Introduction
Registers are defined as semiotic systems which fulfill a specific cognitive function: transforming any semiotic representations they give the means of producing into other ones for getting new information or new knowledge, which is not the case of all semiotic systems used in mathematical activity, for instance gestures. Mathematics requires semiotic systems that fulfill the specific transformation function analyzed by Frege (1892). It consists of substituting one semiotic representation b for another a, if both representations denote the same object, such as for example in calculations. Registers are key tools for analyzing the cognitive processes of mathematical thinking, because they allow separating two kinds of substitution whose cognitive requirements are distinct: between two representations from two different semiotic systems and between two representations within the same semiotic system. The former is called conversion and the latter treatment.
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Duval, R. (2020). Registers of Semiotic Representation. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_100033
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