Teachers’ Responses to Instances of Student Mathematical Thinking with Varied Potential to Support Student Learning

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Keith Leatham and Blake Peterson recently published an article titled “Teachers’ Responses to Instances of Student Mathematical Thinking with Varied Potential to Support Student Learning” in the Mathematics Education Research Journal. Keith has answered a few questions about this article below: 

Who were your co-authors on this article?

Shari L. Stockero, Laura R. Van Zoest, Ben Freeburn, and Blake E. Peterson

Who would you say is the target audience for this article?

Mathematics teacher educators and researchers

What is the big problem you hoped to address with this article?

The big problem is that we don’t know enough about teachers decisions with regards to using student contributions during instruction in order to sufficiently inform work preparing teacher to productively use student mathematical thinking. To contribute to solving this problem we explored the extent to which teachers take into account the potential a given student contribution has to support student learning.

What are some of the key ideas in the article?

We found that teachers tend to explicitly incorporate students’ actions and ideas in their responses to student contributions, an important consideration for productive use.

The study also found that teachers tended to direct responses to the student who had shared the thinking, even when that thinking could be more productively used by redirecting out to the rest of the class.

What are some of the main ideas you hope your audience will take from this article?

Many teachers are not aware of the untapped potential in turning certain student contributions over to the class to make sense of.

What else would you like to say about this article?

The paper also utilizes the “Teacher Response Coding” scheme, as framework that teases apart important aspects of teachers responses that provide substantial nuance to characterizing teachers’ responses.

Abstract:

Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support learning. This study investigated teachers’ responses to a common set of instances of SMT with varied potential to support students’ mathematical learning, as well as the productivity of such responses. To examine variations in responses in relation to the mathematical potential of the SMT to which they are responding, we coded teacher responses to instances of SMT in a scenario-based interview. We did so using a scheme that analyzes who interacts with the thinking (Actor), what they are given the opportunity to do in those interactions (Action), and how the teacher response relates to the actions and ideas in the contributed SMT (Recognition). The study found that teachers tended to direct responses to the student who had shared the thinking, use a small subset of actions, and explicitly incorporate students’ actions and ideas. To assess the productivity of teacher responses, we first theorized the alignment of different aspects of teacher responses with our vision of responsive teaching. We then used the data to analyze the extent to which specific aspects of teacher responses were more or less productive in particular circumstances. We discuss these circumstances and the implications of the findings for teachers, professional developers, and researchers.