Ebook: Exploiting Mental Imagery with Computers in Mathematics Education

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

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The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

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The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-2
Imagery for Diagrams....Pages 3-19
External Representations in Arithmetic Problem Solving....Pages 20-33
Visualization in Mathematics and Graphical Mediators: An Experience with 11-12 Year Old Pupils....Pages 34-51
Visual Organisers for Formal Mathematics....Pages 52-70
Mediating Mathematical Action....Pages 71-81
Mathematical Objects, Representations, and Imagery....Pages 82-94
Front Matter....Pages 95-96
Images and Concepts in Geometrical Reasoning....Pages 97-116
Between Drawing and Figure....Pages 117-124
The Functions of Visualisation in Learning Geometry....Pages 125-141
Geometrical Pictures: Kinds of Representation and Specific Processings....Pages 142-157
Front Matter....Pages 159-160
Overcoming Physicality and the Eternal Present: Cybernetic Manipulatives....Pages 161-177
On Visual and Symbolic Representations....Pages 178-189
The Dark Side of the Moon....Pages 190-201
Ruminations About Dynamic Imagery (and a Strong Plea for Research)....Pages 202-224
On Designing Screen Images to Generate Mental Images....Pages 225-232
Learning as Embodied Action....Pages 233-249
Front Matter....Pages 251-251
The Importance of Mental Perception when Creating Research Pictures....Pages 252-262
Random Images on Mental Images....Pages 263-276
Imagery as a Tool to Assist the Teaching of Algebra....Pages 277-290
Mathematical Screen Metaphors....Pages 291-308
Back Matter....Pages 323-332
Exploiting Mental Imaging: Reflections of an Artist on a Mathematical Excursion....Pages 309-321

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The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-2
Imagery for Diagrams....Pages 3-19
External Representations in Arithmetic Problem Solving....Pages 20-33
Visualization in Mathematics and Graphical Mediators: An Experience with 11-12 Year Old Pupils....Pages 34-51
Visual Organisers for Formal Mathematics....Pages 52-70
Mediating Mathematical Action....Pages 71-81
Mathematical Objects, Representations, and Imagery....Pages 82-94
Front Matter....Pages 95-96
Images and Concepts in Geometrical Reasoning....Pages 97-116
Between Drawing and Figure....Pages 117-124
The Functions of Visualisation in Learning Geometry....Pages 125-141
Geometrical Pictures: Kinds of Representation and Specific Processings....Pages 142-157
Front Matter....Pages 159-160
Overcoming Physicality and the Eternal Present: Cybernetic Manipulatives....Pages 161-177
On Visual and Symbolic Representations....Pages 178-189
The Dark Side of the Moon....Pages 190-201
Ruminations About Dynamic Imagery (and a Strong Plea for Research)....Pages 202-224
On Designing Screen Images to Generate Mental Images....Pages 225-232
Learning as Embodied Action....Pages 233-249
Front Matter....Pages 251-251
The Importance of Mental Perception when Creating Research Pictures....Pages 252-262
Random Images on Mental Images....Pages 263-276
Imagery as a Tool to Assist the Teaching of Algebra....Pages 277-290
Mathematical Screen Metaphors....Pages 291-308
Back Matter....Pages 323-332
Exploiting Mental Imaging: Reflections of an Artist on a Mathematical Excursion....Pages 309-321
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