Students´ Reasoning During a Calculus Two-Stage Exam

Abstract

For a two-stage exam, students first write their exam individually and then repeat it in a small group. This study analyzed the discussions that students had during the group stage of a two-stage exam in a first-year calculus course in order to investigate students’ reasoning and how they arrived at their answers. Data, consisting of 14 transcripts of audio-recordings of the students’ discussions, were analyzed qualitatively, guided by Lithner’s (2007) conceptual framework on mathematical reasoning. The results suggest that, though students primarily used imitative reasoning or rote learning to answer many questions, they also demonstrated creative reasoning by using a novel & plausible approach and grounding their reasoning in mathematics. Further, though the imitative reasoning relied primarily on remembering a theorem or term in calculus, creative reasoning was demonstrated in multiple ways.