The study examined basic counting competencies, difficulties, skill progressions, and variation among 36 moderately retarded and 64 mildly retarded students (ages 5-14). Quantitative and qualitative analyses indicated deficiencies in basic counting competencies and systematic oral- and object-counting errors. Striking individual differences in…

Practical and classroom-tested ideas are suggested for teaching the midpoint theorem and exponents and factorials. (PK)

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

Presents a rationale and activities for using teacher-made laminated strips to teach fraction division concepts. (PK)

This study attempts to understand the American and Japanese cultural and ethnic differences in student's mathematics scores from the perspective of differential cognitive organization of number resulting from differences in primary-language characteristics. The relation between cognitive representation of number and mathematics achievement are…

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)

Game theory is appropriate as a topic for an honors seminar for high school students. Matrices provide a model for analyzing certain situations involving conflict, and probability theory can be used to determine the best strategies for the players. Variations on the ancient game of morra are discussed. (MNS)

After presenting the case for using games to teach higher-level skills, four mathematics instructional games are given. At the comprehension level are Average Hands and Polyhedron Rummy. Prime Plus is at the application level, while In Proportion is at the analysis level. (MNS)

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

Presented are four activities (each accompanied by ready-to-duplicate worksheets) dealing with: colors and shapes (grades K-2); using a coordinate grid in map reading (grades 3-4); order pairs of whole numbers (grades 5-6); and locating ordered pairs of rational numbers in the coordinate plane (grades 7-8). (JN)

Research on fractions and decimals is reviewed. Understanding is vital, and thus children need experiences with concrete materials for the various interpretations of rational numbers. (MNS)

How the computer can become an integral part of mathematics learning at the junior high school level is discussed in terms of mathematics processes. The rationale for activities involving programmed processes and examples of them are given. (MNS)

The author suggests using African mathematical games in school curricula to emphasize the contributions of Afro-Americans to United States' heritage and to study other cultures. Many of the games and skills are interdisciplinary and appealing to children. A stone game, geometric patterns, and counting and money systems are briefly discussed. (MR)

Patterns in decimal expansions are investigated. (DT)