Exploring grade eight students' development of geometric reasoning in a problem solving situation using dynamic geometry software. (c2010)

Abstract

Mathematics educators consider proof as central to the discipline of mathematics. However, the use of Dynamic Geometry Software (DGS), which enables students to create many examples of a single figure, raises questions about the importance of deductive proof. The Lebanese curriculum does not explicitly integrate the use of DGS in geometry teaching. However, some schools are including DGS activities in geometry classes. This study aims at exploring Lebanese students’ development of geometric reasoning in problem-solving situations requiring proving, using dynamic geometry software. Participants are a conveniently accessible group of grade 8 students, at a reputable private school in Mount-Lebanon. The group consists of 35 students, 12 females and 23 males coming from middle socioeconomic background. The study involves several techniques: a semi-structured interview with the teacher, development of a math teaching unit integrating the use of Cabri-Geometer, paper-pencil problem-solving situations requiring proofs prior to unit implementation, implementation of the unit, problem solving situations in DGS context which require proving, and clinical interviews with selected groups of students while solving proof problems. The proofs produced by students using paper-pencil were compared with proofs produced in a DGS context. In addition, the mental models of geometric reasoning of students using paper-pencil were compared with the mental models in DGS context. Data collected was analyzed according to a classification framework developed for this purpose. The following results were found: students were able to produce more correct figures using DGS than when using paper-pencil. They were also able to better experiment and explore the problem. This made them understand the problem and the theorems and properties it involves. Students produced more correct conjectures. Moreover, DGS figures provided students with tools to prove so they did not give any conjecture with no proof. Though some of the proofs produced were empirical most of the proofs reflected more understanding of the concepts. Moreover, while students focused, in the paper-pencil quiz, on the format of proofs produced, they rather focused, in the DGS quiz, on the content and logic of proofs produced.