It is critical that elementary students develop understanding of fractional numbers because understanding concepts such as fraction magnitude predict later mathematics success. Representing fractions in multiple ways assists students in developing a sense of fraction magnitude. A systematic approach to presenting multiple representations is the…

Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…

Interviewed 70 children learning multidigit addition and subtraction in 2 different learning environments. Found that understanding and skill were closely related for tasks in which students had received no instruction and on more difficult tasks even after instruction. The alternative instruction, which encouraged students to develop their own…

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…