There was a breakthrough in my Geometry class today. As part of proving congruent triangles, I had students graphing points that formed triangles and they had to decide if the triangles were congruent. On the first one, I had a young man tell me they were congruent and his reason? Well obviously the first triangle had been rotated and moved to the second location.

That offered a perfect opportunity to discuss that idea and to see how rotation, reflection, and transformation also apply to other things, so I threw in an activity to break up the learning and give their brains a chance to process the information. This is great. We also talked about which theorem would be perfect for this one and the reasons. It was a really good discussion.

Tomorrow I am giving my lower performing students partner tests. They will work in groups of two. Each person has a set of problems. The partners do not have the same problems but they do have the same answers, so if they both get the same answer they know they are right. If they don't, they can help each other check their work to find the mistakes.

I realize that tests are to check their level of understanding but who is to say they can't learn more during a test. Our goal is to make sure they understand the material so I figure this is another way for them to do it. I already allow students three chances to take and retake a test but to retake the test, they must make corrections first. I also divide the test into four parts and they only have to retake the parts of the test they do not show mastery of. I want them to learn and continue learning. This allows that to happen.