Last Monday in Geometry, it was time for my students to ‘discover’ that when two parallel lines are cut by a transversal, corresponding angles are congruent, etc. I think its pretty typical for geometry teachers to have students construct parallel lines and a transversal and measure pairs of angles to determine special relationships. Here’s the activity as suggested by a geometry textbook I have:
I think this is a good activity, and I’ve done it before, but I’ve never been entirely satisfied with it. First of all, invariably someone starts shouting out the conclusions before everyone is done measuring, and students start making assumptions about their own results, and the magic is lost. Second of all, I feel like the teacher usually ends up saying something like, “and every time you draw parallel lines and a transversal, alternate interior angles will be congruent.” I don’t want my students to believe everything I say without evaluating its reasonableness first. They need more evidence than that. I am trying to teach my geometry students to adopt an attitude of skepticism; they shouldn’t be drawing conclusions unless they can explain them.
In an attempt to improve this activity this year, I had students work with partners, but I imposed a strict ban on speaking while they were working, so that no pair’s work would be influenced by that of others. Some students asked me if they could assume certain results would be the case, and I reminded them of the dangers of assuming. I had them submit all of their measurements via a Google Form, and then we looked at the pooled results as a class to see if we could establish patterns. I did this with a class of students that need a lot of direction, and it did not exactly go smoothly: some students measured the wrong angles, some students measured the right angles incorrectly, some students entered their data in the wrong place, but we got it done eventually, and I was still happy I did it.
1) It was a struggle. I wouldn’t confirm or deny anything my students were thinking and saying for most of the activity, so it forced some actual thinking.
2) Our examples and data were student created. They weren’t perfect, but they were real. Not all angles in life are 60 degrees, and sometimes that makes them hard to measure, but you might still have to measure them.
3) There were mistakes. Students didn’t only see their results, but they saw those of their classmates. When something didn’t look right, we could have a conversation about whether someone made a mistake, or whether it was actually the case that the pattern people thought they were seeing wasn’t a pattern at all.
I liked this activity, and I liked how my students’ iPads made it relatively easy to execute. But it got me thinking about something I’m starting to not like about my students having iPads, but that’s a topic for another post…