Mathematical Enculturation

Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Its reputation is awe-inspiring. Everybody knows how important it is and everybody knows that they have to study it. But few people feel comfortable with it; so much so that it is socially quite acceptable in many countries to confess ignorance about it, to brag about one's incompe­ tence at doing it, and even to claim that one is mathophobic! So are teachers around the world being apparently legal sadists by inflicting mental pain on their charges? Or is it that their pupils are all masochists, enjoying the thrill of self-inflicted mental torture? More seriously, do we really know what the reasons are for the mathematical activity which goes on in schools? Do we really have confidence in our criteria for judging what's important and what isn't? Do we really know what we should be doing? These basic questions become even more important when considered in the context of two growing problem areas. The first is a concern felt in many countries about the direction which mathematics education should take in the face of the increasing presence of computers and calculator-related technol­ ogy in society.

Contenu

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.