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 know 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-relevant" 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 "relevant" 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.

{inserted 2/14/08: this page has been intentionally damaged, how and by whom I don't know. There was a script running here, something about which I know nothing, but several paragraphs are missing. For example, I quoted a RS math problem that dealt with buying candy bars, and how bad that is for someone. Then I spoke against the problem. I pick up here where the text seems unmolested}

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?

{other paragraphs are missing here}

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....

## 12 comments:

I don't know if you caught this new study topic:

Ebonics suggested for district

http://www.sbsun.com/Stories/0,1413,208~12588~2969790,00.html

I wonder how they plan to incorporate ebonics into math.

The above, and your story, make me appreciate the German school system my son and daughter attend - plain ole German efficiency: in at 8, out at 12 with no fluff or social justice lessons. Some Germans are concerned about the state of the education here, maybe I'll pass your blog to our friends, and they can see what is happening in the states.

Happy Belated Birthday to your son. My son turns 9 in December, but we'll get him beer and brats in order to help him learn about a different culture.

Given your concern of education, are you happy with your son's teaching?

Cheers

Edward: I'd rather not. Notice Tom Wahl's comment.

Tom -- Please tell me more about the German school system. It is exactly what I need for my younger son (maybe my older one, too). He can have his core academic classes all together and then spend the rest of the day doing what he loves -- very artistic things like composing, recording music, writing, making and editing movies, making his own characters, etc. He cannot get all of this in local high schools.

tHanks!

Elizabeth

Nashville

One of my elementary schools is a 'Reading First' grant recipient (mucho federal dollars to implement research-based reading instruction). While I like most of it, there is an emphasis on relating the reading to student's experiences, culture etc. When this comes up during staff development w/ the state department folks, I generally give an obonoxious eye-rolling display. One of the main reasons (uses, charms, etc) of reading to find out about the world beyond yourself. In other words, I didn't have to

experiencea gulag to comprehend Solzhenitsyn.eeeuuuuww. I've been away for a few days, and then took a few more days to get around to catching up on reading various blogs, and I find this...

I read the original introduction here:

http://www.rethinkingschools.org/publication/math/RM_intro.shtml

before reading Darren's analysis in full, and I found it very hard work. Constantly having to resist the urge to scream at your monitor and/or barf all over it takes a lot of effort...

Aside from pulling apart the nonsensical arguments line by line (as Darren does admirably), the first thing that struck me about the introduction: all of the examples described linked to political issues, I mean, err "social justice" issues, seem to me using very limited expanses of mathematics.

I can see how one can force fit basic arithmetic and statistics into that sort of context, but what about Newtonian mechanics or more abstract pure mathematics? I don't see any obvious route here, and my suspicion is that the mathematics will end up getting watered down rather than admit that there is no "social context" for, say, integral calculus. Wait, I know, how about a lesson "exploring Isaac Newton's role as a member of the upper class social elite"... that should do it. :-(

The second general problem I have with the stated approach is that by bending mathematics teaching as a tool for teaching "social justice", it almost necessarily allows little room for considering any other applications. This is a minor but important variation on the first point. If teachers are supposed to construct all their examples so as to include a "social justice" aspect (as in the farcical candy store/sweatshop example), how does one even begin to consider mechanical engineering problems? Again, as in my first point, if one is required to accept the dogma that there is no such thing as a "neutral" math problem, does it not follow that one is forced to fence off any problem areas which actually are, so as to avoid questioning the dogma?

Having read the intro (and once I'd calmed down), I stepped back a page and happened to catch this rather horrifying review:

"This is an invaluable resource! Rethinking Mathematics has the potential to change the basic ways we think about and teach one of the most important subjects in schools today. With clarity and insight, this book shows how teachers who are dedicated to social justice can act on their commitments in a subject that has, for too long, been seen as simply a technical area."

— Michael W. Apple, John Bascom Professor of Curriculum and Instruction and Educational Policy Studies at the University of Wisconsin-Madison

aaaaaaaaaaaarrrrgggggggghhhhhh. Message for Prof. Apple: yes, indeed, mathematics is "one of the most important subjects in schools today". As an engineer, it is the most important subject I learned and which I need to do my job - and which the nation needs in order to compete. Please, pretty please,

don't f*** with it.Regards

Krill

Edward, my point was that Benezet is the antithesis of the German model of schooling.

Krill, your comment could almost be a post on its own! I agree with your point about simple mathematics and almost made it in my post, but given the length of what I'd already done I assumed someone would bring it up! Do you think the RS people would like my trig problem (extra credit on a test, no less) about pointing a howitzer at an enemy position that's identified by a forward observer? I'm sure they'd go nuts, given their anti-war backgrounds. But what I have found most illuminating about that problem is the several different techniques students have used in order to solve it. Since I hadn't discussed a problem like this before, those who do it show that they grok the math and can apply it to the real world--I don't have to lead them to any answer, as they can find it on their own.

a quick follow up...

After posting my previous comment, I read the table of contents, which includes an article entitled "Integrals and Equity". This stood out in light of my previous comment about not being able to fit integral calculus into a "social justice" context, so I found the article itself (not indexed at the main site, but Google is your friend...). Here it is:

http://www.rethinkingschools.org/archive/19_03/inte193.shtml

it describes the teaching of a "math" lesson by the author allegedly on the subject of integral calculus. Sure enough, after a bit of initial handwaving about "areas under lines" it goes off into the weeds. No actual integral calculus being taught here at all. Is this really the vision of the future of math teaching that

Rethinking Schoolshave in mind?Regards

Krill

Of course it is, Krill, because then *everyone* can do it and *everyone* will have good self-esteem and the achievement gap will go away and we'll all be equal and....

Regarding what Elizabeth in Nashville asked me - well, that would take a bit of space and this isn't my cocktail party. I would just say that if you wish to teach your son the basics, consider home schooling. There are many sources for finding the curriculum you want. You can get the teaching done in the morning and schedule for the afternoon the activities that benefit your son - take the situation into your own hands.

I know this item doesn't fit the topic, but we were talking to friends who have a 9 year old boy in the base public school. The teacher chose to show them the movie Dodgeball during class last year. I'm sure there's a social justice lesson for the kids - like teachers need naps. Why is a movie even shown in class, let alone a PG 13?

Tom

This is where I stopped reading:

I know that every time I add 3 + 4 the answer is going to be 7, no matter what.Unless you're adding modulo 2. Maybe you should rethink the predicatability and replicability.You're right about specifying a base--but once you specify a base, the predictability and replicability return. Every time. No matter what.

To pick such a small nit as a way to dismiss the entire essay speaks volumes about your own agenda regarding this subject.

I was too quick to speak. One could, I suppose argue, that I wouldn't have 3 or 4 when doing modulo 2 arithmetic, but that get's fixed if we think mod 5 or 6.

I need to get upset little less :)

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