Effects of Representation Format in Problem Representation on Qualitative Understanding and Quantitative Proficiency in a Learning Game Context

Reports and surveys by the U.S. government and international organizations have repeatedly acknowledged the achievement problem in math in K-12 regardless of various efforts (e.g., by the U.S. Department of Education) to diminish it. To address the problem in math achievement in K-12, teachers, scholars, and the U.S. government have developed various materials and intervention tools. As a potential platform to address the problem in math achievement, video games generate a large variety of perspectives on their value. Along with the debate on the game's inherent good or bad features, there is also a debate on the effectiveness of video games as a learning tool. Regarding these debates and the ambiguous results on video games as learning tools, Greitemeyer and Mügge (2014) postulated that games can provide both positive and negative impacts according to their content (i.e., violent and pro-social games). However, recent literature investigating the use of video games in varied learning contexts shows that the learning effectiveness of games is still inconclusive. A potential reason is that video games mostly facilitate implicit qualitative understanding. Video games consist of rich interactive experiences that help to foster understanding of qualitative relationships in gameplay more than quantitative proficiency that is required in the formal school system (Clark et al. 2011; Squire, Barnett, Grant, & Higginbotham, 2004). Another reason is that educational game designers have paid little attention to designing and developing learning supports in educational games. Therefore, the current study aims to address a comprehensive question -- How does an educational game, through the use of learning supports, promote the application of acquired qualitative understanding to math problem solving in formal educational contexts? A promising method to address the aforementioned problem is to externalize cognitive and metacognitive processes (Lajoie, 2009). Externalizing Problem Representation (EPR) refers to a cognitive behavior in which a learner constructs her own representations overtly (Cox, 1999). The processes of EPR are to re-order information in problem solving, to clarify ambiguous parts of the problem, and to modify and enact mental representations including mental animations and images. EPR helps to make missing and implicit information or representations explicit. There are several synonyms of Externalizing Problem Representation (EPR), such as external representation (Zhang, 1997), externalized cognition (Cox & Brna, 1995), and re-representation (Ainsworth & Th Loizou, 2003). From the semiotics perspective, EPR can be categorized into two forms by its sign: Iconic and symbolic. Although the potential benefits of externalizing problem representation was claimed in prior research, little attention was paid to investigating the design of EPR in video games. Compared to the studies of mental problem representation, few empirical studies on external representation have been conducted. Hence, it is warranted to examine the efficacy of learning support that promotes externalizing problem representation in two formats (i.e., iconic and symbolic) in the video-game-based learning setting. In light of this, the purpose of this study is to investigate whether EPR-promoting scaffolds (in iconic vs. symbolic formats) enhance qualitative understanding and quantitative proficiency in ratios and proportional relationships in a learning game context. Specifically, the learning game will request players to respond to either iconic or symbolic learning probes that help to externalize the mental representations of the math problems in the game. In this study, quantitative proficiency refers to the problem solving proficiency in both game and formal education context. The current study involves two levels of task complexity (i.e., low complexity vs. high complexity) as a moderating variable. The study addresses the following research questions: 1. Will iconic learning probes promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional reasoning, with the task complexity controlled in the educational game? 2. Will symbolic learning probes promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional reasoning, with task complexity controlled in the educational game? 3. Will iconic learning probes promoting EPR, in comparison to symbolic learning probes promoting EPR, be more effective in enhancing qualitative understanding and quantitative proficiency in ratio and proportional reasoning, with task complexity controlled in the educational game? To accomplish the purpose of this study, learning probes that prompt learners to externalize their internal problem representation were developed in two different formats, iconic and symbolic, based on Mayer's math problem representation model. In the experiment, forty-five participants in this study processed either iconic or symbolic learning probes during their gameplay. Finally, qualitative understanding and quantitative proficiency were measured three times: before this study, after playing the shipping container episode with a low complexity task, and after playing the shipping container episode with a high complexity task. Regarding Research Question 1, the result of repeated-measures ANOVA indicates that, for participants in the Iconic Learning Probe (ILP) group, the difference in qualitative understanding between the pretest, posttest, and posttest 2 was not statistically significant whereas the difference in quantitative proficiency between the pretest, posttest 1, and posttest 2 was statistically significant. Regarding Research Question 2, the result of repeated-measures ANOVA indicates that, for participants in the Symbolic Learning Probe (SLP) group, the difference in qualitative understanding between the pretest, posttest 1, and posttest 2 was statistically significant whereas the difference in quantitative understanding between the pretest, posttest 1, and posttest 2 was not statistically significant. Regarding Research Question 3, since there was a significant interaction between the times of measurement and the types of EPR in regard to both qualitative understanding and quantitative proficiency, pairwise comparisons using the Bonferroni method were drawn. There were significant differences in participants' qualitative understanding between ILP and SLP groups in posttest 1 and posttest 2 whereas there was no significant difference in participants' qualitative understanding between ILP and SLP groups in the pretest. Regarding the quantitative proficiency, there were significant differences in participants' quantitative proficiency between ILP and SLP groups in posttest 1 whereas there was no significant difference in participants' quantitative proficiency between ILP and SLP groups in the pretest and posttest 2. In the final chapter, I discussed major research findings of this study based on the theoretical research reviewed in Chapter 2. Then I described the implications of this study and suggestions for future study.