> So we need to be able to figure out both what students need to know and > what students don't need to know.
This reminded me of an article that I read in Mathematics Education: "the notion of cognitive root (Tall,1989) as a cognitive unit which is (potentially) meaningful to the student at the time, yet contain the seeds of cognitive expansion to formal definitions and later theoretical development." Generalising this idea outside of mathematics education, the idea is that we should be able to identify certain "concepts" that are understandable to students at whatever stage they've reached the time, but that can also be built upon. In other words, once they've learnt the cognitive roots, they shouldn't have to "unlearn" them at any point in order to learn further concepts that depend on them. I admit this doesn't fix the problem of "What will they need to know, but people don't necessarily need to know today?", but might offer a framework for thinking about what students need to know. Rebecca REFS BELOW: ----------- David Tall (2000) Biological brain, mathematical mind & computational computers (how the computer can support mathematical thinking and learning) Plenary presentation for ATCM conference, Chang Mai, Thailand, December 2000. Tall, D. O. (1989). Concept Images, Generic Organizers, Computers & Curriculum Change, For the Learning of Mathematics, 9,3, 37-42. ---------------------------------------------------------------------- PPIG Discuss List ([EMAIL PROTECTED]) Discuss admin: http://limitlessmail.net/mailman/listinfo/discuss Announce admin: http://limitlessmail.net/mailman/listinfo/announce PPIG Discuss archive: http://www.mail-archive.com/discuss%40ppig.org/
