Teacher Responses to Student Thinking: In the Moment and in Reflection

• In Event: 63.085 - MTCC Roundtable Session 26
  In Roundtable Session: 63.085-1 - Investigating Opportunities for Teacher Learning in Online Video-Based Labs

Abstract

It is well-documented that attending to student thinking while facilitating mathematical discussions is a complex undertaking. Teachers need to create a respectful environment in which students feel comfortable critiquing peers and making mistakes while simultaneously shaping the conversation’s mathematical trajectory (eg. Smith & Stein, 2018). This involves quick processing of tenuous student ideas, encouraging use of mathematical evidence, and creating opportunities for different solutions to surface (O’Connor, 2002; Stein, 2001).

To aid teachers with this challenge, professional development often makes use of video with the idea that video provides teachers with extended time to reflect on in-the-moment interactions in a way that is not possible during instruction (Sherin, Jacobs, & Philipp, 2011). The focus of this paper is the relationship between teachers’ in-the-moment noticings and their noticings when they watch video of themselves. Specifically, this study compares teachers’ responses to students’ contributions during mathematical discussions with teachers’ commentary on students’ thinking in later written reflections so as to better understand the affordances of each context and the role that video played in teachers’ sense-making.

Data and Methods
In spring 2018, 10 K-2 teachers participated in an online professional development course on mathematical argumentation. Each week, teachers uploaded videos of themselves leading mathematical discussions and wrote corresponding reflections. For this paper, 19 teacher-uploaded videos and reflections were coded for three types of responses to student thinking: descriptive, evaluative, and interpretive. Descriptions narrated, revoiced, or summarized what students said or did. Evaluations put value labels on students’ ideas or corrected or confirmed students’ ideas. Interpretations made sense of students’ contributions. Reflections were further coded as general or specific and as attending to individual students or groups. Patterns in teacher tendencies were also noted. This coding draws on previous research on the development of teachers’ attention to student thinking (Sherin & van Es, 2009).

Results and Significance
Analysis revealed interesting distinctions between teachers’ responses to student thinking in the moment and in reflections. In the moment, teachers frequently made specific, descriptive statements relating to individual student ideas. They evaluated individual contributions with general terms like “great” and “fascinating,” and also corrected or confirmed some responses. Teachers interpreted individual student contributions in the form of questions that related directly to math. In written reflections, in contrast, teachers frequently made general, descriptive statements about group thoughts, rather than focusing on individual students as they did in the moment of instruction. Teachers broadly evaluated both individuals and groups. In reflections, teachers’ interpretations of students’ ideas related both to math, as well as to characteristics of individual students.

Knowing that attending to student thinking is both complex and important, teacher educators seek opportunities to support teachers in understanding and responding to students’ mathematical ideas. This project contributes to the ongoing discussion of how to make best use of tools for reflection. It raises questions around the tasks, prompts, and language teacher educators might use when supporting teachers in responding to student thinking, whether in the moment or in professional development.

Author

• Mari Altshuler, Northwestern University School of Education and Social Policy Learning Sciences