Abstract
We analyse proof presentation at the tertiary level, using a concept called ‘the flow of a proof’, which relates to proof classroom presentation of proof. We focus on rhetorical features of the flow of a proof that we analyse using our adaptation of Perelman’s ‘New Rhetoric’. We present an analysis of an episode from a lesson in Set Theory, given to prospective mathematics teachers, and demonstrate how the lecturer’s design of the flow enabled her to create a thought-provoking analogy and to trigger a cognitive conflict. The lecturer’s actions created presence of the need for a proof as a tool to solve the conflict, and clarified that analogies may be erroneous; moreover, the discussion highlighted mathematical values that the lecturer wished the students to embrace. The study suggests that mindful planning of the flow of a proof should attend to its rhetorical aspects, so that the flow will promote productive classroom communication that improves proof teaching and learning. Furthermore, a conscious pre-design of the flow may be used by lecturers as a practical pedagogical ‘reflective aid’ that makes them aware of their own premises. This can be used to support ideas that lecturers perceive as important to convey to students.
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Gabel, M., Dreyfus, T. (2022). Creating a Shared Basis of Agreement by Using a Cognitive Conflict. In: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., Winsløw, C. (eds) Practice-Oriented Research in Tertiary Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-14175-1_14
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