Learning Number with TouchCounts: The Role of Emotions and the Body in Mathematical Communication
Article
First Online:
- 779 Downloads
- 16 Citations
Abstract
In this paper we describe a touchscreen application called TouchCounts, which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard’s communicational approach, augmented by a focus both on the role of the body—particularly the fingers and hands—and emotions in the mathematical communication of a child, a teacher and a touchscreen device, we show how two 5-year-old girls learn about counting and adding.
Keywords
Emotions Tools Touchscreen Gestures Goals Number sense Communicational approach Early yearsReferences
- Aubrey, C. (1997). Children’s early learning of number in school and out. In I. Thompson (Ed.), Teaching and learning early number (pp. 20–29). Philadelphia, PA: Open University Press.Google Scholar
- Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48–65). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: the body in/of mathematics. Educational Studies in Mathematics, 83(3), 453–470. Google Scholar
- Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.CrossRefGoogle Scholar
- Fuson, K. C. (1992). Research on learning and teaching addition and subtraction of whole numbers. In G. Leinhardt, R. Putnam, & R. A. Hattrap (Eds.), Handbook of research on mathematics teaching and learning (pp. 53–187). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principles before skill. Cognition, 13, 343–359.CrossRefGoogle Scholar
- Gracia-Baffaluy, M., & Noël, M.-P. (2008). Does finger training increase numerical performance? Cortex, 44, 368–375.CrossRefGoogle Scholar
- Groen, G., & Resnick, L. B. (1977). Can reschool children invent addition algorithms? Journal of Educational Psychology, 69, 645–652.CrossRefGoogle Scholar
- Heyd-Metzuyanim, E. (2013). The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity. Educational Studies in Mathematics, 83(3), 341–368.Google Scholar
- Ladel, S., & Kortenkamp, U. (2011). Implementation of a multi-touch-environment supporting finger symbol sets. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the seventh Congress of the European Society for Research in Maths Education (pp. 1792–1801). Poland: University of Rzeszów.Google Scholar
- Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
- Lange, T., & Meaney, T. (2013). iPads and mathematical play: A new kind of sandpit for young children. In Proceedings of CERME 8. Turkey.Google Scholar
- McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: University of Chicago Press.Google Scholar
- Meece, J. L., Anderman, E. M., & Anderman, L. H. (2006). Classroom goal structure, student motivation, and academic achievement. Annual Review of Psychology, 57, 487–503. doi: 10.1146/annurev.psych.56.091103.070258.CrossRefGoogle Scholar
- Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2013). Playing mathematical instruments: Emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372–415.Google Scholar
- Nemirovsky, R. (2011). Episodic feelings and transfer of learning. Journal of the Learning Sciences, 20(2), 308–337.Google Scholar
- Núñez, R. (2003). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In R. Hersh (Ed.), 18 Unconventional essays on the nature of mathematics (pp. 160–181). New York: Springer.Google Scholar
- Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York: Basic Books.Google Scholar
- Radford, L. (2012). Towards an embodied, cultural, material conception of mathematics cognition. In 12th international congress on mathematical education program, COEX, Seoul, Korea.Google Scholar
- Roth, W.-M. (2011). Geometry as objective science in elementary classrooms: Mathematics in the flesh. New York: Routledge.Google Scholar
- Roth, W. M., & Lee, Y. J. (2007). “Vygotsky’s neglected legacy”: Cultural-historical activity theory. Review of Educational Research, 77(2), 186–232. doi: 10.3102/0034654306298273.CrossRefGoogle Scholar
- Roth, W. M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
- Sfard, A. (2008). Thinking as communicating. New York: Cambridge University Press.CrossRefGoogle Scholar
- Sfard, A. (2014). Creating numbers: Participationist discourse on mathematics learning. In D. Butlen, I. Bloch, M. Bosch, C. Chambris, G. Cirade, S. Clivaz, S. Gobert, C. Hache, M. Hersant, & C. Mangiante (Eds.), Rôles et places de la didactique et des didacticiens des mathématiques dans la société et dans le système éducatif. 17e école d'été de didactique des mathématiques. Nantes du 19 au 26 août 2013. Grenoble: La pensée sauvage. Google Scholar
- Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different? Early numerical thinking revisited. Cognition and Instruction, 23(2), 237–309.Google Scholar
- Sfard, A., & McClain, K. (2002). Analyzing tools: Perspectives on the role of designed artifacts in mathematics learning. The Journal of the Learning Sciences, 11(2&3), 153–161.CrossRefGoogle Scholar
- Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22.CrossRefGoogle Scholar
- Siegler, R. S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.Google Scholar
- Sinclair, N. (2013). TouchCounts: An embodied, digital approach to learning number. In Proceedings of ICTMT12, Bari, Italy.Google Scholar
- Sinclair, N., & Jackiw, N. (2011). TouchCounts [computer software]. Tangible Mathematics Project, Simon Fraser University.Google Scholar
- Sinclair, N., & Moss, J. (2012). The more it changes, the more it becomes the same: The development of the routine of shape identification in dynamic geometry environments. International Journal of Education Research, 51, 28–44.Google Scholar
- Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: The murky and furtive world of mathematical inventiveness. ZDM—The International Journal on Mathematics Education, 45(2), 239–252.CrossRefGoogle Scholar
- Thurston, W. (1990). Mathematics education. Notices of the AMS, 37(7), 844–850.Google Scholar
- Turkle, S. (2011). Evocative objects: Things we think with. Cambridge, MA: MIT Press.Google Scholar
- Vergnaud, G. (2008). The theory of conceptual fields. Human Development, 52, 83–94.Google Scholar
- Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.Google Scholar
- Zimmerman, B. (2000). Self-efficacy: An essential motive to learn. Contemporary Educational Psychology, 25(1), 82–91. doi: 10.1006/ceps1999.1016.Google Scholar
Copyright information
© Springer Science+Business Media Dordrecht 2014