Pre Algebra is on my teaching list this year. The last time I taught it was five or six years ago, and I’ve changed quite a bit as a teacher since then, so I’m building everything again from scratch. (It feels appropriate to note that my philosophy of teaching/learning has shifted more significantly than my actual practice, at least in my other classes.)
For the past week or so we’ve been constructing, measuring, labeling, identifying, and discussing triangles (where the constructing has been mostly with non-digital tools). Given three sides, given three angles, given some combination, similarity, congruence, impossible triangles, etc. Our progress has been frustratingly slow, in large part because my routine of late has consisted of me going into class with an activity and some excitement only to discover that some key element of the activity is seriously flawed. I spend the next evening revising the activity (thereby rekindling my excitement) in order to try it again the next day. I imagine (hope?) our progress won’t be quite as slow next year, but I’m not sure if that’ll be the case.
This is the activity I wrote for today. Since it’s late, I’ll cut to the chase: The conclusions students drew at the end of the activity were on the disappointing side, both in terms of the depth of insight of their observations, as well as their ability to express what they noticed.
This (here and here and here) is what I have planned for tomorrow. I’m hoping that by giving them space to record their measurements (in an organized manner) our debriefing conversation will include more insightful comments from students. We’ll see.
If you’re game, have a look at the handouts and let me know in the comments what you like, what you don’t, and how you’d make it better.