One place where students are called on to think beyond a simple relationship
is with the ideal gas law
PV = nRt
I don't have my sources available but I was reading recently how nearly all
students - including some graduate students in chemistry - faced with a
question like "what will happen if V is doubled?" will either ignore one of
the three variables, or apply them one step at a time in a sequential
reaoning process, usually imagining a two-step process over time.
What is going on is that they are trying to arrive at an answer
algorithmically, when the algorithms won't give them a meaningful answer.
What is needed is to have the students learn to habitually create models of
situations, and consider carefully what all the constraints are on their
models, before trying to crank out an answer.
Students can learn this habit but they won't as a rule come up with it
themselves. Students want the easy way and that ain't it! But once they
learn it they will find it is not just a more powerful way, it's also more
satisfying.
8-)
Chris Horton
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