Hostname: page-component-76d6cb85b7-vdhp9 Total loading time: 0 Render date: 2026-07-15T16:25:38.602Z Has data issue: false hasContentIssue false
  • English
  • Français

Toward an integrative approach to numerical cognition

Published online by Cambridge University Press:  27 July 2017

Tali Leibovich ,
Naama Katzin ,
Moti Salti  and
Avishai Henik
Tali Leibovich
Affiliation:
Department of Math Education, The University of Haifa, Haifa, Israel, 3498838 labovich@gmail.com http://www.numericalcognition.org/people.html
Naama Katzin
Affiliation:
Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, 8499000, Israel naamaka@post.bgu.ac.il Henik@bgu.ac.il http://in.bgu.ac.il/en/Labs/CNL/Pages/staff/naamaka.aspx http://in.bgu.ac.il/en/Labs/CNL/Pages/staff/AvishaiHenik.aspx The Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, 8499000, Beer-Sheva, Israel
Moti Salti
Affiliation:
Brain Imaging Research Center (BIRC) and the Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev and Soroka University Medical Center, Beer-Sheva, 8499000, Israel motisalti@gmail.com http://in.bgu.ac.il/en/bcs/Pages/staff/motisalti.aspx
Avishai Henik
Affiliation:
Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, 8499000, Israel naamaka@post.bgu.ac.il Henik@bgu.ac.il http://in.bgu.ac.il/en/Labs/CNL/Pages/staff/naamaka.aspx http://in.bgu.ac.il/en/Labs/CNL/Pages/staff/AvishaiHenik.aspx The Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, 8499000, Beer-Sheva, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

In response to the commentaries, we have refined our suggested model and discussed ways in which the model could be further expanded. In this context, we have elaborated on the role of specific continuous magnitudes. We have also found it important to devote a section to evidence considered the “smoking gun” of the approximate number system theory, including cross-modal studies, animal studies, and so forth. Lastly, we suggested some ways in which the scientific community can promote more transparent and collaborative research by using an open science approach, sharing both raw data and stimuli. We thank the contributors for their enlightening comments and look forward to future developments in the field.

Information

Type
Authors' Response
Information
Behavioral and Brain Sciences , Volume 40 , 2017 , e194
Check for updates
Copyright
Copyright © Cambridge University Press 2017 

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.)

Article purchase

Temporarily unavailable

References

Baldwin, D. A. (1993) Early referential understanding: Infants' ability to recognize referential acts for what they are. Developmental Psychology 29(5):832–43. doi: 10.1037/0012-1649.29.5.832.Google Scholar
Bugden, S. & Ansari, D. (2016) Probing the nature of deficits in the ‘approximate number system’ in children with persistent developmental dyscalculia. Developmental Science 19(5):817–33. doi: 10.1111/desc.12324.Google Scholar
Calhoun, L. G. (1971) Number conservation in very young children: The effect of age and mode of responding. Child Development 42(2):561–72. doi: 10.2307/1127488.Google Scholar
Cantlon, J. F., Platt, M. L. & Brannon, E. M. (2009b) Beyond the number domain. Trends in Cognitive Sciences 13(2):83–91. doi: 10.1016/j.tics.2008.11.007.Google Scholar
Cantrell, L., Kuwabara, M. & Smith, L. B. (2015b) Set size and culture influence children's attention to number. Journal of Experimental Child Psychology 131:19–37. doi: 10.1016/j.jecp.2014.10.010.Google Scholar
Cicchini, G. M., Anobile, G. & Burr, D. C. (2016) Spontaneous perception of numerosity in humans. Nature Communications 7:12536. doi: 10.1038/ncomms12536.Google Scholar
Clayton, S., Gilmore, C. & Inglis, M. (2015) Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement. Acta Psychologica 161:177–84. doi: 10.1016/j.actpsy.2015.09.007.Google Scholar
Cleland, A. A. & Bull, R. (2015) The role of numerical and non-numerical cues in nonsymbolic number processing: Evidence from the line bisection task. Quarterly Journal of Experimental Psychology 68(9):1844–59. doi: 10.1080/17470218.2014.994537.Google Scholar
Coubart, A., Streri, A., de Hevia, M. D., Izard, V. (2015) Crossmodal discrimination of 2 vs. 4 objects across touch and vision in 5-month-old infants. PLoS ONE 10(3):e0120868. doi: 10.1371/journal.pone.0120868.CrossRefGoogle ScholarPubMed
Deaner, R. O., Isler, K., Burkart, J. & Van Schaik, C. (2007) Overall brain size, and not encephalization quotient, best predicts cognitive ability across non-human primates. Brain, Behavior and Evolution 70(2):115–24. doi: 10.1159/000102973.Google Scholar
Diamond, A. (2013) Executive functions. Annual Review of Psychology 64:135–68. doi: 10.1146/annurev-psych-113011-143750.Google Scholar
Durgin, F. H. (1995) Texture density adaptation and the perceived numerosity and distribution of texture. Journal of Experimental Psychology: Human Perception and Performance 21(1):149–69. doi: 10.1037/0096-1523.21.1.149.Google Scholar
Feigenson, L. (2011) Predicting sights from sounds: 6-month-olds' intermodal numerical abilities. Journal of Experimental Child Psychology 110(3):347–61. doi: 10.1016/j.jecp.2011.04.004.Google Scholar
Féron, J., Gentaz, E. & Streri, A. (2006) Evidence of amodal representation of small numbers across visuo-tactile modalities in 5-month-old infants. Cognitive Development 21(2):81–92. doi: 10.1016/j.cogdev.2006.01.005.Google Scholar
Gebuis, T. & van der Smagt, M. J. (2011) False approximations of the approximate number system? PLoS ONE 6(10):e25405. doi: 10.1371/journal.pone.0025405.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 28(8):923–31. doi: 10.1080/20445911.2016.1221828.CrossRefGoogle ScholarPubMed
Ginsburg, N. & Nicholls, A. (1988) Perceived numerosity as a function of item size. Perceptual and Motor Skills 67(2):656–58. doi: 10.2466/pms.1988.67.2.656.Google Scholar
Izard, V., Sann, C., Spelke, E. S. & Steri, A. (2009) Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America 106(25):10382–85.CrossRefGoogle ScholarPubMed
Jordan, K. E. & Brannon, E. M. (2006) The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences of the United States of America 103(9):3486–89. doi: 10.1073/pnas.0508107103.Google Scholar
Kaminski, J., Call, J. & Fischer, J. (2004) Word learning in a domestic dog: Evidence for “fast mapping.” Science 304(5677):1682–83. doi: 10.1126/science.1097859.Google Scholar
Katzin, N., Katzin, D., Salti, M. & Henik, A. (2016) Convex hull as a heuristic. Poster presented at the Psychonomics Society 57th Annual Meeting, Boston, MA.Google Scholar
Kobayashi, T., Hiraki, K. & Hasegawa, T. (2005) Auditory–visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science 8(5):409–19. doi: 10.1111/j.1467-7687.2005.00429.x.Google Scholar
Kobayashi, T., Hiraki, K., Mugitani, R. & Hasegawa, T. (2004) Baby arithmetic: One object plus one tone. Cognition 91(2):B23–34. doi: 10.1016/j.cognition.2003.09.004.Google Scholar
Konkle, T. & Oliva, A. (2012) A real-world size organization of object responses in occipitotemporal cortex. Neuron 74(6):1114–24. doi: 10.1016/j.neuron.2012.04.036.Google Scholar
Leibovich, T. & Ansari, D. (2016) The symbol-grounding problem in numerical cognition: A review of theory, evidence and outstanding questions. Canadian Journal of Experimental Psychology 70(1):12–23.Google Scholar
Leibovich, T. & Henik, A. (2014) Comparing performance in discrete and continuous comparison tasks. Quarterly Journal of Experimental Psychology 67(5):1–19. doi: 10.1080/17470218.2013.837940.Google Scholar
Leibovich, T., Henik, A. & Salti, M. (2015) Numerosity processing is context driven even in the subitizing range: An fMRI study. Neuropsychologia 77:137–47. doi: 10.1016/j.neuropsychologia.2015.08.016.Google Scholar
Leibovich, T., Kallai, A. & Itamar, S. (2016a) What do we measure when we measure magnitudes? In: Continuous issues in numerical cognition, ed. Henik, A., pp. 355–73. Elsevier. doi: 10.1016/B978-0-12-801637-4.00016-0.Google Scholar
Mandler, G. & Shebo, B. J. (1982) Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General 111(1):1–22.Google Scholar
Mix, K. S., Huttenlocher, J. & Levine, S. C. (2002a) Multiple cues for quantification in infancy: Is number one of them? Psychological Bulletin 128(2):278–94. doi: 10.1037/0033-2909.128.2.278.Google Scholar
Mix, K. S., Levine, S. C. & Huttenlocher, J. (1997) Numerical abstraction in infants: Another look. Developmental Psychology 33(3):423–28. doi: 10.1037/0012-1649.33.3.423.Google Scholar
Mix, K. S., Levine, S. C. & Newcombe, N. S. (2016) Development of quantitative thinking across correlated dimensions. In: Continuous issues in numerical cognition, ed. Henik, A., pp. 1–33. Elsevier. doi: 10.1016/B978-0-12-801637-4.00001-9.Google Scholar
Moore, D., Benenson, J., Reznick, J. S., Peterson, M. & Kagan, J. (1987) Effect of auditory numerical information on infants’ looking behavior: Contradictory evidence. Developmental Psychology 23(5):665–70. doi: 10.1037/0012-1649.23.5.665.Google Scholar
Piaget, J. (1952) The child's conception of number. Psychology Press.Google Scholar
Salti, M., Katzin, N., Katzin, D., Leibovich, T. & Henik, A. (2017) One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks. Behavior Research Methods 49(3):1120–27. doi: 10.3758/s13428-016-0772-7.CrossRefGoogle Scholar
Sokolowski, H. M., Fias, W., Ononye, C. B. & Ansari, D. (2017) Are numbers grounded in a general magnitude processing system? A functional neuroimaging meta-analysis. Neuropsychologia. Available online January 22, 2017. doi: 10.1016/j.neuropsychologia.2017.01.019.Google Scholar
Starkey, P., Spelke, E. S. & Gelman, R. (1983) Detection of intermodal numerical correspondences by human infants. Science 222(4620):179–81. doi: 10.1126/science.6623069.Google Scholar
Starkey, P., Spelke, E. S., & Gelman, R. (1990) Numerical abstraction by human infants. Cognition 36(2):97–127. doi: 10.1016/0010-0277(90)90001-Z.Google Scholar