Numbers, Language, and the Human Mind

Abstract

The acquisition of a counting sequence Pre-numerical props for number assignments Gateway to number Language and the emergence of counting and cardinality 6 The organisation of our cognitive number domain Representation of counting words as numerical tools Concepts of numerical quantity Abstract cardinalities Concepts of measure Concepts of numerical rank Concepts of numerical label The architecture of the number domain 7 Non-verbal number systems Arabic numerals as a non-verbal number sequence The development of non-verbal numerals: From iconic representations to numerical tools Two alternative number sequences: The correlation of counting words and Arabic numerals 8 Numbers in language: The grammatical integration of numerical tools

The faculty of language: what's special about it?

“…For example, the notion of a "week" depends on counting time periods that cannot all be perceived at once; we doubt that such a concept could be developed or learned without the mediation of language. More striking is the possibility that numbers themselves (beyond those that can be subitized) are parasitic on language-that they depend on learning the sequence of number words, the syntax of number phrases, or both (Bloom, 1994a;Wiese, 2004) (though see Grinstead, MacSwan, Curtiss, & Gelman, 1997, for a contrary view). Vast domains of human understanding, including the supernatural and sacred, the specifics of folk and formal science, human-specific kinship systems (such as the distinction between cross-and parallel cousins), and formal social roles (such as "justice of the peace" and "treasurer"), can be acquired only with the help of language.…”

“…As for recursion in language evolving out of recursion in number cognition, if this involves co-opting at all (see Grinstead et al, 1997Grinstead et al, , 2004, for doubts), the proposed direction in HCF's hypothesis would appear to be backwards (Bloom, 1994a;Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999;Wiese, 2004). Recursive language is a human universal or near-universal, emerging reliably and spontaneously in ontogeny.…”

Iconic and non-iconic stages in number development: the role of language

“…This yields iconic representations of set sizes; representations that do not rely on dependent linking, but are associated by individual similarity with the objects they represent: the size of an empirical set is represented by the cardinality of another set (a set of object tokens) or the size of an analog magnitude (in this latter case the representation is not one of discrete cardinality, but of accumulated quantity, suggesting that cardinal concepts based on object tokens play a more central role for the development of discrete numerical representations [8,28,34]). …”

Das competências quantitativas iniciais para o conceito de número natural: quais as trilhas possíveis?

“…Uma vez que, nem o mecanismo de representação de magnitude e nem mesmo o mecanismo de representação mental de objetos individualizados têm as propriedades dos números naturais. As propriedades que definem os números naturais (para uma revisão ver Wiese, 2003) são: as entidades são distintas, elas formam uma progressão e esta progressão é infinita. Desta forma, os números naturais são definidos pelas relações que constituem a progressão infinita e não por representações instanciadas de quantidades.…”

“…No processo de elaboração dessa ideia de número, as representações mentais produzidas pelas crianças são baseadas em processos cognitivos gerais (como por exemplo, o processo da visão, da memória, da percepção tátil dos objetos) sem atrelamento específico a conhecimentos de base numérica, pelo menos inicialmente. Assim, para esses pesquisadores, a construção plena de um conceito de nú-mero que englobe a complexidade de entender o número natural nas dimensões cardinal, ordinal e nominal deriva de um longo processo de desenvolvimento (Clearfield & Mix, 1999Huttenlocher, Duffy, & Levine, 2002;Mix, 2002;Mix, Hutenllocher, & Levine 2002a, 2002bMix & Sandhofer, 2007;Wiese, 2003).…”