Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Analyzed students' reasoning with fractions. Found that skilled students applied strategies specifically tailored to restricted classes of fractions and produced reliable solutions with a minimum of computation effort. Results suggest that competent reasoning depends on a knowledge base that includes numerically specific and invented strategies,…

Discusses ways teachers can encourage students to construct useful meanings for the fractional unit. Provides three examples of representations of common fractions and illustrates misconceptions in fraction problems. Includes a brief summary of constructivist mathematics education and an example in which a teacher misunderstands a fractional unit.…

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

Seven secondary teachers of 57 students with learning disabilities used a videodisc program to teach fractions. Teacher and student reactions were very positive, almost two-thirds of the students reached or exceeded criterion performance, and teaching styles of participating teachers subsequently became more interactive. (JDD)

Investigated (n=124) preservice school teachers' reasoning and concepts of invariance of fractional numbers under numeration systems in different bases. The majority of students believed that fractions change their numerical value under different symbolic representations. (Author/MKR)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)

Three teaching experiments are reported which study aspects of a diagnostic teaching methodology. An experiment in the field of directional quantities showed a positive relationship between the intensity of discussion and amount of learning; one on fractions and another on geometric reflections showed good two-month retention under the…

This study analyzed relations between student achievement in the domain of fractions and the extent to which classroom practices are aligned with principles recommended by current reform frameworks. Hierarchical linear-model analyses revealed that alignment of classroom practices with reform principles was related to student achievement in problem…

Unique associations between three families of mathematical knowledge and individual differences in the mathematics skills of 103 seventh and eighth graders were studied. Conceptual and procedural knowledge adequately explained individual differences in fraction solving and problem set-up accuracy, but only conceptual knowledge adequately expressed…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

Set: Research Information for Teachers, is published twice a year by the New Zealand Council for Educational Research and the Australian Council for Educational Research. This document draws together 16 articles on mathematics from previous issues grouped into three categories: general, primary, and secondary. The titles are: (1) "Contents…

Three studies of five seventh-grade students (ages 12-14) with emotional disturbances were conducted to determine whether a stimulus class would emerge as a result of one conditional discrimination training using direct instruction (implemented with a constant time delay) augmented with instructive feedback. The students were taught to identify…