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Unformatted text preview: Educating student teachers about values Educating in mathematics education in Alan J. Bishop Alan Faculty of Education Faculty Monash University Melbourne Australia <[email protected]> 1 Mathematics educators are increasingly being Mathematics challenged about the goals to which mathematics education should aim: technology, societal demands, scientific development, economic growth…. To a large degree these goals are all about the values we should be inculcating in our students. we Therefore we need to think about what mathematical values teaching we are doing with our student teachers. values 2 Values are the deep affective qualities Values which education aims to foster through the teaching of mathematics. Values are not the same as beliefs, although the two constructs are related, and there is much research on beliefs in mathematics education but little on values. mathematics 3 Whereas it is relatively easy and common in the Whereas teaching of humanities, arts subjects and perhaps also the sciences to discuss the development of values, this is not the case at present in mathematics teaching. present There is a widespread misunderstanding that There mathematics is a value-free subject, and many policy developers (as well as some educators) might initially be concerned about explicit values education in mathematics. 4 What policy developers and others should be What concerned about, however, is that values teaching and learning inevitably goes on in mathematics classrooms. mathematics This is because whenever teaching takes place, This choices are made, which are based on, and therefore reveal, certain values. therefore However there is only a limited understanding at However present of what values are being transmitted, and of how effectively they are being transmitted. transmitted. Perhaps this is because most values appear to Perhaps be taught and learnt implicitly rather than explicitly in mathematics classrooms. 5 Therefore there are new research questions which Therefore can now be asked, such as: What values are teachers of mathematics teaching? teaching? What values are students learning from their What teachers? teachers? Are they learning more significant values from Are their peers than from their teachers? 6 What values are implicitly and explicitly being What transmitted or ‘shaped’ through curricula and textbooks? textbooks? To what extent can teachers be helped to teach To other values than those they currently teach? other Is it possible to develop more effective Is mathematics teaching through the values education of student teachers? 7 Values in mathematics education are of three basic kinds: Mathematical values: values which have developed as Mathematical the subject has developed within the particular culture. the General educational values: values associated with the General norms of the particular culture, of the particular society, and of the particular educational institution. and Mathematics educational values: values embedded in Mathematics the curriculum, textbooks, classroom practices, etc. as a result of the other sets of values. 8 My research approach to these issues has been to focus My on mathematical values, and on the actions and choices concerning them – mathematical value competences mathematical I have used White’s (1959) three component analysis and have terminology: terminology: Ideological values: ‘rationalism’ and ‘objectism’ Sentimental values: ‘control’ and ‘progress’ Sociological values: ‘openness’ and ‘mystery’. Sociological 9 Mathematical value competences Mathematical Ideological Ideological Valuing Rationalism means: Valuing emphasising argument, reasoning, logical analysis, and explanations. Valuing Objectism means: Valuing emphasising objectifying, concretising, emphasising symbolising, and applying the ideas of mathematics. mathematics. 10 Mathematical value competencesSentimental Valuing Control means: emphasising the power of mathematical and emphasising scientific knowledge through mastery of rules, facts, procedures and established criteria. Valuing Progress means: Valuing emphasising the ways that mathematical and scientific ideas grow and develop, through alternative theories, development of new methods and the questioning of existing ideas methods 11 Mathematical value competencesSociological Valuing Openness means: emphasising the democratisation of knowledge, through demonstrations, proofs and individual explanations. Valuing Mystery means: Valuing emphasising the wonder, fascination, and mystique of mathematical ideas. 12 Developing mathematical value Developing competences 1. competences • • • • Making the student teachers aware of Making values in mathematics education. Developing an understanding of the Developing history of mathematics. history Illustrating contrasts between different Illustrating mathematical histories. mathematical Exploring cultural value differences via Exploring ethnomathematics. ethnomathematics. 13 Developing mathematical value Developing competences 2. competences Identifying mathematical values in • school and university textbooks, • writings about mathematics • mathematics examinations and tests • science and engineering textbooks 14 Developing mathematical value Developing competences 3. competences Using the 6 value classification to: Create appropriate teaching materials for Create classroom use. classroom Demonstrate and develop richer Demonstrate pedagogical repertoires. pedagogical Develop more appropriate assessment Develop instruments. 15 Some other points from our Some research research Teachers’ values in the classroom are Teachers’ shaped to some extent by the values embedded in each subject. This implies that changing teachers’ values and understandings of the subject being taught may well change the values they can emphasise in class. 16 Some other points from our Some research research If teachers wish to emphasise values other If than those they currently emphasise, it is possible to learn strategies from their teaching of other subjects. teaching The best time to develop mathematical The value competences is during teacher training. training. 17 ...
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