Doomed ideas (III)

A different sort of lesson for this digital age.

We mentioned, some time ago, that our digital environment has resulted in a decay of some skills that used to be ubiquitous: reading the dial of a clock, for instance, or picking out a precise value from a graph.  Our tutoring consultant in particular has noticed this sort of difficulty in many of his students.  To remedy the situation, he has proposed a workshop on analog methods.

It would start out with a big piece of paper, a compass rose and sets of parallel rulers and dividers.  The students would be given a series of problems involving addition and subtraction of vectors, to be worked out graphically.  And (this is important) they would be graded on the accuracy of their answers.  Even in current classes students are required to do some plotting of vectors; however, the results are crude and inaccurate.  We want to get across the importance of being careful and using the proper technique.  Along the way we hope they might absorb some lessons about uncertainties (a short vector, for instance, has a large uncertainty in direction).

An advanced lesson might involve a chart exercise, where the ship’s position is determined by bearings and distances, and a course must be determined to get where you want to go.  Alternatively, the student might be given data points determining a curve (not a straight line) and required to fill in the rest of the plot using French Curves or similar devices.  Ideally, the curve would not be something that could be calculated numerically from the data points given.  Again, the test would be how accurately the required course or the interpolated points could be determined.

Easier in practice would be an introduction to nomograms.  Closest to our hearts (and maybe easiest to carry out) would be instruction in the slide rule, an ingenious device that has in the past aroused the curiosity of some of our tutor’s students.  Our astronomer looks longingly at a celestial astrolabes, but their complexity puts them in the graduate student class.

Our tutor sometimes covers electrical circuits for the later stages of Physics classes.  He thinks just employing a multimeter with a needle (D’Arsonval movement) instead of a digital display would be very instructive.  Constructing a full-fledged electronic analog computer, however, would again probably be only for graduate students, though a RLC circuit with adjustable elements could be instructive.

As with our previous ideas, it’s almost certain that the analog workshop will never be carried out.  Our tutor can imagine scathing comments from parents about wasting time on material that won’t help get the kids into college.  As a practical matter, the time would arguably be better spent on teaching how to get more out of one’s graphing calculator.  A good feeling for what uncertainty actually is, well, it’s hard to quantify in terms of SAT scores, and it’s difficult to assign a concrete value to accurate compass-and-divider work.

But we’d really like all our students to be able to read a graph.

[Our blog is scheduled for a vacation over the next two weeks.  We should be back after mid-September.]