Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-03T05:22:10.307Z Has data issue: false hasContentIssue false

17 - Numerical Cognition and Executive Functions

Development As Progressive Inhibitory Control of Misleading Visuospatial Dimensions

from Subpart II.2 - Childhood and Adolescence: The Development of Human Thinking

Published online by Cambridge University Press:  24 February 2022

By
Margot Roell ,
Olivier Houdé ,
Grégoire Borst  and
Arnaud Viarouge
Edited by
Olivier Houdé  and
Grégoire Borst
Olivier Houdé
Affiliation:
Université de Paris V
Grégoire Borst
Affiliation:
Université de Paris V
Get access

Summary

Theories have ventured to explain how the human brain has gained the unique ability to develop mathematical concepts and theories. One theory states that mathematics has appeared as a by-product of the human language faculty (Chomsky, 2006). Alternatively, recent cognitive neuroscience research have postulated that mathematics arose from non-linguistic intuitions of numbers and space (Dehaene, 2011; Dillon et al., 2013). Indeed, studies have observed that infants (Starkey & Cooper, 1980; Starkey et al., 1983) and Amazonian indigenous adults with no education in Mathematics and who do not possess number words (Dehaene et al. 2008, Pica et al., 2004) display abstract proto-mathematical intuitions of arithmetic and geometry. These ‘core knowledges’ (Spelke & Kinzler, 2007) have been theorized to be the ontological building blocks that scaffold our ability for representing numbers symbolically and performing exact arithmetic (Starr et al., 2013). They have been found to be predictive of later, more complex mathematical abilities (Gilmore et al., 2010; Halberda et al., 2008; Starr et al., 2013), supporting the idea that complex mathematics would arise from core representations of number and space (Amalric & Dehaene, 2016). Extensive research has shown that numerical and spatial cognition were tightly connected (Hubbard et al., 2005). In some contexts, this relation between number and visuospatial dimensions, such as spatial extent or density, can lead to interferences which can hinder the development of math abilities.

Type
Chapter
Information
The Cambridge Handbook of Cognitive Development , pp. 383 - 407
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adleman, N. E., Menon, V., Blasey, C. M., White, C. D., Warsofsky, I. S., Glover, G. H., & Reiss, A. L. (2002). A developmental fMRI study of the Stroop color-word task. NeuroImage, 16, 61–75.Google Scholar
Ahr, E., Houdé, O., & Borst, G. (2016). Inhibition of the mirror generalization process in reading in school-aged children. Journal of Experimental Child Psychology, 145, 157–165.CrossRefGoogle ScholarPubMed
Aïte, A., Berthoz, A., Vidal, J., Roëll, M., Zaoui, M., Houdé, O., & Borst, G. (2016). Taking a third-person perspective requires inhibitory control: Evidence from a developmental negative priming study. Child Development, 87, 1825–1840.CrossRefGoogle ScholarPubMed
Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences (USA), 113, 4909–4917.Google Scholar
Anobile, G., Cicchini, G. M., & Burr, D. C. (2014). Separate mechanisms for perception of numerosity and density. Psychological Science, 25, 265–270.Google Scholar
Anokhin, A. P., Heath, A. C., & Myers, E. (2004). Genetics, prefrontal cortex, and cognitive control: A twin study of event-related brain potentials in a response inhibition task. Neuroscience Letters, 368, 314–318.CrossRefGoogle Scholar
Ansari, D., Fugelsang, J. A., Dhital, B., & Venkatraman, V. (2006). Dissociating response conflict from numerical magnitude processing in the brain: An event-related fMRI study. NeuroImage, 32, 799–805.Google Scholar
Aron, A. R., Robbins, T. W., & Poldrack, R. A. (2004). Inhibition and the right inferior frontal cortex. Trends in Cognitive Sciences, 8, 170–177.Google Scholar
Bench, C. J., Frith, C. D., Grasby, P. M., Friston, K. J., Paulesu, E., Frackowiak, R. S. J., & Dolan, R. J. (1993). Investigations of the functional anatomy of attention using the Stroop test. Neuropsychologia, 31, 907–922.CrossRefGoogle ScholarPubMed
Besner, D., & Coltheart, M. (1979). Ideographic and alphabetic processing in skilled reading of English. Neuropsychologia, 17, 467–472.CrossRefGoogle ScholarPubMed
Blair, C., Knipe, H., & Gamson, D. (2008). Is there a role for executive functions in the development of mathematics ability? Mind, Brain, and Education, 2, 80–89.CrossRefGoogle Scholar
Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647–663.Google Scholar
Borgmann, K., Fugelsang, J., Ansari, D., & Besner, D. (2011). Congruency proportion reveals asymmetric processing of irrelevant physical and numerical dimensions in the size congruity paradigm. Canadian Journal of Experimental Psychology/Revue Canadienne de Psychologie Expérimentale, 65, 98–104.CrossRefGoogle ScholarPubMed
Borst, G., Ahr, E., Roell, M., & Houdé, O. (2015). The cost of blocking the mirror-generalization process in reading: Evidence for the role of inhibitory control in discriminating letters with lateral mirror-image counterparts. Psychonomic Bulletin & Review, 22, 228–234.Google Scholar
Borst, G., Cachia, A., Vidal, J., Simon, G., Fischer, C., Pineau, A., … Houdé, O. (2014). Folding of the anterior cingulate cortex partially explains inhibitory control during childhood: A longitudinal study. Developmental Cognitive Neuroscience, 9, 126–135.CrossRefGoogle ScholarPubMed
Borst, G., Poirel, N., Pineau, A., Cassotti, M., & Houdé, O. (2013a). Inhibitory control efficiency in a Piaget-like class-inclusion task in school-age children and adults: A developmental negative priming study. Developmental Psychology, 49, 1366–1374.Google Scholar
Borst, G., Simon, G., Vidal, J., & Houdé, O. (2013b). Inhibitory control and visuo-spatial reversibility in Piaget’s seminal number conservation task: A high-density ERP study. Frontiers in Human Neuroscience, 7, 920.CrossRefGoogle ScholarPubMed
Botvinick, M. M. (2007). Conflict monitoring and decision making: Reconciling two perspectives on anterior cingulate function. Cognitive, Affective, & Behavioral Neuroscience, 7, 356–366.Google Scholar
Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., & Cohen, J. D. (2001). Conflict monitoring and cognitive control. Psychological Review, 108, 624–652.Google Scholar
Brainerd, C. J., & Reyna, V. F. (2001). Fuzzy-trace theory: Dual processes in memory, reasoning, and cognitive neuroscience. Advances in Child Development and Behavior, 28, 41–100.CrossRefGoogle ScholarPubMed
Bub, D. N., Masson, M. E. J., & Lalonde, C. E. (2006). Cognitive control in children: Stroop interference and suppression of word reading. Psychological Science, 17, 351–357.CrossRefGoogle ScholarPubMed
Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118, 32–44.CrossRefGoogle Scholar
Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273–293.CrossRefGoogle ScholarPubMed
Cachia, A., Borst, G., Tissier, C., Fisher, C., Plaze, M., Gay, O., … Raznahan, A. (2016). Longitudinal stability of the folding pattern of the anterior cingulate cortex during development. Developmental Cognitive Neuroscience, 19, 122–127.CrossRefGoogle ScholarPubMed
Cappelletti, M., Didino, D., Stoianov, I., & Zorzi, M. (2014). Number skills are maintained in healthy ageing. Cognitive Psychology, 69, 25–45.CrossRefGoogle ScholarPubMed
Cappelletti, M., Lee, H. L., Freeman, E. D., & Price, C. J. (2010). The role of right and left parietal lobes in the conceptual processing of numbers. Journal of Cognitive Neuroscience, 22, 331–346.CrossRefGoogle ScholarPubMed
Chomsky, N. (2006). Language and Mind (3rd ed.). Cambridge: Cambridge University Press.Google Scholar
Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM: The International Journal on Mathematics Education, 47, 759–770.Google Scholar
Cohen Kadosh, R., Cohen Kadosh, K., & Henik, A. (2008). When brightness counts: The neuronal correlate of numerical-luminance interference. Cerebral Cortex, 18, 337–343.Google Scholar
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3, 63–68.CrossRefGoogle Scholar
Dakin, S. C., Tibber, M. S., Greenwood, J. A., Kingdom, F. A. A., & Morgan, M. J. (2011). A common visual metric for approximate number and density. Proceedings of the National Academy of Sciences (USA), 108, 19552–19557.CrossRefGoogle ScholarPubMed
Daurignac, E., Houdé, O., & Jouvent, R. (2006). Negative priming in a numerical Piaget-like task as evidenced by ERP. Journal of Cognitive Neuroscience, 18, 730–736.Google Scholar
de Hevia, M. D., Girelli, L., Bricolo, E., & Vallar, G. (2008). The representational space of numerical magnitude: Illusions of length. The Quarterly Journal of Experimental Psychology, 61, 1496–1514.Google Scholar
de Hevia, M. D., Vanderslice, M., & Spelke, E. S. (2012). Cross-dimensional mapping of number, length and brightness by preschool children. PLoS ONE, 7, e35530.Google Scholar
De Neys, W., Lubin, A., & Houdé, O. (2014). The smart nonconserver: Preschoolers detect their number conservation errors. Child Development Research, 2014, 1–7.Google Scholar
De Neys, W., & Vanderputte, K. (2011). When less is not always more: Stereotype knowledge and reasoning development. Developmental Psychology, 47, 432–441.Google Scholar
Defever, E., Reynvoet, B., & Gebuis, T. (2013). Task- and age-dependent effects of visual stimulus properties on children’s explicit numerosity judgments. Journal of Experimental Child Psychology, 116, 216–233.Google Scholar
Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics (Rev. and updated ed). New York: Oxford University Press.Google Scholar
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371.Google Scholar
Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56, 384–398.Google Scholar
Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21, 355–361.Google Scholar
Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in western and Amazonian indigene cultures. Science, 320, 1217–1220.Google Scholar
Dempster, F. N. (1992). The rise and fall of the inhibitory mechanism: Toward a unified theory of cognitive development and aging. Developmental Review, 12, 45–75.CrossRefGoogle Scholar
Desmet, L., Grégoire, J., & Mussolin, C. (2010). Developmental changes in the comparison of decimal fractions. Learning and Instruction, 20, 521–532.CrossRefGoogle Scholar
DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265.CrossRefGoogle ScholarPubMed
DeWind, N. K., & Brannon, E. M. (2012). Malleability of the approximate number system: Effects of feedback and training. Frontiers in Human Neuroscience, 6, 68.CrossRefGoogle ScholarPubMed
DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39–49.Google Scholar
Diamond, A. (2000). Close interrelation of motor development and cognitive development and of the cerebellum and prefrontal cortex. Child Development, 71, 44–56.CrossRefGoogle ScholarPubMed
Diamond, A., & Goldman-Rakic, P. S. (1989). Comparison of human infants and rhesus monkeys on Piaget’s AB task: Evidence for dependence on dorsolateral prefrontal cortex. Experimental Brain Research, 74, 24–40.CrossRefGoogle ScholarPubMed
Dillon, M. R., Huang, Y., & Spelke, E. S. (2013). Core foundations of abstract geometry. Proceedings of the National Academy of Sciences (USA), 110, 14191–14195.Google Scholar
Dormal, V., & Pesenti, M. (2009). Common and specific contributions of the intraparietal sulci to numerosity and length processing. Human Brain Mapping, 30, 2466–2476.Google Scholar
Dubois, B., Verin, M., Teixera-Ferreira, C., Thierry, A. M., Glowinski, J., Goldman-Rakic, P. S., & Christen, Y. (1994). Motor and Cognitive Functions of the Prefrontal Cortex. Berlin: Springer.Google Scholar
Duncan, E. M., & McFarland, C. E. (1980). Isolating the effects of symbolic distance, and semantic congruity in comparative judgments: An additive-factors analysis. Memory & Cognition, 8, 612–622.CrossRefGoogle ScholarPubMed
Durkin, K., & Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction, 22, 206–214.CrossRefGoogle Scholar
Egner, T., & Hirsch, J. (2005). Cognitive control mechanisms resolve conflict through cortical amplification of task-relevant information. Nature Neuroscience, 8, 1784–1790.Google Scholar
Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A., & Senn, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Developmental Neuropsychology, 26, 465–486.Google Scholar
Fair, D. A., Cohen, A. L., Power, J. D., Dosenbach, N. U. F., Church, J. A., Miezin, F. M., … Petersen, S. E. (2009). Functional brain networks develop from a ‘local to distributed’ organization. PLoS Computational Biology, 5, e1000381.Google Scholar
Fjell, A. M., Walhovd, K. B., Brown, T. T., Kuperman, J. M., Chung, Y., Hagler, D. J., … Gruen, J. (2012). Multimodal imaging of the self-regulating developing brain. Proceedings of the National Academy of Sciences (USA), 109, 19620–19625.Google Scholar
Foltz, G. S., Poltrock, S. E., & Plotts, G. R. (1984). Mental comparison of size and magnitude: Size congruity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 442–453.Google Scholar
Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16, 136–148.Google Scholar
Fuhs, M. W., McNeil, N. M., Kelley, K., O’Rear, C., & Villano, M. (2016). The role of non-numerical stimulus features in approximate number system training in preschoolers from low-income homes. Journal of Cognition and Development, 17, 737–764.Google Scholar
Gabriel, F. C., Szucs, D., & Content, A. (2013). The development of the mental representations of the magnitude of fractions. PLoS ONE, 8, e80016.Google Scholar
Gebuis, T., & Gevers, W. (2011). Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009). Cognition, 121, 248–252.Google Scholar
Gebuis, T., Herfs, I. K., Kenemans, J. L., De Haan, E. H. F., & Van der Smagt, M. J. (2009). The development of automated access to symbolic and non-symbolic number knowledge in children: An ERP study. European Journal of Neuroscience, 30, 1999–2008.CrossRefGoogle ScholarPubMed
Gebuis, T., Kenemans, J. L., de Haan, E. H. F., & van der Smagt, M. J. (2010). Conflict processing of symbolic and non-symbolic numerosity. Neuropsychologia, 48, 394–401.Google Scholar
Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology. General, 141, 642–648.Google Scholar
Gebuis, T., & Reynvoet, B. (2013). The neural mechanisms underlying passive and active processing of numerosity. Neuroimage, 70, 301–307.Google Scholar
Gelman, R. (1972). Logical capacity of very young children: Number invariance rules. Child Development, 43, 75.Google Scholar
Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., … Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS ONE, 8, e67374.Google Scholar
Gilmore, C., Cragg, L., Hogan, G., & Inglis, M. (2016). Congruency effects in dot comparison tasks: Convex hull is more important than dot area. Journal of Cognitive Psychology (Hove, England), 28, 923–931.CrossRefGoogle ScholarPubMed
Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115, 394–406.Google Scholar
Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76, 104–122.Google Scholar
Hadland, K. A., Rushworth, M. F. S., Passingham, R. E., Jahanshahi, M., & Rothwell, J. C. (2001). Interference with performance of a response selection task that has no working memory component: An rTMS comparison of the dorsolateral prefrontal and medial frontal cortex. Journal of Cognitive Neuroscience, 13, 1097–1108.Google Scholar
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668.Google Scholar
Harris, I. M., & Miniussi, C. (2003). Parietal lobe contribution to mental rotation demonstrated with rTMS. Journal of Cognitive Neuroscience, 15, 315–323.Google Scholar
Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10, 389–395.Google Scholar
Ho, C. S.-H., & Fuson, K. C. (1998). Children’s knowledge of teen quantities as tens and ones: Comparisons of Chinese, British, and American kindergartners. Journal of Educational Psychology, 90, 536–544.Google Scholar
Houdé, O. (2000). Inhibition and cognitive development: Object, number, categorization, and reasoning. Cognitive Development, 15, 63–73.Google Scholar
Houdé, O., & Borst, G. (2015). Evidence for an inhibitory-control theory of the reasoning brain. Frontiers in Human Neuroscience, 9, 148.Google Scholar
Houdé, O., & Guichart, E. (2001). Negative priming effect after inhibition of number/length interference in a Piaget-like task. Developmental Science, 4, 119–123.Google Scholar
Houdé, O., Pineau, A., Leroux, G., Poirel, N., Perchey, G., Lanoë, C., … Mazoyer, B. (2011). Functional magnetic resonance imaging study of Piaget’s conservation-of-number task in preschool and school-age children: A neo-Piagetian approach. Journal of Experimental Child Psychology, 110, 332–346.Google Scholar
Houdé, O., Rossi, S., Lubin, A., & Joliot, M. (2010). Mapping numerical processing, reading, and executive functions in the developing brain: An fMRI meta-analysis of 52 studies including 842 children: Meta-analysis of developmental fMRI data. Developmental Science, 13, 876–885.Google Scholar
Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.Google Scholar
Hurewitz, F., Gelman, R., & Schnitzer, B. (2006). Sometimes area counts more than number. Proceedings of the National Academy of Sciences (USA), 103, 19599–19604.Google Scholar
Jacobs, J. E., & Klaczynski, P. A. (2002). The development of judgment and decision making during childhood and adolescence. Current Directions in Psychological Science, 11, 145–149.Google Scholar
Joliot, M., Leroux, G., Dubal, S., Tzourio-Mazoyer, N., Houdé, O., Mazoyer, B., & Petit, L. (2009). Cognitive inhibition of number/length interference in a Piaget-like task: Evidence by combining ERP and MEG. Clinical Neurophysiology, 120, 1501–1513.Google Scholar
Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg, P., Golaszewski, S., … Ischebeck, A. (2005). Neural correlates of distance and congruity effects in a numerical Stroop task: An event-related fMRI study. NeuroImage, 25, 888–898.Google Scholar
Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L.-B., … Ischebeck, A. (2006). Neural correlates of the number-size interference task in children. NeuroReport, 17, 587–591.Google Scholar
Keller, L., & Libertus, M. (2015). Inhibitory control may not explain the link between approximation and math abilities in kindergarteners from middle class families. Frontiers in Psychology, 6, 685.Google Scholar
Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009a). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.Google Scholar
Knops, A., Viarouge, A., & Dehaene, S. (2009b). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception, & Psychophysics, 71, 803–821.Google Scholar
Knops, A., Zitzmann, S., & McCrink, K. (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4, 325.Google Scholar
Koechlin, E., Dehaene, S., & Mehler, J. (1997). Numerical transformations in five-month-old human infants. Mathematical Cognition, 3, 89–104.Google Scholar
Kok, A. (1999). Varieties of inhibition: Manifestations in cognition, event-related potentials and aging. Acta Psychologica, 101, 129–158. https://doi.org/10.1016/S0001–6918(99)00003-7Google Scholar
Konishi, S., Nakajima, K., Uchida, I., Kameyama, M., Nakahara, K., Sekihara, K., & Miyashita, Y. (1998). Transient activation of inferior prefrontal cortex during cognitive set shifting. Nature Neuroscience, 1, 80–84.Google Scholar
Lammertyn, J., Fias, W., & Lauwereyns, J. (2002). Semantic influences on feature-based attention due to overlap of neural circuits. Cortex, 38, 878–882.Google Scholar
Leibovich, T., Henik, A., & Salti, M. (2015). Numerosity processing is context driven even in the subitizing range: An fMRI study. Neuropsychologia, 77, 137–147.Google Scholar
Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From ‘sense of number’ to ‘sense of magnitude’: The role of continuous magnitudes in numerical cognition. The Behavioral and Brain Sciences, 40, e164.Google Scholar
Leroux, G., Joliot, M., Dubal, S., Mazoyer, B., Tzourio-Mazoyer, N., & Houdé, O. (2006). Cognitive inhibition of number/length interference in a Piaget-like task in young adults: Evidence from ERPs and fMRI. Human Brain Mapping, 27, 498–509.Google Scholar
Leroux, G., Spiess, J., Zago, L., Rossi, S., Lubin, A., Turbelin, M.-R., … Joliot, M. (2009). Adult brains don’t fully overcome biases that lead to incorrect performance during cognitive development: An fMRI study in young adults completing a Piaget-like task. Developmental Science, 12, 326–338.Google Scholar
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201–221.Google Scholar
Lubin, A., Rossi, S., Lanoë, C., Vidal, J., Houdé, O., & Borst, G. (2016). Expertise, inhibitory control and arithmetic word problems: A negative priming study in mathematics experts. Learning and Instruction, 45, 40–48.Google Scholar
Lubin, A., Simon, G., Houdé, O., & De Neys, W. (2015). Inhibition, conflict detection, and number conservation. ZDM, 47, 793–800.Google Scholar
Lubin, A., Vidal, J., Lanoë, C., Houdé, O., & Borst, G. (2013). Inhibitory control is needed for the resolution of arithmetic word problems: A developmental negative priming study. Journal of Educational Psychology, 105, 701–708.Google Scholar
Luna, B., Padmanabhan, A., & O’Hearn, K. (2010). What has fMRI told us about the development of cognitive control through adolescence? Brain and Cognition, 72, 101–113.Google Scholar
MacDonald, A. W. (2000). Dissociating the role of the dorsolateral prefrontal and anterior cingulate cortex in cognitive control. Science, 288, 1835–1838.Google Scholar
Marshuetz, C., Smith, E. E., Jonides, J., DeGutis, J., & Chenevert, T. L. (2000). Order information in working memory: FMRI evidence for parietal and prefrontal mechanisms. Journal of Cognitive Neuroscience, 12(suppl 2), 130–144.CrossRefGoogle ScholarPubMed
McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Attention, Perception, & Psychophysics, 69, 1324–1333.Google Scholar
McNab, F., Leroux, G., Strand, F., Thorell, L., Bergman, S., & Klingberg, T. (2008). Common and unique components of inhibition and working memory: An fMRI, within-subjects investigation. Neuropsychologia, 46, 2668–2682.Google Scholar
Mehler, J., & Bever, T. G. (1967). Cognitive capacity of very young children. Science, 158, 141–142.Google Scholar
Miller, E. K. (2000). The prefrontal cortex and cognitive control. Nature Reviews Neuroscience, 1, 59–65.CrossRefGoogle ScholarPubMed
Moskal, B. M., & Magone, M. E. (2000). Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task. Educational Studies in Mathematics, 43, 313–335.Google Scholar
Nieuwenhuis, S., Yeung, N., van den Wildenberg, W., & Ridderinkhof, K. R. (2003). Electrophysiological correlates of anterior cingulate function in a go/no-go task: Effects of response conflict and trial type frequency. Cognitive, Affective, & Behavioral Neuroscience, 3, 17–26.CrossRefGoogle Scholar
Nys, J., & Content, A. (2012). Judgement of discrete and continuous quantity in adults: Number counts! Quarterly Journal of Experimental Psychology, 65, 675–690.Google Scholar
Nys, J., Ventura, P., Fernandes, T., Querido, L., Leybaert, J., & Content, A. (2013). Does math education modify the approximate number system? A comparison of schooled and unschooled adults. Trends in Neuroscience and Education, 2, 13–22.Google Scholar
Odic, D., Hock, H., & Halberda, J. (2014). Hysteresis affects approximate number discrimination in young children. Journal of Experimental Psychology. General, 143, 255–265.Google Scholar
Odic, D., Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Developmental change in the acuity of approximate number and area representations. Developmental Psychology, 49, 1103–1112.Google Scholar
Pardo, J. V., Pardo, P. J., Janer, K. W., & Raichle, M. E. (1990). The anterior cingulate cortex mediates processing selection in the Stroop attentional conflict paradigm. Proceedings of the National Academy of Sciences (USA), 87, 256–259.Google Scholar
Peterson, B. S., Kane, M. J., Alexander, G. M., Lacadie, C., Skudlarski, P., Leung, H.-C., … Gore, J. C. (2002). An event-related functional MRI study comparing interference effects in the Simon and Stroop tasks. Cognitive Brain Research, 13, 427–440.CrossRefGoogle ScholarPubMed
Piaget, J. (1952). The Child’s Conception of Number. London: Routledge and Kegan Paul (original in French, Piaget, J., & Szeminska, A., 1941).Google Scholar
Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of Research in Science Teaching, 2, 176–186.Google Scholar
Piaget, J. (1968). Quantification, conservation, and nativism. Science, 162, 976–979.Google Scholar
Piazza, M., De Feo, V., Panzeri, S., & Dehaene, S. (2018). Learning to focus on number. Cognition, 181, 35–45.Google Scholar
Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547–555.Google Scholar
Piazza, M., Pica, P., Izard, V., Spelke, E. S., & Dehaene, S. (2013). Education enhances the acuity of the nonverbal approximate number system. Psychological Science, 24, 1037–1043.Google Scholar
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503.Google Scholar
Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron, 41, 983–993.Google Scholar
Poirel, N., Borst, G., Simon, G., Rossi, S., Cassotti, M., Pineau, A., & Houdé, O. (2012). Number conservation is related to children’s prefrontal inhibitory control: An fMRI study of a Piagetian task. PLoS ONE, 7, e40802.Google Scholar
Posner, M., & Petersen, S. E. (1990). The attention system of the human brain. Annual Review of Neuroscience, 13, 25–42.Google Scholar
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20, 8.Google Scholar
Roche, A. (2005). Longer is larger – Or is it? Australian Primary Mathematics Classroom, 10, 11–16.Google Scholar
Roell, M., Viarouge, A., Hilscher, E., Houdé, O., & Borst, G. (2019a). Evidence for a visuospatial bias in decimal number comparison in adolescents and in adults. Scientific Reports, 9, 14770.Google Scholar
Roell, M., Viarouge, A., Houdé, O., & Borst, G. (2017). Inhibitory control and decimal number comparison in school-aged children. PLoS ONE, 12, e0188276.Google Scholar
Roell, M., Viarouge, A., Houdé, O., & Borst, G. (2019b). Inhibition of the whole number bias in decimal number comparison: A developmental negative priming study. Journal of Experimental Child Psychology, 177, 240–247.Google Scholar
Rousselle, L., & Noël, M.-P. (2008). The development of automatic numerosity processing in preschoolers: Evidence for numerosity-perceptual interference. Developmental Psychology, 44, 544–560.Google Scholar
Rubinsten, O., Henik, A., Berger, A., & Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81, 74–92.Google Scholar
Sackur-Grisvard, C., & Léonard, F. (1985). Intermediate cognitive organizations in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2, 157–174.Google Scholar
Schwarz, W., & Ischebeck, A. (2003). On the relative speed account of number-size interference in comparative judgments of numerals. Journal of Experimental Psychology: Human Perception and Performance, 29, 507–522.Google Scholar
Siegler, R. S. (1995). How does change occur: A microgenetic study of number conservation. Cognitive Psychology, 28, 225–273.Google Scholar
Siegler, R. S. (1998). Emerging Minds: The Process of Change in Children’s Thinking. New York: Oxford University Press.Google Scholar
Simon, T. J., Hespos, S. J., & Rochat, P. (1995). Do infants understand simple arithmetic? A replication of Wynn (1992). Cognitive Development, 10, 253–269.CrossRefGoogle Scholar
Smith, L. B., & Sera, M. D. (1992). A developmental analysis of the polar structure of dimensions. Cognitive Psychology, 24, 99–142.CrossRefGoogle ScholarPubMed
Soltesz, F., Szucs, D., & Szucs, L. (2010). Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: A developmental study. Behavioral and Brain Functions, 6, 13.Google Scholar
Sophian, C., & Chu, Y. (2008). How do people apprehend large numerosities? Cognition, 107, 460–478.Google Scholar
Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10, 89–96.Google Scholar
St Clair-Thompson, H. L., & Gathercole, S. E. (2006). Executive functions and achievements in school: Shifting, updating, inhibition, and working memory. Quarterly Journal of Experimental Psychology, 59, 745–759.Google Scholar
Stacey, K., Helme, S., & Steinle, V. (2001). Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways. PME Conference, 4, 4–217.Google Scholar
Starkey, P., & Cooper, R. (1980). Perception of numbers by human infants. Science, New Series, 210, 1033–1035.Google Scholar
Starkey, P., Spelke, E., & Gelman, R. (1983). Detection of intermodal numerical correspondences by human infants. Science, 222, 179–181.Google Scholar
Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Infants show ratio-dependent number discrimination regardless of set size. Infancy, 18, 927–941.CrossRefGoogle ScholarPubMed
Steinle, V., & Stacey, K. (2003). Grade-related trends in the prevalence and persistence of decimal misconceptions. International Group for the Psychology of Mathematics Education, 4, 259–266.Google Scholar
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013a). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex; a Journal Devoted to the Study of the Nervous System and Behavior, 49, 2674–2688.Google Scholar
Szűcs, D., Nobes, A., Devine, A., Gabriel, F. C., & Gebuis, T. (2013b). Visual stimulus parameters seriously compromise the measurement of approximate number system acuity and comparative effects between adults and children. Frontiers in Psychology, 4, 444.Google Scholar
Takeuchi, H., Taki, Y., Sassa, Y., Hashizume, H., Sekiguchi, A., Nagase, T., … Kawashima, R. (2012). Regional gray and white matter volume associated with Stroop interference: Evidence from voxel-based morphometry. NeuroImage, 59, 2899–2907.Google Scholar
Tibber, M. S., Greenwood, J. A., & Dakin, S. C. (2012). Number and density discrimination rely on a common metric: Similar psychophysical effects of size, contrast, and divided attention. Journal of Vision, 12, 8.Google Scholar
Tipper, S. P. (2001). Does negative priming reflect inhibitory mechanisms? A review and integration of conflicting views. The Quarterly Journal of Experimental Psychology Section A, 54, 321–343.CrossRefGoogle ScholarPubMed
Tipper, S. P., Weaver, B., Cameron, S., Brehaut, J. C., & Bastedo, J. (1991). Inhibitory mechanisms of attention in identification and localization tasks: Time course and disruption. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 681–692.Google Scholar
Tissier, C., Linzarini, A., Allaire-Duquette, G., Mevel, K., Poirel, N., Dollfus, S., … Cachia, A. (2018). Sulcal polymorphisms of the IFC and ACC contribute to inhibitory control variability in children and adults. eNeuro, 5.Google Scholar
Tokita, M., & Ishiguchi, A. (2010). How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled? Attention, Perception, & Psychophysics, 72, 1839–1853.Google Scholar
Townsend, J., Adamo, M., & Haist, F. (2006). Changing channels: An fMRI study of aging and cross-modal attention shifts. NeuroImage, 31, 1682–1692.Google Scholar
Tzelgov, J., Meyer, J., & Henik, A. (1992). Automatic and intentional processing of numerical information. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 166–179.Google Scholar
Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31, 344–355.Google Scholar
Van Dooren, W., Lehtinen, E., & Verschaffel, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction, 37, 1–4.Google Scholar
Van Hoof, J., Lijnen, T., Verschaffel, L., & Van Dooren, W. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education, 15, 154–164.Google Scholar
Viarouge, A., & de Hevia, M. D. (2013). The role of numerical magnitude and order in the illusory perception of size and brightness. Frontiers in Psychology, 4, 484.Google Scholar
Viarouge, A., Houdé, O., & Borst, G. (2019). Evidence for the role of inhibition in numerical comparison: A negative priming study in 7- to 8-year-olds and adults. Journal of Experimental Child Psychology, 186, 131–141.Google Scholar
Vogel, S. E., Grabner, R. H., Schneider, M., Siegler, R. S., & Ansari, D. (2013). Overlapping and distinct brain regions involved in estimating the spatial position of numerical and non-numerical magnitudes: An fMRI study. Neuropsychologia, 51, 979–989.Google Scholar
Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488.Google Scholar
Westlye, L. T., Grydeland, H., Walhovd, K. B., & Fjell, A. M. (2011). Associations between regional cortical thickness and attentional networks as measured by the attention network test. Cerebral Cortex, 21, 345–356.Google Scholar
Wilkey, E. D., Barone, J. C., Mazzocco, M. M. M., Vogel, S. E., & Price, G. R. (2017). The effect of visual parameters on neural activation during nonsymbolic number comparison and its relation to math competency. NeuroImage, 159, 430–442.Google Scholar
Wilkey, E. D., Pollack, C., & Price, G. R. (2020). Dyscalculia and typical math achievement are associated with individual differences in number-specific executive function. Child Development, 91, 596–619.Google Scholar
Wood, G., Ischebeck, A., Koppelstaetter, F., Gotwald, T., & Kaufmann, L. (2009). Developmental trajectories of magnitude processing and interference control: An fMRI study. Cerebral Cortex, 19, 2755–2765.Google Scholar
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.Google Scholar
Wynn, K. (1995). Infants possess a system of numerical knowledge. Current Directions in Psychological Science, 4, 172–177.Google Scholar
Wynn, K. (1998). Psychological foundations of number: Numerical competence in human infants. Trends in Cognitive Sciences, 2, 296–303.Google Scholar
Wynn, K., Bloom, P., & Chiang, W.-C. (2002). Enumeration of collective entities by 5-month-old infants. Cognition, 83, B55–B62.Google Scholar
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11.Google Scholar
Zacks, J. M. (2008). Neuroimaging studies of mental rotation: A meta-analysis and review. Journal of Cognitive Neuroscience, 20, 31.Google Scholar
Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H., & Dong, Q. (2007). Chinese kindergartners’ automatic processing of numerical magnitude in Stroop-like tasks. Memory & Cognition, 35, 464–470.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×