Research talk and gallery workshop for teachers
Again, similar titles to my previous presentations, but again, a lot has changed in my thinking around our study of slope in 2012. At NCTM 2014, I presented the updates in a research talk and a gallery workshop for teachers. Here are all of the resources for those presentations, as well as a link to the complete unit for teachers and others to use. Please download, modify, and use the tasks with your students!
Gallery workshop for teachers
Research session talk:
I present a local instructional theory for slope that emerged during a design experiment in a high-school Algebra I classroom. In the design experiment, students explored situations related to making predictions. As students engaged with these situations, they reinvented and made-meaningful multiple sub-constructs of slope. I show that this process involved the assemblage and coordination of mathematical artifacts, and I introduce the notion of a cascade of artifacts to describe this process. I suggest that artifacts are inextricably bound with activity, and I discuss the nature of the classroom activities that promoted the development of the cascade of artifacts.