A year or so ago, a decades-long friend and colleague reappeared. My friend also has a strong interest in maths ed, although she takes the “Let’s all be friends” approach. Readers of this blog know well that I’ve given up on that, but still my friend and I can argue amicably about this and that. In particular, she took some issue with my “all modern maths ed sucks” post. While conceding that most educational research is bad, she was unwilling to write off the discipline entirely and she suggested a few things for me to read. I gave them a semi-decent try, and my response was “meh”. While the stuff she suggested was mostly reasonable, or even good, I felt it was, at best, addressing third order issues. One article, however, has had me pondering a little, and I thought it may be worth sharing.
Andrea diSessa is a big shot in education research, particularly in science education and maths education. The particular article that my friend suggested is from the proceedings of a 1991 conference on the psychology of mathematics education, and is titled,
If We Want to Get Ahead, We Should Get Some Theories
DiSessa’s title is clear enough, and his abstract makes it clearer:
In education, or in the learning sciences generally, theory is in a poor state. We have not reached deep theoretical understanding of knowledge or of the learning process, and it is important that we recognize this. Even more importantly, our community does not seem particularly intent or armed to change the situation. This paper is aimed at raising the issue of intent, arguing for new dedication toward theory. It is also aimed at a modest contribution to our toolkit for a more theoretically attentive practice of education research.
Theory is not my thing, and I didn’t read DiSessa’s paper closely. But the paper is well written and it seems interesting enough for the genre. DiSessa, who has a PhD in physics, spends a fair amount of time discussing how theories in physics work, and whether and how the nature and the success of such theories might shed some light on the way theories of learning might work.
For me, one passage of DiSessa’s article stuck out as worth pondering (to the extent any of this is worth pondering). DiSessa frames his quest for theories of learning with explicit reference to his background in physics:
I take three things from my experiences with physics. Each of these provides a “place to look” and a “judgment to make” with respect to the state of theory in an empirical science.
It is the third of these things that struck me.
Respectable theory, when we get it, cleanly transcends common sense.
My last point of extrapolation from physics to our expectations for theory in education really follows from discussion of the above two points. Unless we can unambiguously point to how we have transcended – in generality, precision, clarity, and justifiability – the intuitive sense of mechanism we all build in daily life observing and thinking about psychological matters, we just won’t have adequately prepared theoretical ground. I’ll pick one focus for this exposition, but I think the point is much broader. Commonsense vocabulary just won’t do the job of providing the technical terms of a theory of learning. When we stop with “beliefs,” “knowledge,” “concepts,” and so on, even with a few phrases of elaboration, we are on extremely shaky ground.
To put an edge on this, physics theorizing has always involved ontological innovation. The “force” in Newton’s theory is a new entity that simply does not exist in common sense. Even mass took on a much refined interpretation to make sense in that theory. More evidently, quantum wave functions did not exist before quantum mechanics. My presumption is that we will not have adequate theoretical purchase on learning until concepts, facts, beliefs, skills, and all the rest of our common sense about knowledge and learning become reinterpreted within a fabric of more precise and less intuitively loaded terms. Please, do not mistake: I’m not appealing for obscure language, or for proliferation of new words. I’m appealing for the clarity that can come with ontological innovation.
This seems a very clear and useful phrasing of the challenge. Does any theory of learning, does maths ed theorising in any part or as a whole, transcend common sense? Does anyone even try? If the claim of current practitioners is that maths ed theorising gives back something larger than the ideas it employs, then what is it that it gives?
DiSessa wrote his paper thirty years ago and perhaps the current education guys, even perhaps DiSessa, believe that respectable theories of learning now exist. Perhaps the Brain Boys consider that they have it all under control. If anyone can suggest a theory of learning that answers DiSessa’s challenge, can suggest a theory of learning that gives back more than it takes, I’m willing to listen and to read.
But of course I am as sceptical as ever. From what I’ve seen learning theory is still, at best, truisms. More often, it is falsisms.