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 study examines the learning outcomes and learning environment of a youth organizing program that has been effective in promoting individual as well as social change. Drawing on interviews with 25 former youth organizers from the program, this study explores the lessons that stay with them as they transition to young adulthood and the factors…

Engle's (this issue) analysis of framing students' contributions in learning interactions to construct generality and Marton's (this issue) discussion of learning to discern differences make valuable contributions to the ongoing scientific effort to understand transfer. This commentary characterizes these articles as contributing to 2 valuable…

The purpose of this article is to identify some necessary conditions of learning. To learn something, the learner must discern what is to be learned (the object of learning). Discerning the object of learning amounts to discerning its critical aspects. To discern an aspect, the learner must experience potential alternatives, that is, variation in…