Monday, June 20, 2005

Social justice math

It turns out that those who thought that math was a universal language equally valid in various corners of the world are wrong. Far-left ideologues calling themselves "critical theorists" are pushing hard to turn math instruction into another form of crude political indoctrination.

Many thanks to the inimitable and ever-alert Prof. Plum for calling attention to this renewed assault on a discipline one would have thought was immune to politicization.

Here is a brief excerpt from Diane Ravitch on this trend cited by Prof. Plum:

Those were the days of innocent dumbing-down. Now mathematics is being nudged into a specifically political direction by educators who call themselves “critical theorists.” They advocate using mathematics as a tool to advance social justice. Social justice math relies on political and cultural relevance to guide math instruction. One of its precepts is “ethnomathematics,” that is, the belief that different cultures have evolved different ways of using mathematics, and that students will learn best if taught in the ways that relate to their ancestral culture. From this perspective, traditional mathematics — the mathematics taught in universities around the world — is the property of Western Civilization and is inexorably linked with the values of the oppressors and conquerors. The culturally attuned teacher will learn about the counting system of the ancient Mayans, ancient Africans, Papua New Guineans, and other “non-mainstream” cultures.

Partisans of social justice mathematics advocate an explicitly political agenda in the classroom. A new textbook, “Rethinking Mathematics: Teaching Social Justice by the Numbers,” shows how problem solving, ethnomathematics and political action can be merged. Among its topics are: “Sweatshop Accounting,” with units on poverty, globalization, and the unequal distribution of wealth. Another topic, drawn directly from ethnomathematics, is “Chicanos Have Math in Their Blood.” Others include “The Transnational Capital Auction,” “Multicultural Math,” and “Home Buying While Brown or Black.” Units of study include racial profiling, the war in Iraq, corporate control of the media, and environmental racism. The theory behind the book is that “teaching math in a neutral manner is not possible.” Teachers are supposed to vary the teaching of mathematics in relation to their students’ race, gender, ethnicity, and community.

This fusion of political correctness and relevance may be the next big thing to rock mathematics education, appealing as it does to political activists and to ethnic chauvinists.
Prof. Plum also cites an actual syllabus on Teaching Mathematics for Social Justice taught by one Blidi Stemn at Northeastern University, Boston Campus:

Course Description
This introductory course explores principles of social justice in education as a lens in rethinking school mathematics. The course will provide participants with a) an opportunity to expand their knowledge and awareness of issues of social justice in the context of mathematics education; b) an opportunity to develop a pedagogical model for teaching for social change; c) a process to critically examine the content of school mathematics curriculum and instructional practices from the perspective of social justice; d) an opportunity to contemplate on the role of the teacher as an agent of change and “transformative intellectual”. Throughout the course we will emphasize the relationship between theory and practice in an attempt to understand some of the complexities and challenges in addressing issues of social justice in mathematics teaching and learning.

Sapient Educator has more on social justice math in Multicultural Math? Ethnomathematics? Socially Just Math? No Kidding!

Sapient Educator has dug up the apparent originator of the term Ethnomathematics, a Brazilian called Ubiratan D'Ambrosio. D'Ambrosio sounds like a buddy of Paulo Freire, judging by the grandiose claims made for this form of math. World peace, no less:

Mathematics is absolutely integrated with Western Civilization, which conquered and dominated the entire world. The only possibility of building up a planetary civilization restoring the dignity of the losers and, together, winners and losers moving into the new. [Ethnomathematics, then, is] a step towards peace.
A little bit murky. Something must be lost in translation somewhere.


Catherine Johnson said...


and not in a good way, either

Stephan said...

These are the kind of extra scary things that make me glad I am homeschooling and developing my own math curriculum.
Math is very "multicultural": numbers from India, algebra from the middle east. Trig from the Babylonians, Geometry from the Egyptians, then all the stuff from China.
This is what happens as the Memory Hole keeps getting bigger.

NYC Educator said...

I take exception to your calling idiots with stupid ideas "far left idealogues."

They are simply idiots--as are those who'd deny the theory of evolution and the effectiveness of condom use.

Instructivist said...

"I take exception to your calling idiots with stupid ideas "far left ideologues."

They are simply idiots--as are those who'd deny the theory of evolution and the effectiveness of condom use."

You may want to familiarize yourself with the neo-Marxist origins of the "critical theorists."

See here:


“Critical pedagogy,” a body of education theory represented by the writings of Henry Giroux, Peter McLaren, Michael Apple, and other leftist-leaning thinkers, takes its cue from the Durkheim quotation above, but it carries the notion of schools as agents of moral instruction and socialization far beyond what Durkheim envisioned and what the public expects.

Critical pedagogy extends critical theory—the neo-Marxist examination of the relationship between power and culture, aimed at addressing issues of class, race, gender, and social justice through the remaking of societal institutions—to the realm of schools. The core concern of critical pedagogy is to illuminate the role of schools in perpetuating the established order and to convert them, instead, into instruments for social reform.

Despite its radical bent—bordering on the kind of liberation theology associated with Latin American revolutionary clergy—the critical pedagogy school has managed to carve out a respectable niche in America’s schools of education, enough to get its views aired in journals such as the Harvard Educational Review (see Giroux’s essay in the Winter 2002 issue) and to have its patron saint, Paulo Freire, the Brazilian Marxist, recognized by the New York Times as one of 13 “provocative leaders” in education “on whose shoulders the future is being built.” Marilyn Cochran-Smith, the newly elected president of the influential American Educational Research Association (AERA), is at least sympathetic to the critical pedagogy movement and is the director of a curriculum and instruction doctoral program at Boston College that lists critical pedagogy as one of only four areas of specialization. At its 2002 annual meeting, the AERA program featured more than 40 panels on critical theory and pedagogy.

Admittedly, the critical pedagogues have squarely confronted two of the most enduring issues surrounding the work of education: 1) To what extent should the mission of public schools be focused on character development, societal reform, and other such affective goals, as opposed to cognitive development and academic preparation? 2) To the extent that values should be taught in school, whose values should take precedence? A related issue, first raised by Durkheim and now at the center of critical pedagogy, is: How much emphasis should schools place on promoting individual achievement vis-à-vis collective well-being? Proponents of critical pedagogy view “egoism” as incompatible with societal progress and complain that schools have become too wedded to Social Darwinist competition. By contrast, traditionalists worry that schools have taken the “it takes a village” slogan to such lengths that they risk producing an increasing number of village idiots.

Darren said...

I've written posts about Ethnomathematics and Math For Social Justice over at my blog, In the latter I fisked the Rethinking Schools dogma.

I'll not put the links here; that could be considered poor form. But if you're interested, either scroll through my main page/archives or email me (info through my profile) and I'll be happy to give you the URL.

Instructivist said...


I read your terrific analysis. It deverses widespread exposure. It's not poor form at all to drop important links.

I'll do it for you:

My browser balks when going to your site (the page won't load).

I'd love to have your post in my comment section.

Darren said...

Monday, July 18, 2005
Math For Social Justice, Part II

Rethinking Mathematics is nothing more than an attempt to politicize the teaching of math. In this I hope it fails, because too much of our curriculum has become politicized already.

Let's take some snips from the web site and comment on them, shall we?

In a "rethought" math class, teachers make mathematics more lively, accessible, and personally meaningful for students, who in turn learn in more depth.

This is a common misperception in education today, one I want to dispel right here and now. By "personally meaningful" these authors mean that we should teach math using examples from the students' own lives. Isn't the purpose of education to expand their horizons, to teach them about what's beyond their noses? We need to teach them about what they don't know, not just reinforce what they already know. As for the remainder of their claims, I don't why a "traditional" math classroom cannot be lively and accessible to students. Even though I stand in front of the class and teach most of the period, I'd like to think that my classes are nothing if not lively. These Rethinking Schools people (from here forward known as RS people) have set up a false dichotomy. Rapport and instructional delivery make a class lively and accessible, not necessarily the political applicability of the course.

The articles in this book provide examples of how to weave social justice issues throughout the mathematics curriculum and how to integrate mathematics into other curricular areas. This approach seeks to deepen students' understanding of society and to prepare them to be critical, active participants in a democracy.

What exactly is "social justice"? Is it the belief that people should work and earn their own money and not be mooches on society? Is it the belief that everyone is entitled to exactly what they earn, and nothing more? Is it the belief that despite our perhaps humble beginnings, we all have the same legal footing to pursue life, liberty, and happiness? Is it the belief that welfare payments should be limited in duration, thus providing impetus for a person to seek meaningful work? Or is it the belief that the rich are the cause of all troubles in society, and class warfare is the foundation of our society? If I were placing money on this, I know which of these options I'd bet the RS people would choose. The RS people wouldn't teach students to be critical thinkers; rather, they'd teach them to criticize. There's a big difference.

When teachers weave social justice into the math curriculum and promote social justice math "across the curriculum," students' understanding of important social matters deepens. When teachers use data on sweatshop wages to teach accounting to high school students or multi-digit multiplication to upper-elementary students, students can learn math, but they can also learn something about the lives of people in various parts of the world and the relationship between the things we consume and their living conditions. (See "Sweatshop Accounting," page 53, and "Sweatshop Math," page 160.)

I assert here that a math class is not the place for social science. Math is a "hard science"--that is, it's replicable and predictive. I know that every time I add 3 + 4 the answer is going to be 7, no matter what. Social science is a "soft science"--different people, in different conditions, will act in different ways. Three plus four will always be seven. This attempt to politicize the math classroom, and to politicize with an unambiguous leftward bias, is another in a long string of attempts to water down the math curriculum so that "every student can succeed." What it really does is ensure that no student succeeds because no one learns any real math! The left doesn't believe in absolutes, it doesn't believe in standards, it doesn't believe in individuality. No one is better than anyone else, no one is more capable, we're all one big mass. This is why the left preaches about "group" identities (racial, ethnic, sexual orientation) while the right preaches about individuals. The left thinks we're all equal--hence the union mentality--the right says we all have an equal opportunity to pursue our potential. This is yet another big difference.

Social science should not be injected into a math curriculum. Rather, math (as a hard science) should be injected into the social science curriculum (a soft science)--that would truly be teaching "across the curriculum". Don't bring your politics into math; rather, use math to justify (or disprove) your politics. A wonderful example of someone having done this is Bjorn Lomborg, the environmentalist I wrote about here. Somehow, though, I don't think the RS people would want to use math in quite the way Lomborg did, as his conclusions don't match their politics. For example, he found the following, which he published in his book The Skeptical Environmentalist in 2001:
1. There is more food today, and fewer people are starving.
2. Life expectancy world-wide has risen from 30 to 67 years in the last century.
3. Poverty has been reduced more in the past 50 years than it was in the preceeding 500.
4. Air pollution in the industrialized world has declined--in London the air hasn't been cleaner since medieval times.
5. We're not losing forests. (That doesn't mean Brazilians should clear-cut the Amazon.)
6. Oil won't run out.
7. "The world is not without problems, but on almost all accounts, things are going better and they are likely to continue to do so into the future."

I wrote this in that same post: "Lomborg doesn't say or even imply that man should perform any activity he wants and ignore the environment. Instead, he presents information that allows us to make informed choices about courses of action rather than reacting to rhetoric, emotion, and anecdote." This is the right way to do things. Gather the facts, use the math, and draw conclusions--don't draw conclusions first and then see how you can use math to justify your conclusions. I propose that we live by this quote attributed to Sherlock Holmes: When the facts contradict your expectations, believe the facts. Lomborg did; I doubt the RS people would.

Rethinking Mathematics spotlights several examples of student activism. These include fifth-grade Milwaukee students writing letters to social studies textbook publishers based on their mathematical analysis of slave-holding presidents and textbooks' failure to address this issue (see "Write the Truth," page 140); New York City students who measured their school space, calculated inequities, and then spoke out against these inequities in public forums (see "‘With Math, It's Like You Have More Defense,'" page 81); and students who used math to convince their school administration to stop making so many obtrusive PA announcements (see the activity "Tracking PA Announcements," page 130).

I ask, does a 10-year-old truly have the capacity for independent, critical thought on the subject of slave-owning presidents? Do they truly have enough information, enough knowledge? Cognitive scientists tell us that algebra is difficult for younger students because most aren't able to think abstractly until around age 14. They can't figure out that x=5.5 if 2x+3=14, but at age 10 they can offer political opinions about slaveholding presidents? This is the type of political indoctrination I stand against, this is the dilution of math that I fight. Save that kind of fight for older students in a social science class--5th graders should be learning this material (at least in California) in math class. And there's a quote, the source of which I don't know, which is apropos of this discussion: Context is often the first victim of activism."

Rethinking math also means using culturally relevant practices that build on the knowledge and experiences of students and their communities. Many of these approaches have been developed by teachers and then described and theorized by researchers of color, such as Gloria Ladson-Billings and William Tate. A guiding principle behind much of this work is that teachers should view students' home cultures and languages as strengths upon which to build, rather than as deficits for which to compensate. In "Race, Retrenchment, and the Reform of School Mathematics" (page 31), Tate offers the simple example of a teacher's failure to reach her students because she uses story problems that are not grounded in the students' culture; while Luis Ortiz-Franco ("Chicanos Have Math in Their Blood," page 70) encourages teachers to teach about the base-20 Mayan number system as a way to emphasize, to both Chicano students and others, that math has deep roots in indigenous cultures in the Americas.

This sounds much like so-called ethnomathematics, which I addressed in this post. There's no such thing as "culturally-relavent" math, not if you're trying to teach math in a way to prepare students for the rigors of college and to compete in a world economy. And teaching base-20 numbers? It may be "cultural", but how "relavent" is it? How will it help students learn more complicated math? I again quote from my Ethnomathematics post: Young people need to be shown that they need to accomplish something in their own lives and be proud of that, not to be proud by dubious association with a group hundreds of years and thousands of miles removed from them. Can it be more clear?

Engaging students in mathematics within social justice contexts increases students' interest in math and also helps them learn important mathematics. Once they are engaged in a project, like finding the concentration of liquor stores in their neighborhood and comparing it to the concentration of liquor stores in a different community, they recognize the necessity and value of understanding concepts of area, density, and ratio. These topics are often approached abstractly or, at best, in relation to trivial subjects. Social justice math implicitly tells students: These skills help you understand your own lives — and the broader world — more clearly.

Those sound like social science lessons to me--and that's where they belong.

It's unfortunate that some people are trying to impose their political views in the science classroom--creationism and intelligent design, bogus environmentalism, etc. Let science and math serve as tools, not weapons. Are nuclear weapons "wrong"? That's not a science question, that's a philosophical question. How many liquor stores there are per square mile in a certain area is a straight-forward computation using math; interpreting the meaning or impact of the resulting number is not a math problem, it's a social science problem. And it's probably not an elementary school issue, either.

I'm curious. What's next? Engineering For Social Justice? Of course not. No one wants the bridge to fall down. They want the hard science there, same as they want the rigorous training for the pilot of the airplane on which they're flying. There are absolutes there, and there's no way around them--the bridge either collapes or it doesn't, the plane either flies and lands safely or it doesn't. They can't go after these fields. But math education--it doesn't have a direct and immediate impact on life like the examples above do, so the lefties will try to dilute it.

Let's be blunt. The RS people openly stated that "Rethinking Schools emphasizes problems facing urban schools, particularly issues of race." This tells us immediately that they're looking at the achievement gap between whites and Asians on the one hand, and blacks and Hispanics on the other. While that's good and important--it's what the No Child Left Behind Act does--the RS people take exactly the wrong approach. Instead of working to improve the math knowledge of blacks and Hispanics (the stereotypical urban school students), they want to feed into the culture of victimhood and self-esteem by making the students feel good about themselves without really learning the math that they'll need to move ahead in education. In other words, the RS people will be creating students who have "thought without learning" (referenced in Part I), which is in fact "perilous."

Certainly working in a school that has a conceptually strong foundational mathematics curriculum is helpful. Teachers cannot easily do social justice mathematics teaching when using a rote, procedure-oriented mathematics curriculum. Likewise a text-driven, teacher-centered approach does not foster the kind of questioning and reflection that should take place in all classrooms, including those where math is studied.

I thought they were going to surprise me with that first sentence, I thought they were going to insist on learning numerical facts. Then they throw it all away in the remaining sentences. Rote learning has its place; no one should have to "think" about adding 5 and 3, they should just know it's 8. Not having to think about that calculation, or about the multiplication facts, frees the mind to think about the mathematics needed to solve a problem. Lower elementary students, which RS seems to focus on, should be learning math facts and procedures, the very concepts that RS decries! They'll be adding on their fingers, or using calculators to multiply 8x5, for the rest of their lives, while they try to understand how many liquor stores is too many in a neighborhood. We're not doing them any favors by taking away the knowledge that will move them ahead. Michael Lopez, who authors the Welcome to Highered Intelligence! weblog, said it best: The less consistent your means are with your goal, the less effective your efforts shall be. Their goals are not aligned with their means. In fact, they're antithetical.

Additionally, I take exception to the last sentence I quoted above. Who says that a text-driven, teacher-centered approach does not foster questioning and reflection? A text is only a tool, and a good teacher will use that tool, among others, to teach the students enough so that they can form their own questions! They won't have to be told to count the number of liquor stores in a neighborhood; knowledge, facts, are the foundation of critical thinking--the latter cannot exist without the former. Teach them, and they'll question on their own if there are too many liquor stores in a neighborhood. Give them the Learning, and the Thought will come on its own. Good teaching is the key here, not politicizing the curriculum.

This next quote doesn't deserve comment. Any thinking person will see it as fundamentally wrong, needing no additional commentary from me:

Other, traditional forms of math are often too abstract, promote student failure and self-doubt, and, frankly, are immoral in a world as unjust as ours. Traditional math is bad for students and bad for society.

I'm really trying to be strong here, but there are so many things wrong with that statement! Must--resist--urge--to--point--out--obvious--idiocy! Whew, I just have to remember that my readers are reasonable bright people. There, that helps immensely.

Here's more.

Our perspectives on teaching math for social justice have been shaped by our own involvement in movements for social justice during the past three decades — the Civil Rights Movement, anti-war movements, educational justice movements, and other campaigns. We've also been influenced by educators such as the late Brazilian educator Paulo Freire, who argued against a "banking approach" to education in which "knowledge" is deposited into the heads of students and in favor of "problem-posing" approaches in which students and teachers together attempt to understand and eventually change their communities and the broader world.

Nope, nothing lefty there. At least they're up front about it, and not trying to hide. What about my perspectives on social justice, shaped by being raised in a working-class neighborhood in a family of four children, having divorced parents, being raised by a single parent, being responsible for my own education and school matters (neither parent ever attended one of my track meets, and I ran track for two years), going to West Point, serving in the army, and then being a manufacturing manager? Are my views invalid? I'm sure the RS folks wouldn't approve. Yet we're supposed to accept theirs because they say so. Horse hockey, as Colonel Potter (M*A*S*H) would say.

Let's get to the heart of the matter, though. I assert that math is a subject all its own. It is a tool that is used to understand the other sciences, and as such has no inherent political structure. But the RS people disagree. In fact, in an amazing use of lefty doublespeak, they state that not being political is actually being political.

While reading these articles, some people might question whether it's appropriate to interject social or political issues into mathematics. Shouldn't math teachers and curriculum, they might say, remain "neutral?"

Simply put, teaching math in a neutral manner is not possible. No math teaching — no teaching of any kind, for that matter — is actually "neutral," although some teachers may be unaware of this. As historian Howard Zinn once wrote: "In a world where justice is maldistributed, there is no such thing as a neutral or representative recapitulation of the facts."

I disagree. The facts are there for all to see. Your interpretation of them is what is political.

For example: Let's say two teachers use word problems to teach double-digit multiplication and problem-solving skills. They each present a problem to their students. The first teacher presents this one:

A group of youth aged 14, 15, and 16 go to the store. Candy bars are on sale for 43¢ each. They buy a total of 12 candy bars. How much do they spend, not including tax?

The second teacher, meanwhile, offers a very different problem:

Factory workers aged 14, 15, and 16 in Honduras make McKids children's clothing for Wal-Mart. Each worker earns 43 cents an hour and works a 14-hour shift each day. How much does each worker make in one day, excluding fees deducted by employers?

While both problems are valid examples of applying multi-digit multiplication, each has more to say as well. The first example has a subtext of consumerism and unhealthy eating habits; the second has an explicit text of global awareness and empathy. Both are political, in that each highlights important social relations.

Again, it's the interpretation that makes the politics. Notice the value judgements the RS people assign to the first problem--"consumerism" (bad), and unhealthy eating habits (bad). What if, instead of candy bars, the students were buying apples? Does the "politics" of the problem now change?

The first problem is a straightforward application of mathematics. The assumption I would make, however, is that students would be familiar with multidigit multiplication before transitioning to this word problem. The very basic nature of the word problem is designed to use some knowledge the students most likely already have (they probably all understand what is going on in the problem) to extend their use of mathematics, to show them a type of problem in which multiplication is useful. This type of problem promotes mathematical understanding, which should easily be transferable to other types of math problems.

The second example is entirely different. The second example, by its very wording and nature--indeed, by its design--causes the mathematics to be secondary to the social goals of "global awareness" and "empathy", neither of which is a valid subject for mathematics.

Let me give another example. The first problem would be like a shop teacher's teaching the use of a saber saw. Students would already know the basics of how to hold and power the saw, and the problem causes them to extend this knowledge by actually using the saw to, perhaps, cut a curved line in wood. The second problem assumes from the start that we're going to make a shelf, and it will be a great shelf, and the focus is on the shelf, not the saw. The focus of the lesson in shop class should be the saw, not the uses of the shelf.

Elementary students need the building blocks of knowledge, which include rigorous math instruction. We don't build skyscrapers without starting with the foundation, and master piano players learn scales and Chopsticks before concertos. It amazes that these same people (lefties) who think that these children have the intellectual capacity to solve the world's problems don't think they can handle the memorization of times tables or the stress of taking a standardized test. Hold them to a measurable, identifiable standard? Perish the thought.

In closing, the RS people have things bass-ackwards. We should teach the math first, then the applications, then interpret the findings. Don't try to do it all at once, that only confuses the issue (and the students!). This is an ideal time to point out that we math teachers already do enough cross-curricular instruction in our courses--readings and writings about math and mathematicians, applications to art and science, history of math, etc. The RS people make no secret of their desire to use mathematics for social purposes, so let them do it. How fun would it be to watch social studies teachers apply mathematics to their courses of instruction?! I wonder if they'd gain a new appreciation for having an actual knowledge of math....

Anonymous said...

this entry is bull. social justice math and "ethnomathematics" are two completely different ideas.

social justice math consists of using standards-based mathematics to empower disadvantaged students through the exploration of issues of social justice, like comparing the rates of asthma in wealthy vs poor neighborhoods, where industrial pollutants are typically found.

Anonymous said...

"this entry is bull. social justice math and "ethnomathematics" are two completely different ideas."

The argument is that these different ideas are being merged.