Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Research findings on decimals and money are briefly summarized, followed by suggestions for classroom use. (MNS)

Describes the data collection and interpretation project of primary grade students involving predicting, graphing, estimating, measuring, number problem construction, problem solving, and probability. (MKR)

Investigated the continuous fraction concepts of (n=59) students in grades four, five, and six. Students were confident and accurate when performing sharing tasks, but were much less successful on continuous quantity tasks involving formal fraction language and symbol manipulation fraction tasks. (14 references) (Author/MKR)

Stimulus control technology was used to instruct seven students in grades five and six who demonstrated difficulty with fraction ratio and decimal relations. Students were trained to match pictorial representations of fractions to printed counterpart fraction ratios and to match printed decimals to pictorial representations of counterpart…

Discusses weak links in children's developing power in counting. Presents assessment information for mathematics curriculum planning and activities embedding the subskills of counting into daily routines. (MKR)

Explores abundant numbers and presents a proof that abundant numbers of every order exist. Readers are encouraged to use the included computer program to explore abundant numbers for themselves, look for patterns in the output, and consider further questions. (Author/MKR)

Observations of five-year-olds (n=6) about their understanding of base 10 and numbers greater than 20 showed that although these students did not have adequate skill in use of the base 10 number system to count by 10s, they did demonstrate concepts about big numbers. (21 references) (MKR)

Synthesizes research on content knowledge of rational numbers, the learning of rational number order and equivalence concepts, and teachers' pedagogical reasoning about these concepts. Uses teachers' descriptions of how a hypothetical student would understand rational numbers to sketch a formative model of pedagogical reasoning. (16 references)…

This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)

This article (1) provides a review of "Anno's Counting House," a wordless picture-story and game that engages children in thinking about numbers; and (2) examines a classroom activity from which children learn that the same data, graphed differently, may support a variety of conclusions. (GLR)

Presents activities on writing and learning about cuneiform numerals and some mathematical and numerical topics in the context of Mesopotamian culture. Includes resources for further reading. (ASK)

States that thinking about numerical procedures starts in the elementary grades and continues in successive grades until students can eventually express and reflect on the procedures using algebraic symbolism. Outlines how such thinking can progress to algebraic reasoning. Illustrates how computers can be used to promote this progression through…