Challenges in Measuring Secondary Mathematics Teachers’ Professional Noticing of Students’ Mathematical Thinking

Abstract

Our focus is on teachers’ professional noticing of children’s mathematical thinking which Jacobs et al. (Jacobs, Lamb, & Philipp, 2010) describe as a set of three interrelated skills: (1) attending to students’ strategies, (2) interpreting the students’ mathematical understandings, (3) deciding how to respond on the basis of students’ understandings. We focus on secondary teachers’ professional noticing of children’s mathematical thinking because we believe teachers with expertise in noticing children’s mathematical thinking are better poised to support their students’ mathematical performance and understanding. However, studying teacher noticing at the secondary level presents unique methodological challenges. We first consider methodological issues in measuring K–12 teachers’ professional noticing of children’s mathematical thinking, and then consider three methodological challenges that are particular to secondary mathematics classrooms. These issues center around the challenges of artifact selection, determining the relative sophistication of responses, and the lack of access to experts’ responses at the secondary level. Also, we consider the cultures of teaching in the elementary and secondary contexts.