Fatemeh Ahmadpour

In the present study, 193 groups of three students in grades 4 to 6 were assigned a proof-based problem in the field of number theory. The written responses were analyzed. Not surprisingly, the analysis showed that the majority of them relied on examples to ‘prove’ the given statements. However, there was some variation in the ways that examples had been used. Considering the observed variation, 18 students whose proofs were somehow different from each other were invited and interviewed individually for finding more details about their performances. None of them were able to produce accurate formal proofs. However, their performances had an important similarity to mathematicians’.