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When I saw Murray teaching them how to read
the verniers, it occured to me that it would be a nice exercise to go out into
the parking lot and take sightings of the Inco smokestack, about a mile
away...but just to be safe, I asked Murray if trigonometry was on the
Apprenticeship curriculum, to which he answered: "Level
Three". So I spent one class period explaining the math involved in
triangulation (that would have been the "complex trigonometry", I
presume), and the next day we divided the students into two teams and they each
went out to take their measurements. Then we came back to class and I helped
them work out the numbers. I thought it was a good exercise, not only for the
math but also for the teamwork, problem solving, and use of the equipment.
(Except it turns out they couldn't read the verniers. But then, I don’t suppose
anyone is going around saying that Murray
should have been fired on that account.)

Why was the smokestack controversial? I’m
quite certain it’s because I took math outside the classroom. That was
certainly the perspective of Level 2 student Sam Bird, who vociferously
objected to the exercise on the grounds that “we shouldn’t have to freeze our
asses off just cause you wanna know how high the smokestack is”. (He was dead
serious.) The trigonometry issue is a minor sideshow...surely I wasn’t fired
because I gave a preview of some Level 3 material during a Level 2 session? To
be sure, trigonometry turns out to be not much emphasized in the Provincial
Exam, but as a rookie instructor I would have had no way of knowing that at the
time. And at any rate when I did the smokestack calculation in class, I used
some tricks for small-angles, making use of only the basic formula for the
circumference of a circle (which is certainly on the curriculum), avoiding
sines and cosines altogether. Only when specifically asked if you could do this
with “trig” did I show one student how to use his calculator to obtain the
tangent of the angle.

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