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)

This paper on the language of zero (1) deals with the spoken and written symbols used to convey the concepts of zero; (2) considers computational algorithms and the exception behavior of zero which illustrate much language of and about zero; and (3) the historical evolution of the language of zero. (JN)

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)

The relation between mathematical and computational aspects of recursion are discussed and some examples analyzed. Definition, proof, and construction are considered, as well as their counterparts in computer languages (illustrated with Logo procedures). (MNS)

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)