Today’s New York Times has a fine article by Manil Suri about math education and the development of reasoning skills. Its concluding point is that, while the general contribution of the first to the second is weaker than you might think, math instruction can be improved by bringing the math-reasoning tests themselves into the classroom. I’m pretty confident that Suri is right, since I’ve seen positive results from doing something similar in economics and related areas.
When preparing to introduce a new topic in econ, for instance, I’ll often start by taking stock of what lots of people without an economics background think they know about it. This might mean looking at surveys or some excerpts from news or other websites. It often involves drawing out this information from the class itself. For instance, I’ll divide students up into groups of five or so in which they can say to each other what they believe, or even suspect, about the topic, and then have the groups report in a general way what these views were. (I try to use methods that don’t identify potentially mistaken concepts with specific people, to avoid any sense I’m trying to belittle anyone.) Then we will go on to learn about the question, keeping in mind the misconceptions we’ve found and trying to locate the points at which “pop economics” veers off from the real stuff.*
There are many reasons for doing this. One is frankly political: a lot of the political babble in this country is framed by erroneous economic thinking, such as nearly all the fretting over “the national debt”. (Every time I bring this up in the context of the income accounting identities I see expanding eyeballs all across the classroom.) Another is pedagogical: if you don’t put effort into deconstructing pre-existing beliefs as well as developing new knowledge, what you will see on papers and exams is a weird mishmash of the two. It took me too many years to figure this out. But a third is the insight Suri also came to, that using an external point of reference to step outside oneself and observe one’s own learning process provides a powerful boost to learning of all sorts. The misunderstandings of pop econ provide a baseline from which students can measure their progress; they illuminate what they are learning and how.
The name for this is meta-learning (or deutero-learning in cybernetic-speak). It is foregrounded by activities that help students get outside the technique or concept immediately in front of them and see their learning of it as the object of attention. Like all forms of learning, it is best approached inductively and in context: rather than give lectures on meta-learning, provide exercises that call attention to it in situ. I incorporated material to support meta-learning in my textbooks, more in the second (macro) than the first (micro), since I was learning (and meta-learning!) as I went along.
I’ve come to think that explicit incorporation of meta-learning may be the single most important innovation to transform teaching. For those of you who have this a day (or night) job, give it a try.
*Just to be clear, “real” economics is not mean “sanctified by the mainstream”, just conceptual approaches that can be supported by careful reasoning and empirical data. Some mainstream econ is rather closer to the pop variety than to legitimate analysis.
One of the first things one learns in physics is that an object in motion stays in motion unless there is an outside force. The usual counter intuitive example is to ask where an object will fall when dropped by a moving person or out of a car window. Most people think it will fall straight down from where it was released. The physics lesson is that it continues moving forward as it falls. You have to throw out a lot of prior knowledge to get through Newton’s three laws of motion.
That is logical.
thanks for this. it’s a useful way to think about teaching. i hope it catches on.
but my own experience suggests it may not go as far as you hope. you end up teaching a new (to them) orthodoxy and they will go on their way exhibiting contempt for those who don’t share not only their orthodoxy but their superior methodology.
i do wonder though if the trouble i have “teaching” against the Social Security Big Lie… which at best ends up with “students” adopting a mishmash of what i was trying to teach with what they have always believed (the Big LIe) … if i could learn something from your method.
Ah, if only I had them in a classroom and was giving them a grade upon which their future depended.
don’t misunderstand me. i am a bit jaded about “education”, but you sound like you may actually be doing some good.
unfortunately i have seen freshman physics books written by people who don’t understand Newton’s third law. funny thing is it actually doesn’t hurt their ultimate ability to practice physics as if they actually knew what they were doing.