Why Do Supporters of the National Council of Teachers of Mathematics Insist Only They Are Right?
By Nakonia (Niki) Hayes
Guest Columnist EdNews.org
October, 2006
The history of mathematics education in the United States is a complex one, with long-running philosophical conflicts among various groups. But there’s something to be said about listening to those with credentials, practical experience, and “seasons” on them in the mathematics education field. Since the elders in my culture are respected for their insight and ability to bring clarity to conflicting issues, and I am now an elder, it is not surprising for me to think this way.
Criticism of the undeniable impact, and surely an unintentional disastrous one, of the National Council of Teachers of Mathematics on math education since 1989 in the United States is such an issue. A subsequent “math war” began openly in California in 1996 with professional mathematicians and angry parents who opposed the NCTM pedagogy of “whole (discovery) math,” with its insistence on teaching “process” (concepts) over mathematic principles (basic skills). That conflict has grown among individual school districts in other states, as more pro-fessional mathematicians are joining organized parent groups in their desire to return a balance of both basic skills and concepts to math classrooms in the U.S.
At this time, California, Michigan, and Massachusetts have changed their mathematics standards, moving away from the NCTM program, to reflect such a balance. California, in particular, has continued to serve as a model for such change.
My own strong resistance to NCTM’s reform pedagogy of constructivism is based on training and professional experience in five disciplines: journalism, counseling, special education, mathematics, and administration.
With 17 years in journalism and another 30 in public education, I maintain there is mounting evidence in the NCTM “reformed” mathematics curriculum of the following: inaccurate views based on poor research, reverse discrimination (against white males), stereo-typed learning styles that have helped increase achievement gaps for minorities, opaque and convoluted lessons about mathematical procedures, and a disrespect for the historical importance of texts that represent the rich concepts and principles of mathematics.
Yet, the struggle by mathematicians and mostly middle class parents to stop the financial and human costs of this entrenched curriculum, passionately promoted by those who support its philosophy, including the National Science Foundation, is little recognized or understood by disenfranchised parents and, worse, by legislators. A “critical mass” has yet to understand the consequences of the NCTM domination, with its constructivist programs in math education.
And even though NCTM issued a new document in August of this year called Focal Points, the group strongly resists any suggestion this publication indicates they may have been wrong in their pedagogical stance. They explain the document is simply the “next step” of telling educators which mathematics topics should be the focus at each grade level from kindergarten through eighth grade. They sidestep the critical issue of teaching methodology.
My work in this paper is designed to help people understand the passion and the motives behind the NCTM philosophy, as codified in their discipline-rattling 1989 publication, Curriculum and Evaluation Standards for School Mathematics.
I first use a summarized point, which is based on direct quotes from the 1989 NCTM manual or NCTM officials, except for number 8, which discusses the funding relationship between NCTM and the National Science Foundation. There are some related quotes from A Nation at Risk, another public-rattling publication, from 1983, and clearly a basis for much of the NCTM philosophy. Additional sources are indicated as “boxed” information. My final conclusion regarding each numbered item is then offered.
Bold, italicized, and underlined words indicate my own emphases.
An explanation of how my professional background impacted my thinking on this issue is included as an appendix.
1) NCTM designed their Standards with a primary goal of socially promoting egalitarianism via mathematics education.
1) The opportunity for all students is at the heart of our vision of a quality mathematics program. (p. 5) From A NATION AT RISK: “At the heart of such a [learning] society is the commitment to a set of values and to a system of education that affords all members the opportunity to stretch their minds to full capacity…”
2) The social injustices of past schooling practices can no longer be tolerated. Creating a just society in which women and various ethnic groups enjoy equal opportunities and equitable treatment… Equity has become an economic necessity. (p.4) From A NATION AT RISK: “…public commitment to excellence and educational reform must be made [for] equitable treatment of our diverse population. The twin goals of equity and high-quality schooling have profound and practical meaning for our economy and society.
3) If all students do not have the opportunity to learn this mathematics, we face the danger of creating an intellectual elite and a polarized society. (p. 9) From A NATION AT RISK: “To deny young people a chance to learn…would lead to a generalized accommodation to mediocrity in our society on the one hand or the creation of an undemocratic elitism on the other…John Slaughter, a former Director of the NSF, warned of ‘a growing chasm between a small scientific and technological elite and a citizenry ill-inform-ed, indeed uninformed…”
4) Becoming confident in one’s own ability… doing mathematics is a common human activity. (p.6) From A NATION AT RISK: A high level of shared education is essential to a free democratic society and to the fostering of a common culture…
5) Curriculum Standards for Grades 5-8…No student should be denied access to the study of one topic because he or she has yet to master another. (p.69)
6) Curriculum Standards for Grades 9-12…In view of existing disparities in educational oppor-tunity in mathematics…each standard identifies content or processes [and] activities for all students. (p.123)
The core curriculum provides equal access and opportunity to all students… By… recognizing that there frequently is not a strict hierarchy among the proposed mathematics topics at this [9-12] level, we are able to afford all students more opportunities to fulfill their mathematical potential. (p.130)
In choosing not to trap students in one of the two conventional linear patterns, we ensure that doors to college programs and vocational training are kept open for all students. (p.130)
…no student will be denied access to the study of mathematics because of a lack of computa-tional facility. (p.124)
7) Goals are broad statements of social intent. (p.2) New social goals for education include 1) mathematically literate workers, 2) lifelong learning, 3) opportunity for all, and 4) an informed elector-ate. (p.3)
Historically, societies have established schools to…transmit aspects of the culture to the young…[to] provide them opportunity for self-fulfillment. (p.2)
…[the goal is to] focus attention on the need for student awareness of the… impact [their]… interaction has on our culture and our lives. (p.6)
In “An Overview of the Curriculum and Evaluation Standards,” … the curriculum and evalu-ation standards that reflect our vision of … societal and student goals. (p.7)
…standards are value judgments based on…societal goals… research on teaching and learning, and professional experience. (p.7)
8) Research findings from psychology indicate that learning does not occur by passive absorption alone (Resnick, 1987). (p.10)
9) Implications for the K-4 Curriculum: Overall goals must do the following (p.16):
vAddress the relationship between young children and mathematics.
vRecognize the importance of the qualitative dimensions of children’s learning.
vBuild beliefs …about children’s view of themselves as mathematics learners.
10) [grades 9-12] We believe the opportunity to study mathematics that is more interesting and useful and not characterized as remedial will enhance students’ self-concepts as well as their attitudes …students no longer will be confronted with the demeaning prospect of studying…the same content topics as their twelve-year-old siblings. (p.130) …for each individual, mathematical power involves the development of personal self-confidence. (p.5)
In summary, the [9-12] core curriculum seeks to provide a fresh approach to mathematics for all students—one that builds on what students can do rather than on what they cannot do. (p.131)
Deborah Loewenberg Ball, Imani Masters Goffney, Hyman Bass, “Guest Editorial… The Role of Mathematics Instruction in Building a Socially Just and Diverse Democracy,” The Mathematics Educator, 2005, Vol. 15, No. 1, 2-6: Instead of seeing mathematics as culturally neutral, politically irrelevant, and mainly a matter of innate ability, we see it as a critical lever for social and educational progress if taught in ways that make use of its special resources.
…the disparities in mathematics achievement are tightly coupled with social class and race… learning to examine who and what is being valued and developed in math class is essential.”Mathematics instruction, we claim, can offer a special kind of shared experience with understanding, respecting, and using difference for productive collective work.
David Klein, writes in “A quarter century of U.S. ‘math wars’ and political partisanship,” British Society for the History of Mathematics, 2006, http://www.tandf.co.uk/journals/titles/17498430.asp:
The utilitarian justification of mathematics was so strong that both basic skills and general mathematical principles were to be learned almost invariably through ‘real world’ problems. Mathematics for its own sake was not encouraged.
The arguments in support of these changes took two major themes: social justice in the form of challenging racial and class barriers on the one hand, and the needs of business and industry on the other.
The Standards, buttressed by NCTM’s call for ‘mathematics for all’ and the equity agenda in Everybody Counts, clearly sat in the education-for-democratic-equality [camp]…These powerful indict-ments [of elitism] demanded radical solutions. Mathematics reform was social reform…
The NCTM reform was an attempt to redefine mathematics in order to correct social inequities.
CONCLUSION: Students who master both the concepts of a discipline and its principles, which are used to transcend those concepts across all of life’s domains, have the best opportunity of creating equitable opportunities for themselves, regardless of their backgrounds. And mastering the full body of any discipline formed by many peoples across thousands of years of study, such as mathematics, also helps bring its new learners together with a common respect and under-standing—including a true integration—of their thoughts and actions. Learning the content is a priority of any discipline to be mastered. Methodology is the teacher’s magic for getting it taught successfully, as long as it’s legal, ethical, and moral!
2) The secondary goal of NCTM is development of “problem-solving” skills among all learners, as they prepare for a technological world.
1) The first recommendation of An Agenda for Action (NCTM, 1980): “Problem solving must be the focus of school mathematics.” (p.6)
,…problem solving is much more than applying specific techniques to the solution of classes of word problems. It is a process by which the fabric of mathematics as identified in later standards is both constructed and reinforced. (p. 137)
The standards specify that instruction should be developed from problem situations. (p. 11)
2) Traditional teaching emphases on practice in manipulating expressions and practicing algorithms as a precursor to solving problems ignore the fact that knowledge often emerges from the problems. This suggests that instead of the expectation that skill in computation should precede word problems, experience with problems helps develop the ability to compute. (p.9)
3) A strong emphasis on mathematical concepts and understandings also supports the development of problem solving. (p.17)
4) …present strategies for teaching may need to be reversed; knowledge often should emerge from experience with problems. (p.9)
As reported in “An oral history of New Math and New-New Math – Based on a Series of Postings to the NYC Hold Math Reform Web Group, Nov. 18-19, 2003,” compiled by William Hook, Jan. 15, 2004, the following comments of W. Stephen Wilson, professor of mathematics at Johns Hopkins University, are offered:
I think we [Jim Milgram and Wilson] agree that there is “low level” problem solving, meaning “routine” problem solving, which does not require having an “idea,” but requires mastery of material and the use of a “problem solving algorithm (loosely).” We agree there is “high level” problem solving…for real problem solving, we only have vague ideas of what goes on, and none of how to teach it…[but] at that point the NCTM jumps in and says, “but we know how to teach it; that’s what our reforms are all about.” …Basically, the reformers claim to be able to teach “high level” problem solving without bothering with “low level” problem solving or basic mastery of material…I would claim that mathematicians know enough about “high level” problem solving to know you can’t do it if you can’t do “low level” and you haven’t mastered the material. Consequently, we think it is important to teach mastery of material and “low level” problem solving, since it is certainly a prerequisite to “high level” problem solving. Now it turns out that this is already pretty hard to do…it isn’t hard to teach it, but for some reason it seems to be pretty hard to learn it.
Jim Milgram, professor of mathematics at Stanford University, responded: …we should make a real point of the fact that we don’t know much about problem solving and neither do NCTM members. We should, loudly, defend our ignorance.
But what we shouldn’t do is directly attack NCTM ideology…[from his experience with writing the new California standards, he says…] people in NCTM actually want to learn more mathematics than they know, and if given a chance, will do so…it is probably best to challenge them to learn by making a large point of the fact that what NCTM actually does in “problem solving” is to develop systematic ways to do routine problems, something even the traditional programs always did—though they did them using sequenced series of exercises and problems. What NCTM did was to make a list of standard methods, such as “look for a simpler problem,” and say that this is problem solving.
The confusion comes [when] they talk about problem solving, but what they mean is “routine problem solving.” What we hear is “problem solving”…that means “real problem solving.”…[We] explain there are two kinds of problem solving—what we want, that nobody knows how to teach in a ver-bal way, and the routine part, that does scale up and has been generally understood for many, many years.
CONCLUSION: From the affective side of learning, problem-solving could be compared to developing a new habit, which, according to author Stephen Covey in the Seven Habits of Highly Effective People, requires knowledge (content), skills (process), and the desire for successful completion. A major focus for NCTM, it seems, is creating the desire among students to solve problems. NCTM has chosen to do this by using psychological methods based on questionable research about the learning styles of race and gender. In other settings, this practice would be labeled discriminatory and would not be tolerated.
3)NCTM believes that, historically, mathematics instruction had focused on deductive, analytical, and linear thinking skills in teacher-dominated classrooms, with
a competitive environment that met only the learning styles/needs of white (Anglo) males.
1)These four years [9-12]…will revolve around a broadened curriculum that includes extensions of the core topics and for which calculus is no longer viewed as the capstone experience. (p.125)
2)…a demonstration of good reasoning should be rewarded even more than students’ ability to find correct answers. (p.6)
3)Change has been particularly great in the social and life sciences…the fundamental mathematical ideas needed in these areas are not necessarily those studied in the traditional algebra-geometry-precalculus-calculus sequence, a sequence designed with engineering and physical science applications in mind. (p.7)
Jack Price, president of the National Council of Teachers of Mathematics, said in 1996 during a radio interview, “. . .Women and minority groups do not learn the same way as Anglo males . . . males learn better deductively in a competitive environment . . .” (Reported by Sandra Stotsky in Chapter 13, What’s at Stake in the K-12 Standards War, 2000.)
David Klein, “A quarter century of U.S. ‘math wars’ and political partisanship,” British Society for the History of Mathematics, 2006, http://www.tandf.co.uk/journals/titles/17498430.asp.
In The Math Wars, [Alan] Schoenfeld…describes the traditional curriculum as elitist and portrays the math wars as a battle between equality and elitism… …the traditional curriculum was a vehicle for… the perpetuation of privilege…Thus the Standards could be seen as a threat to the current social order.
“…the traditional curriculum, with its filtering mechanisms and high dropout and failure rates (especially for certain minority groups) has had the effect of putting and keeping certain groups ‘in their place.’
CONCLUSION:Although admittedly limited in number because of historical social constraints, and certainly not mental ones, women and “non-Asian minorities” (see #4 below) indeed have esta-blished themselves with respected places in mathematics. And while the design of mathematics instruction has been the same for 2,000 years—analytical, deductive, and linear—we know its history is rich and powerful because of contributions from many cultures and races—not just white males. To eliminate this historical type of teaching/ learning means 50% to 75% of all students, who learn concretely rather than intuitively, are ignored. (See http://www.virtualschool.edu/mon/Academia/ KierseyLearningStyles.html.) The consequence can be seen with higher failure rates now among boys
in all subjects, as those subjects have become more intuitive, inductive, verbal, and “cooperative” in scope.
4)NCTM used post-1960s research that defined “learning styles” of “non-Asian minorities and girls” as being inductive, intuitive, holistic, group-oriented, cooperative, and non-verbal. This meant such students determined the direction of their learning, needed to work in groups, and should focus on the “bigger picture” of “conceptual understanding” rather than the principles (rules) of mathematics.
Sandra Stotsky, in Chapter 13 of What’s at Stake in the K-12 Standards War, points out that mathematics education has been built upon stereotyped “learning styles” of “non-Asian minorities and girls.” She said there is a strain of thought [among mathematics reformists] that suggests non-Asian minorities and women need to be taught with less emphasis on deductive and analytical methods and more emphasis on inductive, intuitive methods because of gender and racial/ethnic differences in learning.
She wrote that two researchers in math education also suggested that African-American students‘ learning may be characterized as having a social and affective emphasis, harmony in their communities, holistic perspectives, expressive creativity and nonverbal communication. They are flexible and open-minded, rather than structured in their perceptions of ideas.
Stotsky asks, “Does this imply that African-Americans cannot engage in rigorous analytical thinking and articulate their ideas in academic prose?”
In addition, Dr. Stotsky explained how researchers said American Indians are “right brained.” This implies they cannot engage in structured forms of learning because . . . the functions of the left brain are characterized by sequence and order, while the right brain functions are holistic and diffused.
David Klein, “A quarter century of U.S. ‘math wars’ and political partisanship,” British Society for the History of Mathematics, 2006, http://www.tandf.co.uk/journals/titles/17498430.asp,
writes, “Ironically, progressivists’ advocacy of programs [that eliminated basic skills and the intellectual content that depends on those skills] for the supposed benefit of disenfranchised groups contributed to racial stereotying, in contradiction to core progressive values.
CONCLUSION: Rather than racial differences being addressed, the cultural deprivation of stu-dents due to a poverty of parenting and/or home values, for whatever reason, should be the educa-tional community’s mountain to climb. To suggest sweeping, stereotyped patterns of cognitive or mental behavior among a general group of people is bigotry. The use of such stereotyping has balkanized math education within America’s already diverse student body. It has increased achievement gaps among students of color, English language learners, and white students. It has, in fact, caused the loss of mathematical achievement across all subgroups, as the educational focus shifted from the proven discipline of mathematics to the perceived affective-based learning styles of learners.
5)NCTM thus adopted the “constructivist” form of pedagogy, which says children should “construct” their own learning for true cognitive understand-ing. (The terms “constructivist,” ” reform,” and now “progressive” are all used to denote the NCTM agenda.) This resulted in the NCTM curriculum develop-ment around holistic presentations, discovery learning (student-dominated), personal relationships encouraged between activities and students, and literary-based (verbal and written) exchanges among students and teachers about the “processes” of their learning within the activities.
1)Our premise is that what a student learns depends to a great degree on how he or she has learned it. (p.5)
…”instruction should persistently emphasize “doing” rather than “knowing that.” (p.7)
2)…in many situations individuals approach a new task with prior knowledge, assimilate new infor-mation, and construct their own meanings…As instruction proceeds, children often continue to use these [self-constructed] routines in spite of being taught more formal problem-solving procedures…This con-structive, active view of the learning process must be reflected in the way much of mathematics is taught. (p.10
3)…knowledge often should emerge from experience with problems. In this way, students may recognize the need to apply a particular concept or procedure and have a strong conceptual basis for reconstructing their knowledge at a later time. (p.9)
4)Programs that provide limited developmental work, that emphasize symbol manipulation and computational rules, and that rely heavily on paper-and-pencil worksheets do not fit the natural learning patterns of children. (p.16)
5)A conceptual approach enables children to acquire clear and stable concepts by constructing meanings in the context of physical situations and allows mathematical abstractions to emerge from empirical experience.(p.17)
6)Curriculum Standards for Grades 5-8…Instructional approaches should engage students in the process of learning rather than transmit information for them to receive.
7)Learning to communicate mathematically…This is best accomplished in problem situations in which students have an opportunity to read, write, and discuss ideas in which the use of the language of mathematics becomes natural…
8)…mathematics must be approached as a whole. Concepts, procedures, and intellectual processes are interrelated. (p.11)
Howard Gardner, father of “multiple intelligences,” stated in his 1981 book, The Unschooled Mind, that it is higher performing children from motivated families who do well with discovery learn-ing methods. This is due to their “readiness” skills in organization, focus, and learned behavior for school settings. By inference, lower-performing students do not use discovery learning methods successfully.
In his 2006 book, Concept-Rich Mathematics Instruction, Meir Ben-Hur also points out that discovery learning is not effective with children from disadvantaged backgrounds. Ben-Hur is a colleague of Reuven Feuerstein, an Israeli cognitive psychologist who studied with Piaget and is touted by constructivists as “one of their own.” Feuerstein has also stated that discovery learning does not work with at-risk students.
CONCLUSION: Research can be declared on all sides of any pedagogy. Research is not the basis for curriculum choices, however. It is the prioritized values a community wants to find in its classrooms: college prep, applied math for consumer use, self-esteem toward mathematics, equity outcomes, etc. We know that research is then found to support those values.(See “Relationships Between Research and the NCTM Standards,” by James Hiebert, University of Delaware, Journal for Research in Mathematics Education 1999, Vol. 30, No. 1, 3-19.)
Of special significance are the constructivists who declare that “discovery learning” does not work with disadvantaged students. In fact, I studied with both Feuerstein and Ben-Hur in Israel, so I’m confident in quoting them on their views of discovery learning. In addition, the NCTM’s paper by Dr. James Hieber states that standards are chosen because of a community’s values—and then research is found to support those choices.
6) NCTM significantly reduced the need for learning basic skills because, they believed, calculators and computers would replace “tedious” paper-and-pencil practice and the need to know algorithms.
1)Scientific calculators with graphing capabilities will be available to all students at all times… A computer will be available at all times… technology in our society further argues for a curriculum that moves all students beyond computation… By assigning computational algorithms to calculator or computer processing, this curriculum seeks not only to move students forward but to capture their interest. (p.130)
2) Calculators do not replace the need to learn basic facts, to compute mentally, or to do reasonable paper-and-pencil computation…young children take a common-sense view… and recognize the importance of not relying on them when it is more appropriate to compute in other ways. (p.19)
3) Some proficiency with paper-and-pencil computational algorithms is important, but such knowledge should grow out of the problem situations that have given rise to the need for such algorithms. (p.8)
4) By removing the “computational gate” to the study of high school mathematics and recognizing that there frequently is not a strict hierarchy among the proposed mathematics topics at this [9-12] level, we are able to afford all students more opportunities to fulfill their mathematical potential. (p.130)
5) [9-12] Standard 5: Algebra…The proposed algebra curriculum will move away from a tight focus on manipulative facility to include a greater emphasis on conceptual understanding. (p.150)
6) The new technology not only has made calculations and graphing easier, it has changed the very nature of the problems important to mathematics and the methods mathematicians use to investigate them. (p.7)
7) For the core program [9-12], this represents a trade-off in instructional time as well as in emphasis…available and projected technology forces a rethinking of the level of skill expectations. (p.150)
8) …although students should spend less time simplifying radicals and manipulating rational exponents, they should devote more time to exploring examples of exponential growth and decay that can be modeled using algebra. (p.150)
9) No student will be denied access to the study of mathematics in grades 9-12 because of a lack of computational facility. (p.124)
10) Although quantitative considerations have frequently dominated discussions in recent years, qualitative considerations have greater significance. Thus, how well children come to understand mathematical ideas is far more important than how many skills they acquire.(p.16)
11) A strong conceptual framework also provides anchoring for skill acquisition. (p.17)
CONCLUSION: By not recognizing the importance of long division and fractions/ratios as algorithms required in algebra, for example, or the many geometric theorems used in advanced mathematics, NCTM’s conceptual standards have crippled high school and college students in mathematics. This can be seen in data reflecting poor mathematics scores among a wide variety of state, national, and international tests. The $4 billion paid by parents annually for private tutoring, the $80 million tutoring industry on the Internet from India, the 50% of community college students requiring remedial math, and the 25% of university students requiring the same remediation further reflect disturbing data about the conceptually-based NCTM pedagogy.
Pg 2: Why Do Supporters of the National Council of Teachers of Mathematics Insist Only They Are Righ
7) NCTM maintains that basic skills are included in their pedagogy.
1) Although arithmetic computation will not be a direct object of study [grades 9-12]… number and operation sense, estimation skills, and judging reasonableness of results will be strengthened in the context of applications and problem solving…and scientific computation. (p.124)
2) The availability of calculators means, however, that educators must develop a broader view of the various ways computation can be carried out and must place less emphasis on complex paper-and-pencil computation. (p. 19)
3) Basic skills today and in the future mean far more than computation proficiency. Moreover, the calculator renders obsolete much of the complex paper-and-pencil proficiency traditionally emphasized in mathematics courses. (p. 66)
4) Some proficiency with paper-and-pencil computational algorithms is important, but such knowledge should grow out of the problem situations that have given rise to the need for such algorithms. (p.8)
CONCLUSION:The question must be asked of NCTM about when, and how, and how much basic skills instruction is included in the many curriculum materials that have been created by publishers to support the NCTM Standards since 1989. Their assurances that basic skills are not ignored in the Standards must be justified with specifics from NCTM.
8) The alliance forged between NCTM and the National Science Founda-tion, with millions of dollars given to universities, school districts, educators, and private entities to write and support the NCTM Standards, has created a huge power base of money, politics, and ideology.
Ralph Raimi, October, 1995, “Whatever Happened to the New Math?” writes, “The year 1958 kicked off the largest and best financed single reform effort ever seen in mathematics education, the School Mathematics Study Group (SMSG), upon which the National Science Foundation (NSF) spent mllions of dollars over its twelve-year lifetime…the teachers’ colleges, the National Council of Teachers of Mathematics, and all the state and federal departments of education and nurture, who though loosely organized did still govern all teaching below the college level, were compelled for the time being to follow our [mathematicians] lead.
“Experimental scientists like [Oliver Wendell] Holmes understand that reality is not to be pushed round, neither by nine old men nor by a prestigious bunch of mathematical geniuses with a pipeline to the U.S. Treasury…The cadre of teachers already out there had preexisting interests and capabilities, the public patience was shorter than experiments that could lose a generation of children, and the educational experts, the professional education bureaucracy (PEB), was gathering its strength for the political battle that finally turned the pipeline back in their direction.
“The books for grades 1-8 come packaged for teachers with mountainous ‘Teachers’ Guides,’ in which the mathematics is swamped into insignificance by the instructions on engaging the attention and improving the self-esteem of students…”
David Klein, in “A quarter century of U.S. ‘math wars’ and political partisanship,” British Society for the History of Mathematics, 2006, http://www.tandf.co.uk/journals/titles/17498430.asp:
“The conflict [development of new California standards] was more than just a theoretical disagreement. At stake was the use of NCTM aligned textbooks in California, the biggest market in the nation.”
Michael McKeown, What’s at Stake in the K-12 Standards War, Chapter 13, “National Science Foundation Systemic Initiatives: How a small amount of federal money promotes ill-designed mathematics and science programs in K-12 and undermines local control of education.”
A Primer for Educational Policy Makers, edited by Sandra Stotsky (Peter Lang, New York, 2000). Also, see nychold.org.
“Many states and districts have accepted NSF Systemic Initiatives grants to make”fundamental, comprehensive, and coordinated changes in science, mathematics, and technologyeducation through attendant changes in policy, resource allocation, governance, management, content and conduct.” This article shows how it is all for the worse, and explains the dynamics behind acceptance of these grants…
“The NSF has provided many grants for the development and dissemination of fuzzy math programs. For example, here is a listing of some of the NSF grants that supported the Connected Mathematics Project (CMP): #9986372 Connected Mathematics Phase II # #9980760 Adapting and Implementing Conceptually-Based Mathematics Instructional Materials for Developmental-Level Students # #9950679 Preparing Elementary Mathematics Teachers for Success: Implementing a Research-Based Mathematics Curricula # #9911849 Teaching Reflectively: Extending and Sustaining Use of Reforms in the Mathematics Classroom # #9714999 Show-Me Project: A National Center for Standards-based Middle School Mathematics Curriculum Dissemination and Implementation #9619033 The Austin Collaborative for Mathematics Education # #9150217 Connected Mathematics Project.”
In 1977, the president of the National Council of Supervisors of Mathematics (NCSM), created by NCTM, stated, “The most important issue NCSM faced during the seventies was countering the ‘back to basics’ movement. At a 1975 meeting, members called on NCSM to quickly develop a clear and concise position that they could use as ammunition in the back-to-basics battle. NCSM obtained $4,500 of funding from the National Institute of Education to write and publish this influential statement. A defining point for NCSM was the publication of the NCSM Position Paper on Basic Mathematics Skills in 1976.”
The recognized disregard toward “basic skills” in the mathematics education community has been around for at least 50 years.
But it hit is zenith in 1989 when the federal government began massive financial support to the privately-run NCTM in its self-appointed status to determine the national trends in U.S. mathematics education. Parents, educators, and administrators assumed such federal support meant the programs, with their attached dollars, were worthwhile. As the millions of dollars have flowed to NCTM supporters in universities, school districts, consultants, and private businesses, their power, reputations and ideology have become profoundly and rigidly entrenched.
The Math and Science Partnership (MSP) with NSF has granted $600 million in 48 partnerships and more than 30 other “tool-development and evaluation projects, plus $400 million in 10,000 new fund-ing awards in professional and service contracts.
See nychold.org or http://www.nsf.gov/news/news_summ.jsp?cntn_id=105812&org=NSF.
Barry Garelick, “An A-Maze-ing Approach To Math,” Education Next magazine, No. 2, 2005. The National Science Foundation (NSF) promoted the NCTM standards beginning in 1990 and awarded millions of dollars in grant money for the writing of math texts that embraced them and to state boards of education whose math standards aligned with them.
CONCLUSION:When one reads, “A Nation at Risk,” the startling 1983 federal report about America’s decline in public education, it becomes clear why NCTM selected “equity” as its focus. Instead of helping teachers learn how to adapt lessons and activities to the increasingly diverse student populations—much of which can be related to economic classes, rather than racial groups—NCTM converted the “discipline” of mathematics into a manual of “processes” to produce egaliatarianism among American students.
Unless the U.S. Department of Education increases its own influence within mathematics education, as it has been doing under the unpopular No Child Left Behind and through the What Works Clearinghouse (which has established rigorous research standards), mathematics education cannot be rescued from the powerful social engineering of NCTM supporters. (In addition, it appears that better oversight of how NSF is spending tax dollars is needed.)
Schools and districts, one at a time, are being led by parents and professional mathematicians in a battle to bring the balance of basic skills and conceptual understanding back into mathematics education. Only in California, Michigan, and Massachusetts has there been a critical mass of concerned adults that brought such change to those states’ standards, curriculum, and assessments. American school children deserve better than having to wait one state at a time for the greatness of mathematics to make sense to them.
APPENDIX
I have measured my solutions in any field of study against the “ABCs of (good) journalism,” which are accuracy, brevity, and clarity. These were “drilled” into me, I’m glad to say, at a small, rural-based teachers’ college called East Texas State University, which is now part of the Texas A&M University system, where I earned my bachelor’s degree in journalism and art.
As a journalist for 17 years, I learned, and taught students in high school and junior college, not to use clichés, loaded words, and always to verify information for accuracy. Most important: Never put your own beliefs, political views, or values in your work for the general public.
Second most important: Think of a girl’s bikini when you write a story: short enough to be interesting but long enough to cover the subject. (Of course, this was in the 1960s and 1970s.)
With a master’s degree in counseling, I spent most of my time as a high school and middle school counselor unraveling emotionally-laden perceptions of events and bringing clarity to situations.
Getting certified in special education, and subsequently being a teacher for grades 6-12, I learned to resist the subconscious, and even open, stereotyping of learning disabled students and the “sorting” of deficient learners into categories.
Earning my certification in mathematics at age 45, I continued to choose to work with inner-city, high-risk minority kids in both middle and high schools, primarily in central Texas, as I had for 15 years.
Following that were the years in Washington state, where I confronted inappropriate images of American Indians while I served as their K-12 principal and teacher and earned a principal’s certification at Gonzaga University. Administrators, I learned, spend a large proportion of their time unraveling problems among different groups of people,—especially on an Indian reservation that must abide by tribal, federal, and state regulations—finding solutions, and offering clarity on the issues to all stakeholders.
Then, as a K-5 principal in an upper middle class school in Seattle, I worked with teachers to build a written, vertically aligned, and cohesive course of study in mathematics, since individual teachers and administrators—often with varying abilities—do not always offer a consistent learning environment for students. Good books and written materials, however, have historically provided solid references in the lives of all learners—and teachers. Those assets had not been present or utilized in the school, so that became a clear priority.
Finally, before retiring as a principal, I decided to work half-time as a high school math teacher in Seattle. My frustration became unbearable as I saw seniors who couldn’t work with fractions and therefore couldn’t work algebra problems, regular education freshmen who didn’t know their multiplication tables, English language learners who were lost in literary-based mathematics lessons, and special education students in my mainstream remedial classes who were just lost in the whole “processing” of mathematics. After working for 47 years, and seeing the monstrous problems we had allowed to develop in mathematics education, I said, “I’m done.”
Oh, yeah. I even earned 15 semester hours in the doctoral program of mathematics education at the University of Texas. Once I learned my training in mathematics education would be under the control of NCTM supporters with their constructivist philosophy, I had to choose not to continue in that field of study.