In elementary school, I used to get excited right around when we reached p.100 of our math books, because that’s when we would really start doing stuff. Those triple digits meant that lessons would no longer be about practicing addition and subtraction, or rehashing things we were supposed to have learned the year before. Maybe that first month or so of the school year taught me patience, otherwise, I would have gone mad. Unfortunately, as a teacher, I’d fallen into the same trap of needing to do that all-important review as the first unit of the school year. What better way to kill the potential energy built up over the summer and bring whatever momentum had built up to a grinding halt? In retrospect, it seems that “review” seems to make students who already got it last year either check out or get lulled into a sense of complacency. For students who didn’t “get it” last year, instead of starting with a clean slate, it instead drives home the message that this year will be more of the same.
This is not to say that review isn’t important or necessary, but what makes the difference is the way that it is done. This year, a colleague and I rearranged the sequence of topics in the PreCalculus courses that we taught (different schools in the same district). Instead of first semester being largely a rehash of Algebra 2, we started with Trigonometry first. This is the fifth year that I’ve been fortunate enough to teach PreCalculus, and I’m kicking myself for not coming to this realization sooner. Even though we’re starting with a topic that’s new for most students, we’re still able to secretly review solving equations, working with exponents, and working with fractions, all in the context of doing trig. Instead of two separate groups (those who got it last year and those who didn’t), everyone was learning something new, on equal footing, and with a clean slate. I don’t think that there’s anything intrinsically different about the makeup of students this year, but with the new approach, we’ve been able to keep the momentum going from the beginning of the school year when students come back from summer, eager to learn something new. We’ve been able to cover more material, go into more depth, and maintain a healthy pace, especially compared to previous years.
I’m slated to teach Algebra 1 next year and am hoping that this idea is something the team will be willing to run with, or at least consider.