Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially…

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when…

An emerging consensus suggests that guided discovery, which combines discovery and instruction, is a more effective educational approach than either one in isolation. The goal of this study was to examine two specific forms of guided discovery, testing whether conceptual instruction should precede or follow exploratory problem solving. In both…

Statistics is taught at every level of education, yet teachers often have to assume their students have no knowledge of statistics and start from scratch each time they set out to teach statistics. The motivation for this experimental study comes from interest in exploring educational applications of augmented reality (AR) delivered via mobile…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

This study provides empirical evidence of a highly specific use of games in education--the assessment of the learner. Linear regressions were used to examine the predictive and convergent validity of a math game as assessment of mathematical understanding. Results indicate that prior knowledge significantly predicts game performance. Results also…

Does speed provide a "model for" rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the "model for" rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14-15 year old students at…