The research team created the animations based upon an analysis of how geometry students solved the problems that we created for the animations.

Thanks.

This is an excellent question. I am particularly interested in how teachers probe for prior knowledge to get below the surface of what students are saying—and whether different elements of the PD model stimulate different ways of “digging out” or revealing relevant student experiences and knowledge.

Thanks for your questions. Our project takes into account three sources of prior knowledge that are relevant during problem-based lessons: (1) prior knowledge of mathematical content that students use to solve a problem, (2) prior knowledge of the context of the problem, and (3) prior knowledge of out of school mathematical practices that are related to the problem. In the study group, the teachers design problems that would enable students to make use of these three sources of prior knowledge in meaningful ways. This is challenging because it requires teachers to know their students and to consider the mathematical content of the lesson. We show examples of how to take into account these three sources of prior knowledge in the vignettes. We expect that the discussions of the vignettes enable teachers to get ideas about how to use students’ prior knowledge in their lessons. Even though the prior knowledge of school mathematics is the most obvious for math teachers, teachers say that the other sources of prior knowledge increase students’ opportunities to have entry points to the problem. In addition, teachers say that problems that are situated in contexts that are relevant to their students increase students’ engagement and motivation.

Thank you. Appreciate the detail about sources of prior knowledge. It gives teachers more opportunities to make the relevant connections. I am also thinking that many teachers experience “aha” moments in the discussions when they hear the perspectives of other teachers who capitalize on prior knowledge that hadn’t ever occurred to them because of the different “prior knowledge” and cultural diversity of the teachers themselves. Is that the case?

Thank you! The art was created by Annie Lin, our graphic artist. She also makes the animations. We use the animations to show different alternatives when using students’ prior knowledge in a lesson. For example, one vignette can show a teacher highlighting connections with students’ prior knowledge of the context of a problem and in another vignette the teacher discusses students’ prior knowledge of specific mathematical content relevant to solve the problem. The videos are from the actual lessons that teachers taught and they show examples of how students used their prior knowledge in the problem-based lesson that the teachers created.

Annie did a great job with the art. As an animator for our project I’d be interested in talking with her at one point about her approach. Is there a place where we can go to view the animations?

These are important questions that we are investigating in the study. First of all, it can be hard for a teacher to pay attention to student thinking in the middle of the lesson because they may be walking from group to group and they may not have a full picture of how students are solving a problem. So, as in other research on video clubs, we are finding that giving teachers an opportunity to examine one video clip of students working on a problem for an extended period of time promotes a lot of discussion. We encourage teachers to use evidence from the video to make sense of how students are solving the problem. The discussions at the end of the year included more attention to student thinking than at the beginning of the year. Also, the teachers tend to initiate these discussions. The teachers are used their insights for revising the lesson in ways in which they can support students’ mathematical understanding. It seems that the analysis of the videos has enabled them to better anticipate students’ ideas.