Abstract
In this chapter, we present and analyze calculator-based tasks and activities conceived as means for the learning of mathematics in several grades of primary and secondary school. The tasks or activities have been experimented with students and pre-service teachers. The intent is to show how a set of calculator-based tasks can be organized in a way that they promote the development of theoretical aspects. The results show that a high variety of numerical activities can be proposed in such a way, but that a further institutional promotion is necessary. The analyses are based on the concept of ‘milieu’ by Brousseau (Theory of didactical situations in mathematics. Kluwer, Dordrecht, 1997) with an anthropological approach (Chevallard Y, Recherches en Didactique des Mathématiques, 19(2):221–266, 1999; Lagrange JB, Educational Studies in Mathematics 43(1):1–30, 2000).
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Notes
- 1.
In Geneva, secondary teachers follow a two-year training and in the second year they teach half-time in school.
- 2.
It is the official calculator in the schools of Geneva, provided to all 10 years-old students.
- 3.
Starting from zero , that is after a reset of memory.
- 4.
See detailed praxeological analysis below.
- 5.
Our favourite one being ‘a / b is a real solution of equation b x = a with a, b integers and b different from zero , positive real numbers being defined as lengths ’.
- 6.
A TI-92 in this case.
- 7.
There is a CAS part in Geogebra (Geogebra.org); Aplusix is a useful program allowing direct control of numerical equalities and algebraic equivalences (Aplusix.com). Other tools can be easily found on the web , e.g. www.calculatorsoup.com/calculators/math/prime-factors.php.
- 8.
They also are of the opinion that transcendent functions are programmed according to their Taylor series . Most of them ignore the CORDIC algorithms (https://en.wikipedia.org/wiki/CORDIC).
- 9.
There is a way to enhance this ‘symbol gap’. Following Brousseau’s formulation phase (1997), the teacher may propose a contest between groups: he will choose one student from each group, and then give a value for the number of tiles of a side . The student that gives the quicker answer gets a point for her group. The groups have the right and the time to prepare a method. In the subsequent validation phase the contest is about the best methods.
- 10.
The TI30X Multiview , given to all students in the schools of Geneva.
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Floris, R. (2017). Pocket Calculator as an Experimental Milieu: Emblematic Tasks and Activities. In: Aldon, G., Hitt, F., Bazzini, L., Gellert, U. (eds) Mathematics and Technology. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-51380-5_9
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