Experienced and Novice Teachers ’ Choice of Examples

The decisions that teachers make in choosing particulars to illustrate the general are important aspects of their pedagogic role. Examples are used by teachers to exemplify concepts and to illustrate procedures. Worked examples frequently form the basis of a teacher’s explanation. This paper focuses on the examples used by experienced teachers and the justification they give for their choice to novice pre-service teachers. The relation “is an example of ” is fundamental to the discipline of mathematics. Its importance is reflected in popular understanding of both what it means to learn and to do school mathematics. Furthermore this learning is judged by our institutions largely on the basis of success in working examples under exam conditions. Examples are thus an everyday part of life for a mathematics teacher. A typical UK secondary school mathematics teacher will choose examples to introduce ideas to the class and for the class to work on independently of the teacher. Text books typically contain large numbers of worked examples and examples for students to attempt. The language of examples used in school is potentially ambiguous. We talk, sometimes interchangeably, of examples of a concept (examples of triangles, integers divisible by 3