Analysis of the mathematical productionof high school students: a view from the mathematical workspace

Abstract

Research in Didactics of Mathematics shows how important it is to know and understand the student's mathematical task -whether with or without the use of technological resources-either from a cognitivist or epistemological point of view. In this sense, this report uses the Mathematical WorkSpace (MWS) as a theoretical tool to analyze the mathematical production of Chilean high school students (16-17 years old). For this purpose, a learning situation is presented with tasks related to the rate of variationin which GeoGebra is used. From the analysis of the students' productions, it is shown that this theory provides tools to characterize the mathematical production of students. In particular, this theoretical framework allows describing and analyzing the process of progressive construction of the meaning of the rate of variation (leading to the intuitive notion of derivative) from the activation of the semiotic, instrumental and discursive genesis, the coordination of semiotic-instrumental, semiotic-discursive and instrumental-discursive vertical planes, as well as the paradigms of Analysis privileged by the students