Challenges to the preparation of teachers of mathematics

This article attempts a personal answer to the following two connected questions: "What are the most important problems in the preparation of mathematics teachers in view of the tasks, functions, and roles they have or ought to have in contemporary mathematics teaching?", and "What specific challenges to the preparation of teachers of mathematics do these problems generate?" These questions are posed as general ones with no particular reference to any specific country. The answers which this article offers to these questions are based on three "axioms" concerning the job of a mathematics teacher and on a characterisation of the qualities which the "ideal, but unfortunately Utopian, mathematics teacher" ought to possess. From this point of departure six major current problems in the preparation, roles and functioning of mathematics teachers are identified: (i) work- ing and living conditions; (ii) qualitative and quantitative recruitment; (Hi) pre- and in-service preparation and education; (iv) teachers' knowledge, beliefs and perceptions of mathematics; (v) teachers' knowledge, beliefs and perceptions of mathematics education and of the tasks, roles, and positions of mathematics teachers; (vi) professional development. These problems are discussed in some detail and the article concludes by suggesting points which deserve particular attention in efforts to develop and improve the education of mathematics teachers: knowledge and perceptions concerning mathematical content and processes (we are talking about teachers of MATHEMATICS, not just about teachers); the need for enthusiastic and committed TEACHERS rather than people who are somewhat knowledgeable in mathematics and happen to teach it; the need for frameworks and environments for continuing professional growth and development. This is a slightly revised manuscript of a plenary lecture given by the author at the ICMI-China Regional Conference on Mathematics Education, Shanghai, 16-20 August 1994.