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What Schemes Do Preschoolers Develop When Using Multi-touch Applications to Foster Number Sense (and Why)?

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Contemporary Research and Perspectives on Early Childhood Mathematics Education

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

As part of an educational project proposed in Italian pre-schools, an educator followed a protocol that had been used in a previous study (Baccaglini-Frank and Maracci in Digit Exp Math Educ 1:7–27, 2015) proposing two chosen iPad apps to children of ages five to six. This study investigates the schemes developed by the children in response to the apps, and the role the educator’s interventions seemed to play in such development. Analyses of the data collected suggest that her interventions privileged and encouraged schemes involving counting, which limited the variety of schemes enacted and the aspects of number sense strengthened through the protocol.

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Notes

  1. 1.

    There is also another mode, called ‘tap mode’, in which success is reached when the user taps the screen (sequentially) as many times as the numerosity of the dots on the ladybug’s back. This mode seems to mostly encourage students to use counting strategies, and to support only to a limited extent children’s development of number abilities. This is why we chose not to use it.

References

  • Baccaglini-Frank, A., & Maracci, M. (2015). Multi-touch technology and preschoolers’ development of number-sense. Digital Experiences in Mathematics Education, 1, 7–27.

    Article  Google Scholar 

  • Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93, 371–397.

    Article  Google Scholar 

  • Barendregt, W., Lindström, B., Rietz-Leppänen, E., Holgersson, I., & Ottosson, T. (2012). Development and evaluation of Fingu: A mathematics iPad game using multi-touch interaction. In D. Marjanovic, M. Storga, N. Pavkovic, & N. Bojcetic (Eds.), Proceedings of DESIGN 2010, the 11th International Design Conference (pp. 204–207). Dubrovnik, Croatia: ACM.

    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 

  • Butterworth, B. (1999). The mathematical brain. London: Macmillan.

    Google Scholar 

  • Clements, D. H. (2002). Computers in early childhood mathematics. Contemporary Issues in Early Childhood, 3(2), 160–181.

    Article  Google Scholar 

  • Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3, 155–181.

    Article  Google Scholar 

  • English, L., & Mulligan, J. (2013). Reconceptualizing early mathematics learning. Dordrecht: Springer.

    Book  Google Scholar 

  • Fuson, K. C. (1992). Research on learning and teaching addition and subtraction of whole numbers. In G. Leinhardt, R. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 53–187). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

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

    Google Scholar 

  • Ginsburg, H. P., Uscianowski, C., & Almeda Ma. V. (2018). Interactive mathematics storybooks and their friends. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (this volume).

    Google Scholar 

  • Goldin-Meadow, S. (2004). Gesture’s role in the learning process. Theory into Practice, 43(4), 314–321.

    Article  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 

  • Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26(2), 115–141.

    Google Scholar 

  • Ladel, S., & Kortenkamp, U. (2013). An activity-theoretic approach to multi-touch tools in early maths learning. The International Journal for Technology in Mathematics Education, 20(1), 3–8.

    Google Scholar 

  • Levin, B. B. (2002). Using the case method in teacher education: The role of discussion and experience in teachers’ thinking about cases. Teaching and Teacher Education, 1, 63–79.

    Google Scholar 

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

    Google Scholar 

  • Noël, M. P. (2005). Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11, 1–18.

    Article  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. Proceedings of the 29th Annual Conference of the Cognitive Science Society (pp. 1385–1390). Austin, TX: Cognitive Science Society.

    Google Scholar 

  • Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551.

    Article  Google Scholar 

  • Resnick, L. B., Bill, V., Lesgold, S., & Leer, M. (1991). Thinking in arithmetic class. In B. Means, C. Chelemer, & M. S. Knapp (Eds.), Teaching advanced skills to at-risk students: Views from research and practice (pp. 27–53). San Francisco: Jossey-Bass.

    Google Scholar 

  • Ribeiro, M., Mellone, M., & Jakobsen, A. (2016). Interpreting students’ non-standard reasoning: Insights for mathematics teacher education. For the Learning of Mathematics, 36(2), 8–13.

    Google Scholar 

  • Sato, M., Cattaneo, L., Rizzolatti, G., & Gallese, V. (2007). Numbers within our hands: Modulation of corticospinal excitability of hand muscles during numerical judgment. Journal of Cognitive Neuroscience, 19(4), 684–693.

    Article  Google Scholar 

  • Sedig, K., & Sumner, M. (2006). Characterizing interaction with visual mathematical representations. International Journal of Computers for Mathematical Learning, 11(1), 1–55.

    Article  Google Scholar 

  • Sinclair, N. (2018). Time, immersion and articulation: Digital technology for early childhood mathematics. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), Contemporary research and perspectives on early childhood mathematics education (this volume).

    Google Scholar 

  • Sinclair, N., & Baccaglini-Frank, A. (2016). Digital technologies in the early primary school classroom. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 662–686). New York: Taylor Francis/Routledge.

    Google Scholar 

  • Sinclair, N., & Jackiw, N. (2011). Touchcounts [computer software]. Tangible mathematics project, Simon Fraser University.

    Google Scholar 

  • Sinclair, N., & Pimm, D. (2015). Mathematics using multiple senses: 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., & Sedaghat Jou, V. (2013). Finger counting and adding on a touchscreen device. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of European Society for Research in Mathematics Education (CERME 8) (pp. 2198–3207). Ankara, Turkey: Middle East Technical University and ERME.

    Google Scholar 

  • Sinclair, N., & Zaskis, 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 (MEDE) book series (Vol. 8, pp. 175–192). Cham: Springer.

    Chapter  Google Scholar 

  • Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). New York: Macmillan.

    Google Scholar 

  • Thompson, J. C., Abbott, D. F., Wheaton, K. J., Syngeniotis, A., & Puce, A. (2004). Digit representation is more than just hand waving. Cognitive Brain Research, 21, 412–417.

    Article  Google Scholar 

  • Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10, 133–170.

    Google Scholar 

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

    Article  Google Scholar 

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Correspondence to Anna Baccaglini-Frank .

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Baccaglini-Frank, A. (2018). What Schemes Do Preschoolers Develop When Using Multi-touch Applications to Foster Number Sense (and Why)?. In: Elia, I., Mulligan, J., Anderson, A., Baccaglini-Frank, A., Benz, C. (eds) Contemporary Research and Perspectives on Early Childhood Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73432-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-73432-3_12

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