More on Mathphobia
I’ve been reading The Design of Everyday Things, which I recommend as a useful and interesting way of thinking about all sorts of minor frustrations in daily life. It’s also applicable to teaching – I’ve definitely noticed many student problems that have more to do with misunderstanding the nature and purpose of the assignment, than with misunderstanding the concepts involved. I was blown away when I realized that not everyone automatically interprets an expression like “Nc(M)” to mean a quantity Nc that is a function of a variable M, but apparently a dedicated mathphobe in the California public school system can easily escape such basic mathematical acculturation. If we don’t provide some other cue to them that we expect to see several different values of Nc, they will get confused and make mistakes.
Anyway, here’s what Donald Norman has to say about math education:
With badly designed objects – constructed so as to lead to misunderstanding – faulty mental models, and poor feedback, no wonder people feel guilty when they have trouble using objects, especially when the perceive (even if incorrectly) that nobody else is having the same problems. Or consider the normal mathematics curriculum, which continues relentlessly on its way, each new lesson assuming full knowledge and understanding of all that has passed before. Even though each point may be simple, once you fall behind it is hard to catch up. The result: mathematics phobia. Not because the material is difficult, but because it is taught so that difficulty in one stage hinders further progress. The problem is that once failure starts, it soon generalizes by self-blame to all of mathematics. Similar processes are at work with technology. The vicious cycle starts: if you fail at something, you think it is your fault. Therefore you think you can’t do that task. As a result, next time you have to do the task, you believe you can’t so you don’t even try. The result is that you can’t, just as you thought. You’re trapped in a self-fulfilling prophecy.
Mathphobes and math teachers in the audience, does this describe your experience? I find it hard to imagine a math curriculum that doesn’t build on previous lessons, but I can certainly imagine a setup that allows more time and flexibility for teachers to address sticking points before they turn into nightmares.
A couple of old-ish (in blog time, anyway), related discussions from the geoblogosphere, one at Sismordia:
A similar debate is happening at the moment in the Geophysics circles at our lab. We are being asked to open up geophysics teaching to students from a variety of backgrounds, including a number who have little or no mathematical training. The question is how to follow these courses with a master’s or PhD program that necessarily involves a great deal of mathematical analysis?