Comparison of 15 English children (mean age 7.5 years) with specific language difficulties and 12 similar children with mathematical difficulties found few differences in their ability to process 2- and 3-digit numbers. Results suggest that a language difficulty may underlie delayed performance in mathematics. (DB)

Presented is a brief overview of Japanese education followed by specific ideas about important considerations in the teaching of mathematics in elementary grades. Examples are given for teaching flexibility in mathematical thinking. (RH)

Discussed are the results of interviews with 63 Australian children (interviewed in English) and 62 Nigerian children (62 interviewed in English and 60 interviewed in Yoruba) to determine how they used number concepts in discussing five demonstrations manipulating physical matter. Differences between the two groups are considered. (RH)

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…

Compared performance of Malaysian children with that of English children on a test into the understanding of number concepts. Findings indicate that difficulties of Malaysian children may be quite different from those of English children. Among the difficulties identified were misconceptions about the order of operation in division and…

This study systematically examined developmental changes in the flexibility of preschool children's counting skills by assessing their use of counting to solve different kinds of quantitative problems at several preschool age levels. Three principal kinds of quantitative problems were considered: (1) quantifying a given set; (2) generating a set…

The development of a quantitative concept of rational numbers was explored in interviews with 16 fourth and fifth graders in two cities. High performers used a flexible and spontaneous application of concepts of rational number order and fraction equivalence, and a reference point, while low achievers tended not to. (MNS)

Comparison of elementary grade students with (N=42) or without (N=42) learning disabilities (LD) on their logical-mathematical structures of thought found that, though both groups generated grouping relationships, children with LD tendered to generate solutions showing less coordinated structures of thought. For both groups, scores on the…

Reports on a study to determine the development of children's understanding of seven properties of the arithmetic mean and to assess the effects of material used in the testing and the medium of presentation. Some differences were found in children's reasoning. No significant differences were found for materials or medium of presentation. (PK)

Two teaching studies were conducted, based on a descriptive framework and diagnostic interviews described previously. In the pilot study, low-achieving students were taught individually; in the main study, they were taught in a group. Performance improved in both cases. (MNS)

A model is proposed in which the quantification of inverse proportionality is developed beyond the initial qualitative relation. Based on a task analysis, the model was tested with 36 eleven-year-old students in a training experiment using a balance task. (MNS)

The 5-stage model of Ross was used to examine the role of instruction in facilitating children's acquisition of place value knowledge. Compares children from 2 samples on 10 tasks designed to reveal their thinking about place value. Discusses implications for theory and classroom. (YP)

By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…

Described is a procedure for teaching children to learn to count on with finger patterns after they have learned to count with objects. The technique has been found to be successful with children of all ability levels at grades one and two. (RH)