1 Educating student teachers about values in mathematics education Alan J. Bishop Faculty of Education Monash University Melbourne Australia Educating student teachers about values in mathematics education Alan J. Bishop Faculty of Education Monash University Melbourne Australia

2 Mathematics educators are increasingly being 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. Therefore we need to think about what mathematical values teaching we are doing with our student teachers. Therefore we need to think about what mathematical values teaching we are doing with our student teachers.

3 Values are the deep affective qualities 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.

4 Whereas it is relatively easy and common in the 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. There is a widespread misunderstanding that 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.

5 What policy developers and others should be concerned about, however, is that values teaching and learning inevitably goes on in mathematics classrooms. This is because whenever teaching takes place, choices are made, which are based on, and therefore reveal, certain values. However there is only a limited understanding at present of what values are being transmitted, and of how effectively they are being transmitted. Perhaps this is because most values appear to be taught and learnt implicitly rather than explicitly in mathematics classrooms.

6 Therefore there are new research questions which can now be asked, such as: What values are teachers of mathematics teaching? What values are students learning from their teachers? Are they learning more significant values from their peers than from their teachers?

7 What values are implicitly and explicitly being transmitted or ‘shaped’ through curricula and textbooks? To what extent can teachers be helped to teach other values than those they currently teach? Is it possible to develop more effective mathematics teaching through the values education of student teachers?

8 Values in mathematics education are of three basic kinds: Mathematical values: values which have developed as the subject has developed within the particular culture. General educational values: values associated with the norms of the particular culture, of the particular society, and of the particular educational institution. Mathematics educational values: values embedded in the curriculum, textbooks, classroom practices, etc. as a result of the other sets of values.

9 My research approach to these issues has been to focus on mathematical values, and on the actions and choices concerning them – mathematical value competences I have used White’s (1959) three component analysis and terminology: Ideological values: ‘rationalism’ and ‘objectism’ Sentimental values: ‘control’ and ‘progress’ Sociological values: ‘openness’ and ‘mystery’.

10 Mathematical value competences - Ideological Valuing Rationalism means: Valuing Rationalism means: emphasising argument, reasoning, logical analysis, and explanations. emphasising argument, reasoning, logical analysis, and explanations. Valuing Objectism means: emphasising objectifying, concretising, symbolising, and applying the ideas of mathematics.

11 Mathematical value competences- Sentimental Valuing Control means: emphasising the power of mathematical and scientific knowledge through mastery of rules, facts, procedures and established criteria. Valuing Progress means: emphasising the ways that mathematical and scientific ideas grow and develop, through alternative theories, development of new methods and the questioning of existing ideas emphasising the ways that mathematical and scientific ideas grow and develop, through alternative theories, development of new methods and the questioning of existing ideas

12 Mathematical value competences- Sociological Valuing Openness means: emphasising the democratisation of knowledge, through demonstrations, proofs and individual explanations. emphasising the democratisation of knowledge, through demonstrations, proofs and individual explanations. Valuing Mystery means: emphasising the wonder, fascination, and mystique of mathematical ideas.

13 Developing mathematical value competences 1. Making the student teachers aware of values in mathematics education. Making the student teachers aware of values in mathematics education. Developing an understanding of the history of mathematics. Developing an understanding of the history of mathematics. Illustrating contrasts between different mathematical histories. Illustrating contrasts between different mathematical histories. Exploring cultural value differences via ethnomathematics. Exploring cultural value differences via ethnomathematics.

14 Developing mathematical value competences 2. Identifying mathematical values in school and university textbooks, school and university textbooks, writings about mathematics writings about mathematics mathematics examinations and tests mathematics examinations and tests science and engineering textbooks science and engineering textbooks

15 Developing mathematical value competences 3. Using the 6 value classification to: Create appropriate teaching materials for classroom use. Demonstrate and develop richer pedagogical repertoires. Develop more appropriate assessment instruments.

16 Some other points from our research Teachers’ values in the classroom are 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.

17 Some other points from our research If teachers wish to emphasise values other than those they currently emphasise, it is possible to learn strategies from their teaching of other subjects. The best time to develop mathematical value competences is during teacher training.