This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

The integration of emerging technologies in higher education presents a new set of challenges and opportunities for educators. With a growing need for customized lesson plans in online education, educators are rethinking the design and development of their learning environments. "Utilizing Virtual and Personal Learning Environments for…

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/MNS)

The article suggests that Belcastro rods, which retain the basic properties of Cuisenaire rods but allow instant identification by touch, may be useful in teaching mathematical concepts to blind children. Drawings illustrate use of the rods in teaching such concepts as addition and subtraction. (Author/DB)

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)

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)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

Experiments to probe the nature of one mode of thinking, imagined spatial operations, have been devised. Results confirm that the mind can model physical processes, subjecting them to the geometric constraints that hold in the external world. The experimental work and implications are discussed in detail. (MNS)

Two experiments examine the sorts of cues that might be available to facilitate children's ability to discriminate between memories for their own actions. Results suggest that the differences in discrimination performance demonstrate the importance of kinesthetic cues and visible consequences for children's memory discrimination. (Author/RWB)

Proportion problems were given to pupils in grades 3-5. Success rates were high, with elementary strategies based on addition often used. Familiarity with the use of ratios in the context, the presence of a mixture, and the use of manipulatives were variables that influenced performance. (Author/MNS)

Investigated what effects two instructional strategies (related to student use of manipulative materials) would have on second-grade students' (N=96) development of logical structures. Also examined the effects of sex on logical development. Results indicate that supplying manipulative materials alone is not adequate in promoting development of…

Surveyed were 220 teachers in grades one-three in 11 states on their use of 11 devices for teaching mathematics. The percent of teachers who never or seldom used the listed manipulatives ranged from 40.8 to 74.7. (MNS)

The uses that chemistry students (undergraduates, postgraduate, and trainee teachers) make of analog models when relating equations to projects were identified. Although only a restricted use of such models were found, and for none of the reasons valued by practicing chemists, patterns were identified. The implications for chemical education at…

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Reported are data from the first individual interview conducted in 1978 as part of a 3-year study on addition and subtraction using verbal problem solving. The research program is attempting to relate pupil performance on selected arithmetic skills to pupil cognitive processes, instructional materials, and teachers' classroom behaviors. From three…