Willa has sent me off to read more interesting things. In addition to the points she drew out of this post at Rational Mathematics Education, I wanted to highlight what seems to me a very sound argument for the negative political consequences of the dominant mode of mathematics education.
The piece starts with a long, and very interesting, quote from Fred Goodman, in which he elaborates on the importance of games (as distinct from puzzles) in mathematics education. It is from this that Willa quoted and pondered. I note particularly his statement:
As the world moves closer and closer to a world where Gods collide and their followers depend with greater and greater certainty on the correctness of their God’s solution, we need to look more closely at the relations that might exist between games, Gods and grades. If learning is conceived primarily as a matter of finding the one correct answer according to the teacher who already knows the answer, and students’ sense of worth is tied to their ability to discover, understand and accept that correct answer, we may be encouraging, even in our secular schools, a tendency towards sectarian thinking.
As I have been reading about mathematics and physics, I am struck by the sense of uncertainty, of working towards better knowledge but of never having the “right” answer. Indeed in First You Build a Cloud, there is a whole chapter on Right and Wrong, which explains the ways that physicists see these questions. And they are very different from dogmatic approaches. She quotes physicist David Bohm:
The notion of absolute truth is shown to be in poor correspondence with the actual development of science. … Scientific truths are better regarded as relationships holding in some limited domain.
Goldenberg, the author of Rational Mathematics Education, goes on the connect Goldman’s long discussion to the broader issue of democracy:
The mentality that has been used to teach mathematics to the masses in this country (and in many others) has for far too long been grounded in authoritarianism. It cannot be a coincidence that progressive-minded reformers continue to call for approaches to classroom teaching that are more student-centered and which stress communication of mathematical ideas, offering sound reasoning for mathematical answers and procedures, while anti-reformers decry this as “time-wasting,” “fuzzy,” and somehow too “touchy-feely” to matter.
my concern here is for the way that subjects are taught and what the political lessons are that aren’t explicitly stated or acknowledged. And those lessons are fundamentally anti- and undemocratic. The focus upon single right answers that are arrived at by (generally) one approved method speaks volumes towards the underlying values of the teacher, the school, the district, right on up through the state and federal governments. The job of students becomes not learning and thinking, but anticipating what teachers expect exactly as they expect it: no less, and generally no more. And therein lie a host of tragedies, even were there not the anti-democratic issues to consider.
I cannot do justice to the argument with excerpts. The whole piece, basically a long quote from Goodman followed by further discussion by Goldberg, is excellent and raises many important points. As many homeschoolers already know, the idea that learning comes in neatly divided boxes labeled “mathematics”, “civics”, “language”, etc is a fiction. What this article nicely points out is that it is a dangerous fiction.
In the frontispiece of First You Build A Cloud, I find this quote:
Newton himself, as well as those … who attacked him … would have all alike been amazed at the more recent contention that natural science has nothing to do with “values,” that it can and should itself remain “value-free,” and that those seeking a direction for human life have nothing to learn from our best knowledge of the nature of things. Even a little science … is a thing of infinite promise for human values. (John Herman Randall, Jr., Newton’s Philosophy of Nature)
Whatever our values, we need to be aware of how the methods we use to teach are promoting or undermining them.