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We have to be critically aware that our way of thinking is VERY alien
to the beginning students. When we think we are presenting principles
the students see equations to be memorized. When we think we are
presenting connections by showing proofs, the students think we are
telling them it is alright to use the equations. For proof of the
latter assertion see the results of Joe Redish's MPEX survey. When we
present simple clear physical principles the students hear
incomprehensible gobbledygook. They have been trained by years of the
lecture method to ignore the fact that they do not understand, so they
dutifully write down what they thought they heard in their notes. Alas,
this is usually not was intended by the lecturer. For evidence of the
latter assertion see the preface to Feynman's notes where he admits
that his carefully crafted brilliant lectures did nothing to improve
student understanding. I would also refer you to the work of the UMass
Amherst PER group or the Heller's, both of whom have methods that
promote concept based problem solving rather than equation hunting
problem solving.
John M. Clement
Houston, TX