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…