Pre-service teachers’ use of different types of mathematical reasoning in paper-and-pencil versus technology-supported environments

Abstract

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate student all of whom had quite a lot of mathematics courses in their repertoire. The study revealed that participants mostly depended on and were limited to analytical reasoning within paper-and-pencil environments, whereas they were able to refer to practical and creative reasoning with the help of the facilities technology environments provided. On the other hand, although participants made progress and used different reasoning types within technology environments, there were cases where they could not move beyond analytical reasoning even within the presence of technological tools. The reason for such a limitation seemed to be because of the way they treated technology as an analytical tool and they depended on ‘learning from technology’ instead of ‘learning with technology’ [Hanna, G., 1989, Proofs that prove and proofs that explain. In: G. Vernaud, J. Rogalski and M. Artigue (Eds), Proceedings of the International Group for the Psychology of Mathematics Education (Paris: ERIC), pp. 45–51].