Relationships Between Semiotic Representational Transformations and Performance Outcomes in Digital Math Games

The purpose of this study was to examine relationships between students’ semiotic representational transformations and students’ mathematics performance outcomes in digital math games. The study employed a convergent parallel mixed methods design. Students in Grades 4, 5, and 6 (ages 9–12) played nine digital math games. Researchers administered pretests and posttests and gathered video data. Researchers coded the video data to identify the representations used and students’ representational transformations to understand how these related to mathematics performance outcomes. The video data revealed that the most frequent type of semiotic representation used by students was images, followed by symbols. The most common type of representational transformation students made was a conversion (i.e., transforming across two different representational registers), which is more complex than a treatment (i.e., transforming within the same representational register). A difference in proportions test revealed significant differences in test scores when students made representational transformations using language, images, symbols, and gestures. The results showed that some of the digital math games prompted more representational transformations than others; However, all of the games prompted the conversion type of representational transformation. Students who progressed between the pretest and posttest were much more likely to make representational transformations. Students who did not recognize and use representations or make transformations were much more likely to regress between the pretest and posttest. These results show the importance of the recognition and use of semiotic representations and representational transformations to mathematics outcomes when students play digital math games.