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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.