Slide rule versus the Internet in education

September 22, 2015

Parents and teachers support increasing digital technology in the classroom, according to a 2012 survey by the Leading Education by Advancing Digital Commission, a large non-profit with ties to education, investment groups, and the federal government.

The survey found that parents and teachers believe “the world has changed” and schools require technology to catch up. “Large majorities of teachers and parents say that it is better to invest in Web-connected devices for each student than in new science textbooks.”

While the survey questions assume noble goals—personalized instruction based on rapid and detailed feedback, as well as equity for disabled or economically deprived students—there is a piece of technology that doesn’t plug in or connect to the Internet, that would do more than computers to cultivate mathematical understanding and reflexive technical skill in students.

Unfortunately, Keuffel and Esser Corporation presented the last American-manufactured slide rule to the Smithsonian Institution 39 years ago.

William Oughtred and others developed the slide rule in the 17th century based on John Napier’s discovery of logarithms. A slide rule multiplies by addition.

Take an ordinary ruler. To add 3+3, you could find 3, then count 3 more inches to get 6. You could do the same thing backwards to subtract. You could multiply by adding 3 again to get 9.

But the slide rule uses a trick, based on Napier’s work, to do the same thing more quickly. A slide rule has three strips of wood. Two of them are clamped together, and the third slides between them. It works because none of the spaces are the same size.

On most of the scales, the distance between 1 and 2 is longer than between 2 and 3, and that’s longer than 3 to 4, and so on up to 10. The little spaces in between—say 1.5 to 1.6—also shrink as the numbers get bigger.

You can multiply numbers by adding their exponents—22x23, that is 4x8=22+3=25=32. Napier reasoned that every number is a power of ten—one is 100, 10 is 101, etc. He composed a table that included every number to three places in between—3.17=100.5010593.

If you want to multiply 4x8, you’re adding 100.6020600+100.9030900 (note that 0.9030900 is not twice 0.0602066), and your slide rule is made so that 4 and 8 are in the same places as their exponents. Put the 1 on the sliding scale over 4 on the fixed scale, move the hairline to 8 on the sliding scale to get 32 on the fixed scale.

Slide rules can divide as well as multiply. They can find square and cube roots, solve ratio problems, and work easily with pi. They are much faster than pencil-and-paper calculations, and they embody important parts of math history and numbers theory.

A student who becomes adept at using a slide rule will also gradually become skilled at keeping track of orders of magnitude, setting up problems, and estimation.

A 10-inch long gadget can only accommodate the numbers between 1 and 10, so it’s necessary with larger and smaller numbers to use the same scales, judging the appropriate place for decimal points.

It also requires the student to decide in advance which scales to use. The marks etched into the scales are useful to only two or three places, so the student must estimate what number between the marks the hairline rests on.

According to media theorist Marshall McLuhan:

Media, by altering the environment, evoke in us unique ratios of sense perceptions. The extension of any one sense alters the way we think and act—the way we perceive the world...You must talk to the media, not the programmer. To talk to the programmer is like complaining to the hot dog vendor at a ballpark about how badly your favorite team is playing.

Let’s choose classroom tech wisely, and talk to the media about the kind of world we want.


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