A series of learning activities used in grades one and two to teach number conservation and arithmetic are presented in detail. The activity sequence is based on working with one-to-one correspondences for a lengthy period before introducing arithmetic operation. The author claims the approach is very successful. (SD)

A method of using pegboards to illustrate addition of whole numbers is described. (SD)

The examples given in this article served as models for the basic principles of "Peer-Mediated Instruction," the focus of six years of classroom research at Teachers College, Columbia University and one approach to the buddy-system of teaching. (Author/RK)

The work of Ladislav Kosc on dyscalculia is presented. His work on meanings, forms, terminology, diagnosis, correction principles, factors in mathematical ability, language dysfunctions, and publications are each included. (MNS)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

Presented are the purposes served by mathematical investigation--the exploration of open situations in a relatively unstructured way--and an example (investigating numbers adding to 13), with numerous questions and conjectures. (MNS)

Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)

Ten experiments examined the effect on the performance of 265 nursery schoolers through first graders using collection versus class terms to describe sets of familiar objects. No facilitative effect of collection terms occurred on number tasks; in a class-inclusion task, performance was better with collection than class terms. (SLD)

Presents number tricks appropriate for use in workshops, mathematics clubs or at other times when stressing recreational mathematics. (PK)

Examines several uses of the word cancel and suggests alternative terminology. In particular, arithmetic and algebraic examples are used to illustrate problems associated with the term cancel. (PK)

Describes a finger pattern method for teaching subtraction. It is suggested that the method has several advantages over the usual methods children adopt. (PK)

Defines and supports investigative mathematics for schools. Presents several results of an investigation of Fermat's Last Theorem. (PK)

A training experiment with 22 retarded children (IQs from 34 to 74) found that training on a general magnitude comparison rule for numbers 1-10 resulted in experimental subjects significantly outperforming control subjects on both immediate and delayed posttests with some evidence of transfer of training. (Author/DB)

Transformational mnemonic strategies have been effectively used to enhance associative and serial list learning of borderline subjects classified as mentally retarded. Recent applications have involved concrete and abstract native-language vocabulary, numbered or ordered information, and digit span recall. (CB)

Brief articles on producing videotapes of the execution of a program on a microcomputer, an illustration of the sums of numbers and squares, and the distance from a point to a line are included. (MNS)