### Teaching the controversy

Jun. 26th, 2012 08:43 pmHmm. It turns out that despite never having taught this material before, I have firm view about what is right, and what is wrong, and I will tell the students when I think that the textbook is wrong. Where did this come from? Today we talked about quadrilaterals, and the 'hierarchy' - a square is a special kind of parallelogram etc. For some reason, the textbook declares that a trapezoid (that's trapezium to us UK English speakers) is a quadrilateral with one and only one pair of opposite sides parallel - so a parallelogram is not a trapezoid. This makes me cross. Before class I asked The Google, and it turns out that there are different views on this, so I did pointed that out, and explained why I felt it makes more sense to define a trapezoid as a quadrilateral with at least one pair of opposite sides parallel. But I'm still a bit surprised by vehemence of my reaction.

With quadrilaterals out of the way it was time for geometric construction. Since I'd asked them specifically to read the section before class, I made them put their textbooks away, and head for the blackboards. I'd scoured the department for all the blackboard rulers and compasses I could find, so there were enough that they could work in pairs. I gave each pair a construction to draw (e.g given a line and a point on the line, using only straight edge and compass construct a perpendicular to the line passing through the point). They had a lot of fun, and there was a fair amount of head scratching, since they couldn't consult their notes. Hee! The guy who was a math major had taken a higher level geometric construction course, so he was able to show a few really elegant constructions that we hadn't seen before. I added a few extra challenging constructions on some empty blackboards, and quite a few of them stuck around after class playing.