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Ben’s perception of space and subitizing activity: a constructivist teaching experiment

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Abstract

This 22-session constructivist teaching experiment set out to investigate a preschool student’s number understanding relative to his subitizing activity. Subitizing, a quick apprehension of the numerosity of a small set of items, has been found to characterize perceptual and conceptual processes students rely on as their understanding of number develops. The purpose for this study is to investigate how a preschool student’s, Ben, perceptual subitizing activity changed relative to the density of items and the development of his number understanding. Findings indicated that early on in the teaching experiment, Ben’s perceptual subitizing activity was influenced by his primary reliance upon the perceived amount of space between items. Shifts in reasoning when perceptually subitizing indicated physiological and experiential development in Ben’s number understanding, as Ben described the number of items increasing when the perceived amount of space between items decreased. Number conservation was considered as relevant to these findings because Ben’s explanation for why a number could increase or decrease mirrored similar logic when unable to conserve number. Implications of this study suggest nuances in number understanding development which can explain preschool students’ reliance upon a more refined set of perceptual subitizing.

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References

  • Arp, S., & Fagard, J. (2005). What impairs subitizing in Cerebal Palsied children?. Wiley Periodicals, Inc., 47, 89–102. doi: 10.1002/dev.-20069

  • Baroody, A. J., Lai, M. L., Li, X., & Baroody, A. E. (2009). Preschoolers' understanding of subtraction-related principles. Mathematical Thinking and Learning, 11(1–2), 41–60.

    Article  Google Scholar 

  • Borst, G., Simon, G., Vidal, J., & Houdé, O. (2013). Inhibitory control and visuo-spatial reversibility in Piaget's seminal number conservation task: a high-density ERP study. Frontiers in human neuroscience, 7, 1–12. doi:10.3389/fnhum.2013.00920.

    Article  Google Scholar 

  • Canobi, K. H., & Bethune, N. E. (2008). Number words in young children’s conceptual and procedural knowledge of addition, subtraction and inversion. Cognition, 108(3), 675–686.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38(2), 136–163.

    Google Scholar 

  • Clements, D. H., & Sarama J. (2014). Play, mathematics, and false dichotomies. [Web log post]. Retrieved from http://preschoolmatters.org/2014/03/03/playmathematics-and-false-dichotomies/

  • Dehaene, S. (2011). The number sense: How the mind creates mathematics. Oxford University Press.

  • Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics Education for Young Children: What It Is and How to Promote It. Social Policy Report. Volume 22, Number 1. Society for Research in Child Development.

  • von Glasersfeld, E. (1995). Radical constructivism: a way of knowing and learning. NY: Taylor & Francis group.

    Book  Google Scholar 

  • Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of number. The American Journal of Psychology, 62(4), 498–525.

    Article  Google Scholar 

  • LaPointe, K., & O'Donnell, J. P. (1974). Number conservation in children below age six: its relationship to age, perceptual dimensions, and language comprehension. Developmental Psychology, 10(3), 422.

    Article  Google Scholar 

  • Logan, G. D., & Zbrodoff, N. J. (2003). Subitizing and similarity: toward a pattern-matching theory of enumeration. Psychonomic Bulletin & Review, 10(3), 676–682.

    Article  Google Scholar 

  • MacDonald, B. L., & Wilkins, J. L. M. (2015a). Amy’s subitizing activity relative to number understanding: a constructivist teaching experiment. Manuscript forthcoming.

  • MacDonald, B. L. & Wilkins, J. L. M. (2015b). Seven types of subitizing activity characterizing young children’s mental activity. In S. Marx & S. L. Gregory (Eds.), Qualitative research in STEM.

  • Malach, R., Reppas, J. B., Benson, R. R., Kwong, K. K., Jiang, H., Kennedy, W. A., Tootell, R. B. (1995). Object-related activity revealed by functional magnetic resonance imaging in human occipital cortex. Proceedings of the National Academy of Sciences, 92(18), 8135–8139.

  • Mandler, G., & Shebo, B. J. (1982). Subitizing: an analysis of its component processes. Journal of Experimental Psychology: General, 3(1), 1–22.

    Article  Google Scholar 

  • Mehler, J., & Bever, T. G. (1967). Cognitive capacity of very young children. Science, 158(3797), 141–142.

    Article  Google Scholar 

  • Moradmand, N., Datta, A., & Oakley, G. (2013). A computer-assisted framework based on a cognitivist learning theory for teaching mathematics in the early primary years. Australian Educational Computing, 27(2), 39–45.

    Google Scholar 

  • Piaget, J. (1965). The child’s conception of number. (C. Gattegno and F. M. Hodgson, Trans.). New York, NY: W.W. Norton & Company, Inc. (Original work published in 1941).

  • Piaget, J. (1970). Genetic epistemology. (E. Duckworth, Trans.). New York, NY: Columbia University Press. (Original work published in 1968).

  • Pylyshyn, Z. (1989). The role of location indexes in spatial perception: a sketch of the FINST spatial-index model. Cognition, 32(1), 65–97.

    Article  Google Scholar 

  • Ramani, G. B., & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between low and middle-income preschoolers. Journal of applied developmental Psychology, 32(3), 146–159.

    Article  Google Scholar 

  • Rothenberg, B. B., & Courtney, R. G. (1968). Conservation of number in very young children: a replication of and comparison with Mehler and Bever's study. The Journal of Psychology, 70(2), 205–212.

    Article  Google Scholar 

  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: learning trajectories for young children. New York, NY: Routledge.

    Google Scholar 

  • Sasanguie, D., De Smedt, B., Defever, E., & Reynvoet, B. (2012). Association between basic numerical abilities and mathematics achievement. British Journal of Developmental Psychology, 30(2), 344–357.

    Article  Google Scholar 

  • Starkey, G. S., & McCandliss, B. D. (2014). The emergence of “groupitizing” in children’s numerical cognition. Journal of experimental child psychology, 126, 120–137.

    Article  Google Scholar 

  • Steffe, L. P. (1991). The constructivist teaching experiment: illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 171–194). Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Steffe, L. P., & Ulrich, C. (2014). The constructivist teaching experiment. In S. Lerman (Ed.), Encyclopedia of mathematics education. Dordrecht, The Netherlands: Springer. doi:10.1007/978-94-007-4978-8.

    Google Scholar 

  • Ulrich, C., Tillema, E. S., Hackenberg, A. J., & Norton, A. (2014). Constructivist model building: empirical examples from mathematics education. Constructivist Foundations, 9(3), 328–339.

    Google Scholar 

  • Willoughby, R. H., & Trachy, S. (1971). Conservation of number in very young children: a failure to replicate Mehler and Bever. Merrill-Palmer Quarterly of Behavior and Development, 205–209.

  • Zahn, C. T. (1971). Graph-theoretical methods for detecting and describing gestalt clusters. Computers, IEEE Transactions on, 100(1), 68–86.

    Article  Google Scholar 

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Authors and Affiliations

  1. Utah State University, 2805 Old Main Hill, Logan, UT, 84322-2805, USA

    Beth L. MacDonald

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  1. Beth L. MacDonald
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Correspondence to Beth L. MacDonald.

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MacDonald, B.L. Ben’s perception of space and subitizing activity: a constructivist teaching experiment. Math Ed Res J 27, 563–584 (2015). https://doi.org/10.1007/s13394-015-0152-0

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  • DOI: https://doi.org/10.1007/s13394-015-0152-0

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