Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Explores the role of spatial orientation skill in the solution of mathematics problems. Reports the role of estimating the approximate magnitude of a figure; demonstrating the flexibility to change; adding marks to show relationships; moving or assessing the size and shape of figure; and getting the correct answer. (YP)

Discusses the implementation of the National Council of Teachers of Mathematics standards, especially problem solving, into the elementary mathematics curriculum. Presents three examples: measurement and seriation at the primary level; place value for intermediate level; and spatial reasoning and logical thinking at the intermediate level. (YP)

Discusses the planning, organizing, and implementing of a week of mathematics activities at an elementary school. Describes five activity stations, including activities for mental mathematics, calculator mathematics, estimation, geoboards and tengrams, and graphing and estimation exercises. (YP)

Describes four activities to obtain information from maps, use scales and legends, and interpret information on charts. Provides the objectives, directions, extensions, answers, and worksheets for each of the activities. (YP)

Describes seven spatial abilities related to mathematics including eye-motor coordination, figure-ground perception, perceptual constancy, position-in-space perception, perception of spatial relationships, visual discrimination, and visual memory. Discusses the relationship of the spatial abilities to the study of geometry. Lists 19 references.…

Discusses games using number tablets. Describes general advantages of the games over using pencil and paper. Provides needs, skills, players, rules, and variations for eight games. (YP)

This article explores an application of combinations, geometric series, and elementary probability that arises in a Biblical setting. Describes examples of the applications such as the use of "urim and thummin." (YP)

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Proposes elements of a model of knowledge structures used in comprehending and generating graphs. Uses the competence model to attempt to organize and interpret findings on misconceptions in graphing. Discusses two types of common misconceptions; treating the graph as a picture and slope-height confusions. (YP)

Describes investigations of quick cancellation problems in two-digital integers. Generalizes the results to n-digital integer problems. (YP)

Studies of young children's sequence of development from counting to the beginnings of formal arithmetic are reviewed. Four essential basic skills are identified: use of counting words, enumeration, the cardinality rule, and quantitative comparison. The contribution of counting to the development of arithmetical proficiency is stressed. (JDD)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (YP)

Reports the performance of grade six students in the Australian Primary Schools Mathematics Competition for 1990 to 1992 and provides general comparisons across states. Results showed that, overall, boys outperformed girls. Appendix contains selected competition questions. (MKR)