The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

Analyzes the arithmetized geometry from a semantical point of view and compares it with classical synthetic exposition of school geometry. Also analyzes the didactical use of one particular system of arithmetized geometry--namely Pogorelov's system--in the Greek Lyceum. Contains 33 references. (Author/JRH)

Reviews the arguments for the value of practical number apparatus and examines the practical activities for which it is used to try to explain why the theoretical benefits do not seem to be translating into practice. (Author)

In this article, the author describes his experiences when he decided to teach university-level mathematics to Year 8. Handling a particularly able class who had investigated the isoperimetric problem, he was confident that the class was more than up to the challenge and adequately motivated. Using a Powerpoint, he delivered the lessons to the…

Describes some interesting features of the book "Sumario Compendioso," first written in North America so that others can use it to enrich their classes and forge links between mathematics and other subjects. (KHR)

The mathematics concept of fractions was taught to a group of learning disabled, dyslexic, and multiply handicapped students (15-20 years old) by preparing a fruit salad. Enthusiastic student participation and enhanced knowledge illustrated the effectiveness of employing several sensory modes in learning activities. (CB)

In this paper I argue that children have a right to basic numeracy and that studies of adult numeracy suggest that this right is being denied to many in British schools. Because of the way that maths education discourses are structured, we do not have a separately defined discourse around numeracy teaching, and this has implications for young…

Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)

This theoretical analysis articulates verbal rule properties and use implications, describes an empirical study examining characteristics of problem solving performance when verbal rules are instructed as a problem solving method, and discusses role of verbal rules in problem solving and implications for learning procedural skills. (MBR)

Suggestions are made for helping children correct and analyze their own work so they may learn from their own mistakes. (MP)

This classic reprint was first published in 1955. Fehr discusses how to determine what is taught, and makes specific comments on the roles of planning, meaning, practice, learning, and problem solving. (MNS)

In this essay, the authors suggest that there is another, different and more ancient way of looking at the moral and social role of the teacher and the processes of education in which she is involved. This alternative perspective draws on older, more imaginative and complex sources of meaning than the latest Gallup poll or the latest adjusted…

In the social learning perspective the anticipation of rewarding consequences serves as one source of motivation. A second results from the perception of a negative discrepancy between present capabilities and desired performance. To foster motlvation it is necessary that persons accurately appraise their capabilities. Techniques for fostering…