Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice

There is broad acceptance that mathematics teachers’ beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary mathematics teachers, one experienced and the other relatively new to teaching, and considers their beliefs about the nature of mathematics, as a discipline and as a school subject. Possible origins and future developments of the structures of their belief systems are discussed along with implications of such structures for their practice. It is suggested that beliefs about mathematics can usefully be considered in terms of a matrix that accommodates the possibility of differing views of school mathematics and the discipline.