In one year of high school, our beloved math teacher passed away from an out-of-the-blue heart attack. While we were understandably mournful, a substitute came in to cover his classes for the last couple of months. She apparently did well enough that they kept her on for the next year, when I had her for honors calculus. Suffice to say, she was NOT impressive, constantly sounding more confused than the students were, relying on the sample problems in the book and the teacher’s primer with no improvisation, etc. The running joke was that she was only learning the concepts a week before teaching us!
The crown jewel was working with “i”, the imaginary number that’s the square root of negative one. It’s a wonky concept in and of itself, but “the exponential powers of i” turned out to be the easiest lesson because they just went in a loop: i, -1, -i, 1, then start again. So while there were three different ways to figure out the answer, they should have all come out the same… SHOULD.
One problem was “i to the 40th power.” Every student in the class got the same correct answer, 1, except for ONE STUDENT who got -i. It turns out she was the only one who was using the “count out the steps a total number of times” method, because she couldn’t figure out the multiples (this was, again, a Junior honors calculus class.) I and two others help her out, and she did it 39 times instead of 40… She says she did it 40, despite having three other people help her. So she asks the teacher.
The teacher looks over the work. Looks it over again. WRITES IT ON THE BOARD… And having just copied the student’s work verbatim, not listening to the rest of us that you just needed to do the step ONE MORE TIME, comes to the conclusion that “when you do it with different methods, as you get into the higher exponents you get different results.”
Someone yelled out “That is literally not how math works!” She just said “it did this time.” This teacher left after the mid-terms, at which point we hadn’t even finished chapter 2 of an 8 chapter book, with the average grade in the class being a C+. Somehow, she’d gotten a job teaching ADVANCED PLACEMENT math in another school! At least the replacement who ended up becoming the permanent teacher was a joy: we not only finished the book almost a month before the school year ended, the average class grade was now up to a B+ and final exams averaged an A-, and that was WITH us spending about half that last month just doing reviews, and the other half watching movies!