Celia Hoyles

Richard Noss

This book is the culmination of some ten years' theoretical and empirical investigation. Throughout this period, we have come into contact with many who have stimulated our thinking, some of whom belong to the community of Mathematics Educators. Our membership of that community has challenged us to make sense of some deep issues related to mathematical learning, especially the cognitive and pedagogical faces of mathematical meaning making. Alongside this community, we are privileged to have been part of another, whose members are centrally concerned both with mathematics and educa tion. Yet many of them might reject the label of Mathematics Educators. This community has historically been clustered around what is now called the Epistemology and Learning Group at the Massachusetts Institute of Technol ogy. Their work has focused our attention on cognitive science, ethnography, sociology, artificial intelligence and other related disciplines. Crucially, it has forced our awareness of the construction of computational settings as a crucial component of the struggle to understand how mathematical learning happens. We have sometimes felt that few have tried to span both communities. Indeed, an analysis of the references in the literature would, we are sure, reveal that the two communities have often ignored each other's strengths. One reason for writing this book is born of our hope that we might draw together Mathematics Educators and mathematics educators, and assist both communities in recognising that there are insights that might be derived from each other.

Learning Cultures and Computers

Windows on Mathematical Meanings

These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry. In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using? Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.

Learning Mathematics and Logo

Arthur Bakker

Phillip Kent

Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the twenty-first century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies and globalisation. Through a series of case studies from the manufacturing and financial service sectors, the authors argue that there has been a radical shift in the type mathematical skills required for work – a shift not yet fully recognised by the formal education system, or by employers and managers. Examining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions: What mathematical knowledge and skills matter for the world of work today? How does information technology change the necessary knowledge and the ways in which it is encountered? How can we develop these essential new skills in the workforce? With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.

The Need for Techno-Mathematical Literacies

Improving Mathematics at Work

Paul Dowling

The introduction of the National Curriculum has imposed restraints on the way subjects are taught. This book argues that, in the case of mathematics, the limitations have effectively robbed the subject of its true meaning and identity.

Mathematics Versus the National Curriculum

Andrea A. DiSessa

Computers are playing a fundamental role in enhancing exploratory learning techniques in education. This volume in the NATO Special Programme on Advanced Educational Technology covers the state of the art in the design and use of computer systems for exploratory learning. Contributed chapters treat principles, theory, practice, and examples of some of the best contemporary computer-based learning environments: Logo, Boxer, Microworlds, Cabri-Géomètre, Star Logo, Table Top, Geomland, spreadsheets, Function Machines, and others. Emphasis is on mathematics and science education. Synthetic chapters provide an overview of the current scene in computers and exploratory learning, and analyses from the perspectives of epistemology, learning, and socio-cultural studies.

Richard Noss

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