The role of abduction in proving processes

This paper offers a typology of forms and uses of abduction that can be exploited to better analyze abduction in proving processes. Based on the work of Peirce and Eco, we describe different kinds of abductions that occur in students’ mathematical activity and extend Toulmin’s model of an argument as a methodological tool to describe students’ reasoning and to classify the different kinds of abduction. We then use this tool to analyze case studies of students’ abductions and to identify cognitive difficulties students encounter. We conclude that some types of abduction may present obstacles, both in the argumentation when the abduction occurs and later when the proof is constructed.