Discriminating proof abilities of secondary school students with different mathematical talent

A characteristic differentiating mathematically talented students from average students is their ability to solve problems, in particular proof problems. Many publications analyzed mathematically talented students' ways to solve problems, but there is a lack of data about the ways those students learn to make proofs. We present results from a study were we posed some geometry proof problems to secondary school students having different degrees of mathematical ability. We have classified their answers into categories of proofs. Our results suggest that the ability to make proofs of the mathematically talented secondary school students is better than that of the average students in their grade and also that mathematically talented students could be ready to begin learning to make deductive proofs even at secondary school grade 1.