The research on teacher education and beliefs suggests that it is necessary to help pre-service teachers acknowledge their beliefs and then to provide them with experiences to challenge them if their beliefs are counterproductive. Owens (1987) underscored the importance of getting to know the pre-service teachers' beliefs by acknowledging that
The constructs through which pre-service teachers view mathematics and mathematics teaching are important determinants of how
individuals interpret their undergraduate experiences and anticipate their teaching roles. These constructs are integral to the individuals' developing worldviews which perform an important function in structuring their roles as professionals. Knowledge of preservice teachers constructs and worldviews can provide teacher educators with understandings of how individuals perceive their undergraduate experiences, and should play a central role in the design and conduct of these programs (p. 169).
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Ball (1990a) recognising the importance of beliefs in the life of pre-service teachers, said ...I want to provide experiences that lead them to reconstruct what has come before as well as to direct the course of their future with the subject (p. 14).
To change pre-service teachers' beliefs about mathematics teaching and learning was not an easy task as demonstrated by the empirical evidence in the beliefs change literature.
Furthermore, which particular aspects of the beliefs merit attention? The literature (e.g. NCTM, 1989) was very clear that teacher education needs to address issues such as pre-service
teachers' views of mathematics and how they come to know. As Ball (1990a) wrote A course about the teaching and learning of mathematics is
necessarily about mathematics content as well as epistemological issues (Ball, p 14).
In what kind of mathematics should teacher education courses engage their pre-service teachers? There was a debate about whether teacher education courses should have their pre- service teachers learn more mathematics or learn the mathematics that they would eventually teach. Owens (1987) found that pre-service secondary mathematics teachers' study of higher mathematics, or what Freudenthal (cited in Cooney, 1988) described as "sterilized courses of further training in abstract mathematics" only contributed to the pre-service teachers'
conceptions of mathematics as "essentially an exercise in manipulating symbols" (p. 360).
Owens found that college mathematics did not expand the pre-service teachers' conceptions of mathematics but rather they introduced new ideas. I agree with Cooney (1988) who was not against the introduction of new mathematics in teacher education courses but questioned the
"practice of dichotomizing the study of advanced maths on the one hand and of general pedagogy on the other so as to limit the teachers' mathematical experiences only to those involving the study of wholesale new mathematical ideas" (p.360 original emphasis). Besides learning new mathematics Cooney (ibid.) emphasised that
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Teachers need experiences constructing the same mathematics they will be teaching (p. 355)
What seemed evident in the work of Ball, Cooney and Owens was that teacher education needed to
• provide pre-service teachers with experiences to help them be aware of their beliefs about mathematics, mathematics teaching and learning;
• provide them with experiences to challenge their beliefs about mathematics, teaching and learning if these beliefs were counterproductive to their practice;
• have pre-service teachers learn more mathematics to get new ideas about mathematics in a context that is not separate from pedagogical issues;
• learn relationally the concepts and the procedures of the mathematics they would eventually teach in schools, and finally
• address the issue of how learners come to know the mathematics they 'learned'.
The shift in teacher education suggested by the teacher education literature suggests that teachers and pre-service teachers are coming to be seen as thinking professionals. According to this perspective, rather than providing pre-service teachers with step-by-step recipes for teaching, it may be more effective to require them to generate the information to support their own informed decisions in the classroom. This view of teacher education suggests a change in how teacher educators and pre-service teachers view teacher education. It suggests a more humanistic view of teacher education where both teacher educators and pre-service teachers have more autonomy and authority over the process of learning to become mathematics teachers. This process of teacher education, as implied in the literature, suggests a heavy investment of time, human energy and commitment by both parties. I say this because it takes time to encourage pre-service teachers to return to their past and to understand how they
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formed their beliefs about mathematics, mathematics teaching and learning. Time is also needed to realise the implications of those beliefs in their professional and personal life. Time is again needed to engage pre-service teachers in new activities to help them change their beliefs (if necessary) and then for them to gain confidence to work with the alternative ways of teaching mathematics. Central to this process of teacher education is commitment on the part of the teacher educators to change. Nonetheless, it would be consistent with some of the practices that the KBSR expects in the primary classrooms of these future teachers.