What constitutes successful collaborative conjecturing-and-proving processes? Relations between beginning undergraduates’ resources, conjecturing-and-proving processes, and performance

Abstract

Abstract Students’ difficulties with mathematical argumentation, conjecturing, and proving, as well as with collaborating effectively, have long been documented in the literature. While there is some research on what constitutes successful proving processes, systematic investigations of proving process quality are rare. We investigate how individual-mathematical and social-discursive process characteristics during a collaborative conjecturing-and-proving activity relate to students’ performance in conjecturing and proving, as well as their proof-related resources, such as prior proof skills. Based on a multidimensional high-inferent coding of collaborative conjecturing-and-proving processes of N =98 prospective mathematics students who worked in dyads, we test a range of hypotheses on the overall role of process characteristics for students’ performance. Moreover, we investigate which single process characteristics best predict conjecturing-and-proving performance. We find that individual-mathematical process quality mediates the effect of students’ resources on their performance, whereas the investigated social-discursive characteristics were largely unrelated to students’ proof performance. Mathematical argument structure was particularly predictive for performance. Results further indicate that process quality is predicted by the partners’ resources, but not by the partners’ contributions earlier in the process. However, students within a dyad converge in terms of process quality. We derive implications for the conceptualization, measurement, and investigation of process characteristics.