Abstract
This chapter addresses the problem of the development of mathematical symbol use in the context of young children’s play and everyday talk. Starting out from a Vygotskian perspective, it is assumed that in the development of the meaning of everyday mathematics-like terms, these gradually acquire a more definite mathematical meaning as a result of the children’s participation in mathematical activities in school or everyday practices, and of the provoked reflection on the interrelationships between signs and meanings (the so called `semiotic activity’). In order to examine some of the involved assumptions the author reports a number of his previous observational and interview studies with primary school children. From these studies it can be demonstrated that semiotic activity is indeed accessible for young children. If this mechanism is really involved in the development of mathematics-like word meanings towards more specific mathematical meanings, it should be logically derived that the development of these meanings is dependent on the frequency and nature of the semiotic activity involved, and as such we should expect that the development of the meaning of different notions is not a function of ontogenesis as such, but varies over the different notions. This could be demonstrated by the reported interview studies.
We should break the barriers surrounding mathematics
H. Freudenthal (1973, p. 72), Mathematics as an educational task
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van Oers, B. (2002). The Mathematization of Young Children’s Language. In: Gravemeijer, K., Lehrer, R., Van Oers, B., Verschaffel, L. (eds) Symbolizing, Modeling and Tool Use in Mathematics Education. Mathematics Education Library, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3194-2_4
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