The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

What is it that makes learners "think"? What geometrical problem, simply posed, can switch on the thinking processes of students? The author describes one such starting point that worked in a real classroom with Year 9 students. A group of learners for whom "mathematics comes easy" experience being stuck, they learn to handle this unfamiliar…

The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

Thanks to technological progress the world becomes more and more complicated. People stand in front of new and difficult problems that need to be solved. These are problems, the solutions of which are not universal, and cannot be learned. Many solutions require specific data that cannot be learned, as new data is part of the ongoing generation of…

Unlike old perceptions of algebra as a subject that needs to be taught in the upper grade levels of schooling, much of the recent research reports that young students are capable of reasoning algebraically. It is important to note that the recommendation to include algebraic experiences in the early grades is not made simply to introduce typical…

Display took a wide variety of forms ranging from students presenting their initial planning and thought processes, to displays of their finished work, and their suggestions for extending the task should they, or others, have time to return to it in the future. A variety of different media were used from traditional posters in many shapes and…

Decision exercises using a finite state machine and replacement systems are described in this second of two articles. For the first article, see MT No. 62, March, 1973, pp. 50-55. (DT)

Discusses using Alan Bell's "Principles for the Design of Teaching" with student teachers. Discusses choosing genuine and substantial mathematical activities, exposing and resolving cognitive conflict, using flexible tasks in which the degree of challenge can be adjusted or a single starting point can develop into multiple tasks, using feedback,…

The author seeks to clarify the difficulty and complexity of the things youngsters must do to learn mathematics, and to have teachers question their own views about children in redefining mathematics instruction. (MP)

Portions of interviews with children who are engaged in a problem solving activity are presented. The problem used is an "eel question" taken from the work of Piaget. The verbal responses of children are seen as a part of effective teaching, and this method of assessment is encouraged. (MP)

Discussion about the nature and varieties of mathematical understanding is presented. Symbolic understanding is defined as a mutual assimilation between a symbol system and a conceptual structure, that is dominated by the conceptual structure. (MP)

It is argued that a young child's perceptual skills form the basis for all future conceptual and mathematical learning. An experiment supports the argument. (MP)

One girl's achievements in pattern-making are related with the intent of examining the way children think and the character and quality of the intellectual growth. (MP)

Discusses numeracy strategy. Focuses on gaining insight into student understanding of number. Discusses the benefits of this long-overdue numeracy strategy. (ASK)

Children are asked to describe the subtraction process or to describe a context in which subtraction may be used. (JLH)