My students are killing it right now in Geometry. We spent some time learning about rigid motions so that I can use them as the basis for their proofs on congruence. This will save us about 150 pages in the textbook, which I wasn’t really using anyway. It will also provide more access to proof for kids who don’t usually get it, which is most of them. Here you see them hard at work creating a model for a piece of playground equipment that utilizes a composition of two geometric transformations. This group is inventing a swiveling monkey-bar teeter-totter. They made videos of their creations and my son’s sixth grade class will be judging them. I told them that they will be given the chance to show me they learned this material and future material through our quizzes, through individual project presentations, or through student-created assignments and research. I told them they could use a book or online sources such as Khan Academy. Some started doing this and told me that it wasn’t the same thing as our quizzes or the work from class, that it was all based on graphs and coordinates. I told them that was fine, they would learn much more doing their own research and deciding which activities helped them learn, more than from following only one teacher’s way of doing things. So we are going to prove some theorems, do some discovery based lessons, and create more deliverables for our final exhibition in November, but they are going to take more and more ownership. Their grades will become less and less of an obstacle to learning and just a thing we need to do to be in compliance with a system that thinks it means well. They are going to do some perspective drawing as a way to give them some perspective on parallel lines. They will be designing shade structures for parks in town that have little or no shade. They will learn about adventure playgrounds and how handing over control to kids is the best way for them to learn and grow. They will then design their ultimate playgrounds for when professionals come to check out their exhibitions. They will give recommendations to the city about playgrounds and social justice, about their impact on child development and hence the development and health of the city as a whole. They will learn about how something that they took for granted before is worth looking at more deeply. They will be a part of something bigger than themselves. Hopefully they will see how geometric transformations can lead to a real kind of transformation. Big goals, I know, but it’s the only way I can think of to make it worth any of our time to get up and go to school every day.