This study investigated analogical transfer of conceptual structure from a prior-knowledge domain to support learning in a new domain of mathematics: division by fractions. Before a procedural lesson on division by fractions, fifth and sixth graders practiced with a surface analogue (other operations on fractions) or a structural analogue (whole…

The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…

Cognitive development unfolds in many contexts, and one of the most important of these contexts is school. Thus, understanding the school context is critical for understanding development. This article discusses some of the reasons why cognitive developmental researchers might wish to conduct research in schools, describes how to get started…

This study investigated how understanding of the equal sign changes as a function of experience in mathematics and variations in context. Students with different levels of mathematics experience (elementary school, seventh grade, undergraduate, and graduate) were randomly assigned to view the equal sign in one of three contexts: (a) equal sign…