"Cela fait maintenant plusieurs années que l'équipe "Analyse" de l'IREM de Montpellier s'intéresse à l'utilisation des calculatrices graphiques. C'est donc tout naturellement que, dans les stages "modules en seconde et en première", nous... more
"Cela fait maintenant plusieurs années que l'équipe "Analyse" de l'IREM de Montpellier s'intéresse à l'utilisation des calculatrices graphiques. C'est donc tout naturellement que, dans les stages "modules en seconde et en première", nous avons été amenés à faire des propositions d'activités utilisant cet outil. Et à réfléchir sur les conséquences de cette utilisation.
Un exemple, parmi d'autres : il s'agit d'une activité proposée en 1°S, après un premier cours sur la résolution des équations du second degré, et avant toute leçon sur la dérivation.
Le défi (pour les élèves !) : déterminer une parabole tangente à trois droites données
L'objectif (pour le maître! ) fixer le rôle des coefficients a, b et c du trinôme ax2+bx+c. On lira ci-dessous un bilan de l'activité des élèves, et de l'évaluation qui a suivi.
Il en ressort que les images mentales qu'induit, dans la tête des élèves , la manipulation des calculatrices graphiques sont des images animées. Et que ce caractère "dynamique", laissé sans contrôle, peut vite se constituer en obstacle...
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The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the... more
The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students’ learning of the limit concept. As a result of data analysis, it was found that the constructivist learning environment provided positive contribution to learning of the limit concept. It was determined that the experimental group was more successful than the control group in seeing the relations between the limits and the real world. At the same time, experimental group had lesser difficulty in understanding the limits. However, both the experimental and the control groups had difficulty in applying the deltaepsilon approach. It is concluded that this study would guide when learning environment is design to construct mathematical concepts.
The purpose of this study is to investigate the misconceptions emerging in mathematics student teachers’ limit instruction and the reflections of these misconceptions on their teaching. In this study, which used the case study design,... more
The purpose of this study is to investigate the misconceptions emerging in mathematics student teachers’ limit instruction and the reflections of these misconceptions on their teaching. In this study, which used the case study design, regarding the limit concept, four senior mathematics student teachers’ four-hour limit instruction was examined within the context of misconceptions as described in the literature. Mathematics student teachers’ lesson plans, video recordings of the participants’ lessons in which they taught the concept of limitandaudiorecordingsofsemi-structured interviews were used to gather data.Participants carried their instruction mostly by demonstrating that the function’s limit is different than the function’svalueat x=a. However, since mathematics student teachers did not have adequate knowledge of misconceptions regarding the limit concept, some misconceptions emerged in their teaching process. Three of the participants made illustrations by making use of the meaning attributed to limit in daily language, and this situation caused students to perceive the limit concept as the maximum value to be reached and as a boundary not to be exceeded.
This paper describes an alternative approach to homework, which asked the students to create and solve a problem set. The homework was one of several activities in an Introductory Calculus course taught using the Flipped Classroom method.... more
This paper describes an alternative approach to homework, which asked the students to create and solve a problem set. The homework was one of several activities in an Introductory Calculus course taught using the Flipped Classroom method. The homework was meant to replace readings that were usually assigned to prepare students for the next class. Results from the experiment shows that this type of homework had a large impact on increasing students' understanding of the taught material. Students who were given this homework, on average, had a 29.98 grade points increase in posttest scores compared to students who were given the regular reading assignments. This increase can be attributed to students being better prepared for classes. By doing the homework, students were made to review the provided materials and had more problem sets to practice on. Moreover, students' reception of this type of homework was positive.
"A entendre professeurs et élèves parler des calculatrices graphiques, un Martien pourrait à bon droit imaginer qu'il ne s'agit pas pour les uns et les autres du même objet : pour les élèves, une calculatrice graphique (dé)montre les... more
"A entendre professeurs et élèves parler des calculatrices graphiques, un Martien pourrait à bon droit imaginer qu'il ne s'agit pas pour les uns et les autres du même objet : pour les élèves, une calculatrice graphique (dé)montre les propriétés des fonctions. Pour les professeurs une calculatrice graphique est un gadget qui n'a aucune légitimité mathématique. Les uns et les autres s'accordent cependant sur un fait : la maîtrise de cet outil ne nécessite aucun apprentissage particulier.
On défendra ci-dessous la thèse inverse : la manipulation d'une calculatrice graphique n'a rien de naturel, son utilisation non maîtrisée peut peser lourdement sur la construction des connaissances mathématiques.
Et on présentera quelques pistes pour une prise en compte raisonnée de cet outil dans l'enseignement."
