Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.

[1]  David Tall,et al.  Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept , 1992 .

[2]  Pierre Vérillon,et al.  Cognition and artifacts: A contribution to the study of though in relation to instrumented activity , 1995 .

[3]  David Tall,et al.  Functions and Calculus , 1996 .

[4]  Michèle Artigue,et al.  Le Logiciel ‘Derive’ comme revelateur de phenomenes didactiques lies a l'utilisation d'environnements informatiques pour l'apprentissage , 1997 .

[5]  P. Rabardel.  Les hommes et les technologies; approche cognitive des instruments contemporains , 1995 .

[6]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .

[7]  Andrew Boyd,et al.  Interactive video: A bridge between motion and math , 1996, Int. J. Comput. Math. Learn..

[8]  Yves Chevallard,et al.  Concepts fondamentaux de la didactique : perspectives apportées par une approche anthropologique , 1991 .

[9]  Luc Trouche,et al.  Seeing is Reality: How Graphic Calculators May Influence the Conceptualization of Limits , 1996 .

[10]  Celia Hoyles,et al.  Windows on Mathematical Meanings , 1996 .

[11]  G. Vergnaud.  La théorie des champs conceptuels , 1989 .

[12]  Jean-Baptiste Lagrange,et al.  Techniques and Concepts in Pre-calculus Using CAS: A Two Year Classroom Experiment with the TI-92. , 1999 .

[13]  A. Sfard.  On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin , 1991 .

[14]  Luc Trouche,et al.  The Complex Process of Converting Tools into Mathematical Instruments: The Case of Calculators , 1998, Int. J. Comput. Math. Learn..