Table of Contents

  • No teacher of mathematics can afford to ignore the changes that are taking place in mathematical education in the schools. These changes concern method and content and are calculated to improve the mathematical education of all children, having regard to their varying abilities. Mathematics is a basic tool in the development of science, technology, commerce and industry and hence in the economic development of a modern society.

  • The objectives of the school fall into two strands. The first is the narrow but popular aim of enabling the child to have a job or earn a living when he leaves school. On this there is general agreement by the state, the family, the neighbours, the public and sometimes even the child himself.

  • The teaching of mathematics in the primary school by the new approach, otherwise known as “discovery” learning,is a challenging and rewarding experience for children and their teacher. Primary school children, whose ages in most countries range from five to twelve years, learn to discover for themselves mathematical concepts, patterns and relationships and to solve problems in mathematics. In countries like Britain, where syllabuses are not externally imposed and head teachers are free to devise their own schemes of work and classroom methods, it is easy for teachers to try the new approach, which consists of getting children to work in small groups or individually, encouraging them to think for themselves and investigate mathematical problems, which they do in individual and sometimes highly original ways.

  • A consideration of mathematics in secondary schools might begin with three fundamental types of questions. The first type revolves around what to teach and includes such questions as, “In an age of calculating machines need children know multiplication tables? Should we teach manipulation in algebra? If so, how much? Are logarithms obsolete? Should we teach trigonometry at all? If so, why? What parts of recent mathematics ought to come into the school syllabus? What should go out to make room for new topics? More fundamental, what considerations should determine our choice of syllabus?”

  • A few years ago it was apparently easy to examine candidates in mathematics and it seemed comparatively simple to evaluate a mathematics curriculum. At the primary school level the content of the teaching was confined to arithmetic and the debate was in terms of a conventional testing of mechanical and problem arithmetic contrasted with objective, multiple choice tests. The situation at the secondary level was equally stable.

  • There is a shortage of competent teachers of mathematics at all levels. In some countries, the shortage is of qualified teachers; in all there is a dearth of good teachers, competent in action. In several developing countries, there are many teachers who have not been exposed to the new ideas and yet have to teach mathematics.

  • Resources for learning mathematics are part of our total environment, natural and man-made. The “mathematical content” of our natural environment is much the same for all of us, wherever we happen to be located. The shape of the sun; the apparently changing shape of the moon; daily and seasonal patterns of shadows; regularity and symmetry in crystals, leaves, flowers, and seeds; experiences with water, such as reflections, waves and ripples; – these are freely available to all.