Teachers ’ Views of Students ’ Mathematical Capabilities : A Challenge for Accomplishing Ambitious

Building on qualitative research that suggests teachers’ views of their students’ mathematical capabilities matter for the quality of students’ learning opportunities, we investigated the views of 122 middle-grades mathematics across two large, urban districts that were pursuing ambitious instructional reform. Our findings suggest that accomplishing ambitious reform (like the implementation of the Common Core State Standards) will require shifts in teachers’ views of their students’ capabilities. We approached our investigation through a lens of problem framing – we focused on teachers’ diagnoses of the source(s) of students’ difficulties in mathematics as well as their prognoses. Methodologically, we developed an interview-based assessment for eliciting and characterizing teachers’ diagnoses and prognoses. We report descriptive information regarding teachers’ diagnoses and prognoses, as well as on trends in the relations between the two. Our findings suggest that the majority of teachers viewed at least some of their students as incapable of engaging in rigorous mathematical activity, and that when they perceived students were facing difficulty, they tended to describe lowering the rigor of the work in which students were expected to engage. We conclude by considering the implications of our findings for designing and assessing improvement efforts as well as for future research. Students’ Math Capabilities