Christine Keitel

Second international handbook of mathematics education

There is much debate within mathematics teacher education over ways in which professional and academic foci could be made to complement each other. On the one hand, teachers’ craft knowledge is emphasized, mainly as this relates to the particular and local level of teaching; on the other hand, the importance of academic subject knowledge cannot be denied. In this chapter the focus will be on how to blend and balance the two through activities in which teachers learn from other teachers, particularly the co-learning of teachers and teacher educators. It will discuss professional relationships, reflective practice, community building, and research in practice. Examples of research-based programs involving lesson study (LS) and the Learner’s Perspective Study (LPS) have moved the relevant research in this area to yet another level, in which theory and practice are combined. Projects such as these and others from diverse parts of the world will be presented and discussed.This chapter seeks to provide an integrating theoretical framework for understanding the somewhat disparate and disconnected literatures on “modelling” and “technology” in mathematics education research. From a cultural–historical activity theory, neo-Vygtoskian perspective, mathematical modelling must be seen as embedded within an indivisible, molar “whole” unit of “activity.” This notion situates “technology”—and mathematics, also—as an essential part or “moment” of the whole activity, alongside other mediational means; thus it can only be fully understood in relation to all the other moments. For instance, we need to understand mathematics and technology in relation to the developmental needs and hence the subjectivity and “personalities” of the learners. But, then, also seeing learning as joint teaching–learning activity implies the necessity of understanding the relation of these also to the teachers, and to the wider institutional and professional and political contexts, invoking curriculum and assessment, pedagogy and teacher development, and so on. Historically, activity has repeatedly fused mathematics and technology, whether in academe or in industry: this provides opportunities, but also problems for mathematics education. We illustrate this perspective through two case studies where the mathematical-technologies are salient (spreadsheets, the number line, and CAS), which implicate some of these wider factors, and which broaden the traditional view of technology in social context.

Beyond the Tunnel Vision: Analysing the Relationship Between Mathematics, Society and Technology

Enthusiasm about the introduction of computers into mathematics education is widespread, the justifications for it however are very diverse: “Some call the effects of micro-computers on schools a revolution … Nothing before has so stirred schools into action. School systems, teachers, parents and children talk about computers as they never talked about programmed learning, educational television, open education nor raising the school leaving age, for that matter. Schools must have computers! No other educational technology has been thought to have such potential. People talk about how children are captivated by computer … while others stress computer-based jobs. Yet others urge affirmative action and remediation through computer-assisted-learning. Others point to the demands of technological culture when urging schools to use computers. On a different track some see a potential for more and better intellectual and social activities in schools, others stress self-image and self-expression. The range of possibilities is exceptional.”(Olsen 1988,p,9)

From the Few to the Many: Historical Perspectives on Who Should Learn Mathematics

Today we take for granted that everybody should be offered the opportunity to learn mathematics. However, it was not until well into the 20th century that “mathematics for all” became an achievable goal. Before then, the geographical location of schools in relation to children’s homes, the availability (or non-availability) of teachers capable of teaching mathematics, parental attitudes to schooling, economic circumstances of families, and social and psychological presuppositions and prejudices about mathematical ability or giftedness, all influenced greatly whether a child might have the opportunity to learn mathematics. Moreover, in many cultures the perceived difference between two social functions of mathematics—its utilitarian function and its capability to sharpen the mind and induce logical thinking—generated mathematics curricula and forms of teaching in local schools which did not meet the needs of some learners. This chapter identifies a historical progression towards the achievement of mathematics for all: from schooling for all, to arithmetic for all, to basic mathematics for all; to secondary mathematics for all; to mathematical modelling for all; and to quantitative literacy for all.

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.

Social (In)Justice) and International Collaborations in Mathematics Education.

The literature mathematics education contains several references to issues related to social justice, including gender, racial and multicultural aspects, and perhaps to a lesser degree, socioeconomic factors. More commonly, this literature discusses social justice in terms of “equity” and “equal opportunity”. However, very rarely the term social justice is theorised. This chapter aims to: (a) present a theoretical discussion of the construct “social justice” from a variety of perspectives, and (b) apply the theoretical discussion to raise issues of social justice behind several types of international contacts and collaborations between educators in the discipline

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.