PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2013
Denver, Colorado
Critiquing the Reasoning of Others: Devil’s Advocate and Peer Interpretations as Instructional Interventions
Page: 1-285
This study investigated the ways in which college mathematics teachers might encourage the development of student reasoning through critiquing activities. In particular, we focused on identifying situations in which the instructional interventions were implemented to encourage the critiquing of arguments and in which students explained another’s reasoning. Data for the study come from two teaching experiments – one from the domain of combinatorics and the other from real analysis. Through open coding of the data, Devil’s Advocate and Peer Interpretations emerged as effective interventions for the creation of sources of perturbation for the students and for assisting in the resolution of a state of disequilibrium. These two interventions differed in design and in the type of reasoning students evaluate, but they both provoked students to further develop their reasoning, and therefore their understanding. We discuss the implications of these interventions for both research and teaching practice.