Forbidden teaching tips

Banned from the classroom!

Like most teachers, I have my own collection of favorite mnemonic devices, tricks that I share with my students who are having difficulty remembering key facts. Seldom do I use the product rule to differentiate a function without muttering, “The first times the derivative of the second plus the second times the derivative of the first.” I learned it thirty-eight years ago and it really stuck.

I also know some mnemonics that don't do much for me, though I may well trot them out in case they do the trick for some of my students. I remember my first encounter with what my trigonometry teacher called “that famous Indian princess, Sohcahtoa.” He wrote it on the board, all in uppercase letters, with hyphens: SOH-CAH-TOA. Then he explained it was how he remembered the three most important trig functions: “The sine is the opposite divided by the hypotenuse, the cosine is the adjacent divided by the hypotenuse, and the tangent is the opposite divided by the adjacent.” The story of this famous example of Native American royalty left me cold, since I never had trouble with the right-triangle definitions of the trigonometric functions. Some of my students certainly like it, though, and trot it out whenever they are momentarily perplexed.

That ain't right

It was one of my students who helpfully explained to me a memory device he used to recall the names of the three sides of a right triangle. Unlike most triangles, a right triangle has specific names for its sides, labeling the long side as the hypotenuse and the two shorter sides (which always include the right angle) as legs. My student posed his reminder in the form of an amusing riddle. Amusing to him, anyway:

Q: Why do mathematicians love right triangles so much?

A: I don't know. Why do mathematicians love right triangles so much?

Q: Because their legs are spread ninety degrees!

My student paused for laughter at the punchline, which his classmates dutifully and amply delivered. (Yes, he had delivered his riddle in the middle of class.) The only sound that came out of me was a kind of choking sound.

I have not shared the student's memory device with any other classes, despite its wonderful memorability. I also have trouble since then telling my students that right triangles are easy.

Lying down on the job

Professor Jane Doe came bustling into the math department's faculty room after a hectic session of introductory algebra. Jane had a story to tell her colleagues.

She had been in the unit on linear equations and their graphs. Jane had cheerfully explained to her students the difference between vertical lines and horizontal lines, the former having undefined slope while the latter have zero slope. Gesturing vigorously, as she was wont to do, Professor Doe had pointed out that horizontal lines were named after the horizon, so that was an easy way to remember that horizontal lines are flat like the horizon, while vertical lines go up and down.

At the end of the period, a student approached Professor Doe, eager to share her own way of remembering the difference between horizontal and vertical:

“Mrs. Doe, I know a good way to remember which way horizontal lines go. Just remember ‘whore’! Whores do their work horizontal. See?”

Math instructors spluttered their coffee at Jane Doe's story, laughing and choking. Jane was clearly still nonplussed by the student's helpful tip. In the awkward silence that followed, one colleague ventured a comment: “Whores don't do all their work horizontal.”

The faculty room quickly emptied out.