Sociomathematical scaffolding as students engage in revising draft definitions, conjectures, and proofs

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.