The term is over, and I now know that I’ll be back for another term – though it’s still unclear as to what I’ll be teaching: either a whole lot of statistics, or a calculus/precalculus mix. So it’s time to reflect on what went right and what went wrong last term, so that I can work on improving for next semester, particularly if I teach precalc again.

- I gave weekly quizzes in both of my courses; the quizzes were fifteen minute deals, and the questions were taken directly from the homework. This worked very well for my discrete class, in which quiz marks were strongly correlated with test marks; but it did not work at all for my precalc class. I actually had some precalc students get full marks on their quizzes, and
*then*ask me to explain the questions: it turns out they had just memorized their notes and reproduced the solutions on the quiz – a method that did not prepare them for the tests in the least. The discrete class, though, was one in which hard work translated more directly into success, and so high quiz marks did not mislead my students (or me) about their abilities. - My students in all classes were weaker than I expected. This was more of an obstacle for the precalculus crew than for the discrete crew. So, if I end up teaching precalc again, I will spend the entire first week of classes reviewing grade 9, 10, and 11 math. Good topics to review include:
- Solving linear equations
- The bare basics of setting up word problems – though this is something I’ll have to emphasize later on anyway
- In general, expressing one quantity in terms of another
- Working with rational expressions, including plain old fractions
- Basic properties of exponents

- That said: if I teach precalculus again, I need to explicitly establish what students should know coming into my class. I should prepare a worksheet for this purpose, and tell students that they should be comfortable with every single question on it by the second week of class. I should not be afraid to say to some students who ask me questions in class, “That is a Grade 9 question. You have a lot of catching up to do, and you will not be successful in my class until you get to that level. You can see me during my office hours for help, but I am not going to deal with your question here, because it deals with subject matter that is part of the prerequisite for this course.” This would have saved a lot of time in my weak precalc class; it also would have served to clarify my expectations. For students who are still at a grade 9-10 level by the (relatively late) drop deadline, I should advise them to drop my class and sign up for it again when they have met the prerequisites.
- In general, I should invite students to my office more often. This includes students who hassle me in the ten minutes between classes, asking me questions that can’t legitimately be addressed in that amount of time. Last term I often just tried to give quick answers, which didn’t really address most of the issues.
- I need to be more clear about what does and does not constitute acceptable behaviour in my class. In particular, I should dismiss any student whose cell phone goes off in my class; I certainly warn them enough about that. I should not be afraid to tell wilfully obnoxious students to behave, and I should make clearer earlier in the term to some of my female students that even though it is generally considered socially acceptable for them to giggle about how much they hate math and how much they suck at it, I will not tolerate it in my classroom. (I did make this clear in the last few weeks of classes. They were surprised, but they listened.) I think that this failure on my part played a large role in the downfall of my bad precalculus section, which contained a few strong personalities who succeeded in setting a negative tone for the class.
- I should create worksheets. The text is so horrible that the problems, for the most part, don’t address what I think are the central concepts I want to emphasize. Although I complained about students whining about how the tests were so
*different*from the homework, their complaints were not entirely invalid – particularly as the text had this infuriating tendency to ruin a perfectly good question with instructions such as “and now graph it on your graphing calculator…” - I do, for the most part, defend my decision to give tests that differed somewhat from the homework. I should defend that decision in class, vocally, on a regular basis. Some of my students truly seemed to be under the impression that I had merely forgotten to teach some of the material on the tests – none of which required skills or methods that I hadn’t gone over at some point. I should reach out to those students, to try to show them exactly how the course material related to the test questions – and how to better learn the course material and better prepare for subsequent tests. I thinkI succeeded in this with some students, but (understandably, I’m sure) not with the ones who were indignant about their tests and demanded that I change them.
- I am happy with the way I taught how to set up word problems. I am happy with the way that I emphasized how to set up equations by reading the problem carefully and establishing what quantities we knew, what quantities we did not know, and how they were related. Next term, I’ll spend some more time on this and make that section of the course more interactive, because – truth be told – it’s a far more important skill than most of the other things I teach in that class, like factoring quadratics and graphing parabolas.
- Next term, every time a student asks, “Will (suchandsuch) be on the test?” I should put it on the test. That’ll learn ‘em.