Mathematical Enculturation

'Taking a refreshing noneurocentric position which refutes any suggestion that 'West is best' as regards the development of mathematical thinking, Bishop sees mathematical development as being a function of the needs of whatever society in which it arises.' Tony Brown (Manchester Polytechnic), in Mathematics Teaching 'This book is an informed, extremely rational and objective account of some aspects of enculturation and educational activity in the field of mathematics. I would recommend the book to all interested in mathematics education and curriculum design.' Kathryn Crawford (The University of Sydney), in Educational Studies in Mathematics 'What is unique about Bishop's account is his attempt to specify and describe a universal set of activities that have supported and shaped the development of mathematics throughout the world.' J. Stigler, in Journal for Research in Mathematics Education

• 1/Towards a Way of Knowing.- 1.1. The conflict.- 1.2. My task.- 1.3. Preliminary thoughts on Mathematics education and culture.- 1.4. Technique-oriented curriculum.- 1.5. Impersonal learning.- 1.6. Text teaching.- 1.7. False assumptions.- 1.8. Mathematical education, a social process.- 1.9. What is mathematical about a mathematical education?.- 1.10. Overview.- 2/Environmental Activities and Mathematical Culture.- 2.1. Perspectives from cross-cultural studies.- 2.2. The search for mathematical similarities.- 2.3. Counting.- 2.4. Locating.- 2.5. Measuring.- 2.6. Designing.- 2.7. Playing.- 2.8. Explaining.- 2.9. From ‘universals’ to ‘particulars’.- 2.10. Summary.- 3/The Values of Mathematical Culture.- 3.1. Values, ideals and theories of knowledge.- 3.2. Ideology — rationalism.- 3.3. Ideology — objectism.- 3.4. Sentiment — control.- 3.5. Sentiment — progress.- 3.6. Sociology — openness.- 3.7. Sociology — mystery.- 4/Mathematical Culture and the Child.- 4.1. Mathematical culture — symbolic technology and values.- 4.2. The culture of a people.- 4.3. The child in relation to the cultural group.- 4.4. Mathematical enculturation.- 5/Mathematical Enculturation — The Curriculum.- 5.1. The curriculum project.- 5.2. The cultural approach to the Mathematics curriculum — five principles.- 5.3. The three components of the enculturation curriculum.- 5.4. The symbolic component: concept-based.- 5.5. The societal component: project-based.- 5.6. The cultural component: investigation-based.- 5.7. Balance in this curriculum.- 5.8. Progress through this curriculum.- 6/Mathematical Enculturation — The Process.- 6.1. Conceptualising the enculturation process in action.- 6.2. An asymmetrical process.- 6.3. An intentional process.- 6.4. An ideational process.- 7/TheMathematical Enculturators.- 7.1. People are responsible for the process.- 7.2. The preparation of Mathematical enculturators — preliminary thoughts.- 7.3. The criteria for the selection of Mathematical enculturators.- 7.4. The principles of the education of Mathematical enculturators.- 7.5. Socialising the future enculturator into the Mathematics Education community.- Notes.- Index of Names.