Skip to main content

Developing Adaptive Number Knowledge with the Number Navigation Game-Based Learning Environment

  • Chapter
Describing and Studying Domain-Specific Serious Games

Abstract

Research suggests that adaptivity with arithmetic problem solving can be developed by placing more focus on developing students’ understanding of the underlying numerical characteristics and connections during problem solving. For this reason, the present study aimed to explore how primary school students’ game performance using the “Number Navigation Game” (NNG) game-based learning environment was related to their development of adaptive number knowledge. NNG provides extensive opportunities for working strategically with various number patterns and number–operation combinations. Sixth grade students (N = 23) played NNG in pairs, once a week, for 7 weeks during math class. Students completed measures of adaptive number knowledge and arithmetic fluency during pre- and post-testing. Results show that students’ game performance had a unique contribution to explaining students’ adaptive number knowledge during post-test. This suggests that NNG is a promising game-based learning environment for developing adaptivity with arithmetic problem solving by enhancing students’ adaptive number knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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 

  • 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.

    Article  Google Scholar 

  • Blöte, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. Learning and Instruction, 10, 221–247. doi:10.1016/S0959-4752(99)00028-6.

    Article  Google Scholar 

  • Brezovszky, B., Lehtinen, E., McMullen, J., Rodriguez, G., & Veermans, K. (2013). Training flexible and adaptive arithmetic problem solving skills through exploration with numbers. The development of Number Navigation Game. In C. Vaz de Carvalho, & P. Escuderio (Eds.), Proceedings of the 7th European Conference on Game Based Learning (ECGBL2013) (pp. 626–634). Retrieved from http://issuu.com/acpil/docs/ecgbl2013-issuu_vol_2

  • Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2003). Patterns of knowledge in children’s addition. Developmental Psychology, 39, 521–534. doi:10.1037/0012-1649.39.3.521.

    Article  Google Scholar 

  • Chen, Z. -H., Liao, C. C. Y., Cheng, H. N. H., Yeh, C. Y. C., & Chan, T. -W. (2012). Influence of game quests on pupils’ enjoyment and goal-pursuing in math learning. Educational Technology & Society, 15, 317–327. Retrieved from http://dblp.uni-trier.de/db/journals/ets/ets15.html#ChenLCYC12

  • Cheung, A. C., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88–113. doi:10.1016/j.edurev.2013.01.001.

    Article  Google Scholar 

  • Devlin, K. (2011). Mathematics education for a new era: Video games as a medium for learning. Natick, MA: AK Peters.

    Book  Google Scholar 

  • Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23, 45–55. Retrieved from http://www.jstor.org/stable/749163.

  • Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20, 399–483. doi:10.1207/S1532690XCI2004_1.

    Article  Google Scholar 

  • Garris, R., Ahlers, R., & Driskell, J. E. (2002). Games, motivation, and learning: A research and practice model. Simulation & Gaming, 33, 441–467. doi:10.1177/1046878102238607.

    Article  Google Scholar 

  • Gee, J. P. (2003). What video games have to teach us about literacy and learning. Hampshire, England: Palgrave Macmillan.

    Google Scholar 

  • Girard, C., Ecalle, J., & Magnan, A. (2013). Serious games as new educational tools: How effective are they? A meta‐analysis of recent studies. Journal of Computer Assisted Learning, 29, 207–219. doi:10.1111/j.1365-2729.2012.00489.x.

    Article  Google Scholar 

  • Habgood, M. P. J., & Ainsworth, S. E. (2011). Motivating children to learn effectively: Exploring the value of intrinsic integration in educational games. Journal of the Learning Sciences, 20, 169–206. doi:10.1080/10508406.2010.508029.

    Article  Google Scholar 

  • Hatano, G., & Oura, Y. (2003). Commentary: Reconceptualizing school learning using insight from expertise research. Educational Researcher, 32, 26–29. Retrieved from http://www.jstor.org/stable/3700083.

  • Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. The Journal of Mathematical Behavior, 23, 443–463. doi:10.1016/j.jmathb.2004.09.005.

    Article  Google Scholar 

  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81–116. doi:10.2307/30034933.

    Article  Google Scholar 

  • Hwang, G., & Wu, P. (2012). Advancements and trends in digital game‐based learning research: A review of publications in selected journals from 2001 to 2010. British Journal of Educational Technology, 43, E6–E10. doi:10.1111/j.1467-8535.2011.01242.x.

    Article  Google Scholar 

  • Järvelä, S., Lehtinen, E., & Salonen, P. (2000). Socio-emotional orientation as a mediating variable in teaching learning interaction: Implications for instructional design. Scandinavian Journal of Educational Research, 44, 293–306. doi:10.1080/713696677.

    Article  Google Scholar 

  • Ke, F. (2008). A case study of computer gaming for math: Engaged learning from gameplay? Computers & Education, 51, 1609–1620. doi:10.1016/j.compedu.2008.03.003.

    Article  Google Scholar 

  • Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., …von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57, 782–795. doi:10.1016/j.neuroimage.2011.01.070

  • 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.

    Article  Google Scholar 

  • Lehtinen, E., Brezovszky, B., Rodríguez Padilla, G. Lehtinen, H. Hannula-Sormunen, M. M., McMullen, J., … Jaakkola, T. (2015). Number Navigation Game (NNG): Design principles and game description. In J. Torbeyns, E. Lehtinen & J. Elen (Eds.), Developing competencies in learners: From ascertaining to intervening (pp. xx-xx). New York, NY: Springer.

    Google Scholar 

  • Lowyck, J., Lehtinen, E., & Elen, J. (2004). Editorial: Students’ perspectives on learning environments. International Journal of Educational Research, 41, 401–406. doi:10.1016/j.ijer.2005.08.008.

    Article  Google Scholar 

  • Martens, R., Gulikers, J., & Bastiaens, T. (2004). The impact of intrinsic motivation on e‐learning in authentic computer tasks. Journal of Computer Assisted Learning, 20, 368–376. doi:10.1111/j.1365-2729.2004.00096.x.

    Article  Google Scholar 

  • 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 

  • Metsämuuronen, J. (2006). Tutkimuksen tekemisen perusteet ihmistieteissä. [Principles of conducting scientific research in humanities]. Jyväskylä, Finland: Gummeruksen kirjapaino Oy.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM (Ed.), Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/

  • Plass, J. L., O’Keefe, P. A., Homer, B. D., Case, J., Hayward, E. O., Stein, M., & Perlin, K. (2013). The impact of individual, competitive, and collaborative mathematics gameplay on learning, performance, and motivation. Journal of Educational Psychology, 105, 1050–1066. doi: 10.1037/a0032688

  • Räsänen, P., Salminen, J., Wilson, A. J., Aunio, P., & Dehaene, S. (2009). Computer-assisted intervention for children with low numeracy skills. Cognitive Development, 24, 450–472. doi:10.1016/j.cogdev.2009.09.003.

    Article  Google Scholar 

  • Salen, K., & Zimmerman, E. (2004). Rules of play: Game design fundamentals. Cambridge, MA: MIT Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schrank, F. A., McGrew, K. S., & Woodcock, R. W. (2001). Technical abstract (Woodcock-Johnson III Assessment Service Bulletin No. 2). Itasca, IL: Riverside Publishing. Retrieved from http://www.riverpub.com/clinical/pdf/WJIII_ASB2.pdf

  • Seo, Y., & Bryant, D. P. (2009). Analysis of studies of the effects of computer-assisted instruction on the mathematics performance of students with learning disabilities. Computers & Education, 53, 913–928. doi:10.1016/j.compedu.2009.05.002.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Threlfall, J. (2002). Flexible mental calculation. Educational Studies in Mathematics, 50, 29–47. doi:10.1023/A:1020572803437.

    Article  Google Scholar 

  • Threlfall, J. (2009). Strategies and flexibility in mental calculation. ZDM—International Journal on Mathematics Education, 41, 541–555. doi:10.1007/s11858-009-0195-3.

    Article  Google Scholar 

  • Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2009). Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction. Learning and Instruction, 19, 1–12. doi:10.1016/j.learninstruc.2007.12.002.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of “The number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 1–16. doi:10.1186/1744-9081-2-20.

    Article  Google Scholar 

  • Wouters, P., van Nimwegen, C., van Oostendorp, H., & van der Spek, E. D. (2013). A meta-analysis of the cognitive and motivational effects of serious games. Journal of Educational Psychology, 105, 249–265. doi:10.1037/a0031311.

    Article  Google Scholar 

  • Young, M. F., Slota, S., Cutter, A. B., Jalette, G., Mullin, G., Lai, B., … Yukhymenko, M. (2012). Our princess is in another castle. A review of trends in serious gaming for education. Review of Educational Research, 82, 61–89. doi:10.3102/0034654312436980

Download references

Acknowledgment

The present study was funded by grant 274163 awarded to the last author by the Academy of Finland.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Boglárka Brezovszky .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Brezovszky, B. et al. (2015). Developing Adaptive Number Knowledge with the Number Navigation Game-Based Learning Environment. In: Torbeyns, J., Lehtinen, E., Elen, J. (eds) Describing and Studying Domain-Specific Serious Games. Advances in Game-Based Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-20276-1_10

Download citation

Publish with us

Policies and ethics