Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group of 19 grade 6 elementary school students' ability to reason logically, to justify an argument, and to prove mathematical conjectures. The results of this study indicate that, even though the process of justification is difficult for students, they were able to demonstrate skills related to mathematical proof. (Contains 4 tables and 1 figure.)