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January 15, 2005

Anti-Racist MultiCultural Math - Part Two (Zwei, Dos, Deux, Due, Dois, . . )

This is a follow-up to my earlier post Anti-Racist Multicultural Math and I want to focus on some criticisms that Chris Correa is making about the Newton incident. He's disputing the charge that Anti-Racist, Multicultural Math is being taught in Newton, Mass. and believes that this story only has legs because of an agenda driven newspaper reporter and an audience only too willing to believe the worst about the educational establishment.

(Note: This turned out to be a much longer post than I envisioned . . . it's kind of taken on a "everything and the kitchen sink style" because at this point I'm too lazy to edit it, sorry, so the non-Newton stuff starts at the section entitled Know Thy Enemy.)

Let's review the facts:

- The downward trend in 6th grade math scores is unique to Newton and not seen statewide.
- The test is unchanged.
- The demographics are relatively unchanged.
- The SES of the students are relatively unchanged.
- The school district budget is at a record level despite fewer students in the district.
- Teacher turnover is low.
- Political & administrative oversight is unchanged.

The curriculm was changed to emphasize anti-racist core values and the results have been a steady decrease in 6th grade math achievement. Furthermore, in statewide rankings, the Newton School district has declined. In 2004, they ranked 39th in the state, in 2003 they ranked 25th, and in 2002 (the only ranking I could find) they ranked 7th. (See here for district rankings in 2003 and 2004.)Here is the raw data on the 6th grade Math scores:

GRADE 06 MATHEMATICS
PERFORMANCE LEVEL 2001 2002 2003 2004
ADVANCED 42 40 41 37
PROFICIENT 31 35 30 31
NEEDS IMPROVEMENT 16 17 19 21
WARNING 11 8 9 11

Now from what I gather, Chris is arguing that we should look at the current 8th grade math achievement scores because the 8th graders have 3 years of the anti-racist math under their belts and their scores are actually increasing:

GRADE 08 MATHEMATICS
PERFORMANCE LEVEL 2001 2002 2003 2004
ADVANCED 41 37 42 40
PROFICIENT 29 31 32 33
NEEDS IMPROVEMENT 20 21 15 20
WARNING 9 10 10 7

I'm not terribly reassured by an analysis of that data. Also, keep in mind that these current 8th graders were the 2002 class of 6th graders, the best performing cohort in the 4 year time window of that survey. Further, the 8th graders have had instruction under the anti-racist math curricula for only half of their school careers while the 6th graders have suffered for two thirds of their time in school. It's quite likely that the 8th graders were able to salvage some semblence of understanding of mathemetical fundementals in their first 4 years of school. Chris also argues that the test scores are dropping because the proportion of disabled and limited English proficient students is increasing and that the difficulties of teaching students with these impairments is the root cause of the overall decline in 6th grade Math scores. I've taken the liberty of amalgamating the 2002, 2003, & 2004 data into the table below:

GRADE LEVEL 6 - MATHEMATICS
 STUDENTS INCLUDEDPERCENT OF STUDENTS AT EACH PERFORMANCE LEVEL
#%APNIW/F
STUDENT STATUS - 2004
    REGULAR631704835 15 2
    DISABLED246271220 36 33
    LIMITED ENGLISH PROFICIENT2631946 27 8
STUDENT STATUS - 2003
    REGULAR658715234 13 1
    DISABLED237261123 36 30
    LIMITED ENGLISH PROFICIENT2833621 25 18
STUDENT STATUS - 2002
    REGULAR627745134 12 3
    DISABLED216251038 29 23
    LIMITED ENGLISH PROFICIENT91-- - -

Let's look at the trends in the 4 achievement categories. Notice that in the Advanced category, there has been an annual 1% rise in the number of disabled students who qualify while there has been a slightly downward trend for the regular students, and with only two data points for the limited English proficiency students we note a sharp drop off.

In the Proficient category, the regular students remain stable, the disabled students are declining in numbers and the limited English proficiency students are increading.

In the Needs Improvement category, the regular students,are showing a slow, but steady, increase, while 7% more disabled students have moved into this category over 3 years and the limited English proficient students have shown a marginal rise.

Lastly, in the Warning category, the regular students are pretty much holding steady, while 10% more disabled students have moved into this category and 10% fewer of the limited English proficiency students are classified in this lowest category.

Looking at the totality of these trends it's quite obvious that increasing the proportion of disabled and limited English proficiency by 4% doesn't explain the reallocation in performance amongst the groups of students. For Chris's hypothesis to hold, we'd expect to see the performance of regular students remain unchanged and most of the declines occuring amongst the disabled and limited English proficiency students. No such pattern is discernable.

Another explanation that Chris offers, but which I don't find exculpatory, is that none of the official Newton School District literature actually refers to "Anti-Racist Math." Further, if I'm reading him correctly, Chris believes that this whole story is the author's fabrication because the author quotes from a Social Studies Curricula Guide and that there is no anti-racist agenda within the Math curricula.

Let's take a closer look. The author of the newspaper article wrote:

Between 1999 and 2001, under the direction of Superintendent Young and Assistant Superintendent Wyatt, the math curriculum was redesigned to emphasize "Newton's commitment to active anti-racist education" for the elementary and middle schools. This meant that no longer were division, multiplication, fractions and decimals the first priority for teaching math. For that matter, the teaching of math was no longer the first priority for math teachers, as indicated by the new curriculum guidelines, called benchmarks, which function as the primary instructional guide for teaching math in the Newton Public Schools.

Apparently, in looking at the Newton School District webpages, Chris was searching for explicit statements that could have served as the foundation for the above statements and he found none and apparently missed the significance of the statements on core values. Chris is looking at this from a functionalist point of view. By way of analogy consider a manufacturing company that makes quality a core value. No longer is quality strictly within the purvue of the quality control department, it has now become a mission for the entire company, and the first job of people on the assembly line is to ensure that their work meets the quality standards, and thereafter they can concentrate on productivity gains, workflow issues, labor relations, etc.

The Newton School District has adopted Respect for Human Differences and MultiCultural Education as their core values:

Effective multicultural education suggests a reexamination of the history, social constructs and dynamics related to race, class, gender, ethnicity, economics, and culture that impact curriculum and instruction. Multicultural education includes rigorous curriculum and inclusive teaching that challenges all students and staff. We are committed to developing a philosophy of multicultural education that can be infused across transformed curricula. The district-wide Core Value--respect for human differences --set the direction and formed the basis for our continued support of the wide range of offerings above and for our espoused multicultural/anti-racist approach to teaching and learning.

Subsumed under these core values are specific functional objectives, and if these functional objectives are exempt from core values, we'd expect that to be noteworthy. The Mathematics Benchmarks read, in part, as follows:

The Newton Public Schools Mathematics Benchmarks for Elementary Grades (K-5) are organized to reflect the National Council of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics (2000). The Benchmarks include both content strands and process strands.

. . . These process strands are consistent with NCTM Principles and Standards, and with Newton’s commitment to active anti-racist education.

. . . However, the Benchmarks are not explicitly aligned with the 2000 revision of the Massachusetts Mathematics Curriculum Frameworks, as that document does not reflect all of the instructional and philosophical principles of NCTM or of the Newton Public Schools.

. . . In accordance with the core values of the Newton Public Schools, teachers are expected to provide a mathematics program which ensures that every child meets his or her grade level benchmarks, and that every child is challenged at his or her level.

This document is quite explicit in stating that the Newton District curriculm differs from the suggested state curricula by incorporating anti-racist principles developed locally and that the Math curricula is in accord with the dominant core values. I see no reason to conclude that the Math curricula is exempt from the core values of the District.

In the end, Chris asks us to not believe the worst about the educational establishment and asks us to accept the fact that the concept of Anti-Racist Math is something that simply doesn't exist.

KNOW THEY ENEMY

I however, disagree. In the spirit of knowing thy enemy, (Not Chris, but the advocates of fads like anti-racist math) I pull from my bookshelf, Sandra Harding's The Science Question in Feminism. Here are a few relevant quotes:

Page 36.

In the 1950s, the philosopher of science Willard Van Orman Quine indentified two dogmas of empriicism that he thought shoud be abandoned. "Modern empriricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truths which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meanigful statement is equivalent to some logical construct upon terms which refer to immediate experience." Quine argued that both dogmas were illfounded, and that if they were abandoned, we would be inclined to see as less clear the purportedly firm distinction between natural science and specualtive metaphysics. We would also recognize pragmatic standards as the best we can have for judging the adequacy of scientific claims.

Page 39.

If we are not willing to try to see the favored intellectual structures and practices of science as cultural artifacts rather than as sacred commandments handed down to humanity at the birth of modern science, then it will be hard to understand how gender symbolism, the gendered social structure of science, and the masculine indentities and behaviors of individual scientists have left their marks on the problematics, concepts, theories, methods, interpretations, ethics, meanings, and goals of science.

Page 40

But we shall try to locate the pure, value-free core of science responsible for the purportedly inherent progressiveness in scientific method, in model claims in physics, in the mathematical language of science, and in logical reasoning. If, as I shall argue, pure science cannot be found in these places, then where should we try to find it?

Page 44.

I will argue that a critical and self-reflective social science should be the model for all science, and that if there are any special requirements for adequate explanations in physics, they are just that - special. (We will see that much of biology should already be conceptualized as social science . . . )

Page 45

Second, the concepts and hypotheses of physics require acts of social interpretation no less than do those in the social sciences. The social meanings that explanations in physics have for physicists and for the "man and woman in the street" are necessary components of these explanations, not scientifically irrelevant historical accidents. Perhaps it is appealing to imagine that the mathematical formulations of Newton's laws are the explanations of the movements of matter because it takes only a little effort for us modern folk to get a sense of what these formulas mean in ordinary language. But should we think of a formula so long that only a computer could read it in one hour as an explanation of a type of phenomenon? The answer to this question is "no." An explanation is a kind of social achievement. . .

The formula "1 + 1 = 2" is meaningless unless we are told what it is to count as a case of 1, of +, of =, and so on. . .

Scientific formulas are like legal judgements: the laws become meaningful only through learning (or deciding) how to apply them, and doing so is a process of social interpretation.

Page 47

I have been suggesting reasons for reevaluating the assumption that physics should be the paradigm of scientific knowledge-seeking. If physics out not to have this status, then feminists need not "prove" that Newton's laws of mechanics or Einstein's relativity theory are value-laden in order to make the case that the science we have is suffused with the consequences of gender symbolism, gender structures and gender identity.

Page 48

The belief that mathematics has no formal social dimensions - that the "external" social history of mathematics has left no traces on its "internal" intellectual structures - provides grounds for regarding science as fundamentally a set of sentences (such as Newton's laws) and physics as the paradigmatic science. . . . We have already argued that the explanations in physics cannot be "reduced" to mathematical "sentences" shorn of social interpretation.

Page 49

. . . two considerations make it plausible to regard as mythical the possibility of pure mathematics. In the first place, no conceptual system can provide the justificatory grounds for itself. To void vicious circularity, justificatory grounds must always be found outside the conceptual system one is trying to justify. The axioms of mathematics are no exception to this rule. . . . mathematical concepts and theories, too, are tested against historical social worlds they are designed to explain.

Page 50

They did so by replacing the social image of numbers as counting units with the social image of numbers as divisions of a line. These are social images because they reflect what people in historical cultures intentionally do. Not all cultures have been as preoccupied with the measuring - dividing a line - as has ours for the last few centuries. As one comentator points out, such a process of socially negotiating cultural images in mathematics is similar to what we do when we exclude patriotic killing in wartime from the moral and legal category of murder.

Page 51

It may be hard to imagine what gender practices could have influenced the acceptance of particular concepts in mathematics, but cases such as these show that the possibility cannot be ruled out a priori by the claim that the intellectual, logical content of mathematics is free of all social influence. . .

Mathematicians in this century, however, have found it impossible to justify the axioms of mathematics with any logical principles that are not more dubious, more counterintuitive, than the mathematics they are supposed to justify. So it is doubtful that the duty of providing a firm grounding for the truths of mathematics can be assigned to logic. Moreover, a few feminists have proposed ways in which specific assumptions in logic are androcentric. Merrill Hintikka and Jaakko Hintikka, for example, argue that the metaphysical units of a branch of logic called "formal semantics" correspond to masculine but not feminine ways of individuating objects.

OK, that's enough of that. The book goes on for 250 pages and if we substitute discriminatory racial ways of knowing for Harding's analysis of gender discrimation in our ways of knowing, we have an insight into the form that Anti-Racial Mathematics could take.

For us to expect that the Anti-Racist MultiCultural Math threat was simply the work of an agenda driven newspaper reporter, we'd have to discount the theoretical work on race, culture and gender coming from the academy, as well as the education establishment's well known penchant for implementing faddish approaches to education. Consider:

For Stacy Christ, a fourth grader in Fairfax County, Va., a homework problem about pencils and packages was an exercise in frustration.

"The answer required division," her mother, Susan, explained to me, "but she'd never been taught to multiply." . . .

But now "constructivism," as it is sometimes called, has become a force in teaching mathematics -- and the paradox is immense. In a field distinguished by reliance on proof, an unproven approach is being taken in thousands of schools.

The saga of whole math began in earnest in 1989, when the National Council of Teachers of Mathematics published standards that denounced a "longstanding preoccupation with computation and other traditional skills." According to the council, stressing addition, subtraction and, worst of all, memorization made students into "passive receivers of rules and procedures rather than active participants in creating knowledge."

The standards recommended that students get together with peers in cooperative learning groups to "construct" strategies for solving math problems, rather than sit in class with teachers instructing them.

Calculators were a necessity from kindergarten on, the council said, because students liberated from "computational algorithms" could pursue higher-order activities, like inventing personal methods of long division.

Dr. Frank Allen, a former council president and whole-math opponent, has noted that as the standards were being developed, the council's research advisory committee expressed concern about the failure of the standards commission to provide research support for its recommendations. But the standards' writers were undeterred, and today their views drive the direction of curriculums and textbooks in both public and private schools.

Or consider Professor of Education, Martin A. Kozloff's take on fads:

The common view does not adequately capture the history of innovations in education (ranging from questionable to destructive), such as additive-free diets, "gentle teaching," "sensory integration," "full inclusion," and "facilitated communication" for persons with autism and other developmental disabilities; whole language, invented spelling, inquiry learning, discovery learning, learning styles, multiple intelligences, "brain-based teaching," constructivist math, portfolio assessment, authentic assessment, "journaling," self-esteem raising, "learning centers," "sustained silent reading," "developmentally appropriate practices," and "student centered" education for more typical students.

Let's look specifically to racist math:

But DoEd's unqualified embrace of the constructivist approach--sometimes called the "New-New Math" -- prompted a counterattack by the heaviest artillery yet in the Math Wars. On November 18, 1999, Secretary Richard Riley and staff spilled their morning coffee over a full-page Washington Post advertisement signed by 200 mathematicians, scientists, and other experts calling on Riley to withdraw the federal endorsement of the 10 math programs. Among the signers were four Nobel laureates in physics and two winners of the Fields Medal, the highest honor for mathematicians.

The high-powered group protested the absence of active research mathematicians from DoEd's Expert Panel. They also objected that DoEd's Top-10 programs omitted basic skills, such as multiplying multi-digit numbers and dividing fractions.

"These programs [the Top 10] are among the worst in existence," said Cal State/Northridge math professor David Klein, who helped draft the letter. "It would be a joke except for the damaging effect it has on children." Some of the panelists fought back. For example, Steven Leinwand accused the 200 scholars of being interested in "math for the elite" alone. Leinwand, math consultant for Connecticut's education department, said the NCTM and DoEd believe "math needs to empower all students." However, it was Leinwand who in 1994 wrote in Education Week that continuing to teach children multi-digit computational algorithms was "downright dangerous." . . .

Secretary Riley commented that NCTM has published "the prevailing standards in the country, so we thought that would make sense." But critics see a deliberate integration of ideological agendas. The architects of NCTM's 1989 standards declared that social injustices had given white males an advantage over women and minorities in math, and they promised NCTM's reinvented math would equalize scores. Equality would be achieved by eliminating the "computational gate."

For more on this aspect of the problem see this story:

Carson said long division "was completely excised from the programs for quite a while until the backlash got so large that they at least had to make nods toward teaching it.

"In 5th grade they're still drawing pictures to solve problems in multiplication and division."

Her son, who attends the public schools in New York City, was drawing clumps of sticks to solve multiplication problems in the 6th grade, she said.

In the 7th grade, he and his classmates were asked to find the area of a circle. Four weeks were devoted to the task. Traditionally, children were given the formula, but apparently these junior Archimedes were supposed to rediscover the uses of pi.

"Where's algebra?" Carson asked. "This is inquiry-based learning taken to an absurd end. But in schools of education, inquiry-based learning is IT!" . . . .

In both his prepared remarks and in discussion, Klein disparaged colleges of education, which produce most U.S. math teachers. In countries where students score high on standardized tests, teachers have degrees in mathematics, not math education, he said.

Klein said both parents and academic mathematicians are rebelling against the NSF and NCTM programs, which radically de-emphasize basic skill, encourage "rampant" calculator use beginning in Kindergarten, and falsely claim to teach conceptual understanding. "Instead they squander valuable class time on aimless projects with little or no intellectual content," he said. . . .

Carson said NCTM-style math education is closing the "performance gap" in test scores by lowering the achievement of above-average students.

Let's take a look at ethnomathematics:

How tame those struggles seem, however, when compared to the rising vanguard of self-described ethnomathematicians. For some, the new discipline just means studying the anthropology of various measurement methods; they merely want to supplement the accepted canon -- from Pythagoras to Euclid to Newton -- with mind-expanding explorations of mathematical ideas from other cultures. For others, however, ethnomathematics is an effort to supplant the tyranny of Western mathematical standards. . . .

''Mathematics is absolutely integrated with Western civilization, which conquered and dominated the entire world. The only possibility of building up a planetary civilization depends on restoring the dignity of the losers.''

'The practical effect,'' Klein says, ''has been watered-down math books that overemphasize inductive reasoning (like continuing visual patterns), because this is supposed to be good for women and minorities, and de-emphasizing deductive reasoning and mathematical proofs, which is the heart of mathematics, because that supposedly favors white males. . . .

''But mathematics is a worldwide monoculture. Look at the chalkboards in math departments at universities all around the world -- in Africa, Asia, Europe, Latin America. You will see the same symbols everywhere you go on this planet, except perhaps in colleges of education where fads reign supreme.'' Klein says he does spend some class time discussing the math of Mayans, Egyptians and other early civilizations. ''But ancient techniques and early discoveries in math will not take students very far who want to do something in the modern world with mathematics,'' he says. . . .

If you'd like to learn more about ethnomathematics, you can go to the Ethnomathematics Digital Library or you can read The Multicultural Math Classroom: Bringing in the World by Claudia Zaslavsky:

Rationale for introducing multicultural, anti-racist perspectives into the math curriculum, along with practical teaching ideas. Students address community issues through math. Includes sections on numerals, recording and calculating, geometry and measurement in architecture, geometry in art, data analysis, games of many cultures and more. Heinemann, 1996. 240 pp. * $25

Or see Anti-Racist Science Teaching by Gill & Levidow:

This book shows how science and technology embody distinctive values and cultural assumptions, including racist ones. These are in turn reflected in the way science is taught in many schools. Specific case studies present anti-racist approaches to biology, nutrition, and wildlife conservation, as well as one school's experiment with reorganizing the curriculum across disciplinary boundaries. Free Association Books (London), 1987. 324 pp. (01-609-5646/0507.)

Or simply search for "racism" and "math" within the Annotated Bibliography of Multicultural Issues in Mathematics Education.

Here are some resources for teachers interested in teaching Native American Geometry, Multicultural Approaches in Math and Science, and Anti Racist Science Teaching.

Turning the focus back to the Newton District, it's likely that the administration changed the curriculm in order to close the achievement gap and they chose to use Connected Mathematics because of reports that:

Mathematics problem-solving scores for African American students in the two standards-based curricula were significantly higher than scores for African American students in the control group.

However, the administrators were unlikely to have investigated this fad too deeply for they would surely have come across this critique:

Putting aside the fact that the "Control" is neither pre-Standards nor alternatively reform, how good of a study is this? Well, of the 14,000 students in this district, one would assume over 1000 in Grade 6. This study involves 46 of them. Out of this group, 8 students were African American so the conclusion that the "African American students in the two standards-based curricula were significantly higher" is a comparison with performance from 8 students already in a Standards-based curriculum.

Further, if one analyses the performance of Newton's 6th grade African-American students, we actually see that the number of Advanced and Proficient students declines and the Needs Improvement and Warning students increases

The District of Newton's type of social experimentation and classroom indoctrination can lead to sad and devastating results. The first tremors of this quake are being felt in the lowered math performance of the 6th grade students, but as Joanne Jacobs has reported, elsewhere in the country lawsuits have been launched because diplomas are being withheld from students and the suits allege that this is due to culturally biased tests and even students with a 3.0 average can't pass the math portions of these tests:

With a 3.0 grade point average anchoring a solid academic record, Robyn Collins, 18, has big plans once she graduates from Reed High School in Sparks, Nev. . . .

The only problem is that she might not graduate from high school.

Collins is among 2,195 students -- 12 percent of the state's senior class -- who have completed all their course work requirements but will not receive high school diplomas this spring because they have not passed the math portion of Nevada's high school graduation test. . . .

"I've cried so much about this test," said Collins, who learned yesterday that she had failed the exam for at least the fifth time. "I'm not a stupid kid. . . . It is just that in my opinion, the stuff on the test doesn't equate to anything that I've learned in school."

Test proponents, however, contend that the exams are easy enough that the vast majority of students should pass them. They note that there are multiple opportunities to take the test and that many states offer remedial instruction, and they contend that high school graduates should demonstrate competence in basic skills.

Some states, in response to angry uproar about the damage to graduates' self-esteem, have lowered the pass threshold for tests, while others have implemented tests comprised strictly of pre-algebra material for their 10th grade students. Here are the Released Questions from the October 2004 test for California High School Exit Examination. God help us all if this test is too difficult for high school graduates to pass.

Considering the record of the educational establishment, their history of gullibility with respect to ill-considered fads, and academic research on anti-racist math and the availability of teacher resources to assist in eradicating evil racist mathematics from our schools, I find it entirely credible that an Anti-Racist Multicultural Math curriculm has been implemented and is not the figment of a newspaper reporter's imagination. The efforts Chris has made to offer alternate explanations are commendable but entirely unconvincing.

Also, see this guide to curriculm and this related post.

Posted by TangoMan at 08:13 PM