Relevant Literature
 Barab, S.A., Scott, B., Siyahhan, S., Goldstone, R., IngramGoble, A., Zuiker, S.J., Warren, S. Transformational play as a curricular scaffold: using videogames to support science education. Journal of Science Education and Technology 18(4), 305 (2009).
 Clark, D.B., TannerSmith, E.E., Killingsworth, S.S. Digital games, design, and learning: a systematic review and metaanalysis. Review of Educational Research 86(1), 79–122 (2016).
 Crocco, F., Offenholley, K., Hernandez, C. A proofofconcept study of gamebased learning in higher education. Simulation & Gaming 47(4), 403–422 (2016).
 Deterding, S., Dixon, D., Khaled, R., Nacke, L. From game design elements to gamefulness: defining gamification. In: Proceedings of the 15th International Academic MindTrek Conference: Envisioning Future Media Environments, pp. 9–15. ACM (2011)
 Habgood, M.J., Ainsworth, S.E. Motivating children to learn effectively: exploring the value of intrinsic integration in educational games. J. Learn. Sci. 20(2), 169–206 (2011).
 Hwang, G.J., Wu, P.H., Chen, C.C. An online game approach for improving students learning performance in webbased problemsolving activities. Comput. Educ. 59(4), 1246–1256 (2012).
 Ke, F. Designing and integrating purposeful learning in game play: a systematic review. Educ. Technol. Res. Dev. 64(2), 219–244 (2016).
 Lobel, A., Engels, R.C., Stone, L.L., Burk, W.J., Granic, I. Video gaming and childrens psychosocial wellbeing: a longitudinal study. J. Youth Adolesc. 46(4), 884–897 (2017).
 Lomas, D., Patel, K., Forlizzi, J.L., Koedinger, K.R. Optimizing challenge in an educational game using largescale design experiments. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 89–98. ACM (2013).
 Mayer, R.E. Computer Games for Learning: An EvidenceBased Approach. MIT Press, Cambridge (2014).
 Riconscente, M.M. Results from a controlled study of the ipad fractions game motion math. Games Cult. 8(4), 186–214 (2013).
 Schell, J. The Art of Game Design: A Book of Lenses. CRC Press, New York (2014).
 Suh, S., Kim, S.W., Kim, N.J. Effectiveness of MMORPGbased instruction in elementary english education in Korea. J. Comput. Assist. Learn. 26(5), 370–378 (2010).
 Tabbers, H.K., de Koeijer, B. Learner control in animated multimedia instructions. Instruc. Sci. 38(5), 441–453 (2010).
 Wouters, P., Van Oostendorp, H. Instructional Techniques to Facilitate Learning and Motivation of Serious Games. Springer, Cham (2016).
 Yip, F.W., Kwan, A.C. Online vocabulary games as a tool for teaching and learning english vocabulary. Educ. Media Int. 43(3), 233–249 (2006).
 Cordova, D.I., Lepper, M.R. Intrinsic motivation and the process of learning: beneficial effects of contextualization, personalization, and choice. Journal of Educational Psychology 88(4), 715 (1996).
 Flowerday, T., Shell, D.F. Disentangling the effects of interest and choice on learning, engagement, and attitude. Learn. Ind. Differ. 40, 134–140 (2015).
 Lomas, J.D., Koedinger, K., Patel, N., Shodhan, S., Poonwala, N., Forlizzi, J.L. Is difficulty overrated?: the effects of choice, novelty and suspense on intrinsic motivation in educational games. In: Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems, pp. 1028–1039. ACM (2017).
 Malone, T.W. Toward a theory of intrinsically motivating instruction. Cogn. Sci. 5(4), 333–369 (1981).
 Ryan, R.M., Rigby, C.S., Przybylski, A. The motivational pull of video games: a selfdetermination theory approach. Motiv. Emot. 30(4), 344–360 (2006).
 Sawyer, R., Smith, A., Rowe, J., Azevedo, R., Lester, J. Is more agency better? The impact of student agency on gamebased learning. In: Andre, E., Baker, R., Hu, X., Rodrigo, M.M.T., du Boulay, B. (eds.) AIED 2017. LNCS, vol. 10331, pp. 335–346. Springer, Cham (2017).
 Snow, E.L., Allen, L.K., Jacovina, M.E., McNamara, D.S. Does agency matter? Exploring the impact of controlled behaviors within a gamebased environment. Comput. Educ. 82, 378–392 (2015).
 Zimmerman, B.J. Selfefficacy: an essential motive to learn. Contemp. Educ. Psychol. 25(1), 82–91 (2000).
 Zimmerman, B.J. Investigating selfregulation and motivation: historical background, methodological developments, and future prospects. Am. Educ. Res. J. 45(1), 166–183 (2008).
 Glasgow, R., Ragan, G., Fields, W.M., Reysi, R., Wasman, D. The decimal dilemma. Teach. Child. Math. 7(2), 89 (2000)
 Isotani, S., McLaren, B.M., Altman, M. Towards Intelligent tutoring with erroneous examples: a taxonomy of decimal misconceptions. In: Aleven, V., Kay, J., Mostow, J. (eds.) ITS 2010. LNCS, vol. 6095, pp. 346–348. Springer, Heidelberg (2010).
 Stacey, K., Helme, S., Steinle, V. Confusions between decimals, fractions and negative numbers: a consequence of the mirror as a conceptual metaphor in three different ways. In: PME Conference, vol. 4, pp. 4–217 (2001).
 Thipkong, S. & Davis, E.J. (1991). Preservice teacher's misconceptions in interpreting and applying decimals. School Science and Mathematics, 9, 9399. (Considerable difficult that both adults and children have difficulty with decimals; A catalog of decimal misconceptions)
 Swan, M. (1983). Teaching decimal place value: A comparative study of "conflict" and "positive only" approaches. Nottingham: Shell Centre for Mathematical Education.
 Steinle, V. (2004). Detection and remediation of decimal misconceptions. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.), Towards Excellence in Mathematics (pp. 460478). Brunswick: The Mathematical Association of Victoria.
 Steinle, V. & Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in grades 5 to 10. In C. Kanes, M. Goos and E. Warren (Eds), Teaching Mathematics in New Times. Proceedings of the 21st Annual Conference of MERGA, (2) 548555. Brisbane: MERGA.
 Steinle, V., & Stacey, K. (1998a). Students and decimal notation: Do they see what we see? Paper presented at the Thirtyfifth Annual Conference of the Mathematical Association of Victoria. The Mathematical Association of Victoria, Brunswick, Vic.
 Standiford, S. N., Klein, M. F., & Tatsuoka, K. K. (1982). Decimal fraction arithmetic: Logical Error Analysis and Its validation. Research report  University of Illinois at UrbanaChampaign.
 Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Preservice teachers' knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education, 4(3),20525.
 Stacey, K., Helme, S., & Steinle, V. (2001). Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways. In M. v. d. HeuvelPanhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 217224). Utrecht: PME.
 Stacey, K. & Steinle, V. (1998). Refining the classification of students' interpretations of decimal notation. Hiroshima Journal of Mathematics Education, 6, 4969.
 Stacey, K., & Steinle, V. (1999). A Longitudinal study of children's thinking about decimals: A preliminary analysis. Paper presented at the 23rd Conference of the International Group for the Psychology of Mathematics Education, Haifa, Israel.
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CMU HCII Article: Decimal Game Helps Kids Get The Point CMU HCII Article: Decimal Point: Can Having Fun Increase Learning? 