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…

This article examines formative interventions as we understand them in cultural-historical activity theory and reflects on key differences between this intervention research tradition and design-based research as it is conceived in the learning sciences tradition. Three projects, including 2 Change Laboratories, are analyzed with the help of…