Geoffrey Howson

Toward an International Mathematics Curriculum

This chapter revisits the notion of an international curriculum, analyzing the various forces that might push countries toward one and reasons why countries should develop their own distinct curricula. We first describe the term curriculum to set the stage for our later discussion. We then discuss, in turn, common influences for curriculum change, common learning goals, common driving forces of public examinations, common emphases and treatments, and common issues for future curriculum development. Although the tendency for countries to include a more-and-more internationally-accepted core selection of topics in their national curricula is to a great extent both to be welcomed and expected, this move has had a potential negative effect on curriculum development. Significant work also remains to be done to explore the way in which new technology (especially digital technology) could affect both the mathematics included in the curriculum and how it could more effectively contribute to the teaching and learning of mathematics in general.

Curriculum development in mathematics: Curriculum development: an introduction

This century has seen vast changes in school systems everywhere and in the education they offer. For example, in the developed countries, secondary education for all has become a reality; elsewhere, rapid progress to that end is being made. However, not only is education being offered more widely, but it now has different goals. Changes in the social and economic structures of society have had profound implications for education, as have the growth of new technologies and of knowledge. Such changes will continue to occur and to present challenges to the educator and, in particular, to the curriculum developer. The need for curriculum development will not be transient. In this book we describe some of the features of curriculum development as it affects mathematical education. We shall look at the way that curriculum development has taken place in the past – especially within the last two decades; the various forces that have influenced the form that it has taken and the successes it has achieved; the management procedures which have been devised; and the attempts made to evaluate its outcomes. Finally, we look critically at the reform period in retrospect, its achievements and failures, and the lessons to be learned.

The Relationship between Assessment, Curriculum and Society

This quotation is from an article describing attempts to supply evening education to working men which appeared in The Penny Magazine of December 13, 1834, a magazine for the general public. It illustrates two important, and long recognized, facets of assessment. First, the essential part which formative assessment should pay in teaching (although nowadays we take a broader view of this type of assessment than is exhibited in the quotation); secondly, the attendant dangers of dispirited and embarrassed students. The example is, I fear, typical; for, as we shall see, in almost every aspect, assessment procedures must attempt to find some middle path between what is accepted as essential and good and that which is regarded as dangerous and dispensable.

Mathematics Education in the United Kingdom

Each of the four constituents of the United Kingdom, England, Scotland, Wales and Northern Ireland, has its own educational system. However, it is the educational systems of England and Scotland that have historically displayed the greatest differences, and it is on those two countries that this chapter concentrates.

The origins of mathematics education research in the UK: a tribute to Brian Griffiths

The meeting of the British Society for Research into Learning Mathematics held at the University of Southampton on 21st June 2008 was dedicated to the memory of Brian Griffiths, who had died earlier that month. At the meeting it was suggested that I write a paper tracing the development of research in mathematics education in the UK up to the writing of Mathematics: Society and Curricula, a book that Brian and I co-authored, published in 1974. This paper is dedicated to Brians memory: I hope that it will be considered a fitting tribute to a great friend and colleague, and to an outstanding mathematician and mathematics educator.

A History of Mathematics Education in England

1. Robert Recorde 2. Samuel Pepys 3. Philip Doddridge 4. Charles Hutton 5. Augustus De Morgan 6. Thomas Tate 7. James Wilson 8. Charles Godfrey 9. Elizabeth Williams.

Curriculum Development in Mathematics

1. Curriculum development: an introduction 2. The historical background 3. Case studies of curriculum development 4. The practice and management of curriculum development 5. Curriculum theory and curriculum research 6. A retrospective look at curriculum projects 7. Evaluation within curriculum development 8. Lessons for today and tomorrow.

Curriculum development in mathematics: Case studies of curriculum development

Three projects Before embarking on an analysis of how curriculum development in school mathematics has been managed, and how this management reflects various theories of curriculum change, the reader should be aware of the variety of forms that curriculum development can take. In this chapter we present case studies of three curriculum development projects in mathematics: The Fife Mathematics Project of Scotland, the Secondary School Mathematics Curriculum Improvement Study of the USA, and the Individualised Mathematics Instruction Project of Sweden. These three projects were chosen not because they are either typical or exemplary, but because together they serve to illustrate, about as well as three projects can, the variety of approaches that have been taken to the problem of managing mathematics curriculum development. Each project is sketched in turn, and then together they are discussed as they relate to certain issues of management. Reporting on the Allerton Park conference (see p. 88) on styles of curriculum development, Stuart Maclure (1972) noted that to see contrasts in ‘style’ and in underlying values, one should look at issues that divide opinion rather than issues on which there is consensus. Maclure identified three key issues that divided opinion at the conference: (1) the contrast between centralised and decentralised systems, (2) the impact of curriculum development on the role of the teacher, and (3) the relation between the centre and the periphery. We have used these same three issues to illustrate some of the ways curriculum development projects can differ.

Curriculum development in mathematics: Curriculum theory and curriculum research

The legacy of early curriculum theories The early decades of this century saw a rapid expansion in the provision of secondary education in the United States. Public high school enrolments, which stood at about 500 000 in 1900, roughly doubled in each of the following four decades. There was a need then to reconsider school curricula which had to that time not differed significantly from European educational tradition. America needed its own, newly-developed pattern. The result was an autonomous reform movement in pedagogy, based on a pragmatic philosophy, which was to determine the basic reorientation of American curricula. In the field of mathematics education two opposing tendencies emerged: one originated in social practice; the other viewed social practice as the goal of its reformatory intentions. The most significant educational figure to emerge was John Dewey (1859–1952). Dewey derived his conception of learning from his observations of how everyone learns in his environment, i.e. through action and experience. Learning in schools should, therefore, also be conceived of as ‘learning by doing’ and ‘learning by experience’. Dewey rejected the division of content into separate school subjects, since this was alien both to the child and to reality. Instead he proposed project teaching based on real objects.