Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic Geometry software and their evolving Mathematical explanations

ABSTRACT. A key issue for mathematics education is how children can be supported in shifting from ‘because it looks right ’ or ‘because it works in these cases ’ to convincing arguments which work in general. In geometry, forms of software usually known as dy-namic geometry environments may be useful as they can enable students to interact with geometrical theory. Yet the meanings that students gain of deductive reasoning through experience with such software is likely to be shaped, not only by the tasks they tackle and their interactions with their teacher and with other students, but also by features of the software environment. In order to try to illuminate this latter phenomenon, and to determine the longer-term influence of using such software, this paper reports on data from a longitudinal study of 12-year-old students ’ interpretations of geometrical objects and relationships when using dynamic geometry software. The focus of the paper is the progressive mathematisation of the student’s sense of the software, examining their inter-pretations and using the explanations that students give of the geometrical properties of various quadrilaterals that they construct as one indicator of this. The research suggests that the students ’ explanations can evolve from imprecise, ‘everyday ’ expressions, through reasoning that is overtly mediated by the software environment, to mathematical explan-ations of the geometric situation that transcend the particular tool being used. This latter stage, it is suggested, should help to provide a foundation on which to build further notions of deductive reasoning in mathematics. KEY WORDS: appropriation of learning, computer environments, deductive reasoning, dynamic geometry software, geometry, mathematical explanation, mathematisation, medi