Teachers’ noticing of proportional reasoning

Abstract

The importance of understanding what and how mathematics teachers notice is well documented, but more research is needed on content-specific noticing. In particular, knowing how teachers notice proportional reasoning, a vital topic spanning all grades of mathematics, could inform measures that support students’ proportional reasoning. We examined how teachers noticed when responding to two prompts (one student-focused and one teacher–student-interaction-focused) after watching a video of a middle grades proportional reasoning lesson. We analyzed the proportional reasoning reported from 13 elementary and 20 secondary prospective teachers and used cooccurrences along with noticing practices to describe how teachers noticed proportional reasoning and what aspects of proportional reasoning they noticed. Results indicate: (a) the two prompts resulted in differences in what and how participants noticed proportional reasoning, (b) participants were primarily descriptive and not interpretative when describing the proportional reasoning they noticed, and (c) the elementary and secondary prospective teachers both noticed similar aspects of proportional reasoning but showed differences in how the proportional reasoning cooccurred with the noticing practices. These findings reiterate the importance of the prompts used with teachers, the potential of using video to advance teachers’ noticing of proportional reasoning, and the methodological potential of using cooccurrences to examine teachers’ content-specific noticing.