In my quest to effectively include programming in my 9th grade honors physics class, I have been reflecting a lot on the nature of programming in comparison to the nature of traditional problem-solving both as 1) culminating activities in a typical unit of study and 2) as driving forces in defining learning objectives and the accompanying instruction to prepare students for such culminating activities.
Predictions vs. Simulations
Students learn relationships to make calculations to understand or predict conditions at desired instances. Or, students can learn relationships to create a program to make repeated calculations with small changes in time so that conditions are observable at any moment. For example, students can use an equation to predict the position of an accelerating object, given its acceleration, time, and starting position, or they can make a program to simulate an object accelerate at any rate, from any start position, for any amount of time.
The former can be demonstrated using a handful of measurements to make an impressively accurate prediction. The latter is demonstrated when the motion of an object on a screen is realistic to a practical degree (and corroborated with manual calculations).
Paper and pencil predictions are powerful in their simplicity and effectiveness. Programmed computer simulations are wonderful in the richness of possible applications. This contrast seems like it could be another version of the awesome function of a calculator vs. the ennobling practice of operating a slide rule. The difference here is that the act of making a program can add depth of understanding to rival (and/or compliment) the understanding of skilled problem-solving calculations, whereas using a calculator precludes one from the beneficial mental engagement requisite in using a slide rule.
(Here is a random chat room thread about the advisability of committing oneself to learning how to use a slide rule for the sake of reaping its benefits. The upshot is: don't bother. Despite their ingenuity, the practicality and power of calculators have [news flash] made slide rules obsolete. I wonder: could programming skill make traditional problem-solving obsolete?)
My analogy may be flimsy. But I do know that I have a dilemma when it comes to making room in my instruction for students to learn and apply programming in their learning of physics, which is ultimately assessed (currently) by paper-and-pencil problem-solving exercises. This leads me to consider assessment strategies before going too much further. I know students will not commit to learning stuff that does not show up on tests.
Any thoughts?
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*Full disclosure: I don't know how to use a slide rule. I missed out on them by about 5 years. I do know they are based on logarithms and I believe the mere use of a slide rule ingrains valuable math concepts. I have my father's lying around my house, somewhere.
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