Peter Pereira

Becoming a Teacher of Mathematics.

For many years I have engaged future mathematics teachers in activities that focus on emotional dimensions of their learning. Even those teachers who were able to reconstruct themselves as learners of mathematics had difficulties with changing their practice. Through a series of autobiographical stories, I examine my own experiences as a teacher and a learner. These stories—one from a computer class, one from a workshop for elementary teachers, one from college, and one from eighth grade—serve as data from which I draw themes that capture the tensions that I experience as I teach. Sharing these tensions with mathematics teachers has had an impact on the way the teachers talk about their teaching and promises to change how they teach. The paper is written to encourage teacher educators to adopt the practice of sharing teaching and learning stories with their students.

Deliberation and the Arts of Perception.

† An earlier version of this paper was presented at the annual meeting of the American Educational Research Association in Montreal in April 1983 as part of a Division B symposium, ‘What to do about curriculum deliberation’.

What counts in mathematics education

The chapter argues for the value of self-study of teaching and teacher education practices that is focused on a particular disciplinary domain. In this case the domain is mathematics education. We argue that teaching and learning mathematics has unique characteristics, challenges and joys. Self-study of teaching maths helps to identify, articulate and reframe those characteristics and the assumptions underlying them. We discuss the increasing emphasis in maths education on communication, problem solving, reflection and making connections with other concepts and areas, and consider the views and status of maths education existing in different countries. The study of maths suffers from low uptake at the higher levels and static teaching in secondary schools. At the same time primary school teachers often feel anxious about their competence in maths and this anxiety transfers to their students. For this reason, it is essential to disrupt practices and initiate new ones in teacher education programs. Self-study of teaching and teacher education supports this process.

Limits of Perception: What Teacher Trainees See and Don't See in Classrooms

Most teacher-education programs require students to spend time observing in schools. There are good reasons for this. Observation can reacquaint a student with the realities of classroom life, foster the development of the skills and techniques of classroom management, and help to generate an understanding of the ways in which classrooms, and schools, function. In the first case, the classroom is intended to serve as an environment where the trainee can remind himself of what it felt like to be in a classroom. In the second case, a particular classroom is intended to serve as an example for the prospective teacher to follow or avoid. In the third case, the classroom is intended to serve as a laboratory, where the prospective teacher can develop, test, and perfect concepts and principles for analyzing classroom events. Whatever outcome for observation is primarily intended by a teacher-education program, it is harder to achieve than might at first appear. What a person sees (or fails to see), when he observes

Reconstructing Teachers of Mathematics

Reform pedagogy in mathematics requires teachers to reconstruct themselves as learners of mathematics at the same time as they reconstruct themselves as teachers of mathematics. Using data from a middle school geometry course for practicing teachers, I identify difficulties encountered as I tried to help teachers learn mathematics in a new way. Teachers have strong emotions—including their fears of failure, of exposure, and of inadequacy—and their frustration with learning can end up disempowering them. They have strong beliefs about what mathematics is and some well-entrenched habits for teaching it. In particular, they often feel that reform methods will require them to give up control, a feeling that, though inaccurate, is widespread and powerful. As a result, any curriculum designed to reacquaint teachers with who they are as learners and teachers of mathematics will inevitably expand beyond the intellectual aims of the objective content to include emotions inherent in the teaching and learning process. Because this is also true for me, I examine dilemmas and tensions I experienced when teachers did not meet my expectations. I conclude by arguing that what transfers most powerfully from my classroom to theirs is the emotional experience of learning.

Adding Value to Self and Content in Mathematics Education: Working in a Third Space

The chapter discusses the complexities that are an inevitable part of mathematics teaching, introduces the concept of ‘third space’ as a way of thinking about these complexities, shows how the chapters in the book can be located within a third space, and explores ways in which the metaphor of a third space can be used to gain insight and raise questions. The chapter concludes with an appeal to readers to try their own discipline-based self-studies as a way to rejuvenate their own practices.