A case study of different types of arguments emerging from explorations in an interactive computerized environment

This paper presents a description of the different types of arguments that emerged as two students, working in a computerized environment, engaged in an investigation of several number theory concepts. The emerging arguments are seen as a result of the influence of the computerized environment together with collaborative learning. Using qualitative research methods, data are analyzed to show how the students constructed four types of mathematical arguments: basic, compound, elaborated, and general-presented-as-specific. These example-based arguments could serve as a knowledge base for developing formal mathematical proofs.