Switch to: References

Add citations

You must login to add citations.
  1. Children’s mappings between number words and the approximate number system.Darko Odic, Mathieu Le Corre & Justin Halberda - 2015 - Cognition 138 (C):102-121.
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Exact equality and successor function: Two key concepts on the path towards understanding exact numbers.Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene - 2008 - Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • Non-symbolic arithmetic in adults and young children.Hilary Barth, Kristen La Mont, Jennifer Lipton, Stanislas Dehaene, Nancy Kanwisher & Elizabeth Spelke - 2006 - Cognition 98 (3):199-222.
    Download  
     
    Export citation  
     
    Bookmark   63 citations  
  • Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense.Ilona Friso-van den Bos, Evelyn H. Kroesbergen & Johannes E. H. Van Luit - 2018 - Frontiers in Psychology 9.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles.Mathieu Le Corre & Susan Carey - 2007 - Cognition 105 (2):395-438.
    Download  
     
    Export citation  
     
    Bookmark   102 citations  
  • Growth of symbolic number knowledge accelerates after children understand cardinality.David C. Geary & Kristy vanMarle - 2018 - Cognition 177 (C):69-78.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Kant on the Acquisition of Geometrical Concepts.John J. Callanan - 2014 - Canadian Journal of Philosophy 44 (5-6):580-604.
    It is often maintained that one insight of Kant's Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept's acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Does learning to count involve a semantic induction?Kathryn Davidson, Kortney Eng & David Barner - 2012 - Cognition 123 (1):162-173.
    Download  
     
    Export citation  
     
    Bookmark   43 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   44 citations  
  • Language as a Necessary Condition for Complex Mental Content: A Review of the Discussion on Spatial and Mathematical Thinking. [REVIEW]Arkadiusz Gut & Robert Mirski - 2018 - Roczniki Filozoficzne 66 (3):33-56.
    In this article we review the discussion over the thesis that language serves as an integrator of contents coming from different cognitive modules. After presenting the theoretical considerations, we examine two strands of empirical research that tested the hypothesis — spatial cognition and mathematical cognition. The idea shared by both of them is that each is composed of two separate modules processing information of a specific kind. For spatial thinking these are geometric information about the location of the object and (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers — A cross-linguistic study.Maciej Haman, Katarzyna Lipowska, Mojtaba Soltanlou, Krzysztof Cipora, Frank Domahs & Hans-Christoph Nuerk - 2023 - Cognition 235 (C):105383.
    Download  
     
    Export citation  
     
    Bookmark  
  • Learning the Natural Numbers as a Child.Stefan Buijsman - 2017 - Noûs 53 (1):3-22.
    How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • How numerals support new cognitive capacities.Stefan Buijsman - 2020 - Synthese 197 (9):3779-3796.
    Mathematical cognition has become an interesting case study for wider theories of cognition. Menary :1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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).
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Children’s understanding of the relationship between addition and subtraction.Camilla K. Gilmore & Elizabeth S. Spelke - 2008 - Cognition 107 (3):932-945.
    In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Children's Understanding of the Natural Numbers’ Structure.Jennifer Asmuth, Emily M. Morson & Lance J. Rips - 2018 - Cognitive Science 42 (6):1945-1973.
    When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010; Siegler & Opfer, 2003). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011; Cantlon, Cordes, Libertus, & Brannon, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • A dissociation between small and large numbers in young children’s ability to “solve for x” in non-symbolic math problems.Melissa M. Kibbe & Lisa Feigenson - 2017 - Cognition 160 (C):82-90.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Preschool children master the logic of number word meanings.Jennifer S. Lipton & Elizabeth S. Spelke - 2006 - Cognition 98 (3):57-66.
    Download  
     
    Export citation  
     
    Bookmark   11 citations