Abstract
A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In geometry, forms of software usually known as dynamicgeometry environments may be useful as they can enable students tointeract with geometrical theory. Yet the meanings that students gain ofdeductive reasoning through experience with such software is likely to beshaped, not only by the tasks they tackle and their interactions with theirteacher and with other students, but also by features of the softwareenvironment. In order to try to illuminate this latter phenomenon, and todetermine the longer-term influence of using such software, this paperreports on data from a longitudinal study of 12-year-old students'interpretations of geometrical objects and relationships when using dynamicgeometry software. The focus of the paper is the progressivemathematisation of the student's sense of the software, examining theirinterpretations and using the explanations that students give of thegeometrical properties of various quadrilaterals that they construct as oneindicator of this. The research suggests that the students' explanations canevolve from imprecise, `everyday' expressions, through reasoning that isovertly mediated by the software environment, to mathematicalexplanations of the geometric situation that transcend the particular toolbeing used. This latter stage, it is suggested, should help to provide afoundation on which to build further notions of deductive reasoning inmathematics.
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Jones, K. Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations. Educational Studies in Mathematics 44, 55–85 (2000). https://doi.org/10.1023/A:1012789201736
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DOI: https://doi.org/10.1023/A:1012789201736