[update 3/27/16: I described how I use AngLegs to introduce this lesson here]
I lied to my students today. Really, I fantasized, because I wish my lie was true.
I told them that I was going to choose some of their work and send it to Ohio for another math class to critique. Then I told them that I also got work from a class in Ohio (I have no idea why I picked Ohio, but they were into it!) . In reality I was using the materials that the Math Assessment Project includes in the triangle congruence lesson. They constructed their “proofs” first, convincing me that 2 triangles with 2 sides congruent in each triangle & 1 angle do not have to result in congruent triangles. They used mostly diagrams, very few had much of an explanation. They did put more effort into it, thinking that someone else, in Ohio, would be looking at it.
Then I gave them samples of student work.
I teach at an alternative school. These students identify themselves as being “behind” the rest of the world.
They all looked discouraged when I passed them “Jorge’s” work. It looks so nice – sentences, labels, proper notation. Then we read it. They realized that he had some false assumptions. One boy got so excited he asked if he could come to the board and he presented a beautiful argument comparing SAS to ASS and how one would result in congruent triangles but not the other. I immediately realized that I need to keep a charged battery in my camera at all times, just in case. Many of my students were so happy they could logically argue and prove an idea that someone in Ohio cannot!
Then we looked at “Kieran’s” work. Immediately a quiet student in the back yelled out “That’s how I did it!”. His body language changed, he sat up straight. he decided he was just as competent, maybe more, than students in Ohio!
Wouldn’t it be awesome if I didn’t have to lie…If we sometimes exchanged work with students in another state, maybe even share video clips of other students discussing one of my students real work. I don’t know how to start, but I have to find a way to make this happen.