Re: [Phys-L] kinematics objectives

["W. Trevor King" <wking@tremily.us>]

On Wed, May 08, 2013 at 07:02:27PM -0500, John Clement wrote:
> But if you make concepts the core, and then bring in methods
> afterwards, the students can learn efficient problem solving.  I
> would strongly disagree with the idea that thought is brought in
> afterwards.  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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