Helping children to bridge the gap between physical materials and symbolic representations is the focus of this article. Examples are drawn from numerical topics, with several hierarchies illustrated. (MNS)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

Computational skills in multiplication and division are reinforced and practice is provided on these worksheets on estimating, finding factors, and determining divisibility. (MNS)

Developmental differences in reasoning ability and item processing demands are analyzed in a study of cognitive determinants of number analogy performance in two IQ levels of elementary school children and college students. The amount of solution-related information in working memory was the crucial processing demand. Process differentiations of…

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

This study looked at student difficulties with fractions by focusing on understanding of part/whole relationships. The sample consisted of two sixth-grade and two eighth-grade classes. A lack of substantial improvement from sixth to eighth grade on many fraction tasks was noted and viewed as cause for concern. (MP)

This article considers the sum of a finite geometric series as applied to numeric data storage in the memory of an electronic digital computer. The presentation is viewed as relevant to programing in several languages and removes some of the mystique associated with syntax constraints that any language imposes. (MP)

The study looked at the initial learning of decimal concepts at grades three, four, and five. Helping children understand the concepts of decimals prior to computational use is promoted as a major goal for elementary education. The investigation is seen to have provided insights that could be applied to instruction. (Author/MP)

Showed that in a task requiring judgments about the concept of "more" based on the relative numerosity of sets, three- to four-year-old children may base their judgments on such parameters as the extent to which the sets are homogeneous with respect to the color of their components. (Author/DB)

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

This study investigated whether there was a difference in achievement by first graders between their ability to solve open sentences presented in vertical form and in horizontal form. It was recommended that the horizontal form be avoided in grades one and two. (MP)

Pre-experimental interviews conducted with three children to investigate three aspects of the nature of counting are detailed. Sixteen findings related to the counting of perceptual items are summarized. (MP)

A different method of teaching students the basic addition facts is presented. If a child is able to conserve quantity, then the organized program designed to aid in the memorization of facts is possible. (MP)

In presenting a rationale for allowing--even encouraging--children to count on their fingers, the author illustrates finger counting systems from African and American Indian tribes and the medieval European system cataloged by the Venerable Bede. She cites number words from many languages which derive from names for gestures. (SJL)

Points out how figurate numbers (numbers that can be represented by dots on particular geometrical polygonal arrays) can be used to permit upper elementary and secondary students to creatively search for patterns within and among series of figurate numbers. (RH) (RH)