The importance of the semiotic representations and their relations with the cognitive processes have been shown by many researches in Mathematics Education (Artigue, D’Amore, Duval, Gagatsis, Mackie, Pavlopoulou, Tall). Deep learning, that is the conceptual acquisition of a concept, occurs when the pupil is able to pass from a representation in a given register to another one in another register or in the same register. In this paper we want to show how CAS, with direct and active involvement of the student, can improve learning in the above sense. This is because such environments are multiple representation systems, symbolic, graphical, numerical, parametric, logical, … Students are often in front of diverse answers to the same questions (for example solving systems of linear equations in Derive can be done by SOLVE or SOLUTIONS or simply by PLOT) so they are stimulated to concentrate their attention to the meaning of the results obtained by the computer, to establish links among different ways of seeing same formal expression which acquire different meaning in diverse contexts. The ability to recognize such different representations and their common properties conduces to construct the “abstract” concept of a mathematical object or process. Such abstraction is foster by CAS use.

### On the CAS and the coordination of semiotic registers

#### Abstract

The importance of the semiotic representations and their relations with the cognitive processes have been shown by many researches in Mathematics Education (Artigue, D’Amore, Duval, Gagatsis, Mackie, Pavlopoulou, Tall). Deep learning, that is the conceptual acquisition of a concept, occurs when the pupil is able to pass from a representation in a given register to another one in another register or in the same register. In this paper we want to show how CAS, with direct and active involvement of the student, can improve learning in the above sense. This is because such environments are multiple representation systems, symbolic, graphical, numerical, parametric, logical, … Students are often in front of diverse answers to the same questions (for example solving systems of linear equations in Derive can be done by SOLVE or SOLUTIONS or simply by PLOT) so they are stimulated to concentrate their attention to the meaning of the results obtained by the computer, to establish links among different ways of seeing same formal expression which acquire different meaning in diverse contexts. The ability to recognize such different representations and their common properties conduces to construct the “abstract” concept of a mathematical object or process. Such abstraction is foster by CAS use.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11386/1071972`
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