In article <[EMAIL PROTECTED]>, Thom <[EMAIL PROTECTED]> wrote: >Herman Rubin wrote: >> There are many which can be done with one side, and MRI >> studies show little on the other. These are "thinking" >> tasks, not those involving vision or bodily motion.
>That's odd. Most "thinking" tasks involve both hemispheres - and most >activity is cortical. There's a reason why there are masses of >connections between the hemispheres. >> >I'm not quite sure what you mean, but there is a lot of research on >> >insight and intuitive problems solving and much of suggests that the >> >division between sudden and incremental solutions is rather fuzzy. >> It is rather difficult to check this; I do know of a >> study by Suppes and others around 1960 on mathematical >> concept formation in children. This involved teaching >> simple concepts, and using multiple choice tests, on >> children aged 5 to 7. The results clearly show that >> there is only a small amount of learning before the >> concept is completely learned (no further errors); there >> is no gradual decrease in errors. >> BTW, the study also checked for "transfer". The results >> again were clear; children taught one concept took longer >> to learn a related one than those learning that as the >> initial concept, and the interference was greatest in >> going from more special to more general. This agrees >> with my beliefs, and suggest that we are using the worst >> order in teaching. >> We can teach concepts and formalism directly, and then >> apply it. The practice of "working up" to a concept is >> both time wasting and requires UNlearning, most difficult. >That doesn't accord with my experience. It's fairly easy to teach a >superficial understanding on many concepts, but takes time, experience >and effort to get a deeper understanding. Of course it may depend on >what he concepts are. At least one major philosopher thinks that some >concepts are innate. If that were true I could imagine that some >concepts could be educated (in the literal sense of drawn out) fairly simply. There is no such thing as a "superficial understanding"; concepts are essentially understood or not. Lest one give the case of the integers, there are at least two, and maybe more, concepts involved, some of which may be contained in others. So-called "depth" is really getting practice in using the concept, not in developing it. The mistake is in even trying to gradually develop a concept. There seems to be a small amount of it "catching on", but this is not development. Remember that mathematical concepts are abstract from the beginning, and "abstract" does NOT mean an abstraction from more "concrete" situations. The use of a more-or-less phonetic alphabet is abstract, but the previous ideas of representing a language are of no help in understanding the use of it. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
