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  1. Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
    Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...)
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  • Nonsymbolic approximate arithmetic in children: Abstract addition prior to instruction.(Manuscript under review.Hilary Barth, Lacey Beckmann & Elizabeth S. Spelke - 2008 - Developmental Psychology 44 (5).
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  • Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys.David Barner, Justin Wood, Marc Hauser & Susan Carey - 2008 - Cognition 107 (2):603-622.
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  • Calibrating the mental number line.Véronique Izard & Stanislas Dehaene - 2008 - Cognition 106 (3):1221-1247.
    Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...)
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  • The Developmental Trajectory of the Operational Momentum Effect.Pedro Pinheiro-Chagas, Daniele Didino, Vitor G. Haase, Guilherme Wood & André Knops - 2018 - Frontiers in Psychology 9.
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  • Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.Maja Rodic, Tatiana Tikhomirova, Tatiana Kolienko, Sergey Malykh, Olga Bogdanova, Dina Y. Zueva, Elena I. Gynku, Sirui Wan, Xinlin Zhou & Yulia Kovas - 2015 - Frontiers in Psychology 6.
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  • Apes are intuitive statisticians.Hannes Rakoczy, Annette Clüver, Liane Saucke, Nicole Stoffregen, Alice Gräbener, Judith Migura & Josep Call - 2014 - Cognition 131 (1):60-68.
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  • Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual‐Task Study With Preschoolers.Iro Xenidou‐Dervou, Ernest C. D. M. Lieshout & Menno Schoot - 2014 - Cognitive Science 38 (1):101-127.
    Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of children's math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a (...)
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  • The innateness hypothesis and mathematical concepts.Helen3 De Cruz & Johan De Smedt - 2010 - Topoi 29 (1):3-13.
    In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist (...)
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  • Perceptual addition of continuous magnitudes in an ‘artificial algebra’.Nicola J. Morton, Cameron Hooson-Smith, Kate Stuart, Simon Kemp & Randolph C. Grace - 2024 - Cognition 244 (C):105710.
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  • Where our number concepts come from.Susan Carey - 2009 - Journal of Philosophy 106 (4):220-254.
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  • Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling.Camilla K. Gilmore, Shannon E. McCarthy & Elizabeth S. Spelke - 2010 - Cognition 115 (3):394-406.
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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.
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  • Quantity evaluations in Yudja: judgements, language and cultural practice.Suzi Lima & Susan Rothstein - 2020 - Synthese 197 (9):3851-3873.
    In this paper we explore the interpretation of quantity expressions in Yudja, an indigenous language spoken in the Amazonian basin, showing that while the language allows reference to exact cardinalities, it does not generally allow reference to exact measure values. It does, however, allow non-exact comparison along continuous dimensions. We use this data to argue that the grammar of exact measurement is distinct from a grammar allowing the expression of exact cardinalities, and that the grammar of counting and the grammar (...)
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  • The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters.Iro Xenidou-Dervou, Camilla Gilmore, Menno van der Schoot & Ernest C. D. M. van Lieshout - 2015 - Frontiers in Psychology 6.
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  • Free-ranging rhesus monkeys spontaneously individuate and enumerate small numbers of non-solid portions.Justin N. Wood, Marc D. Hauser, David D. Glynn & David Barner - 2008 - Cognition 106 (1):207-221.
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  • What do monkeys know about others’ knowledge?Lindsey A. Drayton & Laurie R. Santos - 2018 - Cognition 170 (C):201-208.
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  • Spontaneous number representation in mosquitofish.Marco Dadda, Laura Piffer, Christian Agrillo & Angelo Bisazza - 2009 - Cognition 112 (2):343-348.
    While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated that in fish the same set of signature limits that characterize non-verbal numerical systems in primates is present but yet to provide any demonstration that fish can really represent number rather than basing their (...)
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  • Commentary: “An Evaluation of Universal Grammar and the Phonological Mind”—UG Is Still a Viable Hypothesis.Iris Berent - 2016 - Frontiers in Psychology 7.
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