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  1. Preschoolers and Multi-Digit Numbers: A Path to Mathematics Through the Symbols Themselves.Lei Yuan, Richard W. Prather, Kelly S. Mix & Linda B. Smith - 2019 - Cognition 189:89-104.
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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, or on the ability to approximate quantities, or both, (...)
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  • Bootstrapping of Integer Concepts: The Stronger Deviant-Interpretation Challenge.Markus Pantsar - 2021 - Synthese 199 (3-4):5791-5814.
    Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...)
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  • Linear Spatial–Numeric Associations Aid Memory for Single Numbers.John Opfer, Dan Kim, Christopher J. Young & Francesca Marciani - 2019 - Frontiers in Psychology 10.
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  • Children’s Mappings Between Number Words and the Approximate Number System.Darko Odic, Mathieu Le Corre & Justin Halberda - 2015 - Cognition 138 (C):102-121.
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  • Of Huge Mice and Tiny Elephants: Exploring the Relationship Between Inhibitory Processes and Preschool Math Skills.Rebecca Merkley, Jodie Thompson & Gaia Scerif - 2015 - Frontiers in Psychology 6.
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  • Expert Attention: Attentional Allocation Depends on the Differential Development of Multisensory Number Representations.Pawel J. Matusz, Rebecca Merkley, Michelle Faure & Gaia Scerif - 2019 - Cognition 186 (C):171-177.
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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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  • Children’s Non-Symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability.Yanjun Li, Meng Zhang, Yinghe Chen, Zhijun Deng, Xiaoshuang Zhu & Shijia Yan - 2018 - Frontiers in Psychology 9.
  • Deficits in Approximate Number System Acuity and Mathematical Abilities in 6.5-Year-Old Children Born Extremely Preterm.Melissa E. Libertus, Lea Forsman, Ulrika Adén & Kerstin Hellgren - 2017 - Frontiers in Psychology 8.
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  • A Rational Explanation for Links Between the ANS and Math.Melissa E. Libertus, Shirley Duong, Danielle Fox, Leanne Elliott, Rebecca McGregor, Andrew Ribner & Alex M. Silver - 2021 - Behavioral and Brain Sciences 44.
    The proposal by Clarke and Beck offers a new explanation for the association between the approximate number system and math. Previous explanations have largely relied on developmental arguments, an underspecified notion of the ANS as an “error detection mechanism,” or affective factors. The proposal that the ANS represents rational numbers suggests that it may directly support a broader range of math skills.
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  • Gesture as a Window Onto Children’s Number Knowledge.Elizabeth A. Gunderson, Elizabet Spaepen, Dominic Gibson, Susan Goldin-Meadow & Susan C. Levine - 2015 - Cognition 144 (C):14-28.
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  • Growth of Symbolic Number Knowledge Accelerates After Children Understand Cardinality.David C. Geary & Kristy vanMarle - 2018 - Cognition 177 (C):69-78.
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  • The Number Sense Represents (Rational) Numbers.Sam Clarke & Jacob Beck - 2021 - Behavioral and Brain Sciences 44:1-57.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...)
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  • Do Analog Number Representations Underlie the Meanings of Young Children’s Verbal Numerals?Susan Carey, Anna Shusterman, Paul Haward & Rebecca Distefano - 2017 - Cognition 168 (C):243-255.
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