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 discusses number sense. Suggests a variety of activities appropriate for primary students that will help develop number sense. (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)

A series of nine activities that illustrate prime factorization and other elementary number theory ideas in concrete, representative, and symbolic form are described. (MNS)

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)

Programs are listed for integer powers and fractional powers, with discussion of how to use them in instruction. (MNS)

Four worksheets are provided for developing decimal concepts. For levels 1-2, dollars and cents is the focus; for levels 4-5, tenths and hundredths; for levels 5-7, comparing and ordering decimals; and for levels 6-8, estimating with decimals. Teaching suggestions are included. (MNS)

Studies five-year-olds' relative number judgements of small and large number displays with and without perceptual aids. Children were found to respond to local rather than global density differences and to benefit from the provision of perceptual aids on both small and large number displays. (Author/AS)

Described are activities for thinking through patterns using toothpicks, paper strips, wooden cubes, and people patterns; thinking with attribute items such as geocards, namestrips, and treasures; and thinking with geometric materials such as geoboards and dot paper, cubes, and simple puzzle pieces. (MNS)