The development of mathematical abstraction in the nursery

The aims of this article are to document the types of signs that young children make to represent their mathematical thinking, and to determine the extent to which features of usage-based language acquisition are evident in children’s early graphical communications made in mathematical contexts. Studies of young children’s symbolic principles in ontogeny and research into the acquisition and development of language provide insights into the rich foundational knowledge on which they build their early mathematical inscriptions. The study conceives of children’s mathematical abstractions as emergent cognitive representations, originating in their need to communicate within personally meaningful contexts. The collected ethnographic data comprise mathematical inscriptions from seven children aged three to four years in their nursery school and written observations from their teachers and the first researcher. Analysis follows an interpretive, social-semiotic paradigm; the inscriptions were analysed to show how they convey their emerging mathematical understandings, and how this supports their emergent abstractions. The findings illuminate children’s strategies as they communicate their thinking, indicating the importance of symbolic number knowledge in acquiring the abstract graphical language of mathematics.