Yesterday when there was a sub in my class I gave my geometry students a few pretty challenging angle chasing problems involving parallel lines and transversals. As expected, many of them found them difficult, but some were able to solve them correctly, with many other getting a good start but just hitting a point where they weren’t sure where to go from there. That said, my favorite part of discussing the solutions was when students suggested ways to solve the problems that I hadn’t initially thought of. My way of solving the problems was very different than some of theirs, but we all ended up at the same place. It’s a nice reminder that students sometimes see and think about things in very different ways than us teachers, and we all have a lot to learn from each other.