Findings from a study with first-grade children on addition and subtraction help make a case for a conceptual rather than a mechanized approach to the operations. How base ten blocks were used in the program is illustrated. (MNS)

Research on fractions and decimals is reviewed. Understanding is vital, and thus children need experiences with concrete materials for the various interpretations of rational numbers. (MNS)

Children trained in the clustering-operations approach showed greater achievement than those trained in a traditional approach. The clustering approach presents all four operations simultaneously. (MP)

This report summarizes a project to develop computational estimation materials for students in grades 6, 7, and 8. In chapter 1, the need for estimation skills is discussed and the goals of the project are stated: to develop a carefully sequenced set of lessons, activities, and maintenance work on estimation with whole numbers, fractions,…

Nine children were tested to determine the appropriateness of Piaget's part-whole fraction concept interpretation for both the discrete case and the continuous cases of length and area. (MP)

Research findings on children's understanding of fractions, gleaned from interviews, are briefly noted. (MNS)

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)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

Results of interviews with students regarding their conceptual understanding of fractions are discussed. Fewer than 10 percent had acquired an adequate conceptual base. (MP)

Investigates validity of scores derived from the measurement procedure involving number lines by assessing its unique contributions to performance differences in criterion measures of rational number knowledge and skills, including fraction computation, application, and explanation. States that 205 fifth-grade and 208 sixth-grade students…

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…

What makes a fraction meaningful and a definition of the quantitative notion of fractions are discussed. Then observations from teaching experiments are presented. (MNS)

Investigated was how girls and boys who were discrepant in their spatial and verbal performance used spatial visualization skills in solving word problems and fraction problems. It was concluded that low spatial visualization skill may be more debilitating to girls' mathematical problem solving than to boys'. (MNS)