Decoding a proof of Fermat's Little Theorem via script writing

• Problematic issues identified by 12 pre-service teachers in a given proof are presented.
• The participants’ understanding of the elements of the proof is characterized.
• Dialogic method of presenting proofs is presented.
• Affordances and limitations of this dialogic method of presenting proofs are exposed.

Twelve participants were asked to decode – that is, interpret and make sense of – a given proof of Fermat's Little Theorem, and present it in a form of a script for a dialog 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 dialogs. 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.