When speaking to young children, adults adapt their language to that of the child. In this article, we suggest that this child-directed speech (CDS) is the result of a transactional process of dynamic adaptation between the child and the adult. The study compares developmental trajectories of three children to those of the CDS of their caregivers.…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

A generalized Rasch model is presented for measuring attitudes; it is based on the concepts of Thurstone's method of successive intervals. Benefits of the model are illustrated with a study of students' (N=4,035 fifth through ninth graders) interest in physics. (SLD)