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  • 1 Hungarian Academy of Sciences and Pázmány Péter Catholic University, Piliscsaba
  • 2 University of Technology and Economics, Budapest

Whereas it is a well-established fact that young children can perform intuitive addition and subtraction, it is an open question whether they are capable of multiplicative operations on sets before receiving formal training. Earlier studies devoted to the study of intuitive arithmetic sought for evidence of intuitive multiplication in children’s ability to distinguish proportional relations between quantities and numerosities. This paper claims that multiplication operations are present in children’s everyday communication, in their understanding and producing sentences with two numerical quantifiers and a distributivity marker such as the Hungarian Mindhárom gyerek két autóval játszik ’Every one of three kids is playing with two cars’, and Három gyerek két-két autóval játszik ’Three kids are playing with two cars apiece’. The paper gives account of an experiment testing how 5–7-year-old Hungarian children with no training in arithmetic operations interpret such sentences. The experiment shows that they have access to the multiplicative readings of distributive constructions; they not only accept them as true but at the age of 6–7 they can also actively compute the product of multiplication. The results also outline the acquisition path of multiplication, showing that children first multiply sets of concrete objects, then they represent the objects by their fingers, before they learn to manipulate sets mentally. Our results highlight the fact that language and mathematics are intertwined not only on the lexical level. Grammatical operations involving quantified expressions, among others, encode logical or mathematical operations on sets. Even if linguistic encoding is often ambiguous, grammatically encoded mathematical operations pave the way for abstract mathematics.

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