How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Pre-experimental interviews conducted with three children to investigate three aspects of the nature of counting are detailed. Sixteen findings related to the counting of perceptual items are summarized. (MP)

Presents a number of transcript examples of correct and incorrect transferences by children. Considers the objects of transference including spoken words, written symbols, models and diagrams, arithmetic procedures, and structures. Discusses the use of transference in arithmetic education. (YP)

Investigates children's behaviors and conceptual achievements in the transition from informal calculation strategies to a written division algorithm. Describes five different strategies observed in the solution of division problems. Discusses the implications of the children's behavior. (YP)

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)