Programming for the Sake of Mental Skills

Tutor recommends learning programming

“Word problems” often appear to strike fear into the hearts of the students I tutor in physics and, to a lesser degree, mathematics. Long ago, when I was a student I noticed the same thing among my peers. It baffled me back then but puzzles me less today.

It has always seemed to me that word problems should be easier than ones that simply present an equation and say to solve it. Unlike a more abstract question that contains little more than symbols, a word problem provides a physical context that makes it possible to leverage real world experience and intuition. How could anyone not like that?

The answer is that word problems require students to get out of their comfort zones and do more thinking. More specifically, they require students to make a leap from the familiar to the abstract.

To start with, word problems require students to read exactly what the questions are saying. Normally every single word matters and has been chosen with care in order to avoid ambiguity. In physics energy means the capacity to do work. There’s nothing psychological about it. It has nothing to do with enthusiasm or how much sleep you got last night. “Work” means exerting force through a distance. It has nothing to do with potentially exhausting activities like reading books or writing essays. The scary part though seems to be that word problems require the mental feat of expressing a physical question in the abstract language of mathematics.

Unfortunately, there is no magic way to teach this transformation from words to mathematical symbols. Tedious theories of education aside, it still comes down to the way most skills have to be learned, by repetition and variation. That’s why math and physics students have to do so many problem sets. It’s very much like music students having to practice, practice, practice.

However, I have noticed something interesting. Many students take optional computer programming courses in school but those are very rarely the ones who come to me for help with math or physics. One reasonable interpretation is that being naturally good at those subjects is what makes them want to learn programming. The interpretation I prefer is that the skills developed when learning to program include those very skills required to produce a symbolic representation of a real world situation, as is demanded by math and physics word problems.

This Guardian article has some good ideas about helping kids get an early start with programming.

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