Proofs gone wrong

This past Tuesday, I finished teaching the lesson I began last Friday in Geometry CP on proving isosceles triangle conjectures for the hour and a half class. Part of the lesson that I had planned involved completing two flowchart proofs together, both from the textbook. In both of the proofs in the book a lot of information was already given to the students, leaving them to only have to complete some of the remaining information themselves. I decided to take out some of the information to challenge the students to think. I went through them and took out about one piece of information from every pair given. I used the think-pair-share method of problem solving so that they students would have to think by themselves, work with each other, and share their reasoning with the class.

While we were going over the proof, I discovered that I should have been more careful and strategic about the information that I omitted. There were two adjacent boxes dealing with linear pairs: one of which had the reason of the definition of a linear pair and the other of which had the reason of the linear pair conjecture. There was one student who absolutely could not understand why the reasons for the two boxes could not be interchanged. I tried having the students explain first, followed by myself explaining that the definition was in one box and the conjecture was in the other box, so the reasons could not be changed. We must have spent at least ten minutes going over just that part of the proof. I didn't know what to do because it was only one student who was really struggling with the concept while the others seemed to have grasped it. I tried to explain a couple of times and then had to move on, but I went over to her individually afterward to ask if she had any other questions. The entire experience was a bit frustrating for both me and the students as we found it very difficult to communicate with each other.

Looking back, I think that I perhaps should have given them both reasons so that the students would not have been as confused. From this entire experience, I have learned the importance of really thinking through each problem to detect any potential problems that students may have and to create/edit problems accordingly. From now on, I will try to look at each problem in the students' eyes to see how they will approach the problem and think about explanations that address these ahead of time.