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Mathematical Enculturation


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Table of Contents

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.- 5.2.1. Representativeness.- 5.2.2. Formality.- 5.2.3. Accessibility.- 5.2.4. Explanatory power.- 5.2.5. Broad and elementary.- 5.3. The three components of the enculturation curriculum.- 5.4. The symbolic component: concept-based.- 5.4.1. Counting.- 5.4.2. Locating.- 5.4.3. Measuring.- 5.4.4. Designing.- 5.4.5. Playing.- 5.4.6. Explaining.- 5.4.7. Concepts through activities.- 5.4.8. Connections between concepts.- 5.5. The societal component: project-based.- 5.5.1. Society in the past.- 5.5.2. Society at present.- 5.5.3. Society in the future.- 5.6. The cultural component: investigation-based.- 5.6.1. Investigations in mathematical culture.- 5.6.2. Investigations in Mathematical culture.- 5.6.3. Investigations and values.- 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.- 6.1.1. What should it involve?.- 6.1.2. Towards a humanistic conception of the process.- 6.2. An asymmetrical process.- 6.2.1. The role of power and influence.- 6.2.2. Legitimate use of power.- 6.2.3. Constructive and collaborative engagement.- 6.2.4. Facilitative influence.- 6.2.5. Metaknowledge and the teacher.- 6.3. An intentional process.- 6.3.1. The choice of activities.- 6.3.2. The concept-environment.- 6.3.3. The project-environment.- 6.3.4. The investigation-environment.- 6.4. An ideational process.- 6.4.1. Social construction of meanings.- 6.4.2. Sharing and contrasting Mathematical ideas.- 6.4.3. The shaping of explanations.- 6.4.4. Explaining and values.- 7/The Mathematical 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.- 7.3.1. Ability to personify Mathematical culture.- 7.3.2. Commitment to the Mathematical enculturation process.- 7.3.3. Ability to communicate Mathematical ideas and values.- 7.3.4. Acceptance of accountability to the Mathematical culture.- 7.3.5. Summary of criteria.- 7.4. The principles of the education of Mathematical enculturators.- 7.4.1. Mathematics as a cultural phenomenon.- 7.4.2. The values of Mathematical culture.- 7.4.3. The symbolic technology of Mathematics.- 7.4.4. The technical level of Mathematical culture.- 7.4.5. The meta-concept of Mathematical enculturation.- 7.4.6. Summary of principles.- 7.5. Socialising the future enculturator into the Mathematics Education community.- 7.5.1. The developing Mathematics Education community.- 7.5.2. The critical Mathematics Education community.- Notes.- Index of Names.


`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

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