P[65]'s response to Q3a,b: a) This is one way to prove it but I would have not chosen this way. The way I do it is [algebraic manipulations follow]. b) No [the teacher] would want [the students] to do what I said above beca[use] this is the official proof.

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... task gave ample opportunity to us to explore the interplay of deductive and authoritarian proof schemes in the student responses, especially in terms of what they value as proof themselves (3a) and what their teacher may prioritise (3b). For instance, in the student response, we sample in ( Kanellos et al., 2018, p. 287) -see also Figure 3 -P [65] writes for Q3a that trying specific values for a and b is "one way" to prove that (a + b)(b − b) = a 2 − b 2 . This led us to labelling this response E.I. ...