|« IQ Insanity | Gene Expression Front Page | La Griffe's Latest »|
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 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:
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:
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:
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.
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.
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:
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.
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.
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?
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 . . . )
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. . .
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.
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.
. . . 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.
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.
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. . .
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.
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.
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.
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. . . .
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.
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. . . .
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.