Fusionner des représentations mathématiques machinalement ou en réfléchissant : expériences d’utilisation de calculatrices graphiques

Abstract

In designing mathematics learning with the mediation of computerized tools, one of the crucial questions to be considered is how much and in what way we would like the tool «to do the work » for the students. In problem situations where the solution is achieved mostly via graphical representatives, and algebraic models are mostly used as «keys » for obtaining graphical representatives on the screen, the algebraic representatives and their form seem minimized in importance, and students may tend to generate them from tables by mechanistic-algorithmic procedures. The above questions will be mainly demonstrated within the description and analysis of a case study involving a group of three 10th graders (about 16 years of age) working together to investigate and solve a problem situation on the topic of functions, having graphing calculators (TI-83 Plus) at their disposal. The role of contextual factors is highlighted by means of contrasts with the work of students on the same problem from another country.