The political implications of pedagogy

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.

I got the same impression from the Keith Devlin book that I reviewed a few weeks ago.

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.

and later

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.


3 thoughts on “The political implications of pedagogy

  1. Thanks for the compliments. I’m glad you found the piece useful and provocative. Just one small correction: the guy I quote at length is Fred Goodman, not Goldman. He was my mentor at U of Michigan School of Education. Still a vital guy, though now an emeritus professor living in southern California. He still gets out here to Ann Arbor with regularity. The other fellows whose work informed my post are Layman E. Allen, still a law professor at U of M, and Sheldon Wolin, whom I treat in detail in an earlier blog post.

    I will have to look at the physics sources you mention. The idea of uncertainty as used in quantum physics may not really have a correlation to macro-phenomena, but philosophically I’ve long been suspicious of absolutism, a mindset that seems to dominate anti-progressive reformers, especially in mathematics education. As Nietzsche said before quantum uncertainty was around, “There are no truths, only interpretations.”


  2. I’ve fixed the error. I used Goodman the first time and Goldman the second. I suspect my mind got muddled between Goodman and Goldberg. Sorry.

    I’m not sure if I meant uncertainty in the sense used in physics or just how that sort of epistemological uncertainty is evident in the physics and mathematics reading I’d been doing. I’m a sociologist, who used to live in a (maybe even “the”) cultural studies department. So I am fascinated by the resonances between these discussions and some of the post-modern or post-structuralist debates in the social sciences and humanities.


  3. (For some reason I have only just had your last 10 posts come through on my Newsgator aggregator. thought you’d been quiet).

    I was having an argument with someone at dinner the other night on (I think) a related subject; he maintained that we would one day know everything there is to know about the human body and other scientific endeavours.
    I disagree so much with this – I think we are looking at such things in one framework now (well, no, in several, but the scientific community are largely using one framing) and are managing to find out more from that point of view. However, it seems to me that the more we find out about a thing, the more we see the limitations of what we know, and the uncertainties about whether we are asking the ‘right’ questions, and seeking answers in the best ways.
    My Dad is a physicist, and I think this is something he always assumed about science – that what we discover depends on our questions, our views, who we are etc.

    Enjoyed this post, thanks.


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