## Commentaries
## Wolin, Democracy, and The Math WarsPosted: 2008-06-27
from
One need not be a scholar of the Math Wars to recognize it's no coincidence that the military language Wolin mentions informs that particular phenomenon. Words like "entrenched," "battle," "fight," "shots fired," and many other martial terms are common to the passionate debates about how to best/better teach mathematics to American students. Undeniably, the rhetoric is often inflammatory and combative. But what really resonates is the mentality Professor Wolin describes, and the philosophy and politics that inform so much of the commentary. Articles appear almost daily that reflect an enthusiastic embrace or tacit acceptance of the shift in focus from education as something to develop diverse and individual potentialities to one of creating drones for the workforce. And anti-reform pundits and commentators, as well as some journalists who no doubt see themselves as either neutral or even progressive buy into the notion that "schools should be judged by their contribution to the economic health of society." Of course, this assumption is hardly one Wolin would buy into as a sound basis for effective education, and neither would I. But it fits well the mentality that informs many educational conservatives and, I believe, goes some distance in accounting for their opposition to many changes in math teaching and curricula. Progressive Math Education and Democracy To begin with, NCTM-style reformers and many progressive educators who work independently of NCTM's various reform volumes, have long believed that a major detriment to effective teaching and learning of mathematics is the idea that the authority for mathematical truth lies outside the student and even outside the teacher. Generally, if the teacher isn't seen as the authority, it's "the textbook." Of course, a book can't be an authority. The book is merely a symbol of the authority of one or more authors who are presumed to be authorities and whose work has been sanctioned by even more expert authorities in the general community of mathematics and mathematics teaching. But a distant author, let alone an even more distant reviewer or endorser, can't know the needs of individuals teachers or students. The author can, at best, offer a finite number of topics, along with treatments of them, examples, applications, exercises, etc. in one specific fixed order. If the author is John Saxon, there is no room for a teacher or student to skip ANYTHING or change the order of anything. Saxon books are to be taken as holy texts. No wonder that many educational conservatives adore Saxon Math and promote it above everything else as the absolutely best way to teach the subject. And better yet, in their minds, it's touted as "teacher-proof." Surely this is Eden for anti-reform advocates. No room for variation, individuality, independence, freedom. Just Prussian military precision and strictures, in keeping with the anti-progressive educational restructuring of the early 20th century in this country. But even when John Saxon doesn't rule, teachers and students alike often defer to the textbook as the authority. Teachers often do not dare to stray or modify math lessons from district mandated texts, even when they are not proscribed from doing so by anyone. This is typical in the lower grade bands. At the high school level, it is more likely that the teacher will believe and promote the belief among students that s/he is the authority. It goes without saying that this is the rule at the university level, where instructors are, for the most part, professional mathematicians with PhDs. In only the rarest of cases does one see mathematics teaching that promotes the idea that the authority for mathematical truth must in no small part rest within the students themselves, both individually and collectively. This is not to say that if a student or class believes that something patently false is in fact true that the false believe becomes "true" through force of will or a cockeyed notion that mathematical truth depends upon a vote. However, if students do not themselves have to struggle with mathematical truth as an issue, it is unlikely that they will ever engage in the questions that real mathematicians grapple with on a daily basis. Moreover, they will not even be able to successfully work through the problems of mathematics they are asked to deal with "at grade level." Instead, they will become passive recipients of received mathematical truth, always based in some external authority. And they will resent being asked to determine truth for themselves. Ironically, this implies that the very complaints one hears so frequently from anti-reformers about how it is "fuzzy" reform that makes students unwilling to engage in proof, the real culprit may be the way elementary mathematics is taught as promoted by those same anti-reformers. The lack of opportunity for students to struggle with their own ideas about mathematics should be anathema to real mathematicians who would, one thinks, recognize the necessity for this process based on personal experience. Why, then, are some mathematicians, both prominent or relatively obscure, so vehemently opposed to progressive ideas about how to promote mathematics learning for young children?
I think Professor Wolin has identified correctly the anti-democratic sentiment that fuels regressive ideas about education, particularly in the public sphere where the masses of our children are likely to have the opportunities to receive whatever version of education we support as a culture and society. The kinds of activities and discourse that progressive mathematics educators promote generally call for learning communities that are highly democratic in nature. On multiple levels, a democratic approach to mathematical discourse communities is prone to grow children who are a serious threat to the anti-democratic forces that are currently at work in our country and elsewhere among nations that ostensibly are democratic. It makes a great deal of sense to think that those who fear that the poor will become better equipped to rise up against the gross imbalances that are increasing daily between haves and have-nots in the United States should the latter become literate and numerate would oppose precisely the kinds of educational practices that inherently promote independent thought, meta-cognition, challenging assumptions, questioning authority, and self-reliance for truth. Once again, I need to stress that I'm not arguing for mathematical or any other sort of anarchy. The idea is not for students to come to believe that anything goes in mathematics, but rather that they are obligated to improve their abilities to judge mathematical validity themselves, rather than to passively accept whatever explanation the teacher or book might offer (especially when it is quite possible that either source might be in error, be that from a misremembering, a misstatement, a printer's error, or an actual misunderstanding of the truth). So-called traditional education as currently construed is very much about social control and truth imparted from above and passively accepted. The last thing one would expect those who support that vision of education to accept would be active, student-centered learning that stresses real arguments in class in the context of honest, open, logical debate (hmm, a clever acronym might be hiding there). Finally, I think Wolin is particularly on point when he talks of the sorting function implicit in the current vision of education, and the need to create a system in which the haves can readily rationalize that the have-nots were given a "fair shake" to succeed and didn't make the most of it, hence that they deserve their sad lot and those who "have" need not feel either guilty or responsible for inequities past, present, or future. For all the rhetoric to the contrary, the anti-reformers at Mathematically Correct and NYC-HOLD have long ago given their game away with their hatred of student-centered teaching, their obsession with direct instruction, their aversion to anything that smacks of either discovery learning of content or "self-discovery" in the broader sense. Wolin's vision of developing diverse potentialities is at the opposite pole from the regimented classrooms being promoted by the anti-reform side of the Math Wars. And so they undermine the sorts of real mathematical learning that they claim to be fighting for, all because their real agenda is something that can't survive the sort of independent thinking that such learning necessitates. |

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