A dialogic method of presenting proofs: Focus on Fermat's Little Theorem

Twelve participants were asked to decode a proof of Fermat’s Little Theorem and present it in a form of a script for a dialogue between two characters of their choice. Our analysis of these scripts focuses on issues that the participants identified as ‘problematic’ in the proof and on how these issues were addressed. Affordances and limitations of this dialogic method of presenting proofs are exposed, by means of analyzing how the students’ correct, partial or incorrect understanding of the elements of the proof are reflected in the dialogues. The difficulties identified by the participants are discussed in relation to past research on undergraduate students’ difficulties in proving and in understanding number theory concepts.