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Eliciting preschoolers’ number abilities using open, multi-touch environments

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Abstract

Research has highlighted the potential of digital technology to support the development of children’s number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task design and implementation in more open environments where several different solution strategies are available. To explore this direction, we chose to study TouchCounts, an open environment that combines multi-touch affordances with aural, visual and symbolic ones as well. Using tasks that were designed to address different number sense abilities, we experimented with 4-year-old preschoolers. In this paper we present two tasks, their expected potential with respect to strengthening number sense abilities, and analyses of data collected during the preschoolers’ interactions with TouchCounts. The analyses reveal that the children used different strategies in response to the two tasks, and that a broad range of abilities related to number sense were elicited, including both cardinality and ordinality. An important contribution of this study is also a theoretical framework capable of identifying children’s learning in a multi-touch environment.

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Notes

  1. We see such abilities not as innate but as a cultural product, in accordance with the TSM.

  2. The names of the two environments are connected with this difference: in the Enumerating World children create the counting numbers in sequence, advancing with each touch; while in the Operating World children can explore basic number operation concepts, by manipulating previously created herds.

  3. Fred answered 4 of the 13 initial interview questions correctly, i.e. the minimum number to be selected for the tasks; while Maria answered 10 questions correctly, i.e. the maximum number reached by the involved children.

  4. Sinclair and Zazkis (2017) describe how the request of “making four all-at-once” in TC “requires that the children produce an action (quickly lifting up their fingers and pressing them on the screen, instead of pressing fingers one by one) based on an oral prompt” (p. 185).

References

  • Baccaglini-Frank, A. (2018). What schemes do preschoolers develop when using multi-touch applications to foster number sense (and why)? In I. Elia, et al. (Eds.), Contemporary research and perspectives on early childhood mathematics education. ICME-13 monographs (pp. 223–243). Berlin: Springer.

    Chapter  Google Scholar 

  • Baccaglini-Frank, A., & Maracci, M. (2015). Multi-touch technology and preschoolers’ development of number-sense. Digital Experiences in Mathematics Education,1(1), 7–27. https://doi.org/10.1007/s40751-015-0002-4.

    Article  Google Scholar 

  • Barendregt, W., Lindstrom, B., Rietz-Leppanen, E., Holgersson, I., & Ottosson, T. (2012). Development and evaluation of Fingu: A mathematics iPad game using multi-touch interaction. IDC 2012 (pp. 1–4), June 12–15, 2012, Bremen, Germany.

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, et al. (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York: Routledge.

    Google Scholar 

  • Bèguin, P., & Rabardel, P. (2000). Designing for instrument-mediated activity. Scandinavian Journal of Information Systems,12, 173–190.

    Google Scholar 

  • Brissiaud, R. (1992). A toll for number construction: Finger symbol sets. In J. Bidaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number. Children’s developing numerical abilities. New Jersey: Lawrence: Erlbaum Associates.

    Google Scholar 

  • Broda, M., Tucker, S., Ekholm, E., Johnson, T. N., & Liang, Q. (2018). Small fingers, big data: Preschoolers’ subitizing speed and accuracy during interactions with multitouch technology. The Journal of Educational Research, online first,. https://doi.org/10.1080/00220671.2018.1486281.

    Article  Google Scholar 

  • Bullock, E. P., Shumway, J. F., Watts, C. M., & Moyer-Packenham, P. S. (2017). Affordance access matters: Preschool children’s learning progressions while interacting with touch-screen mathematics apps. Technology Knowledge and Learning,22, 485–511.

    Article  Google Scholar 

  • Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry,46, 3–18.

    Article  Google Scholar 

  • Coles, A. (2014). Ordinality, neuroscience and the early learning of number. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 329–336). Vancouver, Canada: PME.

  • Coles, A., & Sinclair, N. (2018a). Re-thinking ‘normal’ development in the early learning of number. Journal of Numerical Cognition,4(1), 136–158.

    Article  Google Scholar 

  • Coles, A., & Sinclair, N. (2018b). Re-thinking ‘concrete to abstract’: Towards the use of symbolically structured environments. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd conference of the international group for the psychology of mathematics education (Vol. 2, pp. 275–282). Umeå, Sweden: PME.

  • Elia, I., Mulligan, J., Anderson, A., Baccaglini-Frank, A., & Benz, C. (2018). Contemporary research and perspectives on early childhood mathematics education. ICME-13 monographs. Berlin: Springer.

    Book  Google Scholar 

  • Fraenkel, A. (1942). Introduction to mathematics. Tel-Aviv: Masada.

    Google Scholar 

  • Fuson, K. C., & Hall, J. W. (1983). The acquisition of early number word meanings. In H. Ginsburg (Ed.), The development of mathematical thinking (pp. 49–107). New York: Academic.

    Google Scholar 

  • Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge: Harvard University Press.

    Google Scholar 

  • Goodwin, K., & Highfield, K. (2013). A Framework for Examining Technologies and Early Mathematics Learning. In L. English & J. Mulligan (Eds.), Reconceptualizing Early Mathematics Learning. Springer, Dordrecht: Advances in Mathematics Education.

    Google Scholar 

  • Gracia-Bafalluy, M. G., & Noël, M. P. (2008). Does finger training increase young children’s numerical performance? Cortex,44, 368–375.

    Article  Google Scholar 

  • Holgersson, I., Barendregt, W., Emanuelsson, J., Ottosson, T., Rietz, E., & Lindström, B. (2016). Fingu: A game to support children’s development of arithmetic competence—Theory, design and empirical research. In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives. Mathematics education in the digital era (pp. 123–146). Berlin: Springer.

    Google Scholar 

  • Jackiw, N., & Sinclair, N. (2014). Touchcounts [computer software]. Tangible mathematics project. Burnaby: Simon Fraser University.

    Google Scholar 

  • Lafay, A., Thevenot, C., Castel, C., & Fayol, M. (2013). The role of fingers in number processing in young children. Frontiers in Psychology,4, 488. https://doi.org/10.3389/fpsyg.2013.00488.

    Article  Google Scholar 

  • Lyons, I., & Beilock, S. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition,121(2), 256–261.

    Article  Google Scholar 

  • Margolinas, C., & Wosniak, F. (2012). Le nombre à l’école maternelle. Une approche didactique. Bruxelles: De Boeck.

    Google Scholar 

  • Moeller, K., Martignon, L., Wessolowski, S., Engel, J., & Nuerk, H.-C. (2011). Effects of finger counting on numerical development? The opposing views of neurocognition and mathematics education. Frontiers in Psychology,2, 1–5. https://doi.org/10.3389/fpsyg.2011.00328.

    Article  Google Scholar 

  • Moyer-Packenham, P., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson-Pence, K. L., Westenskow, A., et al. (2015). Young children’s learning performance and efficiency when using virtual manipulative mathematics iPad apps. Journal of Computers in Mathematics and Science Teaching,34(1), 41–69.

    Google Scholar 

  • Mulligan, J., Verschaffel, L., Baccaglini-Frank, A., Coles, A., Gould, P., He, S., et al. (2018). Whole number thinking, learning and development: Neuro-cognitive, cognitive and developmental approaches. In M. G. Bartolini Bussi & X. H. Sun (Eds.), Building the foundation: whole numbers in the primary grades. New ICMI study series (pp. 137–167). Berlin: Springer.

    Chapter  Google Scholar 

  • Nesher, P. (2018). Whole number thinking, learning and development: A commentary on chapter 7. In M. G. Bartolini Bussi & X. H. Sun (Eds.), Building the foundation: Whole numbers in the primary grades. New ICMI study series (pp. 169–179). Berlin: Spinger.

    Chapter  Google Scholar 

  • Penner-Wilger, M., Fast, L., LeFevre, J. A., Smith-Chant, B. L, Skwarchuk, S. L, Kamawar, D., & Bisanz, J. (2007). The foundations of numeracy: Subitizing, finger gnosia, and fine motor ability. In D. S. McNamara & J. G. Trafton (Eds.) Proceedings of the 29th annual conference of the cognitive science society (pp. 1385–1390). Austin, TX: Cognitive Science Society.

  • Rothschild, M., & Williams, C. C. (2015). Apples and coconuts: Young children ‘Kinecting’ with mathematics and sesame street. In T. Lowrie & R. Jorgensen (Eds.), Digital games and mathematical learning potential, promises and pitfalls (pp. 123–141). Berlin: Springer.

    Google Scholar 

  • Sedaghatjou, M., & Campbell, S. (2017). Exploring cardinality in the era of touchscreen-based technology. International Journal of Mathematical Education in Science and Technology,48(8), 1225–1239. see https://www.tandfonline.com/doi/full/10.1080/0020739X.2017.1327089

    Article  Google Scholar 

  • Sinclair, N., & Baccaglini-Frank, A. (2016). Digital technologies in the early primary school classroom. In L. English (Ed.), Handbook of international research in mathematics education (pp. 662–686). New York: Taylor and Francis.

    Google Scholar 

  • Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with TouchCounts: The role of emotions and the body in mathematical communication. Technology, Knowledge and Learning,19, 81–99.

    Article  Google Scholar 

  • Sinclair, N., & Pimm, D. (2015). Mathematics using multiple sense: Developing finger gnosis with three-and four-year-olds in an era of multi-touch technologies. Asia-Pacific Journal of Research in Early Childhood Education,9(3), 99–109.

    Article  Google Scholar 

  • Sinclair, N., & Sedaghatjou, M. (2013). Finger counting and adding with touch counts. In B. Ubuz, C. Haser, M. A. Mariotti (Eds.), Proceedings of the 8th congress of the European society for research in mathematics education (pp. 2198–2207). Antalya: Turkey.

    Google Scholar 

  • Sinclair, N., & Zazkis, R. (2017). Everybody counts: Designing tasks for TouchCounts. In A. Leung & A. Baccaglini-Frank (Eds.), Digital technologies in designing mathematics education tasks, mathematics education in the digital era 8 (pp. 175–191). Berlin: Springer.

    Chapter  Google Scholar 

  • Tucker, S. I., Moyer-Packenham, P. S., Westenskow, A., & Jordan, K. E. (2016). The complexity of the affordance-ability relationship when second-grade children interact with mathematics virtual manipulative apps. Technology Knowledge and Learning,21, 341–360.

    Article  Google Scholar 

  • Vergnaud, G. (2009). The theory of conceptual fields. Human Development,52(2), 83–94.

    Article  Google Scholar 

  • Vygotsky, L. (1986). Thought and language. Translated and edited by Alex Kozulin. Cambridge, MA: MIT Press.

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Authors and Affiliations

  1. Dipartimento di Matematica, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Anna Baccaglini-Frank

  2. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, University of Naples “Federico II”, Naples, Italy

    Gemma Carotenuto

  3. Faculty of Education, Simon Fraser University, Vancouver, Canada

    Nathalie Sinclair

Authors
  1. Anna Baccaglini-Frank
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  2. Gemma Carotenuto
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  3. Nathalie Sinclair
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Correspondence to Anna Baccaglini-Frank.

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Baccaglini-Frank, A., Carotenuto, G. & Sinclair, N. Eliciting preschoolers’ number abilities using open, multi-touch environments. ZDM Mathematics Education 52, 779–791 (2020). https://doi.org/10.1007/s11858-020-01144-y

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