Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…

The present research sought to determine if primary school students differentiate between classes that are challenging and those that are difficult, and how these distinctions relate to their motivation and achievement. Results indicated that there are three types of challenges/difficulties. "Challenging" classes are those that are…

Technology-rich learning environments (TREs) provide opportunities for learners to engage in complex interactions involving a multitude of cognitive, metacognitive, and affective states. Understanding learners' distinct learning progressions in TREs demand inquiry approaches that employ well-conceived theoretical accounts of these multiple facets.…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…