Saturday, June 21, 2008

Wolin, Democracy and The Math Wars

The new vision of education is the acquisition of the specific job skills needed in a high-tech society. There are some striking consequences of this definition of education or, rather, the redefinition of it.

One is that the principal purpose of education is no longer conceived primarily in terms of the development of the person. In the past, the person was understood in complex terms of diverse potentialities. The academic subjects to be studied represented not only different methods of understanding but elements of a different sensibility. Becoming a person meant embarking on a quest for the harmonizing of diverse sensibilities.

The rejection of that conception of person can be measured by the disappearance of the older rhetoric about “personal discovery,” “the exploration of diverse possibilities,” or “initiation into a rich cultural heritage.” In its place is an anti-sixties rhetoric which is really an attack on education as the representation of human diversity. Or it is the rhetoric of “core courses” which work to dismiss the very subjects they profess to be defending. The new education is severely functional, proto-professional, and priority-conscious in an economic sense. It is also notable for the conspicuous place given to achieving social discipline through education.

It is as though social planners, both public and private, had suddenly realized that education forms a system in which persons of an impressionable age are “stuff” that can be molded to the desired social form because for several years they are under the supervision of public and private authorities. (Parenthetically, it is in this light that private religious schools have found great favor in the eyes of public and private policy makers: these are perceived as superior means for imposing social discipline, although that discipline is usually described as moral or religious education and as anti-drugs and -sexual permissiveness. Such schools represent the privatization of public virtue.) Third, and closely related, the new conception is tacitly a way of legitimating a policy of social triage. High-tech societies are showing themselves to be economic systems in which a substantial part of the population is superfluous, and so is the skill-potential of perhaps a majority of the working population. Such economies tend to dislocate workers, replace them by automation, or relegate them to inferior, less demanding, and less remunerative types of work. If such a population is not to be a menace, its plight must be perceived as its just desserts, that is, the failure must be theirs, not the system’s. More prisons, not social and educational programs, must be seen as the rational response. The schools should operate, therefore, to sort out people, to impose strict but impersonal standards so that responsibility for one’s fate is clear and unavoidable.

Sheldon S. Wolin: THE PRESENCE OF THE PAST: Essays on the State and the Constitution, “Elitism and the Rage Against Postmodernity” (pp. 60-61)

The above may be and probably should be some of the most important words you read this year about education, mathematics or otherwise. Written by Sheldon Wolin, emeritus professor of political philosophy at Princeton University, they are part of a brilliant essay on, in part, Alan Bloom's THE CLOSING OF THE AMERICAN MIND, as well as the vehement reaction from various quarters against postmodernism and contemporary university education. Moreover, they show that this reaction is above all else part of the opening salvo of neo-conservative Straussism, or at least aspects of Strauss' work as interpreted by what Wolin refers to as that philosopher's epigones that informed or provided justification for, however doubtful it might be that Leo Strauss himself would have agreed with it, the neoconservative movement that dominated the first George W. Bush administration and shaped much of the second until the ship clearly began to sink in 2006.

In reading the quotation from Professor Wolin, I was struck by the eerie similarity between what he describes there and the mind-set of so many anti-reformers in mathematics education that I and many others have struggled against during the past 15 years or more. His essay continues a couple of paragraphs later with this insightful commentary on the Bell Commision's oft-cited A Nation At Risk report:
Although the Bell Report never suggests how it had come about that the nation was at risk, its remedy was remarkable for its pared-down vision of education, its emphasis upon the disciplinary role of schools, and its martial rhetoric. It warned of 'a rising tide of mediocrity' in educational performance, and it likened that prospect to 'an act of war.' It compared current educational practices to 'an act of unthinking, unilateral educational disarmament.' While one might dismiss this as mere hype, the uncomfortable fact is that this rhetoric was chosen in order to establish the context in which the problem of education was to be resolved. Military language is inherently uncongenial to thinking about individual growth but not about adapting individuals to organizational functions. Its barracks language of pseudo-democracy is also a way of brushing off problems of minorities and of the poor. Indeed, the coercive language of war, crisis, and mobilization is so antithetical to what education has traditionally symbolized that it should alert us to the radical recontextualization being proposed for education.

One need not be a scholar of the Math Wars to recognize that it is no coincidence that the military language Wolin mentions informs this particular phenomenon. Words like "entrenched," "battle," "fight," "shots fired," and many other martial terms are common to the passionate debates about how to better or "best" teach mathematics to American students. Undeniably, the rhetoric is often inflammatory and combative. But what really resonates here is the mentality Professor Wolin describes, and the philosophy and politics that inform so much of the commentary in the Math Wars, formal and informal. 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 accept as a sound basis for effective education, and neither would I. But it fits well the mentality that informs the writing of most educational conservatives and, I believe, goes some distance towards accounting for their opposition to many pending or already-implemented 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 its 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 primarily or exclusively outside the student and even outside the classroom teacher (at the K-12 level). Generally, where the teacher isn't seen as the authority, "the textbook" is. 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 communities 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, along with examples, applications, exercises, etc. in one specific and fixed order. If the author is John Saxon, there is explicitly no room for a teacher or student to skip or change the order of anything. Saxon books are intended 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 has been touted by its creator as "teacher-proof." Surely this claim represents an Eden for anti-reform advocates: no room for variation, individuality, independence, or 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 where 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 who for the most part are (and desire to be) viewed as gods.

In only very rare 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 belief becomes "true" through force of will, or a cockeyed notion that mathematical truth depends upon a majority vote. However, if students do not themselves have to struggle with mathematical truth and sense-making 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 and nearly-always do become passive recipients of received mathematical truth, always grounded in and authenticated by external authority. And they will predictably resent being asked to determine truth for themselves.

Ironically, this implies that the very complaints one hears so frequently from anti-reformers about how "fuzzy" reform mathematics education makes students unwilling to engage in proof, the real culprit may well be the sort of elementary mathematics teaching 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 be expected to 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 currently at work in our country (and elsewhere in some nations that ostensibly are democratic). It makes a great deal of sense that those who fear that the poor will become better equipped to struggle against the gross imbalances that are increasing daily between haves and have-nots (particularly in the United States), should the latter become more literate and numerate, would oppose precisely the kinds of educational practices that inherently promote independent thought, meta-cognition, the challenging of assumptions, the questioning of authority, and self-reliance for determining 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, (in opposition to passive acceptance of whatever explanation the teacher or book might offer, particularly when it is quite possible that either source might be in error). So-called traditional education as currently construed is very much about social control, with 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 free 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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