How External Representations Propel Development and Future Learning

Stanford University, Stanford CA

Investigators

Abstract

Mathematics, diagrams, and other formal representations help scientists discover and organize complex relations. This research will test whether this is also true for the developing child. The studies will examine how explicit, culturally developed symbol systems propel the development of higher-order cognition in pre-adolescent and adolescent children in the domains of proportions, fractions, hypothesis testing, and game playing. The studies will alter the characteristics of symbolic tools and children's interactions with them to uncover specific properties of symbol systems and their social environments that support development and transfer. The research will evaluate conceptual maturity not only by the problems children can solve but also by the problems they are prepared to learn to solve in a transfer setting, a potentially much more sensitive measure of development. For example, some children will be encouraged to "invent" mathematics to explain how weight and distance compensate on a balance scale, whereas others will simply use words to explain. Afterwards, to assess the immediate effects of explanations using mathematics versus words, children in both groups will solve new balance scale problems. Most importantly, they will also attempt to learn to solve new compensation problems, for example, involving gears of different sizes. The leading hypothesis is that children who have opportunities to work with symbolic tools to learn to solve benchmark developmental tasks will be more prepared to learn to solve analogous transfer tasks compared to students who do not receive opportunities to use symbolic tools. The findings and methodologies of this research will integrate work in cultural, cognitive, and developmental psychology and will have a direct bearing on instructional theory. The use of symbols is something that instruction can control, and preparation for future learning is what instructors care about. The work will set the stage for specific methods and classroom technologies designed to propel development and prepare children to learn in science and mathematics.