Abstract:

Research has long acknowledged the centrality of the use of examples in the teaching and learning of mathematics at primary and secondary level. This research has shown that the type of examples that are used by the teacher in teaching mathematical concepts can either constrain or enable learners’ access to mathematical knowledge. As Goldenberg and Mason (2008) argue, learners develop meaning through the use of examples that illustrates particular concepts or principles in mathematics.

Unlike teaching in schools, there are multidimensional layers involved in teacher education especially when preparing multilingual pre-service teachers who would, themselves teach mathematics to multilingual learners at the end of their qualifications.

The teacher educator is at once:
1) teaching for learning of mathematics content
2) teaching for teaching of mathematics
3) teaching for teaching of mathematics in multilingual contexts
4) teaching for learning of mathematical practices
5) teaching for the development of proficiency in the language of teaching and learning.

Even though exemplifying as a practice in mathematics has been well researched, there is a dearth of research into the use of examples in pre-service teacher education and how this can support or impede the pre-service teachers’ development of the multiple layers of teacher education. In my research involving four teacher education classrooms, I investigated the question: How do teacher educators use examples in mathematics classrooms, and for what purpose? In answering this question, I also engage with what opportunities the examples used by the four teacher educators open up for the development of the multidimensional layers of teacher education.

In order to address the questions which this research sought to explore, a qualitative study approach was adopted. The wider study for this research consisted of a sample of four universities in a province in South Africa. For the study reported in this paper, four teacher educators teaching in four different classrooms were selected from two of these universities. The four teacher educators who were selected from these universities were video-recorded while teaching a mathematics concept from start to finish. Both teacher educators and pre-service teacher educators’ voices were part of the classroom observation because both teaching and learning were in focus in the study.

Using the anthropological perspective of situativity as a lens, preliminary findings reveal that teacher educators use examples only for the purpose of developing the pre-service teachers as learners of mathematics content and as teachers of mathematics. The mathematical process of exemplifying (what makes a good example in particular topic areas, etc) was backgrounded. In other words, exemplifying was generally used by the teacher educators to explain procedure for solving mathematical problems in the same way definitions were used to explain procedures. Since the pre-service teachers’ attention was not drawn to the importance of the choices of examples when working with their future learners, it can be argued that exemplifying as a practice was solely anchored in making the pre-service teachers more knowledgeable in the mathematics content at hand. Recommendations will be made for teacher development.

Keywords:

Teacher education, exemplification, situative perspective.