How Not to Teach Slope

When I was fired six years ago by University College of the North, the College President gave three examples of improper teaching which were basis for my dismissal: the smokestack, the water heater, and "the slope example". I've talked about the first two cases already, so today we're going to pick up the story at the point where I deal with Exhibit C.

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By now it should be clear that I offended my fellow teachers by taking math outside the traditional classroom. These are the incidents which stuck in their minds as being offensive long after I was gone. Which brings us at last to Exhibit C, the one Ms Henning refers to as “the slope example”. Just what was this?

My first inkling that “slope” was an issue came during an absurd conversation late in January with my supervisor, who worked out of The Pas, five hours away. On one of his infrequent visits, he made a vague reference to problems with the way I taught slope. When I tried to ask him what kind of problems he was talking about, he became visibly flustered and said “slope is just an example”. Then he abruptly announced that he had no more time to talk because there was a taxi waiting to pick him up for his return trip to The Pas, and he rushed down the stairs and out the door! My written follow-ups were not answered, and that was the last I heard about slope.

I’m quite sure I know now what this was all about. Yes, I do teach slope differently. If a roof slope is 5:12, I draw a little triangle and label the sides. Then I draw another triangle to represent the rafter. The horizontal length is given: say, its fourteen feet. The height x is the unknown. Then, pointing at the triangles, I recite:  “Five is to x as twelve is to fourteen”; and as I say the words, I write the formula equating the two fractions. That’s how I teach it, and the reason I teach it that way is because for as long as I can remember, that’s how I’ve done it myself. And the problem is that my method is quite different from the way everyone else teaches it.