Devolution and Autonomy in Education

5 Foreword

6 Introduction

7 Begin Reading

8 List of Authors

9 Index

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2 iii

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Education Set

coordinated by Angela Barthes and Anne-Laure Le Guern

Volume 9

Edited by

Pablo Buznic-Bourgeacq

First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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© ISTE Ltd 2021

The rights of Pablo Buznic-Bourgeacq to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2021936092

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Data A CIP record for this book is available from the British Library

ISBN 978-1-78630-698-2

The concept of devolution, introduced by Brousseau (1982), is at the heart of the theory of didactical situations in mathematics, which itself has called for some research observations in didactics of mathematics, particularly in France, since the 1970s. I will then come back to the concept of “devolution”, which leads us to introduce a fundamental distinction between situational knowledge and institutional knowledge and to characterize the process of devolution. We will then be able to question the roles of the teacher, as well as of the student before concluding on the implications for the disciplines.

The term “didactics” refers to many points of view that depend on the history of research communities in different disciplinary didactics. In didactics of mathematics, a broad anthropological point of view prevails (Sarrazy 2005), which is reflected, for example, in the following definitions:

[…] the didactics of mathematics [is] the science of studying and helping to study (questions of) mathematics (Bosch and Chevallard 1999, p. 79).

It is the science of the specific conditions regarding the diffusion of mathematical knowledge necessary for human occupations (broad sense) (Brousseau 2003, p. 2).

Both of these definitions consider the didactics of mathematics a “normal” science (Kuhn 1970) that includes both foundational and applied research (International Council for Science 2004). Its object of study is specified, and it specifically concerns mathematics; however nothing refers to school or teaching, which represent institutional and historical choices concerning only part of the diffusion of mathematical knowledge or the study of it. In the continuation of the previous quotation, Brousseau, when he specifies the “restricted meaning”, indicates a “teaching” institution but assigns to it a meaning that is not necessarily that conferred on it by contemporary usage (employee in national education).

The didactics of mathematics deals (in a restricted sense) with the conditions where an institution considered a “teaching” institution attempts (mandated if necessary by another institution) to modify the knowledge of another “taught” institution when the latter is not able to do so autonomously and does not necessarily feel the need to do so. A didactic project is a social project to enable a subject or an institution to appropriate knowledge that has been or is in the process of being created. Teaching includes all the actions that seek to achieve this didactic project (Brousseau 2003, p. 2).

In this quotation, a very important point that will be developed is that the “taught institution” does not necessarily feel the need to change its knowledge and is not able to do so autonomously. As I am only interested here in one teaching institution, the school, I will speak of students and teachers.