Exploiting Mental Imagery with Computers in Mathematics EducationRosamund Sutherland, John Mason Springer Science & Business Media, 1995 - 326 ページ 1. Emphasizing the External.- Imagery for diagrams.- External representations in arithmetic problem solving.- Visualisation in mathematics and graphical mediators: an experience with 11-12 year old pupils.- Visual organisers for formal mathematics.- Mediating mathematical action.- Mathematical objects, representations, and imagery.- 2. Imagery in Support of Geometry.- Images and concepts in geometrical reasoning.- Between drawing and figure.- The functions of visualisation in learning geometry.- Geometrical pictures: kinds of representation and specific processings.- 3. Linking Screen and Mental Imagery.- Overcoming physicality and the external present: cybernetic manipulatives.- On visual and symbolic representations.- The dark side of the Moon.- Ruminations about dynamic imagery (and a strong plea for research).- On designing screen images to generate mental images.- Learning as embodied action.- 4. Employing Imagery.- The importance of mental perception when creating research pictures.- Random images on mental images.- Imagery as a tool to assist the teaching of algebra.- Mathematical screen metaphors.- Exploiting mental imaging: reflections of an artist on a mathematical excursion. |
目次
Imagery for diagrams | 3 |
External representations in arithmetic problem solving | 20 |
an experience with 1112 year old pupils | 34 |
Visual organisers for formal mathematics | 52 |
Mediating mathematical action | 71 |
Mathematical objects representations and imagery | 82 |
Imagery in Support of Geometry | 95 |
Images and concepts in geometrical reasoning | 97 |
On visual and symbolic representations | 178 |
The dark side of the Moon | 190 |
Ruminations about dynamic imagery and a strong plea for research | 202 |
On designing screen images to generate mental images | 225 |
Learning as embodied action | 233 |
Employing Imagery | 251 |
The importance of mental perception when creating research pictures | 252 |
Random images on mental images | 263 |
Between drawing and figure | 117 |
The functions of visualisation in learning geometry | 125 |
kinds of representation and specific processings | 142 |
Linking Screen and Mental Imagery | 159 |
cybernetic manipulatives | 161 |
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多く使われている語句
abstract abstract objects accretion disc actions activity algebraic analysis arithmetic arrow schemes aspects black hole Cabri Cabri geometry Cabri-géomètre circle cognitive cognitive science complex concepts construction counting cube Descartes diagrams didactic discussion domain drawing dynamic Edited environment example experience experimental expression external representations film formal function geometrical figure graph graphical heuristic hypotenuse ideas image schemata imagine important interaction interpreted inverse inverse problems involved language learners manipulation mathematical discourse mathematical objects mathematics education meaning mental imagery mental images mental models metaphor metonymies movement NATO natural numbers notation notion operative apprehension particular perception physical plane possible problem solving properties pupils rational numbers reasoning recursive relationships represented result Right Strophoid role sense sequence situation sketch Sketchpad spatial sprite strategies structure SuperPaint symbolic teacher Technology theorem thinking triangle understanding visual imagery visual images visualisations