Connected Mathematics: Teaching Math Through Problem-Solving with AI

A.J. Edson: "We come into the world as problem-solvers. If you think about babies or toddlers, they're always problem-solving, figuring out how to get food, how to walk. Everything is a problem-solving process. Not only are humans problem-solvers, but the discipline of mathematics has evolved from the activity of solving problems. Over the history of the world, different civilizations and cultures have invented new mathematics based on solving problems."

A.J. Edson: "This is how classrooms actually operate. They start out, they've got a problem for the day, they launch it, the teacher launches it in a whole class discussion. Students take up those problems in small groups, they work together, and then they come back together in a whole group conversation and talk about what happens and the strategies that they use."

A.J. Edson: "Think about it. You're in a class, and you've got all these different kinds of strategies going on. The teacher has to make sense of all these different strategies as they're walking around the room, and you as a student have to make sense of your own thinking, and the thinking in your group, and the thinking in your class. So it's a lot of information, a lot of student work, a lot of happening all at once."

Student (from video): "I can make a mistake and get rid of it, I can try again. But if I'm just on paper and pencil, there's something more permanent about the paper and pencil environment. It doesn't allow me to take risks and try different examples."

A.J. Edson: "We really believe that if we're gonna incorporate or integrate AI into the classroom, it really needs to help students and teachers do the things that they're doing all the time and that they're having issues with... We spend a lot of time helping teachers think about what students know, but I don't think that we spend a lot of time helping students know what they know."

A.J. Edson: "For teachers, they have the dashboard. But now, teachers can sort through all of the work in their class in real time and say, okay, what's this group doing? How many of them are using tables? How many of them are using graphs? Are any of them building up or down? Any of them scaling up with unit rates?... Students can click and say, okay, AI told me that I was using this strategy, but why did AI tell me I was using this strategy?"

A.J. Edson: "Math is kind of tricky, because we want math to be accurate. We don't want math to be wrong, so we don't want AI to be wrong... PhotoMath, you take a picture with your phone of any problem in your textbook, and then it uses large language models, and then it translates it, switches it over to symbolic AI, gives the accurate answer, and then brings it back over here to large language model to give you your answer."