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…

A gulf exists between prior work testing metacognitive instructional interventions and teacher practices that may support metacognition in the classroom. To help bridge this gulf, we designed an observational protocol to capture whether and how teachers provide metacognitive support in their talk and examined whether these supports were related to…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Achievement goals are the reasons for pursuing competence-related tasks. Much prior work has shown that they can affect student motivation, learning, and performance outcomes. They are typically measured in classroom settings vis-à-vis self-report surveys about students' goals or the perceived goal structure of the class. Less work has measured…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…