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|As to problem solving we know quite well that students can be pretty good
|problem solvers while at the same time they lack the concepts. The really
|superb problem solvers have to use the concepts.
I've always wondered about the above statement (in its various guises). I suspect the validity of it hinges critically upon the "problems". Are you asking problems that allow for rote-algorithmic responses for success? If so, then I believe it. (These would be the traditional plug and chug variety; often substitute into a single appropriately chosen equation; then I believe it.
OTOH, if the problems require understanding the concepts to answer, than I don't believe it; and one can write this style of problem. For example, a problem requiring a derivation (not memorized from the text) (but eminently doable, if one understands the concepts and has a reasonable subset or the prerequisite math skills.). Often a 2-3 step (concept) equation hunting problem can serve the purpose as well or even derivations from the text; then I'm not sure my experience matches up with the above statement.
|So problem solving is not a
|good test. If you want to combine the two use the MBT. Actually students
|want to memorize procedures for problem solving and that is what happens in
|the conventional classes.
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