ABSTRACT
Several themes will be explored in this chapter relevant to principles of a constructivist epistemology as it might be applied in mathematics teacher education. I take up the issues of understanding the nature of the mathematics teacher against the context of traditional mathematics instruction, the relation between learning and control, and the exhausting effect of the ‘classroom press’. The implications of shifting control over one’s learning from the teacher, to the students and teacher together, is discussed. The role of language in communications about mathematics is addressed with reference to the idea of a consensual domain, or culture of the classroom. The necessity to make explicit how language serves the learning process, and the need for opportunities to clarify meanings for terms, is illustrated by examples from teacher education classes I have taught recently. The significance of the unexpected response in communicating with students is discussed, highlighting the need for teachers to become engaged in ongoing networks of mathematics practice. Teachers need to be active mathematically. The importance of a program component which emphasizes the mathematical activity of teachers and opportunities to broaden and deepen personal networks of mathematical concepts is underlined. Finally, I return to the issue of classroom culture, and suggest that beginning teachers will be influenced positively by role models who are actively seeking better to understand their own practice. I propose a special experimental laboratory that would serve as a half-way house between the university campus and the school classroom where the education of mathematics teachers could be focused.
