Young Students' Ability on Understanding and Constructing Geometric Proofs

Abstract

The present study investigated early secondary education students' ability to understand and construct geometric proofs before and after typical instruction in Euclidean Geometry. At the primary education level, proof is related to reasoning, while at the secondary level, the formation of mathematical proof is introduced. Students' difficulties can be examined within the framework of a possible gap. The research tools were designed 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 in proofs presented to them. There were two main phases of measurement: before and after the teaching of Euclidean Geometry for the first time in the early grades of secondary education. Results indicated that the majority of students recognized the value of using mathematical symbols and the necessity of presenting a logical structure of arguments in order to construct a proof, while many students also preferred the semi-empirical proof as an acceptable form of constructed mathematical proof. Additionally, results indicated that students experienced considerable difficulties in solving tasks related to geometric proofs that were presented verbally and without figures. Based on the results of the present study, students' difficulties in studying and constructing geometric proofs are discussed in relation to the teaching practices of the concept of proof in the early grades of secondary education.