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(reminder: all quotes here are fiddled, probably.)

mathmatica makes students miss the point?

Walk versus Wait: The Lazy Mathematician Wins

In this recreational mathematics note, we address a simple, yet instructive question:

Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the starting point. At each bus stop, Justin is faced with a choice: to walk or to wait. If he walks on, he can still catch a bus at the next bus stop--but if a bus passes him while he walks, he is almost assured a longer wait.

We model Justin's decision constraint and completely solve the model in a special case. The answer is intuitive: the optimal strategy is the laziest.

16 Puzzles for International Puzzle Day

Flipping Out over Technology in Education

In one of the two main examples cited in the study, the students waste time carefully and cleverly using Mathematica to solve a difficult integral that, it turns out, they didn’t need to solve in the first place because it cancels out. Why does it cancel out? Because if it didn’t, this wouldn’t be a homework problem; it would be way too hard to solve by hand.

A student who didn’t have Mathematica but did have rudimentary test-taking skills would have realized immediately that the problem couldn’t be that hard, and would have started looking for ways around the integral.

You can call that a higher level of thinking, and blame Mathematica for leading the students astray, but I think this misses the point. In any sort of real-world scientific problem, chances are you actually would need to solve the integral. Are we really serving our students well by shielding them from this reality and encouraging them to look for tricks and shortcuts they know must be there simply by virtue of the fact that they’re working on a homework problem and not a real-world problem?

Schools are not just about teaching practical skills, they are about our hope for the future. They must help our children think with depth and clarity, see the world with open eyes, and ultimately be our worthy successors in the great enterprise we call civilization.



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