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THE WALL STREET JOURNAL
June 11, 1997
President Clinton's Mandate for Fuzzy MathMarianne Jennings, an Arizona State business professor, has brought enlightenment to the multitudes. With her commentaries on her daughter Sarah's eighth grade math book ("MTV Math" she calls it, for its colorful pictures, disconnected ideas, and generally casual attitude), she has helped parents across the country realize they are not the only ones dismayed by current mathematics education.
Kids are writing about "What We Can Do to Save the Earth," and inventing their own strategies for multiplying. They're learning that getting the right answer to a math problem can be much less important than having a good rationale for a wrong one.
Sometimes called "whole math" or "fuzzy math," this latest project of the nation's colleges of education has some formidable opponents. In California, where the school system embraced whole math in 1992, parents and dissident teachers have set up a World Wide Web site called Mathematically Correct to point out the follies of whole-math instruction.
The credentials of the organizers are impressive - a molecular biologist, a geophysicist, a statistician. And their left-of-center politics give them an advantage in battling an educational establishment that typically dismisses all critics as far-right reactionaries.
"Usually, the first words out of my mouth are "I'm a liberal Democrat," says Mike McKeown, a faculty member of the Salk Institute and a member of Mathematically Correct. As a result of their efforts, several members have been appointed to panels that will influence future math curricula in California.
But such victories will be moot if President Clinton gets his way. The president wants a national test for eighth grade mathematics. Judging from the committee the administration recently picked to oversee the exam, fuzzy thinkers will soon rule the land. The chairman is John A. Dossey, one of the brains behind ("conceptualizers" of) the Addison-Wesley textbook Sarah Jennings uses. Mr. Dossey and the committee's vice chairman, Gail Burrill, are both past presidents of the National Council of Teachers of Mathematics, the group largely responsible for bringing whole math to the schools.
In 1989, Mr. Dossey served on the NCTM commission that issued standards for mathematics that denounced the schools' "longstanding preoccupation with computation and other traditional skills." It was no longer crucial, the commission suggested, for students to be able to add, subtract, multiply, and divide. Giving such "computational algorithms" over to calculators, the standards declare, would free students to develop a conceptual understanding of mathematics and to become "active participants in creating knowledge."
The NCTM commission envisioned classrooms in which teachers operate on the sidelines. Instead of instructing, they encourage "cooperative learning." Such classrooms have become a reality in many U.S. schools. Mathland, a curriculum widely used in California, advises teachers not to "indicate in any way the rightness or wrongness of different answers" but to let students "convince" one another and reach a conclusion on their own.
Whole-math advocates say their methods will bring American math achievement up to world-class levels. But in fact kids in Japan, usually among the top performers on international assessments, do plenty of memorization and drill. Only after they have mastered basic skills are they allowed to use calculators. Moreover, during problem-solving discussions in Japanese classrooms, the teacher leads, making sure that students arrive at the solutions in the optimal way.
Whole-math advocates also argue their methods will eliminate the advantage that white males have in mathematics. In the NCTM's view, the social injustices of past schooling practices" are responsible for minorities and women being underrepresented in advanced math study, and the reinvented math curriculum will help them succeed.
The NCTM claims that removing the "computational gate" to high school mathematics will provide "equal access and opportunity." In other words, women and minorities would benefit if no one were required to master basic skills before moving on to high school. Other whole-math proselytizers speak of minorities' and women's special need for cooperative learning (thus the emphasis on working in groups) and for connecting what they study to social concerns (thus the emphasis on saving the planet).
These "theories" are nothing more than stereotypes, backed - like much of whole math - by research so anecdotal it barely deserves the name. But that has not kept whole-math ideas from being influential, and they will become more powerful still if they are embedded in a national test. Odds are, this will happen. Like Mr. Dossey and Ms. Burrill, the overwhelming majority of the math committee members are whole-math advocates.
What would a national exam based on whole math look like? Here's a hint: A few years ago Mr. Dossey proposed a change to the National Assessment of Educational Progress math test, the exam committee is using as a starting point. He wanted a scoring system under which students would get only half credit for right answers if they didn't make clear how they arrived at them. Wrong answers would get full credit if accompanied by "appropriate strategies."
Those who are worried about a future in which everyone from doctors to actuaries to aircraft designers holds mathematical accuracy in low regard will be able to express their concerns at two public hearings the math committee is holding: one June 17 in Denver and another Aug. 5 in San Francisco. Governors are also targets for protest. They can decide whether their states will adopt the national math exam, and they should hear from citizens who do not want to participate in the further ruination of America's schools.
Mrs. Cheney is a senior fellow at the American Enterprise Institute
[In 2002 she is the wife of the Vice President of the United States]
Compare HER words, above, with the role played by "Tipper
Gore," the wife of the past vice president -- in her advocacy for mental health
technologies -- that flow directly out of Wundt and Rockefeller. There could not
possibly be a larger difference between two woman than the difference between
Mrs. Cheney, and Mrs. Gore.
Copyright 1997, The Wall Street Journal
Used by permission.
"There is a mathematically correct solution"
This web site is devoted to the concerns raised by parents and
scientists
about the invasion of our schools by the
New-New Math
and the need to restore basic skills to math education.
Mathematically Correct is the informal, nationwide organization that
fights the Establishment
on behalf of sanity and quality in math education. -- David
Gelernter, NY Post
Mathematics achievement in America is far below what we would like it to be. Recent "reform" efforts only aggravate the problem. As a result, our children have less and less exposure to rigorous, content-rich mathematics .
The advocates of the new, fuzzy math have practiced their rhetoric well. They speak of higher-order thinking, conceptual understanding and solving problems, but they neglect the systematic mastery of the fundamental building blocks necessary for success in any of these areas. Their focus is on things like calculators, blocks, guesswork, and group activities and they shun things like algorithms and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.
Concerned parents are in a state of dismay and have begun efforts to restore content, rigor, and genuinely high expectations to mathematics education. This site provides relevant background and information for parents, teachers, board members and the public from around the country.
NYC HOLD (Honest Open Logical Debate on Mathematics Education Reform) Web Site
NYC HOLD is a nonpartisan advocacy organization that provides parents, educators, mathematicians and other concerned citizens opportunities to work together to improve the quality of mathematics education in the New York City schools.
We have followed our children's experience and progress in NCTM
Standards-based mathematics programs and have grown increasingly concerned.
We have studied the materials and teaching approaches in our children's
schools. Some of us have researched the programs and their use in other
regions and found that we are not alone in our concerns, rather, our
experiences and worries are shared by parents across the country.
We have been dismayed and frustrated by teachers' reports that their hands
are tied, that they're not free to teach with the materials and methods they
believe best suited for our children. We have learned that mathematicians
and scientists have confirmed our suspicions that the programs lack adequate
skills development, important topics, and the rigor necessary to prepare our
children for advanced high school math and science courses and pursuit of
college math-based courses and majors.
Is Los Angeles dictating bad use of a good math book?
Is LA turning a silk purse into a sow's ear? An Open Letter to the superintendent and school Board suggests LA's Algebra I pacing plan is disastrous and undermines both the California math standards and state approved textbooks.
A Plan for Improving the Quality of Exposition in High School Mathematics by Frank B. Allen
In order to raise the level of student achievement in secondary school mathematics, which everyone agrees is urgently necessary, there must be major improvements in the expository procedures employed by teachers.
How the NCEE Redefines K-12 Math: An Analysis of the NCEE Math Performance Standards by Bill Quirk
The NCEE is satisfied with entry level math. Their "vision" is limited to the needs of everyday life. The concept of prerequisite knowledge is never mentioned. They're not concerned with setting the stage for learning more advanced math. Many of their high school math examples belong at the elementary school level. They claim to emphasize conceptual understanding, but give no evidence that they understand how math ideas are connected. They appear blind to the vertically-structured nature of the math knowledge domain.
Mathematics Education in California
A review of Geometry: tools for a changing world
David E. Joyce provides this review of the Prentice-Hall Geometry text, noting ... It's the content that bothers me, in particular, the lack of logical content. The review covers each chapter in a way that is especially informative for those required to use this text.
Does Two Plus Two Still Equal Four? What Should Our Children Know about Math?
Despite efforts to improve mathematics education in the United States, the August 2001 National Assessment of Educational Progress report found that a majority of children are still unable to perform at a basic level in mathematics and that an achievement gap between white and minority students continues to persist in that subject. The link provides information and transcript of the seminar at AEI.
Stand and Deliver Revisited by Jerry Jesness
The untold story behind the famous rise -- and shameful fall -- of Jaime Escalante, America’s master math teacher.
TERC Hands-On Math: A Snapshot View by Bill Quirk
A review of the TERC (Investigations in Number, Data, and Space) mathematics program shows:
Also read the full report, TERC
Hands-On Math: The Truth is in the Details.
A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein
Mathematics education policies and programs for U.S. public schools have never been more contentious than they were during the decade of the 1990s. The immediate cause of the math wars of the 90s was the introduction and widespread distribution of new math textbooks with radically diminished content, and a dearth of basic skills. This led to organized parental rebellions and criticisms of the new math curricula by mathematicians and other professionals.
New Front in the New York City Math Wars
In NYC, organized parent and teacher opposition to the new math programs
began in District 2, one of the city's best; and now extends to District 3,
District 10 and District 15. Bronx high school teachers have organized to
express opposition to next years' requirement they use only the Interactive
Mathematics Project (IMP), an experimental high school math program. The
teachers worry the program lacks important mathematical content necessary to
prepare large numbers of their students for the Regents A exam and college
level coursework.
The new programs, many without student texts, are based on a "constructivist"
teaching philosophy, which discourages teachers from teaching mathematical
rules and procedures. Instead, teachers guide students, through group
activities, to their own "discovery" of personal solutions. Students are
encouraged to seek help from each other, rather than from the teacher.
Content Review of CPM Mathematics
A point by point review of CPM Mathematics vis-a-vis the California Standards. Much of Volume 1 actually detracts from developing algebraic competence. Almost all of the mathematical content is at the level of the Grade 7 standards or below ... This is not algebra and it is not college preparatory math, no matter what it calls itself. Eventually, Volume 2 starts teaching some algebra but it is too little and too late.
California Mathematics Program Adoptions for 2001
The list of K-8 programs approved by the State Board of Education on January 10, 2001. These programs were seen as the best fit to the state Mathematics Standards [.pdf file 504k] and the guidelines in the Mathematics Framework [.pdf file 1748k].
California State Adopted Middle School Math Programs
This site provides reviews of textbooks adoped in California for middle school, including texts in algebra 1. The report helps to identify the strengths and weaknesses of these adopted programs.
This is the press release for the report from Pacific Research Institute for Public Policy. The full text [.pdf file 741k] of the report, Facing the Classroom Challenge Teacher Quality and Teacher Training in California’s Schools of Education is also available.
How To Respond When Your School Announces a New-New Math Program, by Kevin Killion
What do you say? How do you respond when your school tells you that your child's math program is going to be replaced? What is your reaction when the replacements main advantages are a "Tokyo by Night" layout, fuzzy-headed but politically correct examples, oddball algorithms and methods (or no methods at all), and a big emphasis on writing essays and playing games?
The Math Wars, by David Ross
My disagreement with my father contained the essential elements of the current Math Wars, the debate that is going on today over the way that mathematics should be taught.
Excerpts from Poor Performance Review
Ralph A. Raimi, professor emeritus of mathematics at the University of Rochester, talks about MSPAP, the examination system Maryland uses to assess student performance. He notes that, The system was of no value for its announced purpose. For the full story see the Washington Times of Sunday, April 1, 2001.
Big Business, Race, and Gender in Mathematics Reform, by David Klein
Opposition to California's mathematics standards from reform leaders
continues as of this writing. Former NCTM president Jack Price wrote in a
letter published by the Los Angeles Times on May 10, 1998:
...if the state board had adopted world-class mathematics standards for the 21st century instead of the 19th century, there would have been a great deal of support from the 'education' community.
This sententious observation encapsulates the topics discussed in this essay. For the reformers, "world-class mathematics standards for the 21st century" eluded the Stanford mathematicians who wrote California's 1998 math standards. Missing are the greater emphasis on technology--an end in itself--and pedagogical directives harmonious with the reified "cognitive styles" of the racially diverse populations of the 21st century. The "19th century" arithmetic, algebra, geometry, and trigonometry highlighted in California's 1998 standards will have diminished value in the postmodern epoch of technological wonderments envisioned by math reformers. Perhaps the academic community should consider whether the discipline of mathematics education--much more so than mathematics--needs fundamental alterations for the 21st century.
NCTM Math in the NCEE America's Choice Performance Standards
2+2=5: Fuzzy Math Invades Wisconsin Schools, [.pdf file 80k] by Leah Vukmir
This level of parental outrage and concern is certainly not confined to McFarland. According to Parents Raising Educational Standards in Schools, a Wisconsin-based parent organization, math education has become the number one concern of parents calling for information and assistance. In the last two years it has supplanted the "Reading Wars" and is causing parents across Wisconsin and the nation to organize and rebel.
Standards in School Mathematics [.pdf file, 52k, see second page]
Ralph Raimi discusses the new Principles and Standards for School Mathematics (PSSMP) from the NCTM.
I warn you that these "principles and standards" cannot be appreciated by reading only a few pages. In the small the document sometimes sounds good. But if PSSM in the large informs our vision, then self-esteem is better than knowledge, dictionaries can replace a ready (memorized?) vocabulary, and higher-order thinking skills will boil stones into soup.
Cognitive Child Abuse in Our Math Classrooms, By C. Bradley Thompson
Whole math must lead to a miasma of confusion, boredom, and despair. Rather than encouraging independent, conceptual-level thinking, it is thoroughly anti-conceptual. It dooms children to function on a primitive, perceptual level—i.e., to flounder in a chaotic sea of concretes with no objective principles to guide them. This is cognitive child abuse. Whole-math defenders are shrinking the cognitive capacities of their students to those of infants or even animals.
Romancing the Child by E. D. HIRSCH JR.
"The progressive way of running a school is essentially the opposite of what the 'effective schools' research has taught us." So says Hirsch in the new journal, Education Next
Open Letter on the Department of Education's List of Programs
The U.S. Department of Education issued a statement endorsing some of the worst mathematics programs available. This prompted a rebuttal endorsed by over 200 of the nation's leading mathematicians and has resulted in a congressional hearing.
Testimony to the House of Representatives regarding the Department of Education
Testimony from the appropriations subcommittee that deals with the Department of Education.
Although high-stakes standardized tests are often controversial, Reality Check picks up few signs of public backlash. Neither parents, teachers, nor students themselves voice significant dissatisfaction with testing in their own schools. Large majorities of all groups express strong support for their own district's efforts to raise standards and for using standardized tests to enforce standards ...
Clinton's Proposed National Voluntary Mathematics Test
Noting the inadequate achievement in school mathematics in the United States, President Clinton proposed a voluntary national test as a way to combat the problem. Examinations can be an effective way to stimulate achievement gains, but the devil is in the details. Clinton's plan got off to a bad start. The first committee working on it was full of fuzzy math supporters, and the initial plans were dismal. The test design was shifted from the initial committee to the National Assessment Governing Board. The progress was often delayed and funding was restricted by congress.
The Truth About The REVISED NCTM Standards: Arithmetic is Still Missing! by William G. Quirk, Ph.D.
Similar to the original NCTM Standards, PSSM is vague about the major components of arithmetic mastery:
1.Memorization of of basic number facts
2.Mastery of the standard algorithms of arithmetic
3.Mastery of fractions
The NCTM has toned down the constructivist language, but they still stress content-independent "process skills" and student-centered "discovery learning". Similar to the NCTM Standards, PSSM emphasizes manipulatives, calculator skills, student-invented methods, and simple-case methods.
Mathematics "Council" Loses Hard-Earned Credibiility
By Frank B. Allen
The National Council of Teachers of Mathematics, now led by theoreticians from our Schools of Education, imposes policies that distort the teaching process and heavily impair the learning of school mathematics. Can the NCTM accept the challenge to Save Our Schools?.
Brown Center Report on American Education [.pdf file 43k]
The academic achievement of American students has risen since the 1970s but only at a snail’s pace. Performance in arithmetic remained static or declined slightly. Results for thirteen year olds suggest large numbers of students have not mastered the basic arithmetic skills that are necessary before moving on to algebra.
High Achievement in Mathematics: Lessons from Three Los Angeles Elementary Schools
In a paper commissioned by the Brookings Institution, David Klein describes characteristics and academic policies of three low income elementary schools in the Los Angeles area whose students are unusually successful in mathematics.
The Wall Street Journal Editiorial of January 4, 2000 addressed the so-called reform in mathematics education. The editorial concludes that New Math will take its casualties, especially among the poor, adding to the already mounting costs of the decline in national educational standards.
Why Education Experts Resist Effective Practices, by Douglas Carnine
American education is under intense pressure to produce better results. The increasing importance of education to the economic well-being of individuals and nations will continue feeding this pressure. In the past—and still today—the profession has tended to respond to such pressures by offering untested but appealing nostrums and innovations that do not improve academic achievement.
Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education [.pdf file 54k], by H. Wu
The truth is that in mathematics, skills and understanding are completely intertwined. In most cases, the precision and fluency in the execution of the skills are the requisite vehicles to convey the conceptual understanding.
Knowing and Teaching Elementary Mathematics [.pdf file 73k], by Richard Askey
The U.S. Department of Education has announced the results of an exercise to identify "expemplary" and "promising" texts. Connected Mathemaitcs, a series for grades 6-8, is one the department has deemed exemplary. I do not understand why it deserves that rating. I am quite familiar with this series, as I reviewed it as part of a textbook adoption process. Regarding fractions, for example, Connected Math has some material on the addition and subtraction of fractions, but nothing as systematic as described by the Chinese teachers interviewed by Ma. There is less on multiplication of fractions, and nothing on the division of fractions. If our students go through grade 8 without having studied the division of fractions, where are our future primary teachers going to learn this? The criteria used by the Department of Education review should be rewritten now that Liping Ma's book has provided us with a model of what school mathematics should look like.
Reform Mathematics Education: How to "Succeed" Without Really Trying
The reform designs open the door to claims of successfully teaching mathematics without really doing so. The reform writings and methods are many and varied, but a common feature is that they end up obscuring the failure to teach mathematics. In reform mathematics education, the goal of success for all is not supported by achievement but rather by redefining success and, mostly, by obscuring failure.
Recent Directions in San Diego Mathematics Education
It is obvious that the district is planning to used dumbed-down mathematics in the focus schools. They are taking the approach we have fought so hard to avoid - lowing expectations while claiming otherwise.
San Diego Draft Framework Critique
Is San Diego trying to snatch defeat from the jaws of victory? After the release of state and district standards and a state framework that all align to set high expectations for student learning and clearly detail the course of mathematics instruction, San Diego has released a draft of a local framework that seems devoid of substance. See this review for more details.
The curriculum problems in Santa Monica are complicated by an insidious form of discrimination where students in the more affluent neighborhood schools have the benefit of a State approved, State content aligned curriculum and the schools in less affluent southern part of the District have MathLand and CPM, neither of which is State approved for educational content ... With nearly one-sixth of the students in our elementary and middle schools in danger of retention at the end of June, 2000, giving parents complete and truthful information was an important step in helping children succeed. We formed a coalition of parents and other interested parties to address the issues at the District level, Santa Monicans Working for Equity and Excellence in Public Schools (SMWEEPS).
Mountain View Achievement is a group of concerned parents, teachers and community volunteers who believe that all children can achieve academic success when given appropriate opportunities and tools. We are dedicated to improving educational opportunities, and we invite every member of the community to join us in this endeavor.
From Mathematics: A Text for 6th Graders
by Enn R. Nurk and Aksel E. Telgmaa
© 1995 Drofa, Moscow
Translated from the Russian by Willis Harte
University of Iowa College of Education
The Role of Long Division in the K-12 Curriculum
Reviews the reasons that most math educators today depreciate the topic and other topics in the curriculum that derive from it, methods for teaching long division in such a way that the underlying concepts can be understood by students, the ways in which these concepts develop in later mathematics course, and why they are so important.
By showing topic development across grade levels, it becomes easier to evaluate any particular piece of mathematics content relative to the California standards. The California grade level of content from textbooks or tests or other sets of mathematics standards can thus be more easily identified.
Community response in NYC and across the country has erupted in what have become known as the "math wars." Critical parents, joined by mathematicians and scientists advocate clarity and balance in math reform: urging the inclusion of grade by grade goals, explicit teaching of standard procedures, basic skill building and rigor along with the inclusion of some of the creative exercises in the new programs. The pendulum has swung too far and must be corrected.
The Mathematics Framework in Massachusetts
Massachusetts has been going through quite a struggle over arithmetic in their state mathematics framework. Links include background and the details of the story of the attack by Hyman Bass on the Massachusetts Deputy Commissioner of Education.
If you are concerned about the changes to the mathematics curriculum, you should:
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