Theorizing the interactive nature of teaching mathematics: contributing to develop contributions as a metaphor for teaching
Abstract
The teachers’ role in teacher-student interaction in mathematics has received increased attention in recent years. One metaphor used to describe teaching in teacher-student interaction is to describe teaching as a learning process itself, in terms of learning to develop learning. The aim of the present study is to contribute to the conceptualization and understanding of this view of teaching mathematics. This is done by introducing and elaborating on a new conceptual framework, describing teaching as Contributing to Develop Contributions (CDC). The CDC framework is constructed by combining the theory of symbolic interactionism with a complementing metaphor for learning; learning as contribution. The CDC-framework is illustrated in the context of experimentation-based, interactive teaching of probability. The analysis shows how the CDC-framework helps in coming to understand how teachers develop their own contributions to manipulate the negotiation of meaning of mathematics in the classroom and thereby also develops the students’ contributions. In the presented case we can see how CDC particularly helps in giving account of how a teacher develops her way of using symbols and indications and adjust her own interpretations during a whole class discussion where the teacher and students interpret the empirical results of a random generator. In addition, the analysis also illustrates how the framework draws our attention to how a teacher can contribute to the negation of meaning, and so, to students’ opportunities to learn, by making her own interpretations and ways of ascribing meaning to objects transparent to the students in the interaction.
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