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…

Analyzes a teaching experiment conducted within the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. Analyses of the teaching ex-periments document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded…