Secondary teachers' knowledge of elementary number theory proofs: The case of general-cover proofs

In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine the validity of an argument made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and more difficult to understand.