Triangles

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.

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3 comments

1. I’m curious — what’s the role of the “notice” questions in the activity?

2. mjfenton says:

Michael, thanks for your question.

First, some background. I’ve historically been a direct instruction-heavy teacher. I’m trying to shift away from that so students are more active in their learning. With an activity like this, I’ve found that the “debriefing” time at the end is crucial (though I haven’t mastered it yet), otherwise my students will often miss the point of a lesson. So in a general sense, those “notice” questions are designed to grease the skids for our debriefing time.

In this particular activity, my goal was for students to observe/notice/learn that scaling the sides of a triangle by a factor of n does not affect the angle measures, and that scaling the side length by n multiples the area by n^2.

Additional thoughts? Are there salvageable parts to the activity? Things to rewrite or throw out? Or back to the drawing board?

3. Help me out here. What’s the student learning target? What standard are you working toward? It’s been awhile since I taught Pre-Algebra too.
Also, I’d like to know how long it’s been since you started removing yourself from direct instruction. Last school year (around this time) is when I started removing myself from direct instruction. It’s definitely a transition for both you and your students, especially if you’re doing it sometime during the course of the school year.
Are you putting student work/conjectures up during their exploration time for the class to see and critique? As much as I’d love to completely abandon my students and let them figure it all out on their own, I realistically can’t entirely do that. I have to nudge them somehow at times, but I prefer to show them student work. Find something in the class that is completely wrong or has a shred of possibility and let the students build from there. Sorry, if I’m making some false assumptions. Pre-Algebra is a tough beast for a tough age.
I do like the graphic organizer for tomorrow.