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The Nature of Scaffolding in Undergraduate Students' Transition to Mathematical Proof.

This paper explores the role of instructional scaffolding in the development of undergraduate students' understanding of mathematical proof during a one-year discrete mathematics course. We describe here the framework adapted for the analysis of wholeclass discussion and examine how the teacher scaffolded students' thinking. Results suggest that students who engage in whole-class discussions that include metacognitive acts as well as transactive discussions about metacognitive acts make gains in their ability to construct proof. Moreover, students' capacity to engage in these types of discussions is a habit of mind that can be scaffolded through the teacher's transactive prompts and facilitative utterances.