Learning from Computers: Mathematics Education and Technology

1. Microworlds/Schoolworlds: The Transformation of an Innovation.- 1.1 The story of microworlds.- 1.2 The genesis.- 1.3 From designers to mathematics educators.- 1.4 Generating mathematics through microworlds: some illustrations.- 1.5 Evocative computational objects and situated abstractions.- 1.6 Microworlds in school mathematics.- 1.7 Microworlds in the curriculum.- 1.8 Reflections and implications.- 2. Computer Algebra Systems as Cognitive Technologies: Implication for the Practice of Mathematics Education.- 2.1 CAS: Some examples of symbol manipulations.- 2.2 Computers and computer algebras in relation to pure mathematics.- 2.3 Computer Algebra Systems in relation to mathematics education.- 2.4 Opposition to instructional uses of Computer Algebra Systems.- 2.5 Strengths of Computer Algebra Systems as learning tools.- 2.6 Computer algebra in an educational context: One example.- 2.7 CAS: From amplifiers to reorganisers.- 3. The Computer as Part of the Learning Environment: The Case of Geometry.- 3.1 The dual nature of geometrical figures.- 3.2 Difficulties of students.- 3.3 The notion of geometric figure as mediated by the computer.- 3.4 Changes brought by computers to the relationship to the figure.- 3.5 Interactions between student and software.- 4. Software Tools and Mathematics Education: The Case of Statistics.- 4.1 Didactical transposition and software tools.- 4.2 The revolution in statistics.- 4.3 Graphical and interactive data analysis: an example.- 4.4 Making sense of statistical software tools.- 4.5 Statistics education.- 4.6 Statistics and a re-defined school mathematics.- 5. Didactic Design of Computer-based Learning Environments.- 5.1 Understanding mathematics and the use of computers.- 5.2 Designing QuadFun - A case description.- 5.3 Interlude: Experimental aspects of mathematics.- 5.4 Design issues.- 5.5 A systemic view of didactic design.- 6. Artificial Intelligence and Real Teaching.- 6.1 Didactical interaction revisited.- 6.2 The input of artificial intelligence.- 6.3 Student-computer interaction, an overview.- 6.4 Educational software in the classroom, a new complexity.- 6.5 Open questions for future practice.- 7. Computer Use and Views of the Mind.- 7.1 The notion of cognition.- 7.2 Cognitive reorganization by using tools.- 7.3 Cognitive models and concreteness of thinking.- 7.4 Situated thinking and distributed cognition.- 7.5 The computer as a medium for prototypes.- 7.6 Modularity of thought.- 7.7 Conclusion.- 8. Technology and the Rationalisation of Teaching.- 8.1 The rationalisation of social practice.- 8.2 The elusive rationality of teaching.- 8.3 The marginal impact of machines on teaching.- 8.4 The dynamics of pedagogical change.- 8.5 The programming microworld.- 8.6 The tutoring system.- 8.7 The computer and the rationalisation of teaching.- 9. Computers and Curriculum Change in Mathematics.- 9.1 Locating the curriculum.- 9.2 Curriculum change as institutional change.- 9.3 Redefining school mathematics.- 9.4 Planning curriculum change.- 9.5 Alternative scenarios.- 10. On Determining New Goals for Mathematical Education.- 10.1 Goals for mathematics education.- 10.2 Goals for mathematics learners.- 10.3 Role of the teacher and the educational institution.- 10.4 Needed research on goals in mathematics education.- 11. Beyond the Tunnel Vision: Analysing the Relationship Between Mathematics, Society and Technology.- 11.1 Setting the stage.- 11.2 Technology in society.- 11.3 Mathematics shaping society?.- 11.4 Living (together) with abstractions.- 11.5 Mathematical technology as social structures.- 11.6 Structural problems in an abstraction society.- 11.7 Mathematics education as a social enterprise.- 11.8 Mathematics education as a democratic forum.- 11.9 Reflecting on computers in the classroom: Hardware-software-be(a)ware.- 12. Towards a Social Theory of Mathematical Knowledge.- 12.1 The Mechanistic Age - a historical introduction.- 12.2 Mathematical and social individuation.- 12.3 How can we master technology?.- 12.4 Engineers versus mathematicians since the turn of the century.- References.- Software.