Matching and mismatching between the pedagogical design principles of a math game and the actual practices of play P. Lindström,* A. Gulz,* M. Haake† & B. Sjödén* *Lund University Cognitive Science, Lund University, S-22200 Lund, Sweden †Department of Design Sciences, Lund University, S-22200 Lund, Sweden Abstract The article reports and discusses a long-term qualitative study of forty 8–10-year-old students who regularly played a math game during math lessons for 9 weeks. The goal was to explore the relations between (i) some of the pedagogical principles that underlie the game and (ii) the playing practice in terms of what actually takes place when students play the math game during regular math lessons. The article discusses indications of matches and mismatches between pedagogical principles and playing practice as they appear in analyses of observations and video recordings. The result highlights the difficulty of predicting areas in which possible mismatches appear between the intentions of the pedagogues and designers of educational technology and the actual use of the technology by the students. This also applies to educational materials that have already been pilot tested and used on a smaller scale. We emphasize the need to observe actual use for extensive periods of time, i.e. to go beyond short-time user testing. Keywords design, educational game, game playing in practice, math understanding, pedagogical principle. Introduction Base-10 concepts as gate-keeping concepts in mathematics School mathematics often focuses on training students’ calculating skills and their abilities to apply certain kinds of routine problems. However, having routine computing skills does not necessarily mean that one has an equivalent understanding of mathematical concepts and principles. For example, most children can easily learn how to count to 20, but they may do so without knowing that the number 2 in 20 stands for two sets of 10. Likewise, they may be able to count in the hundreds, but without under- standing that the one in the hundreds column is equal to 10 sets of 10. Actually, the understanding of mathemati- cal concepts related to the base-10 position system, including operations of carrying, borrowing and estima- tion, is an unresolved bottleneck for many elementary school children.Yet, such an understanding is critical to all future mathematics learning and can thus be labelled ‘gate keeping’ (Russell & Ginsburg 1984; Carpenter et al. 1993). Mathematical symbols are complex in that they may have multiple meanings (Arcavi 1994). This can be dif- ficult for a young child who might overextend the one- to-one principle she already knows for connecting symbols to magnitudes – as in ‘3’ means three things – and also interpret ‘11’ as a single ‘name’ instead of one Accepted: 14 July 2010 Correspondence: Agneta Gulz, Lund University Cognitive Science, Kungshuset, Lundagard, S-22222 Lund, Sweden. Email: Agneta.Gulz@lucs.lu.se doi: 10.1111/j.1365-2729.2010.00380.x Original article 90 © 2010 Blackwell Publishing Ltd Journal of Computer Assisted Learning (2011), 27, 90–102