How Do Secondary Mathematics Teachers Manage Students' Responses?

• In Event: Responding to Student Thinking in Secondary Mathematics Classrooms: Studying and Supporting Teaching Practice

Abstract

Objectives

This study describes different ways in which secondary mathematics teachers respond to correct and incorrect student thinking in early algebra.

Perspectives

Despite widespread agreement and evidence of the importance of how teachers respond to students (e.g., NCTM, 2000; Pierson, 2008), research in this area is still ongoing. Specifically, there are three important methodological gaps that warrant attention. First, though there is an impressive range of mathematical content explored—from whole-number operations (e.g., Jacobs, Lamb, Philipp, 2010) to proofs of the Pythagorean Theorem (Zazkis and Zazkis, 2016)—there is need to more deeply explore teacher responses in the context of the “gatekeeper” early algebra. Second, most student response prompts used are either correct or incorrect. Utilizing both types and then contrasting teacher responses to each has the potential to surface important nuances in teacher responses. Third, many teacher responses are obtained in conditions with minimal fidelity to teaching (i.e., the student answers and teacher responses are written not oral, there are no time pressures, etc.). Painting a more accurate picture of the work of teaching necessitates utilizing data collection methods with higher fidelity.

Methods and Data

A novel teaching simulation in which teachers respond orally, under time-constraints, to video clips of student responses was used to collect teacher responses to three different student answers (one correct, one incorrect with information about the source of the error, and one incorrect without that information). The participants were 24 secondary mathematics teachers: 19 inservice and five preservice who predominantly self-identifying as White (23) and Female (18).

Teachers’ initial responses were identified then coded using the Teacher Response Coding scheme (TRC) (Peterson, Van Zoest, Rougée, Freeburn, Stockero, & Leatham, 2017). The TRC captures: who is being engaged and in what, as well as responsiveness (through the take-up of language and ideas) and what mathematics is pursued.

Results

Across all three types of student responses two interesting patterns emerge. First, teachers seem inclined to re-engage the same student who provided the answer (40 out of 72, a little over half) rather than the whole class, or another student for example. Second, teachers seem inclined to repeat part or all of a student’s contribution verbatim (44 teacher responses explicitly used the students’ language or 17 of the 24 teachers did so in two of their three responses).

When contrasting teacher responses to correct versus incorrect answers, most teachers (17) displayed evaluative patterns, though seven teachers did not. These seven teachers provided responses that predominantly engaged the same student or the whole class in all three of their responses and provide responses that were clear (versus imprecise or confusing) but that did not completely give away the underlying mathematical idea to be pursued.

Scholarly Significance

The findings of this study have several implications for teacher education. In particular, by understanding what teachers already seem to do well (take-up student’s language), where they struggle, and what some teachers do when they display less evaluative patterns, teacher education can provide targeted interventions to support teachers in this complex work.

Author

• Annick Rougee, Washington State University - Tri-Cities