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On Wed, May 08, 2013 at 07:02:27PM -0500, John Clement wrote:
But if you make concepts the core, and then bring in methodssolving. I would
afterwards, the students can learn efficient problem
strongly disagree with the idea that thought is brought inafterwards.
That is the currently conventional approach to math and it is not
working well. Whitehead might have changed his mind if he saw the
research that we have now.
I imagined that he was referering to something like "chunking" [1].
After reading Mahajan and Hake on Benezet-Berman [2], I think
"algorithms" = abstract math (2x = 4, solve for x)
"concepts" = science (force * mass = acceration, where
"force" is .)
Although even for "abstract math", you need to have a
conceptual grasp of multiplication, equality, variables,
commutativity, .. I see students thrashing about hoping to
stumble on a solution, and this thrashing occurs because they
don't have a good grasp of *something*, but the thing they're
missing runs the gamut from 'multiplication' to 'moment of
inertia'. I doubt categorizing these misconceptions in a
hierarchy of concept importance is particularly useful, but I
don't have numbers to back that up.
Cheers,
Trevor
[1]:
http://www.csun.edu/science/ref/reasoning/how-students-learn/2.html
[2]: http://arxiv.org/abs/physics/0512202v1
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