Teachers' in-the-moment noticing of students' mathematical thinking: a case study of two teachers

Liu, Yanjun

Teachers' in-the-moment noticing of students' mathematical thinking: a case study of two teachers

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March 22, 2019

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Liu, Yanjun
- Affiliation: School of Education

Abstract

The purpose of this research is to access teachers' in-the-moment noticing of students' mathematical thinking, in the context of teaching a unit from a reform-based mathematics curriculum, i.e., Covering and Surrounding from Connected Mathematics Project. The focus of the study is to investigate the following research questions: 1.How and to what extent do teachers notice students' mathematical thinking in the midst of instruction? 2.How and to what extent does teachers' in-the-moment noticing of students' mathematical thinking influence teachers' instruction? Conceptualized as a set of interrelated components in this study, the construct of teachers' in-the-moment noticing of students' mathematical thinking includes attending to students' strategies, interpreting students' understandings, deciding how to respond on the basis of students' understandings, and responding in certain ways. A review of literature reveals that much of the research on teacher noticing does not examine teacher noticing as it occurs in the midst of instruction. Rather, it involves asking teachers to analyze and reflect on videos outside the context and pressure of in-the-moment instruction. Thus, in order to access teachers' in-the-moment noticing in a more explicit and direct way, the researcher in this study applied a new technology to explore teacher noticing, enabling two teacher participants to capture their noticing through their own perspectives while teaching in real time. Findings indicate that teacher participants noticed for a variety of reasons, including student thinking, instructional adaptations, assessment, content, and student characteristics, focusing primarily on student thinking and instructional adaptations. Furthermore, these participants noticed student thinking in the midst of instruction to different extents, and made adjustments to instruction in different ways. Examination of the data also suggests that teachers' noticing of student thinking was shaped by teachers' beliefs, knowledge, and goals. Therefore, influenced by these constructs, teachers noticed student thinking to different extents, influencing students' opportunities to think mathematically in different ways. A diagram that illustrates the paths through which teachers traveled in the process of noticing is presented, as one of the findings.

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