Abstract

SAMPER, Carmen  and  VARGAS, Claudia. Negation: A contribution to the construction of definitions in a geometry classroom. Educ. mat. [online]. 2019, vol.31, n.3, pp.39-60.  Epub June 15, 2020. ISSN 2448-8089.  https://doi.org/10.24844/em3103.02.

In this article, we present an analysis of the arguments of seven tenth grade students (14 to 16 years old) when they try to define a geometric figure unknown to them, and justify their decision, for which they use the negation of propositions. The objective of our study was to find the characteristics of the use of negations, to determine whether what many researchers in mathematics education have found is true: the use of negations in arguments entails difficulties. The research strategy used was case study method, because our data were the transcriptions of the video and audio registers of the student's work. We conclude that the type of tasks proposed to the students, designed to favor the mathematical processes defining and justifying and the use of a dynamic geometry software, promotes spontaneous use of negations. We identify under what circumstances the students recurred to the use of negations to justify their assertions.

Keywords : argument; negation; defining; justifying; dynamic geometry.

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