Why don't students like proofs?? I think after 21 years of teaching I may have found the answer! Well, at least part of the answer from attending a talk at ATMOPAV (Association of Teachers of Mathematics of Philadelphia and Vicinity) last Saturday. The reason students don't like proofs...(insert drumroll here)...is because they don't understand them! Thanks to Annie Fetter (@MFAnnie) from The Math Forum for helping me re-think this based on ideas from her talk "Ever Wonder What They'd Notice (If Only Someone Would Ask)?"
Gee - students don't like proofs, because they don't understand them. Not really an earth-shattering piece of information there, Leigh. I agree, but do we ask students to understand what is in front of them before they see the given information or what it is that they are to prove? Do we require them to take some time to notice and wonder what is happening in a given diagram? I know I had never done that before with my students.
So on Sunday night, I found a problem from our textbook that I would turn into a 2 day "Notice & Wonder" problem. The image shown here is what my students got from me. Notice that it doesn't have any information about angles or segments. There is no "Given" information.
First, my students worked individually for a few minutes, completing what they noticed and wondered about the diagram. Then, they were put into randomly assigned groups (Did I mention that I love playing cards for random assignment?) to discuss what they noticed and wondered. Last, we came together as a class to compile a master list.
Before I share their lists with you, what do you notice and wonder? Be sure to check back to see their lists and how we moved some items from the wonder column to the notice column.