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)

This study of 73 children sought to determine if children's perceptual comprehension of numerals is higher when they are shown symmetrical rather than asymmetrical arrangements of pegs, and if comprehension scores related to age, sex, and/or social class. The main hypothesis was rejected but some age and class differences were found. (SJL)

A teaching sequence providing a smooth transition from concrete materials to the subtraction algorithm is presented. (MP)

A teaching sequence for the division algorithm is detailed. (MP)

How computer methods can be applied to an old problem and how computer efficiency affects the solution to that problem are illustrated. (MK)

The hypothesis was tested that students with a field-independent cognitive style would learn most about numeration systems if they had minimum guidance and maximum opportunity for discovery through the use of manipulative materials. Data were gathered on 46 prospective elementary school teachers. The hypothesis was supported. (Author/MH)

Activities to develop counting skills are given. (MK)

Programed instruction accelerated the ability of 62 children, ages four to six, in acquiring the concept of number conservation. (CP)

Reviews evidence against theories about preschool childrens' egocentricity and cognitive ineptness in the areas of classification, communication, number and order concepts, memory skills, and capacity for reasoning about causal relationships. Holds that preschoolers have been misunderstood because researchers tend to approach them with tasks…

Attainment relative to six cognitive operations and four number and computational skills was assessed for 90 elementary students using clinical procedures. Variance associated with conservation of number, seriation, and logical classification competency accounted for a significant proportion of the variance in achievement scores. (Author/MK)