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Number Navigation Game (NNG): Design Principles and Game Description

  • Erno LehtinenEmail author
  • Boglárka Brezovszky
  • Gabriela Rodríguez-Aflecht
  • Henrik Lehtinen
  • Minna M. Hannula-Sormunen
  • Jake McMullen
  • Nonmanut Pongsakdi
  • Koen Veermans
  • Tomi Jaakkola
Part of the Advances in Game-Based Learning book series (AGBL)

Abstract

This chapter describes the Number Navigation Game (NNG), a game-based learning environment aimed at the promotion of flexibility and adaptivity with arithmetical problem solving in 10- to 13-year-old students. The game design is based on an integrated approach in which the different elements of the game are directly related to the mathematical content, i.e., the use of rich networks of numerical connections in solving arithmetic problems. The interface of the game is a hundred square superimposed on various maps of land and sea, where players have to strategically navigate a ship by using different combinations of numbers and arithmetic operations. The game has two different modes encouraging the use of different arithmetic operations and number combinations. The openness of the gameplay allows players the opportunities to explore different numerical connections in an environment where there are no right or wrong answers. Future directions of the game development include additional game features and extensions to larger numbers and rational numbers.

Keywords

Adaptive number knowledge Arithmetic problem solving Game design Hundred square 

Notes

Acknowledgment

The present study was funded by grant 274,163 awarded to the first author by the Academy of Finland.

References

  1. Aebli, H. (1980). Denken: das Ordnen des Tuns. Bd. 1: Kognitive Aspekte der Handlungstheorie. Stuttgart, Germany: Klett-Cotta [Thinking: putting actions in order].Google Scholar
  2. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1–33). London, England: Lawrence Erlbaum.Google Scholar
  3. Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24, 294–323. doi: 10.2307/749464.CrossRefGoogle Scholar
  4. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology, 6, 626–641.Google Scholar
  5. Devlin, K. (2011). Mathematics education for a new era: Video games as a medium for learning. Natick MA: AK Peters.CrossRefGoogle Scholar
  6. Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23, 45–55.Google Scholar
  7. Fuchs, L. S., Geary, D. C., Fuchs, G., Compton, D. L., & Hamlett, C. L. (2014). Sources of individual differences in emerging competence with numeration understanding versus multidigit calculation skill. Journal of Educational Psychology, 106, 482–498. doi: 10.1037/a0034444.CrossRefGoogle Scholar
  8. Geary, D. C., Bow-Thomas, C. C., Lin, F., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and americal children: Influence of age, language, and schooling. Child Development, 67, 2022–2044.CrossRefGoogle Scholar
  9. Habgood, M. P. J., & Ainsworth, S. E. (2011). Motivating children to learn effectively: Exploring the value of intrinsic integration in educational games. The Journal of the Learning Sciences, 20, 169–206. doi: 10.1080/10508406.2010.508029.CrossRefGoogle Scholar
  10. Jacobson, M. J., & Spiro, R. J. (1995). Hypertext learning environments, cognitive flexibility, and the transfer of complex knowledge: An empirical investigation. Journal of Educational Computing Research, 12, 301–333. doi: 10.2190/4T1B-HBP0-3F7E-J4PN.CrossRefGoogle Scholar
  11. Klein, A. S., Beishuizen, M., & Treffers, A. (1998). The empty number line in Dutch second grades: Realistic versus gradual program design. Journal for Research in Mathematics Education, 29, 443–464. doi: 10.2307/749861.CrossRefGoogle Scholar
  12. Laski, E. V., Ermakova, A., & Vasilyeva, M. (2014). Early use of decomposition for addition and its relation to base-10 knowledge. Journal of Applied Developmental Psychology, 35, 444–454. doi: 10.1016/j.appdev.2014.07.002.CrossRefGoogle Scholar
  13. Laski, E. V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50, 853–864. doi: 10.1037/a0034321.CrossRefGoogle Scholar
  14. Malone, T. W., & Lepper, M. R. (1987). Making learning fun: A taxonomy of intrinsic motivations for learning. In R. E. Snow & M. J. Farr (Eds.), Aptitude, learning and instruction: III. Conative and affective process analyses (pp. 223–253). Hilsdale, NJ: Erlbaum.Google Scholar
  15. McMullen, J., Brezovszky, B., Rodríguez Padilla, G., Pongsakdi, N., & Lehtinen, E. (2015). Adaptive number knowledge: exploring the foundations of adaptivity with whole-number arithmetic. Manuscript submitted for publication.Google Scholar
  16. Moreno, R., & Mayer, R. E. (2005). Role of guidance, reflection, and interactivity in an agent-based multimedia game. Journal of Educational Psychology, 97, 117–128. doi: 10.1037/0022-0663.97.1.117.CrossRefGoogle Scholar
  17. Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fisher, M. H. (2011). Extending the mental number line: A review of multi-digit number processing. Zeitschrift für Psychologie/Journal of Psychology, 219, 3–22. doi: 10.1027/2151-2604/a000041.CrossRefGoogle Scholar
  18. Nuerk, H. C., Willmes, K., & Fias, W. (2005). Perspectives on number processing: Editorial. Psychology Science, 47, 4–9.Google Scholar
  19. Rodríguez Padilla, G., Brezovszky, B., Pongsakdi, N., Jaakkola, T., Hannula-Sormunen, M., McMullen, J., & Lehtinen, E. (2015). Number Navigation Game-based learning environment: Experience and motivational effects. In J. Torbeyns, E. Lehtinen & J. Elen (Eds.), Developing competencies in learners: From ascertaining to intervening (pp. xxxx). New York, NY: Springer.Google Scholar
  20. Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47, 1525–1538. doi: 10.1037/a0024997.CrossRefGoogle Scholar
  21. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428–444. doi: 10.1111/j.1467-8624.2004.00684.x.CrossRefGoogle Scholar
  22. Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games-but not circular ones-improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545–560. doi: 10.1037/a0014239.CrossRefGoogle Scholar
  23. Thomas, N. (2004). The development of structure in the number system. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the international group for the psychology of mathematics education (Vol. 4, pp. 305–312). Bergen, Norway: Bergen University Collage.Google Scholar
  24. Threlfall, J. (2002). Flexible mental calculation. Educational Studies in Mathematics, 50, 29–47. doi: 10.1023/A:1020572803437.CrossRefGoogle Scholar
  25. Threlfall, J. (2009). Strategies and flexibility in mental calculation. ZDM—The International Journal on Mathematics Education, 41, 541–555. doi: 10.1007/s11858-009-0195-3.CrossRefGoogle Scholar
  26. Tobias, S., Fletcher, J. D., Dai, D. Y., & Wind, A. P. (2011). Review of research on computer games. In S. Tobias & J. D. Fletcher (Eds.), Computer games and instruction (pp. 127–222). Charlotte, NC: Information Age.Google Scholar
  27. Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335–359. doi: 10.1007/BF03174765.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Erno Lehtinen
    • 1
    Email author
  • Boglárka Brezovszky
    • 1
  • Gabriela Rodríguez-Aflecht
    • 1
  • Henrik Lehtinen
    • 1
  • Minna M. Hannula-Sormunen
    • 2
  • Jake McMullen
    • 1
  • Nonmanut Pongsakdi
    • 1
  • Koen Veermans
    • 1
  • Tomi Jaakkola
    • 1
  1. 1.Department of Teacher EducationCentre for Learning Research, University of TurkuTurkuFinland
  2. 2.Department of Teacher EducationTurku Institute for Advanced Studies, University of TurkuTurkuFinland

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