The real problem isn’t math, it’s epistemology. What we want from our students is that they understand how they know what they know. In the sciences, that often distills down into some properly applied mathematics and that common injunction on exams to “show your work.” It’s what we do in those peer-reviewed papers, which are all step-by-step explanations of how we got a particular answer. I suspect that one common thread among academics in all disciplines is that what we really like in a good paper is the logic and the story and the clever details that lead up to the conclusion, that what counts is the process.
The real problem is that so many people want the shortcut to the “right” answer… It’s Bronowski’s conflict between knowledge and certainty: most people prefer certainty, especially when knowledge might give them an answer they don’t like. And they especially favor certainty when it requires nothing more than learning a single datum, rather than the work it takes to do a calculation or derivation or document a chain of evidence. …
Our students aren’t buying a finished product, they’re getting a toolbox (with math at the heart of it) and instructions in how to use it. When they don’t realize that central fact, that’s when mutual disappointment occurs.
I think the parallels with teaching history (or other humanities disciplines) are clear. Yes, perhaps there are more ‘right’ and ‘wrong’ answers in (some branches of) science than in humanities disciplines, with significant implications for how practitioners view their craft, how confident they tend to be about their conclusions. (But how many people in the world have the comparative knowledge to judge that?) Science students are (perhaps) that much more likely to come to a question knowing that a correct answer to it does exist, that a score of 100% is possible. But it isn’t just about putting down that correct answer, even then. The process is vitally important too: show us your workings, how you got to the answer, show that you understood why and how. PZ himself points out parallels with history teaching: “historians have students who want history to be just the memorization of events that actually happened, rather than a difficult exercise in thinking and learning and evaluating.”
There’s one other difference, to my mind. The toolbox metaphor is fantastic – but I’m not sure that a historian’s toolbox would ever have a single core (ie, maths). Maybe the key skills of source criticism do represent that core, but I can’t help thinking that the historian’s toolbox is going to be a lot more ramshackle and thrown-together and idiosyncratic than that of a scientist. Thoughts, anyone?
PS: a question for linguists. Why do Americans do ‘math’ and the British do ‘maths’?