Judith Mousley

Mathematics teacher education and technology

Various applications of electronic technology have contributed to the field of mathematics teacher education, but the array of tools now available to teacher educators in developed countries can be somewhat daunting. In this chapter, the authors present an overview of some of these tools and the ways that they are being used. In addition, they address issues surrounding the development and applications of digital technology in teacher education programs in a number of countries. In particular, they present recent applications of videotapes, multimedia resources, internet-based communities, and tutorial conferencing facilities in pre-service and in-service education of mathematics teachers. As professionals who have used technology in teacher education, the authors blend their own insights into this review of technological tools and relevant issues.

Mathematics education and genre: Dare we make the process writing mistake again?

Abstract The process writing movement in language education has informed current moves towards process methods in mathematics pedagogy. This has led to limited expectations of narrative recounts in students’ writing about mathematics. An examination of primary and secondary mathematics classes and commonly‐used textbooks shows that genre expectations are both limited and limiting. Given that mathematics is text, and that mathematicians need to operate competently within a number of different genres, it is argued that teachers should broaden the scope of task specification so that a wider range of mathematical genres is experienced in classrooms. This paper examines a number of mathematical genres that are accessible to students.

Caution: Classroom under observation

In this article, it is argued that there are serious difficulties in observing someone else teach for the purpose of providing evaluation or corrective feedback on their teaching. The article reports on responses from a group of teacher educators who watched a videotaped classroom lesson. Their written critiques were surprisingly contradictory, so much so as to call into question the reliability of lesson critiques. It is suggested that, where observation and critique of classroom teaching are used, summative judgements be avoided, and that a major goal of observations be to stimulate debate about different teaching styles and individual and cooperative reflection. Most importantly, observers must acknowledge the variety of intentions and perspectives of classroom teachers.

Knowledge Construction: Individual or Social?

For many years, battles raged between those who saw knowledge as perception of a given reality and those who saw it as being constructed through rational activity. More recently, epistemological debates have focused on that activity being essentially individual or social. Initially, the International Group for the Psychology of Mathematics Education (PME) was heavily influenced by the idea that mathematical knowledge is constructed by individuals, and particularly by von Glasersfeld’s “radical” constructivism. The social constructivist thesis that mathematics is a social construction challenged this dominant notion, but Steve Lerman critiqued the “shared consciousness” interpretation of social constructivism and articulated the sociocultural idea of the centrality of social interactions. His influence led a strong turn to the social, with a focus on intersubjectivity in mathematical knowledge and mathematics learning. Steve not only challenged individual people’s ideas but also drew PME into a position where sociocultural and other poststructural theories are in regular use.

Using a Model for Planning and Teaching Lessons as Part of Mathematics Teacher Education

This chapter describes a task for prospective teachers in which they use a particular planning and teaching model as a way of coming to understand the challenges and opportunities in non-routine tasks, and in particular considering the steps that are necessary in converting the tasks into learning opportunities. A particular focus of the planning and teaching model is the way that it addresses the needs of low achieving students, and especially those who may be disadvantaged due to social circumstances. The planning and teaching model involves using content specific open-ended tasks; planning a hypothetical trajectory of tasks; making the relevant pedagogies explicit; ensuring there is sufficient shared experience to allow meaningful discussions and review; and, developing enabling prompts to support students experiencing difficulty as well as extending prompts to engage students who complete the set work. Each of these elements can form the content of teacher education programs for prospective and practising mathematics teachers.