Monday, March 14, 2011

Prometheus and Education

Via Sanjoy Mahojan's excellent TED(ish) talk, here is a good quote:
The goal [of teaching] should be, not to implant in the student's mind every fact that the teacher knows now; but rather to implant a way of thinking that will enable the student, in the future, to learn in one year what the teacher learned in two years. Only in that way can we continue to advance from one generation to the next.
-Edwin T Jaynes
Yet this is a goal that's completely absent from any education reform movement of any flavor. Generally, the reformers try to change some aspect of schools or teachers in order to improve proficiency levels variously measured, ie smaller class sizes or merit pay.

What the quote illustrates is a broader point about education: that the process by which we teach must become efficient in time as we gain knowledge, or else our ability to advance the frontier of education necessarily slows down. Otherwise, people will take so long to advance to the frontier of knowledge that they have less time for active discovery, resulting in a Great Stagnation in research.

These teaching efficiencies have somehow happened anyway, at least in the math/science areas, without us being too aware of it. Calculus is now routinely taught in High Schools, while it was once at the frontier of knowledge. I'm not sure what advances in math education have allowed that to happen, but certainly students are being exposed to "deeper" knowledge at younger and younger ages.

I think this points to the importance of figuring out how to develop meta-cognitive tools that allow people to learn more in less time. ie, improvements in teaching pedagogy that really focus on reducing the actual time involved to learn a skill. I think this particular goal -- which aims for a steady reduction in the age at which students master given skills -- isn't really on the radar for any particular group, but it should be.

There are a couple of other creative ways to get at this idea. We can try more tracking-based systems, so children have more time to focus on learning in a particular direction. We can extend the hours that children spent learning, perhaps by using video games. Alternatively, we should be actively pruning the set of things taught in school as various forms of knowledge become less useful. Geometry and trigonometry seem to be widely taught, yet this is due largely to the importance of those tools to practical engineering applications in the 19th century, as well as reflecting the legacy of a particular mathematical tradition dating back to Euclid and beyond. Seems to me they ought be pruned to make way for mathematical tools of greater practical importance today, like statistics or street fighting math. In general, we should focus away from empirical facts (which are growing like kudzu) towards general reasoning; and in particular innovations that allow for rapid growth in the rate of general reasoning skills.

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