Concreteness Fading of Algebraic Instruction: Effects on Learning

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 perceptual support. Although most work on concreteness focuses on conceptual support through examples or analogies, here we consider notational concreteness—perceptual-motor supports that provide access into the dynamic structure of a representation itself. We hypothesize that perceptual support may be maximally beneficial as an initial scaffold to learning so that later static symbol use may be interpreted using a dynamic perspective. This hypothesis meshes with other findings using concrete analogies or examples, which often find that fading these supports over time leads to stronger learning outcomes. In an experiment exploring this hypothesis, we compared gains from the fading out of dynamic concrete physical motion of symbols during instruction with the introduction of motion over the course of instruction. In line with our theoretical perspective, concreteness fading led to significantly better achievement than concreteness introduction after Day 2 of the intervention.