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One solution is to provide the "tricks" but, at the same time, teach
them to understand the basic idea of where the tricks come from and why.
I do not think this works for many students, as they will continue to
ignore anything other than the "tricks". A lot of students are really
good at "faking it".
So, I guess I am asking whether a better solution would be to simply
remove the "tricks" from the student's arsenal. Yes, teach them how to
solve problems without the tricks. But don't provide students with
anything that could be potentially used as "tricks."
I'm reminded of a tale a friend of mine told me. After graduating from
college and ROTC he chose to go to the Army electronics school. As a
pretest he was asked what are the three most important laws of
electronics. Well he thought about that a while and chose j=sigma* rho,
and Kirchoffs laws. As it happened what they expected was
V=IR, I = V/R and R = V/I
scary
From our point of view as teachers, it is easy to come up withassignments that are complicated enough to defeat the Rain Man