralized education policies arguably served the nation well during the economic boom years, when it needed a relatively uniform work force for its factories and corporate ranks.

But globalization has placed a premium on imaginative individuals able to question authority and reason through problems. These abilities, many believe, are not tolerated–and so, hardly encouraged–in the education system.

In spite of its new, soft approach, the Education Ministry is as control-oriented as ever, critics say. Kazuo Nishimura, a math professor at Kyoto University and head of a group opposed to the new curriculum, says the bureaucrats are way too meddlesome in some areas and way too relaxed in others.

On the one hand, large class size and rigid standards still leave little room for local autonomy or diversity. On the other, textbooks have been dumbed down, with most explanations, difficult problems or sample exercises removed, he says. And the number of hours spent in class is among the lowest for industrialized nations–and getting lower, he adds.

“‘Zest for living’ sounds nice, but their policy is actually quite the opposite,” Nishimura says. “There’s a crisis in Japanese education. The entire system isn’t working well.”

As with education issues in many countries, there has been lots of finger-pointing. Some experts blame politicians for promising reform and not carrying through. Others knock parents for not fostering a love of learning, teachers for a shortage of imagination and schools for their lack of accountability…

(6) “New Program Will Put Artists In Asheville And Buncombe Schools To Support Academic Curriculum” by Barbara Blake

Source: Asheville Citizen-Times – 29 January 2001

Come next fall, students in Asheville and Buncombe County’s public schools will be learning math through clogging, studying the solar system through modern dance, and otherwise embracing reading, writing and ‘rithmetic through the arts, from drama and theater to music and painting.

Frivolous, you say? No way, say educators who have become true believers in the results of a massive research project showing that students – especially at-risk students – who are consistently exposed to the arts perform higher academically across the board than those who are “arts poor.”

Armed with that evidence, and in partnership with the Asheville Area Arts Council and the North Carolina Arts Council, the two school systems will begin a new “Arts in Education” program when school starts up next August, drawing from a pool of more than 40 artists from all disciplines who will work with students in the classroom…

Among the plethora of information that has caught the eye of educators across the nation is a 1999 report called “Champions of Change: The Impact of the Arts on Learning,” a research project authorized by the President’s Committee on the Arts and the Humanities and the Arts Education Partnership, a private, nonprofit coalition of more than 100 national education, arts, business, philanthropic and government organizations.

The report, which former U.S. Education Secretary Richard Riley said contains “ground-breaking quantitative and qualitative data and analysis, as articulated by leading American educational researchers,” says that there is “clear evidence that sustained involvement in particular art forms – music and theater – are highly correlated with success in mathematics and reading.”

Another component of the project, based on 10 years of research involving dozens of after-school programs for disadvantaged youth, studied programs in three categories: sports-academic, community involvement and the arts.

The research showed that youth in all three programs are doing better in school and their personal lives than were other young people from the same socioeconomic categories. To the researchers’ surprise, however, the youth in the arts program were doing the best – even though those students were considered the most “at risk” of all the students in the three programs…

Davis said she and other artists doing residencies have been told repeatedly by teachers and students and parents that “this student wouldn’t have come to school today if it wasn’t for this (class in the arts) – no ifs, ands or buts”…

Steinert admits freely that he was once skeptical about the impact the arts can have on academic success.

“I came to this table kicking and screaming,” he said. “Once I read the research, and once you see that students who are the most at risk are the students who benefit most, and after you see study after study and anecdote after anecdote – I am a true believer.”

Another true believer is Aaron LaFalce, a former self-described “uncool” freshman who is now student body president at Reynolds High School and a member of the school’s renowned chorale.

“I had no direction in my life, and a few times I even though I couldn’t wait until I turned 16 so I could drop out of school and get on with my life,” said LaFalce, who now takes honors classes…

“From my experience in schools, for the past 13 years, classrooms are like a big church of knowledge that needs a revival,” he said. “And I think that revival is going to be through the arts.”

(7) “Education Consultant Tells Teachers To Have Higher Expectations; Author Of `Nothing’s Impossible’ Says Harlem School Shows Way To Excellence” by Michelle Melendez

Source: [Texas] Star-Telegram – 2 February 2001

…[Lorraine Monroe, author of “Nothing’s Impossible,”] spent decades as a teacher and principal in New York’s Harlem section before founding the Frederick Douglas Academy there in 1991. She took the 150 middle school students with the poorest records, told them they were chosen for the new school because they were gifted, hired teachers who actually were gifted, and worked hard. A year later, the school rose from last place to No. 11 in student test scores. By the second year, it ranked fourth, she said.

It all has to do with expectations, she told the teachers.

When children show up at school late, and without notebooks, she doesn’t want to hear teachers say: “What do you expect? The mother has 12 children and drinks and the father ain’t around.” Or, “I don’t care if you learn. I get paid anyway.”

She admonished teachers to watch what they say because children remember, both the good and the bad. “What you believe gets in the way of what you do,” she said…



English Language Development in Mathematics Content (ELD-MC) Symposium

Source: The California Mathematics Project (CMP)


  • Dates: 7-8 March 2001
  • Cost: $50 per person (includes all meals and materials)
  • Location: Sheraton Gateway Hotel, Los Angeles International Airport
  • Keynote Speaker: Dr. Gilbert Cuevas, University of Miami

“It’s All in the Balance” — Professional development models that integrate mathematics content and language teaching strategies must balance mathematics content knowledge and language content components to provide teachers with the necessary knowledge and skills to help ELL (English Language Learner) students reach high levels in mathematics learning. The keynote and symposium will provide a framework from which participants can discuss the development of models that fit the constituencies they serve.

For more information, contact Lee Yang at (310) 825-8814 or at by 14 February 2001.