Young Students' Ability on Understanding and Constructing Geometric Proofs

The present study investigated early secondary education students' ability to understand and to construct geometric proofs before and after the typical teaching of the Euclidean Geometry. At primary education the proof is related to reasoning, while at secondary education the formation of mathematical proof is introduced. Students' difficulties can be examined under the framework of a possible gap. The research tools which were constructed, aimed to investigate the impact of students' conceptions about the structure of proof (experimental, semi-experimental and formal) on their ability to construct geometric proofs and to identify errors on presented to them "proofs". There were two main phases of measurement, before and after the teaching of Euclidean Geometry for the first time at the early grades of secondary education. Results indicated that the majority of the students recognized the value of using mathematical symbols and the necessity of presenting a logical structure of the arguments in order to construct a proof, while at the same time many students preferred the semi-empirical proof as an acceptable form of a constructed mathematical proof. Additionally, results indicated that students had plenty of difficulties to solve tasks related to geometric proof which were presented to them verbally and without any figure. Based on the results of the present study the students' difficulties on studying and constructing geometric proofs are discussed in relation to the teaching practices of the concept of proof at the first grades of secondary education.