Windows on Mathematical Meanings

"Noss and Hoyles take on the field of Mathematics Education as a whole to develop a coherent theoretical framework that will encompass its psychological, social, pedagogical and epistemological dimensions. Their pages abound with socratic flies to torment anyone who claims to understand concepts like abstract, concrete, formal, common-sensical and even mathematics, without the context of an elaborated theory. At the same time they present the most elaborated theoretical discussion to date of how the computer presence might contribute to the development of the field." Seymour Papert, Massachusetts Institute of Technology 'I would say that the book is very readable, and contains a number of interesting details as well as the construction of a theory. It is one important step in developing a theoretical framework for the use of technology in mathematics education.' Nordic Studies in Mathematical Education, 3 (1997)

• 1. Visions of the mathematical.- 1. Reshaping mathematics, revisioning learning.- 2. Computers.- 3. …and cultures.- 4. Windows on methodologies.- 2. Laying the Foundations.- 1. Introduction.- 2. Meanings in mathematics education: a brief survey.- 3. Vignette: The N-task.- 4. The influence of setting on mathematical behaviour.- 5. Street mathematics.- 6. A way out of the cul-de-sac?.- 7. Rethinking abstraction.- 3. Tools and technologies.- 1. Computers and educational cultures.- 2. A preliminary case for programming.- 3. The development of a programming culture.- 4. Micro worlds: the genesis of the idea.- 5. Opening windows on microworlds.- 6. Objects and structures.- 4. RatioWorld.- 1. What do we — and learners — know?.- 2. Building an alternative methodology.- 3. The data set.- 4. The microworld activities and student responses.- 5. Quantitative windows on learning.- 6. Reflections.- 5. Webs and situated abstractions.- 1. Reviewing the foundations.- 2. Webs of meaning.- 3. Domains of situated abstraction.- 6. Beyond the individual learner.- 1. Extending the web.- 2. Collaborative activity in mathematics.- 3. A study of groupwork.- 4. Opening new windows.- 7. Cultures and change.- 1. Innovation and inertia.- 2. Visions of Logo.- 3. Myths and methodologies: a case study of Logo research.- 4. The struggle for meanings.- 8. A window on teachers.- 1. Investigating teachers’ attitudes and interactions.- 2. Teachers making meanings.- 3. Connections and cultures.- 9. A window on schools.- 1. The background to the case study.- 2. The teachers’ voices.- 3. The students’ voices.- 4. Meanings in conflict.- 10. Re-visioning mathematical meanings.- 1. Reviewing the scene.- 2. Epistemological revisions: six examples.- 3. Reconnecting mathematics and culture.- References.