ISBN-10:
1848219261
ISBN-13:
9781848219267
Pub. Date:
08/08/2016
Publisher:
Wiley
Interactions on Digital Tablets in the Context of 3D Geometry Learning / Edition 1

Interactions on Digital Tablets in the Context of 3D Geometry Learning / Edition 1

by David Bertolo
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Product Details

ISBN-13: 9781848219267
Publisher: Wiley
Publication date: 08/08/2016
Pages: 224
Product dimensions: 6.40(w) x 9.30(h) x 0.80(d)

About the Author

David Bertolo, Université de Lorraine, France, is a researcher in information technology at the LCOMS laboratory at the University of Lorraine in France, in the field of Man-Machine Interactions and more specifically on interactions and innovative interfaces that facilitate learning. He is also a teacher of mathematics and mathematical teaching.

Table of 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

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

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

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