Herman Rubin wrote:
HR wrote:
>>>I doubt that the psychologists can understand abstract
>>>reasoning, especially that it is not incremental. The
>>>place where it is most clear is in mathematical concepts,
>>>and few outside of abstract mathematicians even see these,
>>>which can be understood without too much difficulty by
>>>children, but apparently not by those in "education".
>
>
TB replied:
>>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.
>
>
HR:
> 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.
Is this the paper you're referring to?
P. Suppes & R. Ginsberg. (1962) Experimental studies of
mathematical concept formation in young children. Science
Education, 46, 230-240.
I found the reference on this website for a Patrick Suppes
(under Papers on Psychology):
http://www.stanford.edu/~psuppes/
It looks like an interesting paper. But my local library's
subscription to Science Education only goes back as far as
January 1996.
Cheers,
Bruce
--
Bruce Weaver
[EMAIL PROTECTED]
www.angelfire.com/wv/bwhomedir/
.
.
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