Teachers' Noticing of Students' Slope Statements: Attending and Interpreting

In this study, we investigate a sample of in-service teachers' professional noticing of slope. The analysis focuses on which elements of students' statements about slope teachers attend to, and how teachers interpreted those elements. Study results suggest that teachers attended to the vocabulary and mathematical focus of students' statements. Teachers' interpretations were, for the most part, rather consistent across teachers and in line with the researchers' anticipations for elicited slope components. In fact, even for vague student statements expected to elicit a variety of interpretations by teachers, there was a noted lack of diversity in teachers' interpretations. Results for teachers' interpretations suggest they place great academic value on nonvisual slope reasoning and attribute the ability to solve real-world problems to students who used "rate of change" terminology. Other real-world interpretations of slope were interpreted as disconnected from the mathematical meaning of slope or only trivially linked to contextual situations. Findings from this study imply that teachers should be provided with professional development opportunities involving slope. Specifically, teachers need experiences interacting with tasks that build robust notions of steepness through explicit connections to a variety of physical contexts by allowing students to develop imagery and mathematical terminology in rich and meaningful ways. In addition, professional development should help uncover the meaning behind students' vocabulary rather than having them focus on buzz words and catch phrases, which may be used without understanding.