Task Design In Mathematics Education

Abstract

This book is the outcome of ICMI Study 22: Task design in mathematics education .The proposal was presented to the International Commission on Mathematics Instruction (ICMI) in 2011 and accepted.Co-convenors and an International Programme Committee (IPC) were appointed from across the world and met in Oxford early in 2012.Following this, a discussion document and call for papers were prepared for the study conference to be held in July 2013.It was decided to organize the study under fi ve themes, each theme having shared responsibility among two or three of the IPC members.Introductory text and orienting questions for each theme were prepared by the IPC members.The conference was announced for July 2013 in Oxford and a call for papers issued in May 2012.There was a robust response, and we are grateful to Ellie Darlington for the academic administration.The size of the study conference was limited strictly to 80 attenders in order to ensure effective working groups, so papers were reviewed not only on the basis of quality but also to ensure an optimal coverage of relevant issues.The acceptance rate for papers was about 45 %.It was explained to authors that the fi nal book would not consist of a collection of their papers, but there would be online publication of the conference proceedings.IPC members would develop a book which synthesised the papers and discussions that took place within each theme.Authors of high-quality papers which could not be accepted because of overlap of contents were encouraged to seek publication elsewhere.One author from each paper was invited to attend the conference.In addition, four plenary speakers were invited, each representing a particular approach to the principles, practice, and implementation of task design from across the world.Each of them has contributed a chapter to this book.Presentations were invited from the Shell Centre, the Freudenthal Institute, and the TDS/ATD approach to didactic engineering, and a panel presentation was given by attenders who use variation theory as a design tool.The majority of the conference time was spent in working groups organised and led by IPC members.Two cross-theme meetings provided an opportunity to explore contrasts and overlaps in content and approach.viThe IPC decided to structure the book as fi ve main chapters, one for each theme, to be co-authored by IPC members drawing on the papers accepted for the conference, high-quality papers submitted or published elsewhere, relevant literature from the research fi eld, and discussions at the study conference itself.The contribution of co-authors of accepted papers and authors who were prevented from attending is also recognised in each chapter.Four more chapters were provided by the plenary speakers; there is no separate chapter about variation theory as it informs ideas in several chapters.Michèle Artigue and Ken Ruthven were invited to provide commentaries.The fi ve theme chapters were reviewed internally by the IPC and also by the study co-convenors.Through this process, cross-referencing was developed as much as possible, and there was careful examination of any overlaps.Where different chapters have treated similar ideas in different ways, we have tried as far as possible to clarify the differences and indicate cross-references.We want to acknowledge the particular roles played by three members of the IPC: Claire Margolinas edited the online proceedings which can be found at https:// hal.archives-ouvertes.fr/hal-00834054; Peter Sullivan reviewed all the theme chapters in order to comment on overall coherence; and Denisse Thompson, also a member of the IPC, undertook a considerable amount of technical editing.We are indebted to these colleagues for their support and practical wisdom.We are also grateful to Bill Barton who, as president of ICMI when the proposal was submitted, was encouraging and supportive, and to Lena Koch who manages the ICMI website.Finally, we wish to thank the task designers and researchers who have been bringing their work to publication more and more during the last two decades and those who supported and advised the original proposal.We are committed to the idea that task design is at the heart of effective teaching and learning of mathematics and are delighted to be part of the growth of research attention to this focus.