Reasoning about student written work through self-comparison: how pre-service secondary teachers use their own solutions to analyze student work

ABSTRACT

Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students’ mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students’ written work. In interviews, participants solved mathematical tasks and the analyzed student written work in order to make assertions about student understanding. Analysis of participants’ assertions revealed three primary reasoning strategies: mathematical reasoning, pedagogical reasoning, and reasoning through self-comparison. Self-comparison involved participants comparing the student work directly with their own work on the task. This strategy showed promise, as it could be used to help make inferential assertions about student understanding. It also highlighted areas of caution around how beginning pre-service teachers might make use of evidence. This study contributes to the existing literature around noticing student thinking in written work by highlighting the significance of reasoning through self-comparison.

KEYWORDS:

• Analyzing and interpreting student thinking
• reasoning strategies
• pre-service secondary mathematics teachers
• noticing
• self-comparison
• student written work

Acknowledgments

An earlier version of this paper was presented at the National Council of Teachers of Mathematics Research Conference, April, 2015, Boston, MA. I am grateful for feedback and support I received from my STaR Manuscript Review Group 2016, Jen Munson, Sue Staats, Megan Parise Schmidt, Bismark Akoto, and anonymous reviewers. The research for this paper was conducted at as part of a dissertation study at Stanford University, and was supported in part by a Stanford Graduate School of Education Dissertation Support Grant.

Notes

1. Problems in different content areas were selected for the larger study in order to investigate the extent to which knowledge developed in an abstract algebra course for teachers might be applied in algebraic and non-algebraic contexts. For this study, the differences help illustrate a wider range of participant reasoning about student work.