This study investigated the effects of (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

This study investigated the effects of: (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and…

Well-designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th-grade students' (N =…

New educational technologies that utilize students' interaction data and visualizations provide a means to expand our understanding of learning processes. In this study, we apply two advanced and novel data visualization techniques, called the "Indivisualizer" and a "Sankey diagram," to explore how middle school students (N =…

New educational technologies that utilize students' interaction data and visualizations provide a means to expand our understanding of learning processes. In this study, we apply two advanced and novel data visualization techniques, called the "Indivisualizer" and a "Sankey diagram," to explore how middle school students (N =…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

We apply an advanced data visualization technique, "Sankey diagram," to explore how middle-school students (N = 343) solved problems in a game-based algebraic notation tool. The results indicate that there is a large variation in the types of students' strategies to solve the problems, with some approaches being more efficient than…