Interactions on Digital Tablets in the Context of 3D Geometry Learning: Contributions and Assessments

229 Pages·2016·16.838 MB·English

by  Bertolo, David

INFORMATION SYSTEMS, WEB AND PERVASIVE COMPUTING SERIES
HUMAN–MACHINE INTERACTION SET
Volume 2
Interactions on Digital
Tablets in the Context of
3D Geometry Learning
David Bertolo

Interactions on Digital Tablets in the Context of
3D Geometry Learning

Human–Machine Interaction Set
coordinated by
Jérôme Dinet
Volume 2
Interactions on Digital
Tablets in the Context of 3D
Geometry Learning

David Bertolo
First published 2016 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,
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undermentioned address:
ISTE Ltd John Wiley & Sons, Inc.
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www.iste.co.uk www.wiley.com

© ISTE Ltd 2016
The rights of David Bertolo 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: 2016941694

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-926-7
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1. Construction of Spatial
Representation and Perspective in Students . . . . . . . . . . . . . . . . 1
1.1. Spatial representation in children according to Piaget . . . . . . . . . . . 3
1.1.1. From perception to representation . . . . . . . . . . . . . . . . . . . . 3
1.1.2. Projective space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3. Euclidean space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2. The representation of geometric objects:
the status of drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.1. Status of drawings in mathematics:
drawings versus figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.2. Use of geometrical representations . . . . . . . . . . . . . . . . . . . 18
1.2.3. The three main functions of drawings in geometry . . . . . . . . . . 25
1.3. From the physical shape to its planar representation . . . . . . . . . . . . 25
1.3.1. The institutional perspective . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.2. Teaching 3D geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.3. Different representations of 3D objects . . . . . . . . . . . . . . . . . 29
1.3.4. The conflict between the SEEN and the
KNOWN in children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.4. Benefits of new technologies and dynamic 3D geometry . . . . . . . . . 37
1.4.1. Advantages of 3D geometry programs . . . . . . . . . . . . . . . . . 38
1.4.2. Limits of 3D geometry programs and
consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.4.3. Partial conclusions and initial hypotheses . . . . . . . . . . . . . . . 46
vi Interactions on Digital Tablets in the Context of 3D Geometry Learning
Chapter 2. Mobile Devices and 3D Interactions . . . . . . . . . . . . . . 49
2.1. Why mobile devices? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.1.1. A long-standing tradition in mathematics . . . . . . . . . . . . . . . . 51
2.1.2. Interest from the educational community . . . . . . . . . . . . . . . . 54
2.1.3. A field reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.2. Mobile devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.1. Different types of mobile devices . . . . . . . . . . . . . . . . . . . . 58
2.2.2. Entry systems of mobile terminals . . . . . . . . . . . . . . . . . . . . 61
2.3. Interactions on mobile devices and physiology . . . . . . . . . . . . . . . 70
2.3.1. Specificities of mobile devices . . . . . . . . . . . . . . . . . . . . . . 70
2.3.2. Limitations due to physiologic characteristics . . . . . . . . . . . . . 71
2.4. 3D interaction techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.1. Mathematical reminders . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.2. 3D selection/manipulation and
navigation interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5. “Language” of interactions and classifications . . . . . . . . . . . . . . . 88
2.5.1. Language and grammar of gestures . . . . . . . . . . . . . . . . . . . 89
2.5.2. Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 3. Elaboration and Classification
of Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1. Human-centered design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.1.1. A definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.1.2. Principles of the user-based approach . . . . . . . . . . . . . . . . . . 97
3.2. Study of the needs and behaviors of users . . . . . . . . . . . . . . . . . . 98
3.2.1. Study of pre-existing 3D geometry software . . . . . . . . . . . . . . 98
3.2.2. Study of users’ behaviors and needs . . . . . . . . . . . . . . . . . . . 103
3.3. Our grammar and interaction language . . . . . . . . . . . . . . . . . . . 109
3.3.1. Classification of tactile movement interactions . . . . . . . . . . . . 109
3.3.2. Definition of the grammar . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.3.3. The prototype: FINGERS
(Find INteractions for GEometry leaneRS) . . . . . . . . . . . . . . . . . . 112
3.3.4. Our gestural language of interactions . . . . . . . . . . . . . . . . . . 114
3.4. Evaluation of the acceptance of interactions
(selection, translation and rotation) . . . . . . . . . . . . . . . . . . . . . . . . 133
3.4.1. Experimental challenges and constraints . . . . . . . . . . . . . . . . 133
3.4.2. Preliminary evaluation of the acceptance
of rotation and point of view change interactions . . . . . . . . . . . . . . . 134
3.4.3. Comparison between gyroscope,
face-tracking and multi-touch . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.4.4. Student learning of prototype interactions . . . . . . . . . . . . . . . 147
3.5. Conclusion and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Contents vii
Chapter 4. Evaluation of the Educational
Benefits for 3D Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.1. Partnerships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.1.1. The schools in the field . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.1.2. The ESPÉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.1.3. Mathematics teachers’ associations . . . . . . . . . . . . . . . . . . . 157
4.2. Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.2.1. Ethical: the equality of chances for students . . . . . . . . . . . . . . 157
4.2.2. Practical: progression of the concepts
throughout the year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.3. Evaluation of problem solving aids . . . . . . . . . . . . . . . . . . . . . . 158
4.3.1. In the field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.3.2. Laboratory (EEG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.4. Evaluation of the benefits in learning 3D geometry . . . . . . . . . . . . 174
4.4.1. Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
4.4.2. Material and experimental conditions . . . . . . . . . . . . . . . . . . 174
4.4.3. Experimental plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.4.4. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.5. Partial conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203