Attributes of Instances of Student Mathematical Thinking that Are Worth Building on in Whole-Class Discussion

ABSTRACT

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making). Findings illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of these high potential instances that could be used to help teachers more easily recognize them. Implications for researching, learning, and enacting the teaching practice of building on student mathematical thinking are discussed.

Acknowledgments

The authors thank Lindsay Merrill, Brigham Young University, for her contributions to the coding and analysis of the data.

Funding

This work was funded by the U.S. National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. Portions of this article were presented at the 2015 Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Notes

¹ We recognize the “impossibility of directly accessing the thoughts of students” (Leatham et al., 2015, p. 93) and use the phrase “student (mathematical) thinking” to refer to evidenced-based inferences about student thinking based on what students say and do.

² Note that these MOSTs were selected to illustrate our data analysis procedures, not our data set. Thus, to reduce the number of contexts that needed to be described, some of the MOSTs are from the same lesson.

Additional information

Funding

This work was funded by the U.S. National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. Portions of this article were presented at the 2015 Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education.