Hoyles / Lagrange Mathematics Education and Technology-Rethinking the Terrain

The 17th ICMI Study
1. Auflage 2009
ISBN: 978-1-4419-0146-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 13, 494 Seiten

Reihe: New ICMI Study Series

Mathematics Education and Technology-Rethinking the Terrain revisits the important 1985 ICMI Study on the influence of computers and informatics on mathematics and its teaching.  The focus of this book, resulting from the seventeenth Study led by ICMI, is the use of digital technologies in mathematics teaching and learning in countries across the world. Specifically, it focuses on cultural diversity and how this diversity impinges on the use of digital technologies in mathematics teaching and learning. Within this focus, themes such as mathematics and mathematical practices; learning and assessing mathematics with and through digital technologies; teachers and teaching; design of learning environments and curricula; implementation of curricula and classroom practice; access, equity and socio-cultural issues; and connectivity and virtual networks for learning, serve to organize the study and bring it coherence. Providing a state-of-the-art view of the domain with regards to research, innovating practices and technological development, Mathematics Education and Technology-Rethinking the Terrain is of interest to researchers and all those interested in the role that digital technology plays in mathematics education.

Autoren/Hrsg.

Lagrange, Jean-Baptiste

Hoyles, Celia

Inhaltsverzeichnis

1;Hoyles_FM.pdf;1
2;Hoyles_Ch01.pdf;13
2.1;Chapter 1;13
2.1.1;Introduction;13
2.1.1.1;1.1 Introduction;13
2.1.1.2;1.2 Background and Challenges to ICMI study 17;14
2.1.1.3;1.3 The Study Conference;15
2.1.1.4;1.4 Summary of the Book;17
2.1.1.4.1;Section 1: Design of Learning Environments and Curricula;17
2.1.1.4.2;Section 2: Learning and Assessing Mathematics with and Through Digital Technologies;18
2.1.1.4.3;Section 3: Teachers and Technology;20
2.1.1.4.4;Section 4: Implementation of Curricula: Issues of Access and Equity;21
2.1.1.4.5;Section 5: Future Directions;22
2.1.1.5;1.5 Conclusion;23
2.1.2;References;23
3;Hoyles_Ch02.pdf;24
3.1;Chapter 2;25
3.1.1;Introduction to Section 1;25
4;Hoyles_Ch03.pdf;28
4.1;Chapter 3;28
4.1.1;Designing Software for Mathematical Engagement through Modeling;28
4.1.1.1;3.1 Introduction;28
4.1.1.2;3.2 Case Study 1: Graphs ‘n Glyphs: Animation Software for Mathematics Learning;30
4.1.1.2.1;3.2.1 Aims and Description of the Software;30
4.1.1.2.2;3.2.2 Main Issues in Software Design;31
4.1.1.2.3;3.2.3 Notable Characteristics of the Software;33
4.1.1.2.4;3.2.4 Major Achievements;37
4.1.1.2.5;3.2.5 Major Challenges;39
4.1.1.2.5.1;3.2.5.1 Reflections on Design;40
4.1.1.3;3.3 Case Study 2: Lunar Lander, a Prototype Web-Based Space Travel Games Construction Kit;41
4.1.1.3.1;3.3.1 Aims and Description of the Software;41
4.1.1.3.2;3.3.2 The Activity Sequence;43
4.1.1.3.3;3.3.3 Main Issues in Software Design;45
4.1.1.3.4;3.3.4 Notable Characteristics of the Software;46
4.1.1.3.5;3.3.5 Snapshots of Learning;47
4.1.1.3.6;3.3.6 Challenges and Reflections on Design;49
4.1.1.4;3.4 Conclusions;50
4.1.2;References;52
5;Hoyles_Ch04.pdf;55
5.1;Chapter 4;55
5.1.1;Designing Digital Technologies and Learning Activities for Different Geometries;55
5.1.1.1;4.1 Geometry, Technology, and Teaching and Learning;55
5.1.1.2;4.2 Working with Different Geometries on the Flat Screen;56
5.1.1.3;4.3 Designing Digital Technologies for Different Geometries;58
5.1.1.3.1;4.3.1 2D Dynamic Geometry Environments;58
5.1.1.3.2;4.3.2 Software for 3D Geometry;60
5.1.1.3.3;4.3.3 Software for Various Non-Euclidean Geometries;62
5.1.1.4;4.4 Designing Learning Activities to Engage Students with Different Geometries;63
5.1.1.5;4.5 Shaping, and Being Shaped by, Digital Technologies;65
5.1.1.5.1;4.5.1 Coda;66
5.1.1.5.2;4.5.2 Notes;66
5.1.2;References;67
6;Hoyles_Ch05.pdf;69
6.1;Chapter 5;69
6.1.1;Implementing Digital Technologies at a National Scale;69
6.1.1.1;5.1 Introduction;69
6.1.1.2;5.2 Overview of the Projects;70
6.1.1.2.1;5.2.1 Enciclomedia;71
6.1.1.2.2;5.2.2 [e-mail];72
6.1.1.2.3;5.2.3 Isfahan Mathematics House: E-Content;72
6.1.1.2.4;5.2.4 Mathematics 9 and 10 with The Geometer’s Sketchpad;73
6.1.1.2.5;5.2.5 Sketchpad for Young Learners;74
6.1.1.3;5.3 Comparing and Contrasting the Projects;75
6.1.1.3.1;5.3.1 Curriculum Content;75
6.1.1.3.2;5.3.2 Teaching Practices;77
6.1.1.3.3;5.3.3 Activity Design;78
6.1.1.4;5.4 Emerging Themes Across the Projects;81
6.1.1.4.1;5.4.1 Shifts in Audience: Moving Toward More Teacher Participation;81
6.1.1.4.2;5.4.2 Shifts in Value: From Pragmatic to Epistemic;81
6.1.1.5;5.5 Concluding Remarks;84
6.1.1.6;5.6 Looking Forward;84
6.1.2;References;85
7;Hoyles_Ch06.pdf;87
7.1;Chapter 6;88
7.1.1;Introduction to Section 2;88
7.1.1.1;6.1 The Points of Departure;88
7.1.1.2;6.2 A Guided Tour Through the Chapters;89
7.1.1.3;6.3 Looking Back at the Original Issues;91
7.1.1.3.1;6.4 Concluding Remarks;93
7.1.2;References;94
8;Hoyles_Ch07.pdf;95
8.1;Chapter 7;95
8.1.1;Integrating Technology into Mathematics Education: Theoretical Perspectives;95
8.1.1.1;7.1 Introduction;95
8.1.1.2;7.2 Looking Back;96
8.1.1.2.1;7.2.1 The Evolution of Technology and Its Use in the Mathematics Education Community;97
8.1.1.2.2;7.2.2 The Emergence of Theory from the Integration of Technology Within Mathematics Education;98
8.1.1.2.2.1;7.2.2.1 Tutor, Tool, Tutee;99
8.1.1.2.2.2;7.2.2.2 White Box – Black Box;99
8.1.1.2.2.3;7.2.2.3 Microworlds and Constructionism;100
8.1.1.2.2.4;7.2.2.4 Amplifier – Reorganizer;101
8.1.1.2.3;7.2.3 Theoretical Ideas Emanating from the Literature on Mathematical Learning;101
8.1.1.2.3.1;7.2.3.1 Process-Object;102
8.1.1.2.3.2;7.2.3.2 Visual Thinking vs. Analytical Thinking;102
8.1.1.2.3.3;7.2.3.3 Representational Issues;103
8.1.1.2.4;7.2.4 From Past to Present;104
8.1.1.3;7.3 Current Developments;104
8.1.1.3.1;7.3.1 Learning Theories from Mathematical Didactics;105
8.1.1.3.1.1;7.3.1.1 From Scaffolding and Abstraction to Webbing and Situated Abstraction;106
8.1.1.3.1.2;7.3.1.2 Theory of Didactical Situations: the Concept of Milieu;108
8.1.1.3.1.3;7.3.1.3 Perceptuo-Motor Activity in Mathematical Learning;110
8.1.1.3.1.4;7.3.1.4 Discussion;112
8.1.1.3.2;7.3.2 Instrumentation;112
8.1.1.3.2.1;7.3.2.1 Artifact and Instrument;114
8.1.1.3.2.2;7.3.2.2 Instrumental Genesis;114
8.1.1.3.2.3;7.3.2.3 Schemes and Techniques;115
8.1.1.3.2.4;7.3.2.4 Examples;116
8.1.1.3.2.5;7.3.2.5 Orchestration;118
8.1.1.3.2.6;7.3.2.6 Affordances, Constraints, Perspectives;119
8.1.1.3.3;7.3.3 Mediation and Semiotic Mediation;119
8.1.1.3.3.1;7.3.3.1 Representation and the Semiotic Approach;120
8.1.1.3.3.2;7.3.3.2 Mediation;121
8.1.1.3.3.3;7.3.3.3 Mediation According to a Semiotic Approach;122
8.1.1.3.3.4;7.3.3.4 Examples of Semiotic Mediation;124
8.1.1.4;7.4 Summary and Future Developments;126
8.1.1.4.1;7.4.1 Summary;126
8.1.1.4.2;7.4.2 Technological Developments;127
8.1.1.4.3;7.4.3 Theoretical Developments;127
8.1.1.4.4;7.4.4 The Remath Integrative Theoretical Framework;128
8.1.2;References;131
9;Hoyles_Ch08.pdf;139
9.1;8;139
9.1.1;Mathematical Knowledge and Practices Resulting from Access to Digital Technologies;139
9.1.1.1;8.1 Overview of the Chapter;139
9.1.1.1.1;8.1.1 Preface;140
9.1.1.2;8.2 Mathematical Knowledge in a Technological World;142
9.1.1.2.1;8.2.1 What Is Mathematical Knowledge?;142
9.1.1.2.2;8.2.2 The Influence of Technology on the Nature of Mathematical Knowledge;143
9.1.1.2.3;8.2.3 Mathematical Knowledge: Operational and Notational Aspects;145
9.1.1.2.4;8.2.4 Contexts for Learning Mathematics;146
9.1.1.2.5;8.2.5 A New Learning Ecology;147
9.1.1.2.6;8.2.6 Example Cases of Effective Technologies;148
9.1.1.2.6.1;8.2.6.1 The Fractions Project: Using Technology with High Levels of “Cognitive Fidelity”;149
9.1.1.2.6.2;8.2.6.2 The SimCalc Project: Introducing the Mathematics of Change in Middle School – Technology with High Levels of “Mathem;151
9.1.1.2.6.3;8.2.6.3 Dynamic Geometry Environments;153
9.1.1.2.7;8.2.7 Summary of Students’ Mathematical Knowledge in a Technological World;156
9.1.1.3;8.3 Mathematical Knowledge“Within” Technologies;156
9.1.1.3.1;8.3.1 Numbers and Arithmetic;156
9.1.1.3.2;8.3.2 CAS and Problem Spotting;157
9.1.1.3.3;8.3.3 Geometry with Linear Algebra;157
9.1.1.3.4;8.3.4 Who Has to Know What About the Underlying Mathematical Assumptions and Processes of Spreadsheets, DGEs, Statistical Pa;158
9.1.1.4;8.4 New Mathematical Practices;159
9.1.1.4.1;8.4.1 Link Between Knowledge and Practice;159
9.1.1.4.2;8.4.2 Interactions Among Students, Teachers, Tasks, and Technologies: Shifts in Empowerment;161
9.1.1.4.3;8.4.3 Role of Feedback in Practice;164
9.1.1.4.4;8.4.4 Example Technologies that Promote New Mathematical Practices;165
9.1.1.4.4.1;8.4.4.1 New Mathematical Practices in Dynamic Geometry Environments;165
9.1.1.4.4.2;8.4.4.2 Technologies that Encourage New Practices in Statistics;168
9.1.1.4.4.3;8.4.4.3 Children’s Mathematical Practices Using Robotics and Digital Games;170
9.1.1.4.5;8.4.5 Summary of New Mathematical Practices Made Possible with Technology;172
9.1.1.5;8.5 Final Words: An Adaptation of Our Didactical Tetrahedron;174
9.1.2;References;175
10;Hoyles_Ch09.pdf;184
10.1;Chapter 9;184
10.1.1;The Influence and Shaping of Digital Technologies on the Learning – and Learning Trajectories – of Mathematical Concepts;184
10.1.1.1;9.1 Introduction;184
10.1.1.2;9.2 Theoretical Overview;186
10.1.1.2.1;9.2.1 On Learning Trajectories;186
10.1.1.2.2;9.2.2 The Possible Influence and Mediating Role of Digital Technologies on Learning and Learning Trajectories;187
10.1.1.2.3;9.2.3 Digital Technological Environments as Domains of Abstraction;188
10.1.1.2.4;9.2.4 Hypothetical Learning Trajectories in DT Environments: Building on the Microworld Idea and Design;189
10.1.1.3;9.3 Affordances of Digital Technologies that Might Influence Learning Trajectories, and Considerations for the Design of HLT;189
10.1.1.3.1;9.3.1 Technical Aspects;191
10.1.1.3.1.1;9.3.1.1 The Choice of the Technological Tool(s) and Their Design;191
10.1.1.3.1.2;9.3.1.2 The Role of Representations;191
10.1.1.3.1.3;9.3.1.3 The Computational and Dynamic Capabilities of DT;192
10.1.1.3.1.4;9.3.1.4 The Networking Capabilities of DT;193
10.1.1.3.2;9.3.2 Pedagogical and Contextual Aspects (Task Design, the Role of the Teacher and the Didactical Context);193
10.1.1.3.2.1;9.3.2.1 The Pedagogical Setting;193
10.1.1.3.2.2;9.3.2.2 Context of Inquiry of the Activity;194
10.1.1.3.2.3;9.3.2.3 Level of Openness of a DT-Based Activity;194
10.1.1.3.2.4;9.3.2.4 Sequencing of Tasks Within an Activity;195
10.1.1.3.2.5;9.3.2.5 Mathematical Content;196
10.1.1.3.2.6;9.3.2.6 The Possibility of Earlier Engagement (Shifts in Trajectories);196
10.1.1.3.2.7;9.3.2.7 The Teacher’s Role and the Importance of Appropriate Intervention;197
10.1.1.3.3;9.3.3 The Learner Perspective;197
10.1.1.3.3.1;9.3.3.1 Affect and DT: The Role of Engagement and Motivation for Learning;197
10.1.1.3.3.2;9.3.3.2 The Role of the Feedback from DT;198
10.1.1.3.4;9.3.4 Introduction to the Following Sections;198
10.1.1.4;9.4 An Example of the Design of a Hypothetical Learning Trajectory Through Exploratory Tasks;199
10.1.1.4.1;9.4.1 Context of Inquiry;199
10.1.1.4.2;9.4.2 Mathematical Content;200
10.1.1.4.3;9.4.3 The Choice of the Technological Tool;200
10.1.1.4.4;9.4.4 Level of Openness;201
10.1.1.4.5;9.4.5 Representations;201
10.1.1.4.6;9.4.6 Sequencing of Tasks within the Activity;202
10.1.1.4.7;9.4.7 Comments;202
10.1.1.5;9.5 Learning Trajectories Within and Across Various Platforms: An Example with Dynamic Geometry and CAS;202
10.1.1.5.1;9.5.1 The Construction of a Dynamic Representationof the Problem;203
10.1.1.5.2;9.5.2 From Geometry to Algebra;206
10.1.1.5.3;9.5.3 Discussion;207
10.1.1.6;9.6 Emergence of Learning Trajectories from the Engagement with DT: An Example with Spreadsheets;208
10.1.1.7;9.7 Shifts in Trajectories: Possibilities of Earlier Engagement with Powerful Ideas Afforded by DT, and the Development of I;211
10.1.1.7.1;9.7.1 Using DT for Developing Intuitive Thinking;212
10.1.1.7.1.1;9.7.1.1 Early Accessto Powerful Mathematical Ideas: An Example of Early Algebra;214
10.1.1.7.1.1.1;The Case of Rodrigo;215
10.1.1.7.1.1.2;The Case of Ana Karen;216
10.1.1.7.1.2;9.7.1.2 The Role of Spreadsheets in the Transition Towards the Algebraic Method for Solving Word Problems;216
10.1.1.7.2;9.7.2 Early Access to Powerful Mathematical Ideas: Exploring Infinity-Related Notions;219
10.1.1.7.2.1;9.7.2.1 A Logo Microworld for the Exploration of Infinite Processes;219
10.1.1.7.2.2;9.7.2.2 Exploration of Infinite Sequences, Series and the Cardinality of Infinite Setswith ToonTalk;221
10.1.1.7.3;9.7.3 Early Access to Powerful Mathematical Ideas: Long-Term Impact;223
10.1.1.8;9.8 Concluding Remarks;224
10.1.2;References;225
11;Hoyles_Ch10.pdf;232
11.1;Chapter 10;232
11.1.1;Micro-level Automatic Assessment Supported by Digital Technologies;232
11.1.1.1;10.1 Introduction;232
11.1.1.2;10.2 Principle of CAA;234
11.1.1.2.1;10.2.1 How to Implement an Assessment?;234
11.1.1.2.2;10.2.2 Structure in the Tasks or Students Generated Mathematical Objects;237
11.1.1.2.2.1;10.2.2.1 Handling Algebraic Expressions;238
11.1.1.2.2.2;10.2.2.2 Handling Geometric Figures;240
11.1.1.2.3;10.2.3 Generation of Feedback for Students and for Teachers;243
11.1.1.2.3.1;10.2.3.1 Qualitative Feedback for Formative Assessment;243
11.1.1.2.3.2;10.2.3.2 Cohort Achievement Data;244
11.1.1.3;10.3 Results of Actual CAA Use;245
11.1.1.3.1;10.3.1 New Ways of Undertaking Mathematical Tasks;247
11.1.1.3.2;10.3.2 Limits and Difficulties of Using CAA;248
11.1.1.3.3;10.3.3 Interpreting Students’ Solutions in Simple Geometry Tasks;250
11.1.1.4;10.4 Conclusions and the Future;253
11.1.2;References;254
12;Hoyles_Ch11.pdf;256
12.1;Chapter 11;256
12.1.1;Technology, Communication, and Collaboration: Re-thinking Communities of Inquiry, Learning and Practice;256
12.1.1.1;11.1 Introduction;257
12.1.1.1.1;11.1.1 Social Perspectives on Learning;257
12.1.1.1.2;11.1.2 Socio-Constructivism;258
12.1.1.1.3;11.1.3 Socio-Culturalism;258
12.1.1.1.4;11.1.4 Communities of Practice;259
12.1.1.1.5;11.1.5 Voice and Discourse;261
12.1.1.1.6;11.1.6 Distributed Cognition;262
12.1.1.2;11.2 The Growth in Social Perspectives on Teaching and Learning with Technology;263
12.1.1.2.1;11.2.1 Early Accounts;264
12.1.1.2.2;11.2.2 A New Millennium;264
12.1.1.2.3;11.2.3 Current Climate;265
12.1.1.2.4;11.2.4 The Role of Technology in Collaborative Mathematical Practice;265
12.1.1.3;11.3 Different Technological Typologies for Fostering Communication, Collaboration, and Communities of Inquiry;267
12.1.1.3.1;11.3.1 Technologies Designed for Both Mathematics and Collaboration;268
12.1.1.3.1.1;11.3.1.1 Internet-Based Networks;268
12.1.1.3.1.2;11.3.1.2 Classroom-Based Networks;269
12.1.1.3.1.3;11.3.1.3 Non-networked Software;270
12.1.1.3.2;11.3.2 Technologies Designed for Mathematics but Not Specifically for Collaboration;271
12.1.1.3.3;11.3.3 Technologies Designed for Collaboration but Not Necessarily Mathematics;273
12.1.1.3.3.1;11.3.3.1 Enhancing the Learning Environment;274
12.1.1.3.3.2;11.3.3.2 Distance Learning;275
12.1.1.3.4;11.3.4 Technologies Designed for Neither Mathematics nor Collaboration;276
12.1.1.4;11.4 Future Developments;277
12.1.1.4.1;11.4.1 New Forms of Communities of Learners;277
12.1.1.4.1.1;11.4.1.1 Amplifying, Enhancing, Broadening Classroom-Based Communities;277
12.1.1.4.1.2;11.4.1.2 Online Communities: Virtual Communities of Learners;278
12.1.1.4.2;11.4.2 Extending the Role of the Teacher;279
12.1.1.4.3;11.4.3 New Forms of Voice and Discourse;280
12.1.1.4.4;11.4.4 Other Issues;281
12.1.1.4.4.1;11.4.4.1 The Case of Marginalised Members of a Community;281
12.1.1.4.4.2;11.4.4.2 Emergent Uses of Technology;281
12.1.1.4.4.3;11.4.4.3 Unit of Analysis;282
12.1.1.5;11.5 Conclusion and Final Remarks;282
12.1.2;References;283
13;Hoyles_Ch12.pdf;290
13.1;Chapter 12;291
13.1.1;Introduction to Section 3;291
13.1.1.1;12.1 Introduction;291
13.1.2;References;295
14;Hoyles_Ch13.pdf;297
14.1;Chapter 13;297
14.1.1;Working with Teachers: Context and Culture;297
14.1.1.1;13.1 Introduction;298
14.1.1.2;13.2 Context, Culture and Teachers’ Practices;298
14.1.1.3;13.3 Case 1: Using Inquiry Cycles in Activity Design;301
14.1.1.4;13.4 Case 2: Half-Baked Microworlds as Catalysts for Instrumentalisation;304
14.1.1.5;13.5 Case 3: Communal Design of a Tool for Statistical Explorations;308
14.1.1.5.1;13.5.1 Designing as Learning: From Means and Spread to Distribution as a Space of Possible Values;309
14.1.1.5.2;13.5.2 Distributing the Instrumental Genesis Process?;311
14.1.1.6;13.6 Reflections on the Case Studies;312
14.1.2;References;313
15;Hoyles_Ch14.pdf;315
15.1;Chapter 14;315
15.1.1;Teachers and Teaching: Theoretical Perspectives and Issues Concerning Classroom Implementation;315
15.1.1.1;14.1 Theoretical Perspectives;316
15.1.1.1.1;14.1.1 Instrumental Genesis;317
15.1.1.1.2;14.1.2 Zones and Affordances;320
15.1.1.1.3;14.1.3 Instrumentation Theory Applied to a Zone/Affordances Excerpt;322
15.1.1.1.4;14.1.4 Zone Theory and Affordances Applied to an Instrumental Genesis Excerpt;323
15.1.1.1.5;14.1.5 Complexity Theory;323
15.1.1.1.6;14.1.6 Theoretical Perspectives: What Is the Teacher’s Role in Technology Integration?;325
15.1.1.1.7;14.1.7 Factors Influencing Technology Integration in Schools;325
15.1.1.1.7.1;Vignette #1: Novice (Pre-service) Teacher;326
15.1.1.1.7.2;Vignette #2: Experienced Teacher;327
15.1.1.1.8;14.1.8 Factors Influencing Technology Integration in University Mathematics Departments;327
15.1.1.2;14.2 Classroom Implementation;328
15.1.1.2.1;14.2.1 Defining Criteria for Effective Use;328
15.1.1.2.2;14.2.2 Identifying Change;329
15.1.1.3;14.3 Future Visions;330
15.1.2;References;331
16;Hoyles_Ch15.pdf;333
16.1;Chapter 15;333
16.1.1;Teacher Education Courses in Mathematics and Technology: Analyzing Views and Options;333
16.1.1.1;15.1 Introduction;333
16.1.1.2;15.2 Examples of Teacher Development Courses;335
16.1.1.2.1;15.2.1 In Service Teacher Development Course “Mathematics Investigations” (MathInquiry) (Based on Alagic 2006);335
16.1.1.2.2;15.2.2 A Bachelor of Education Course at the Institute of Education for Women in India (BecIEW) (Based on Das 2006);336
16.1.1.2.3;15.2.3 Mieux Apprendre la Géométrie avec l’Informatique1 (MAGI) (Based on Assude et al. 2006);336
16.1.1.2.4;15.2.4 A Teacher Development Course for Prospective Primary Mathematics Teachers (TdcPt) (Based on Hunscheidt and Peter-Koop;336
16.1.1.2.5;15.2.5 The Bachelor of Education “ITeach Laptop Learning Program” (BEdITeach) (Based on Jarvis 2006);337
16.1.1.3;15.3 Characterizing the Varied Views that Underpin Teacher Development Programs in Technology;337
16.1.1.3.1;15.3.1 Views Concerning the Implementation of Technology in the Classroom and in Teacher Education;337
16.1.1.3.2;15.3.2 Views About Changes in Teachers’ Role, Activity and Practices Underpinning a Course;339
16.1.1.3.3;15.3.3 Views About How to Prepare Teachers;340
16.1.1.4;15.4 Identifying the Various Practical Decisions Related to Course Organisation;342
16.1.1.4.1;15.4.1 Contents Proposed in the Courses;342
16.1.1.4.1.1;15.4.1.1 Content 1: The Impact of Technology on Mathematics and the Resulting Evolution of the Curriculum;343
16.1.1.4.1.2;15.4.1.2 Content 2: The Potential of Computer Applications for New Alternatives in Mathematics Learning;344
16.1.1.4.1.3;15.4.1.3 Content 3: The Ideas of Instrumental Genesis and Intertwined Mathematical and Instrumental Knowledge;344
16.1.1.4.1.4;15.4.1.4 Content 4: Creating New Tasks and Making Them Work Together with Older Tasks;344
16.1.1.4.1.5;15.4.1.5 Content 5: New Teaching Abilities;345
16.1.1.4.1.6;15.4.1.6 Content 6: Introducing Technology into a Professional Context;345
16.1.1.4.2;15.4.2 Teacher Educator Strategies;345
16.1.1.4.2.1;15.4.2.1 Strategy 1: Demonstration (Showing How to Achieve a Specific Goal);346
16.1.1.4.2.2;15.4.2.2 Strategy 2: Role Playing (Teacher as a Student);346
16.1.1.4.2.3;15.4.2.3 Strategy 3: In Practice (Teacher as Reflective Practitioners);347
16.1.1.4.2.4;15.4.2.4 Strategy 4: Learning in Communities;347
16.1.1.5;15.5 Conclusion;347
16.1.2;References;348
17;Hoyles_Ch16.pdf;350
17.1;Chapter 16;351
17.1.1;Introduction to Section 4;351
17.1.1.1;16.1 Introduction;351
17.1.1.2;16.2 Mathematics Curricula;352
17.1.1.2.1;16.2.1 Intended, Implemented and Attained Curricula;352
17.1.1.2.2;16.2.2 The Mathematics Curricula of Different Countries;353
17.1.1.2.3;16.2.3 The Mathematics Curricula of Different Sectors;355
17.1.1.2.4;16.2.4 Factors Influencing Implemented Curricula;356
17.1.1.3;16.3 Access and Equity;358
17.1.1.4;16.4 Conclusion;359
17.1.2;References;360
18;Hoyles_Ch17.pdf;363
18.1;Chapter 17;363
18.1.1;Some Regional Developments in Access and Implementation of Digital Technologies and ICT;363
18.1.1.1;17.1 Introduction;364
18.1.1.2;17.2 Macro Perspective on Education for the Twenty-First Century by Linda S. Posadas;364
18.1.1.3;17.3 Regional Reports;366
18.1.1.3.1;17.3.1 Case 1: Russia by Alexei Semenov;366
18.1.1.3.2;17.3.2 Case 2: Hong Kong (A Special Administrative Region of China) by Allen Leung;366
18.1.1.3.3;17.3.3 Case 3: Vietnam by Nguyen Chi Thanh;368
18.1.1.3.4;17.3.4 Case 4: South Africa (and Some Developments in Sub-Saharan Africa) by Cyril Julie;370
18.1.1.3.5;17.3.5 Case 5: Latin-America by Ana Isabel Sacristán;373
18.1.1.3.5.1;17.3.5.1 Latin-American Countries with Mainly Small-Scale Efforts of Integration of Digital Technologies Due to Individual I;374
18.1.1.3.5.2;17.3.5.2 Latin-American Countries with Large-Scale, Either Government-, or Privately-Sponsored, Projects;375
18.1.1.3.5.2.1;Brazil;375
18.1.1.3.5.2.2;Costa Rica;376
18.1.1.3.5.2.3;Mexico;377
18.1.1.3.5.2.4;Colombia;379
18.1.1.3.5.2.5;Chile;380
18.1.1.3.5.2.6;Venezuela;381
18.1.1.4;17.4 Conclusions;382
18.1.2;References;383
19;Hoyles_Ch18.pdf;386
19.1;Chapter 18;386
19.1.1;Technology for Mathematics Education: Equity, Access and Agency;386
19.1.1.1;18.1 Introduction;386
19.1.1.2;18.2 Definitions of Equity Including Access and Agency;387
19.1.1.2.1;18.2.1 Access;388
19.1.1.2.2;18.2.2 Resources for Equity;388
19.1.1.2.3;18.2.3 Equitable Pedagogies;389
19.1.1.2.4;18.2.4 Equitable Outcomes;390
19.1.1.2.5;18.2.5 Agency;391
19.1.1.3;18.3 Research Studies;392
19.1.1.3.1;18.3.1 Equity and Mathematics Learning with Technology;392
19.1.1.3.2;18.3.2 Equity and Attitudes, Beliefs, and Values Associated with Technology Use for Mathematics Learning;395
19.1.1.3.3;18.3.3 Resources for Mathematics Learning with Technology;397
19.1.1.3.4;18.3.4 Access to Mathematical Learning with Technology;398
19.1.1.3.5;18.3.5 Agency as an Outcome of Mathematical Learning with Technology;399
19.1.1.4;18.4 Conclusion;400
19.1.2;References;401
20;Hoyles_Ch19.pdf;405
20.1;Chapter 19;405
20.1.1;Factors Influencing Implementation of Technology-Rich Mathematics Curriculum and Practices;405
20.1.1.1;19.1 Introduction;405
20.1.1.2;19.2 Typology of Factors;406
20.1.1.2.1;19.2.1 The Social, Political, Economical and Cultural Level;406
20.1.1.2.2;19.2.2 The Mathematical and Epistemological Level;408
20.1.1.2.3;19.2.3 A School or an Institutional Level;410
20.1.1.2.4;19.2.4 The Classroom and Didactical Level;411
20.1.1.2.5;19.2.5 Multi-level Factors;412
20.1.1.3;19.3 Explaining the Problem;413
20.1.1.4;19.4 Conclusion;416
20.1.2;References;417
21;Hoyles_Ch20.pdf;420
21.1;Chapter 20;421
21.1.1;Introduction to Section 5;421
22;Hoyles_Ch21.pdf;423
22.1;Chapter 21;423
22.1.1;Design for Transformative Practices;423
22.1.1.1;21.1 Introduction;423
22.1.1.2;21.2 Potentialities of Dynamic Software for Teaching Challenging But Difficult Topics;424
22.1.1.2.1;21.2.1 Making Traditionally Difficult Topics Appear More Straightforward;424
22.1.1.2.1.1;21.2.1.1 Calculus: Illustrating Integrals, Areas and Volumes;424
22.1.1.2.1.2;21.2.1.2 Data Treatment: Understanding the Central Limit Theorem;425
22.1.1.2.2;21.2.2 Topics That Could be Re-introduced to Mainstream Post-16 Teaching;425
22.1.1.2.2.1;21.2.2.1 Differential Equations: Seeing What’s Going On;425
22.1.1.2.2.2;21.2.2.2 Bringing Back the Study of 3D Lines and Planes;426
22.1.1.2.3;21.2.3 Making Teaching More Effective and More Fun;426
22.1.1.3;21.3 Software for Mathematical Explorations: Attempting to Make a Curricular Agenda Visible;426
22.1.1.3.1;21.3.1 Clearing the Confusion Regarding the Role of Technology;427
22.1.1.3.2;21.3.2 From Bodily Actions to Symbolizing and Meaning Production;428
22.1.1.4;21.4 Attention to Detail: Broadening Our Design Language;429
22.1.1.4.1;21.4.1 Design Detail Counts;429
22.1.1.4.2;21.4.2 Well-Developed Design Discourses from Which to Draw;430
22.1.1.4.3;21.4.3 Paradigms of Embodied Interaction;431
22.1.1.5;21.5 Designing a 3D Dynamic and Interactive Environment;432
22.1.1.5.1;21.5.1 A Vision: Technology to Operate an Epistemological Shift;434
22.1.2;References;434
23;Hoyles_Ch22.pdf;436
23.1;Chapter 22;436
23.1.1;Connectivity and Virtual Networks for Learning;436
23.1.1.1;22.2 Developing Microworlds for On-LineCollaborative Learning;438
23.1.1.1.1;22.2.1 Background Issues;438
23.1.1.1.2;22.2.2 A Further Example;439
23.1.1.1.3;22.2.3 Some Reflections and Observations;440
23.1.1.1.4;22.2.4 Some Concluding Remarks;441
23.1.1.2;22.3 Connectivity: New Challenges for the Ideas of Webbing and Orchestrations;441
23.1.1.2.1;22.3.1 Introduction;441
23.1.1.2.2;22.3.2 Some Elements on the Experiment;443
23.1.1.2.3;22.3.3 Some Results;444
23.1.1.2.4;22.3.4 Questions to Be Considered in More Depth;446
23.1.1.2.5;22.3.5 Some More General Considerations;447
23.1.1.3;22.4 Concurrent Connectivity: Using Netlogo’s Hubnet Module to Enact Classroom Participatory Simulations;449
23.1.1.4;22.5 Designing for Exploiting Connectivity Across Classrooms;452
23.1.1.4.1;22.5.1 The Playground Project;452
23.1.1.4.2;22.5.2 The Weblabs Project;455
23.1.1.4.3;22.5.3 Concluding Remarks;457
23.1.2;References;457
24;Hoyles_Ch23.pdf;460
24.1;Chapter 23;460
24.1.1;The Future of Teaching and Learning Mathematics with Digital Technologies;460
24.1.1.1;23.1 Introduction;460
24.1.1.2;23.2 A Personal Journey with Digital Technologies;461
24.1.1.2.1;23.2.1 From Programming to Visualization and Experimentation: A First University Experience;461
24.1.1.2.2;23.2.2 Working with Low Achievers in Geometry with Logo Technology;462
24.1.1.2.3;23.2.3 The CAS Experience;463
24.1.1.2.4;23.2.4 From Microworlds and Open Software to Tutorial and on Line Resources;465
24.1.1.2.5;23.2.5 European Cooperation and Theoretical Connections;466
24.1.1.3;23.3 Towards a Vision: Some Crucial Directions;467
24.1.1.3.1;23.3.1 The Theoretical Perspective;467
24.1.1.3.2;23.3.2 The Teacher Perspective;468
24.1.1.3.3;23.3.3 The Institutional and Curricular Perspectives;469
24.1.1.3.4;23.3.4 Collaboration and Connectivity;470
24.1.1.3.5;23.3.5 Equity and Accessibility;470
24.1.1.4;23.4 Some Concluding Comments;471
24.1.2;References;471
25;Hoyles_Index.pdf;473
25.1;Hoyles_Author Index.pdf;473
25.2;Hoyles_Index.pdf;480