The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)

Fraction strips are suggested as good conceptual models to focus on the meaning of fractions. Making the strips, beginning activities, connecting symbols, more concept activities, and working with two fractions are each illustrated. (MNS)

The use of Logo to develop mathematical concepts is advocated. Children's comments as they work with Logo are presented. (MNS)

The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)

The effects of a teaching program in probability devised for students in grades five to seven were analyzed. Most of the notions were too difficult for fifth graders; 60-70 percent of the sixth graders and 80-90 percent of the seventh graders were able to understand and use correctly most of the concepts. (MNS)

Discusses use of microcomputers to assist teachers in diagnosing student errors. Examines what can be diagnosed, whether diagnosis helps, what diagnosis programs can do, what goes into a diagnosis program, and how the programs can be used. Suggests that software be developed for this purpose. (JN)

Based on the numerous ways physical constants are used daily. A knowledge of the meaning of a constant is deemed necessary. Various studies done by elementary school children are presented. (EB)

Using this four CD-ROM disc set, teachers can have their very own math problem solving mentor as a leading expert in Singapore Math guides them through a lively presentation, working through math problems and explaining how Singapore has become the world's leading method in math. The expert's explanation of how to use Singapore's model-drawing…

This paper addresses the nature of child-initiated episodes of mathematical patterning prior to formal schooling. In a multi-site case study, children's engagement in mathematical patterning experiences was investigated as was the teachers' involvement and influence in these experiences. A conceptual framework was used to guide the examination of…

This pilot study determined some typical cognitive-motivational profiles of Finnish lower secondary students dealing with fractions and decimal numbers. Forty seven students from grades 7-9 participated in a number concept test, where also the motivational aspects, such as self-efficacy, certainty and tolerance were measured. Four distinctively…

We examine eight cases of argumentation in relation to a proportional reasoning task--the "Paint" task--in which the "constant sum" strategy was a significant factor. Our analysis of argument follows Toulmin's (1958) approach and in the discourse we trace factors which seem to facilitate changes in argument. We find that the arguments of "constant…

In this paper we deal with the problem of the genetic relationship between the sensual and the conceptual in knowledge formation. Transcript and videotape analyses of two small groups of a regular Grade 11 mathematics class shed some light on the dialectics between semiotic activity and artefact-mediated kinesthetic actions. The analyses point to…

This report focuses on teachers' individual curricula. An individual curriculum includes contents and reasoning and can be structured in a quasi-logical system of goals and methods, which is the result of teachers' planning of mathematics instruction. There is consent that the planning of individual curricula or the instructional practice is a…

Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

In this paper, the theory of variation in the tradition of phenomenographic research approach is placed in the context of Dynamic Geometry Environment (DGE). Central concepts of discernment, variation, simultaneity and space of learning in the theory of variation are discussed for simple dragging episodes in DGE to illustrate the potential…