Students\u27 views on learning proof in high school geometry: An analytic-inductive approach

This study is a micro-ethnography describing the students\u27 perspective of learning proof in high school geometry within the classroom setting. The research design is based on modified analytic induction. This procedure is employed when the focus is a specific issue. In this case the issue is that of students\u27 learning of geometry and proof. To facilitate the mechanical aspects of coding and analysis, the computer program QUALOG was used. The study was carried out in one urban high school in New York. Four Course II Sequential Mathematics classes taught by three teachers were observed for an eight month period. Students were selected for interviewing consistent with the qualitative methodology employed. In all 41 students were interviewed (13 9th-graders, 23 10th-graders, 5 11th-graders). Teacher interviews and classroom observations provided background information for the students\u27 perspectives. Findings center on classroom routines, the roles of teachers and classmates, as well as on mathematical content. Student comparisons between mathematics and English and social studies classes defined listening as a strategy for learning mathematics. Students interpreted questions about mathematical content to reflect the classroom context in which they experienced learning mathematics. For these students, their understanding of mathematics was inseparable from their understanding of classroom life. Proof in geometry was seen as a process--a logical explanation--or a product--a series of steps. Proof was not seen as a tool for analyzing conjectures. Students did not speak about the meaning of proof. Theorems, axioms, definitions and geometry as an axiomatic system had no significance. In writing proofs, students saw proofs as textbook exercises with the goal being to complete them quickly. Students perceived a partially completed proof as incorrect. To be correct, a proof had to be complete. The results argue that any research which focuses on learning must bring to the forefront the context in which the learning takes place. One cannot understand the former without investigating the latter. They further suggest that mathematics classrooms must change if students are to learn to think mathematically because teachers and classroom routines strongly influence students\u27 beliefs about mathematics