Investigating Mathematics Teaching: A Constructivist Enquiry

By Barbara Jaworski | Go to book overview

Chapter 6

Clare: Origins of the Teaching Triad

I met Clare opportunely. I was about to move into Phase 2 of my research, and knew that I wanted to study teachers who were established in working in an investigative way. Clare expressed interest in the research and invited me to observe in her classroom. She had been teaching for five years and was recognized in her school as being competent and successful. She was a pastoral team leader for a group of staff having care of a number of classes within the school. Her care for, and interest in, students’ social as well as academic well-being was apparent in her relations with students in mathematics lessons. I observed her, principally, teaching a mixed ability Year 10 class whose students she had taught in Year 9. Thus at the beginning of Year 10 she already knew them very well. Although I saw her teach other classes, and she talked to me about her teaching more widely, most of the episodes which I quote arose from the Year 10 class.

After very few lessons it became clear that Clare was an ideal subject for my second phase of research. The reasons for this judgment are bound up in the dilemma of characterizing an investigative approach without first defining what an investigative approach might involve. This case study is an account of my analysis of observations of Clare’s teaching over a year. Its purpose is to convey not only a sense of Clare’s teaching and her thinking about teaching, but also the complex issues involved in characterizing the teaching and justifying its investigative nature.


Background

My initial observations were directed at gaining a sense of Clare’s style and the wider context of her teaching. I tried to be as unobtrusive as possible in her lessons. I took only written field notes and did not try to use audiovisual equipment. I also did not attempt to initiate talk with students, although, when particular students showed an interest, I did not avoid conversations with them. These observations took place over the autumn term. During this time Clare and the class became used to my presence and a relaxed relationship developed which allowed me to suggest the use of recording equipment. Thus, in the spring term I recorded all lessons on either audio or video-tape or both. Towards the end of this term I also interviewed some of the students in the class. Throughout the observations I had long ‘conversations’ with Clare herself.

My data from these two terms of observation was extensive. It could be seen

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