Abstract
This chapter aims at describing research on Fingu, a virtual manipulative housed in a game environment, which is designed to support young children’s learning and development of number concepts and flexible arithmetic competence. More specifically Fingu targets the understanding and mastering of the basic numbers 1–10 as part-whole relations, which according to the literature on early mathematics learning is critical for this development. In the chapter, we provide an overview of the theoretical grounding of the design, development and research of Fingu as well as the theoretical and practical design rationale and principles. We point out the potential of Fingu as a research platform and present examples of some of the empirical research conducted to demonstrate the learning potential of Fingu. Methodologically, the research adopts a design-based research approach. This approach combines theory-driven design of learning environments with empirical research in educational settings, in a series of iterations. In a first series of iterations, a computer game—the Number Practice Game—was designed and researched, based on phenomenographic theory and empirical studies. In a second series of iterations, Fingu was designed and researched, based on ecological psychology in a socio-cultural framing. The design trajectory of NPG/Fingu thus involves both theoretical development and (re)design and development of specific educational technologies.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akkerman, S. F., & Bakker, A. (2011). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169.
Barendregt, W., Lindström, B., Rietz-Leppänen, E., Holgersson, I., & Ottosson, T. (2012). Development and evaluation of Fingu: A mathematics iPad game using multitouch interaction. In IDC 2012 (pp. 1–4). June 12–15, Bremen, Germany.
Baroody, A. J., Bajwa, N. P., & Eiland, M. (2009). Why can’t Johnny remember the basic facts? Developmental Disabilities Research Reviews, 15, 69–79.
Baroody, A. J., Eiland, M., Purpura, D. J., & Reid, E. E. (2013). Can computer-assisted discovery learning foster first graders’ fluency with the most basic addition combinations? American Educational Research Journal, 50(3), 533–573.
Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–178.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., Schauble, L., & Sessa, A. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Cole, M. (2009). The perils of translation: A first step in reconsidering Vygotsky’s theory of development in relation to formal education. Mind, Culture, and Activity, 16(4), 291–295.
Dehaene, S. (2011). The number sense (2nd ed.). New York: Oxford University Press.
Edwards, L. D., & Robutti, O. (2014). Embodiment, modalities, and mathematical affordances. In L. D. Edwards, F. Ferrara, & D. Moore-Russo (Eds.), Emerging perspectives on gesture and embodiment in mathematics. Charlotte, NC: Information Age Publishing.
Engeström, Y., & Sannino, A. (2010). Studies of expansive learning: Foundations, findings and future challenges. Educational Research Review, 5, 1–24.
ENRP. (2015). http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/Pages/enrp.aspx
Fischer, M. H., Kaufmann, L., & Domahs, F. (2012). Finger counting and numerical cognition. Frontiers in Psychology, 3, 1. doi:10.3389/fpsyg.2012.00108
Gee, J. P. (2003). What video games have to teach us about learning and literacy. New York: Palgrave Macmillan.
Gibson, J. J. (1986). The ecological approach to visual perception. Hillsdale, NJ: Lawrence Erlbaum.
Gibson, E. J. (2000). Perceptual learning in development: Some basic concepts. Ecological Psychology, 12(4), 295–302.
Gibson, J. J., & Gibson, E. J. (1955). Perceptual learning: Differentiation or enrichment? Psychological Review, 62, 32–41.
Gibson, E. J., & Pick, A. (2000). An ecological approach to perceptual learning and development. Oxford University Press.
Ginsburg, H. P., & Baroody, A. J. (2003). Test of early mathematics ability (3rd ed.). Austin: Pro-ed.
Goffman, E. (1974). Frame analysis: An essay on the organization of experience. London: Harper and Row.
Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic. Journal for Research in Mathematics Education, 25, 116–140.
Hodkinson, P., Biesta, G., & James, D. (2008). Understanding learning culturally: Overcoming the dualism between social and individual views of learning. Vocations and Learning, 1, 27–47.
Holgersson, I., Barendregt, W., Rietz, E., Ottosson, T., & Lindström, B. (2016). Can children enhance their arithmetic competence by playing a specially designed computer game? CURSIV, 18, 177–188.
Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer. New York: Wiley.
Kaptelinin, V., & Nardi, B. A. (2006). Acting with technology: Activity theory and interaction design. Cambridge, MA: The MIT Press.
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkman, J. (1949). The discrimination of visual number. American Journal of Psychology, 62, 498–525.
Kellman, P. J., & Garrigan, P. (2009). Perceptual learning and human expertise. Physics of Life Reviews, 6, 53–84.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Kühnel, J. (1916). Neubau des Rechenunterrichts. Leipzig: Julius Klinkhardt.
Linderoth, J. (2012). Why gamers don’t learn more: An ecological approach to games as learning environments. Journal of Gaming and Virtual Worlds, 4(1), 45–62.
Lindström, B., Marton, F., Emanuelsson, J., Lindahl, M., & Packendorff, M. (2011). Pre-school children’s learning of number concepts in a game-enhanced learning environment. In J. Häggström, et al. (Eds.), Voices on learning and instruction in mathematics (pp. 119–141). National Centre for Mathematics Education: University of Gothenburg.
Marton, F. (2015). Necessary conditions of learning. London: Routledge.
Marton, F., & Booth, S. (1997). Learning and awareness. Hillsdale, NJ: Lawrence Erlbaum Associates.
Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. Journal of the Learning Sciences, 15(2), 193–220. doi:10.1207/s15327809jls1502_2.
McMullen, J., Hannula-Surmonen, M. M., & Lehtinen, E. (2014). Spontaneous focusing on quantitative relations in the development of children’s fraction knowledge. Cognition and Instruction, 32(2), 198–218.
McMullen, J., Hannula-Surmonen, M. M., & Lehtinen, E. (2015). Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later. ZDM Mathematics Education. doi:10.1007/s11858-015-0669-4
Mehan, H. (1979). “What time is it Denise?”: Asking known information question in classroom discourse. Theory into Practice, 28(4), 285–289.
Neisser, U. (1976). Cognition and reality: Principles and implications of cognitive psychology. W. H. Freeman & Company.
Neuman, D. (1987). The origin of arithmetic skills. A phenomenographic approach. Gothenburg: Acta Universitatis Gothoburgensis.
Neuman, D. (2013). Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen. (To change work methods and culture in primary arithmetic instruction.). Nordic Studies in Mathematics Education, 18(2), 3–46.
Papert, S. (1980). Mindstorms: children, computers and powerful ideas. Brighton: Harvester P.
Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44(2), 162–169.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research—Learning trajectories for young children. New York, NY: Routledge.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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: Moyer-Packenham, P. (eds) International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives. Mathematics Education in the Digital Era, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-32718-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-32718-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-32716-7
Online ISBN: 978-3-319-32718-1
eBook Packages: EducationEducation (R0)