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cutJohn doesn't really argue against my advocacy of "magic X",
because I am not advocating sticking symbols into equations.
Actually I was thinking of the texts which say "X marks the spot" and then
proceed to use X almost
Often the student needs to generate in
intermediate step such as a graph. Then there is the necessity of using
metacognition in the process.
One of the few texts that actually has students translate between all
representations is Minds on Physics from the U.Mass Amherst research group.
It actually has students write equations and also solve problems using
calculus ideas (area & slope) without the calculus formalism. Much of the
text looks simple, but some of it is challenging to college students.
One of the activities out of MOP that I find interesting, but I am not sure
if it worked well in my hands, was translating graphs to physical
situations. Students were given all kinds of crazy graphs and then were
required to us simple objects to reproduce the motion.
My objection to most math teaching is that it concentrates almost
exclusively on equations. While graphing calculators can be helpful, having
the students graph and measure on paper or with real objects is just as
vital.
John M. Clement
Houston, TX