Children completed three types of equivalent cardination tasks which assessed the influence of different stimulus configurations (linear, linear-nonlinear, and nonlinear), and density of object spacing. Prior results reported by Siegel, Brainerd, and Gelman and Gallistel were not replicated. Implications for understanding cardination concept…

Exponential growth provides an interesting setting for exploration. A sequence of activities and questions which will help students become better acquainted with large numbers and scientific notation, as well as computer notions, is given. (MNS)

Young children's understanding of correspondences and numerical differences between disjoint sets was studied in three experiments. Findings appeared to restrict the theory that young children are limited to perceptually based forms of mathematical reasoning. (Author/MP)

This exercise in mathematical modelling requires understanding of geometric progressions, inequalities, and absolutes. It presents a problem on credit creation in the banking system. (MNS)

Activities using paper punches are described, dealing with one-to-one correspondence, place value, large numbers, prime and composite numbers, operations, geometric shapes, and measurement. (MNS)

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)