Exploiting Mental Imagery with Computers in Mathematics Education

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
Front Matter....Pages 251-251
Exploiting Mental Imaging: Reflections of an Artist on a Mathematical Excursion....Pages 309-321
Back Matter....Pages 323-332