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  1. Testimony and Children’s Acquisition of Number Concepts.Helen De Cruz - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge: Approaches From Psychology and Cognitive Science. New York: Routledge. pp. 172-186.
    An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine).
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  • Seven does not mean natural number, and children know more than you think.Barbara W. Sarnecka - 2008 - Behavioral and Brain Sciences 31 (6):668-669.
    Rips et al.'s critique is misplaced when it faults the induction model for not explaining the acquisition of meta-numerical knowledge: This is something the model was never meant to explain. More importantly, the critique underestimates what children know, and what they have achieved, when they learn the cardinal meanings of the number words through.
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  • Learning to represent exact numbers.Barbara W. Sarnecka - 2015 - Synthese 198 (Suppl 5):1001-1018.
    This article focuses on how young children acquire concepts for exact, cardinal numbers. I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey. In this framework, the (...)
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  • Assessing the knower-level framework: How reliable is the Give-a-Number task?Elisabeth Marchand, Jarrett T. Lovelett, Kelly Kendro & David Barner - 2022 - Cognition 222 (C):104998.
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  • Cognitive Structuralism: Explaining the Regularity of the Natural Numbers Progression.Paula Quinon - 2022 - Review of Philosophy and Psychology 13 (1):127-149.
    According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...)
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