### Examining Preservice Secondary Mathematics Teachers’ Responses to Student Work to Solve Linear Equations

#### Abstract

This study examined proposed teacher responses to students’ work to investigate how they respond, what characteristics of a good response are more difficult than others to achieve, and whether particular student error types are more difficult to respond to appropriately. Sixteen preservice secondary mathematics teachers’ proposed responses to five students’ work to solve linear equations were analysed based on four characteristics of a good response: work toward student learning objective, draw on presented student thinking, draw on research on students’ mathematical development, and leave space for student’s future thinking. The preservice teachers’ responses consistently met the last characteristic, but their skill at meeting the other characteristics differed markedly based on the type of student error in the work sample. An implication is the need to help preservice teachers learn how to address conceptual issues in their responses rather than solely focusing on procedural errors that are often irrelevant to meeting the learning objective.

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