Interactive development of subject matter in the mathematics classroom |
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| Authors: | Rainer Bromme Heinz Steinbring |
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| Institution: | (1) Institut für Didaktik der Mathematik IDM, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Deutschland |
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| Abstract: | There are considerable differences among mathematics teachers with regard to the quatlity of their way of developing mathematical knowledge in the classroom. Such differences are analysed. To develop mathematical meaning requires both a consistent presentation of the mathematical symbols and of the referential meaning of these symbols with respect to the given task. On the basis of this conception we assume that the quality of teaching will differ according to how teachers cope with the relation between these two sides of meaning. From a sample of 26 teachers, an  expert teacher and a non-expert teacher were selected by means of classroom observation with scales of instructional quality variables. For each of these two teachers, two lessons introducing probability (sixth grade) are analysed. For this purpose, teacher and student contributions are coded. For the expert teacher, graphic visualizations of the development of mathematical concepts across time show soft transitions between the different aspects of mathematical meaning. These transitions are made possible by a consistent explication of the relation between formal symbols and the given mathematical task. In the case of the other teacher, explication of the relationship between the object side and the symbol side of mathematical meaning is much rarer, and there are sudden switches from one aspect of meaning to another. Further differences concern the handling of student contributions.We gratefully acknowledge the help of Wolfgang Barz, Regina Dietrich and Claudia Krüger with recording, transcribing or coding lessons. For their comments on draft versions of the paper the authors thank Deborah Ball, Jere Brophy, Willibald Dörfler, Alexander Gruza and two anonymous reviewers. |
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