Abstract
Instructors manage several tensions as they engage students in defining, conjecturing, and proving, including building on students’ contributions while maintaining the integrity of certain mathematical norms. This paper presents a case study of a teacher-researcher who was particularly skilled in balancing these tensions in a laboratory setting. We introduce sociomathematical scaffolding, which refers to the scaffolding of normative aspects for mathematical discourse. We found that the teacher-researcher’s sociomathematical scaffolding entailed inquiring into the students’ intended meaning of their draft and then supporting students in revising their draft to adhere to mathematical norms. We illustrate this pattern in three episodes in which the teacher-researcher supported a pair of students to revise their drafted (1) definition of unbounded above sequences, (2) conjecture of the Archimedean Property, and (3) proof by contraction of the Archimedean Property.
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Notes
We do not claim this is an exhaustive list of tasks and procedures that comprise sociomathematical scaffolding but ones that were important for interpreting our results.
This heuristic is known as guided reinvention.
All names are pseudonyms.
This cycle relates to Smith and Stein’s (2018) work in which instructors aim to assess or advance students’ thinking.
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Acknowledgements
We would like to thank Dr. Sean Larsen for his detailed comments on an earlier draft of this manuscript. We would also like to thank the anonymous reviewers for their feedback, which greatly improved our work.
Funding
Partial financial support was received from the Advancing Students’ Proof Practices in Mathematics through Inquiry, Reinvention, and Engagement project (NSF DUE #1916490). The opinions expressed do not necessarily reflect the views of the NSF.
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Vroom, K., Ellis, B. Sociomathematical scaffolding as students engage in revising draft definitions, conjectures, and proofs. Educ Stud Math (2024). https://doi.org/10.1007/s10649-023-10294-1
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DOI: https://doi.org/10.1007/s10649-023-10294-1