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One could focus on many different aspects of improving the quality of mathematics teaching. For a better understanding of children’s mathematical learning processes or teaching and learning in general, reflection on and analysis of concrete classroom situations are of major importance. On the basis of experiences gained in a collaborative research project with elementary school teachers, several ideas about a professional reflection on one’s own instruction activities are explained. The paper focuses on joint reflection between teachers and researchers on the participating teacher’s own classroom interaction by means of concrete examples. It becomes clear that changes of one’s own interaction behavior will take place only in the long-term. Nevertheless such a joint professional reflection should be an essential component of teachers’ professional knowledge in a natural way. 相似文献
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Heinz Steinbring 《Educational Studies in Mathematics》2005,59(1-3):313-324
This is a commentary paper in the volume on “Teachings situations as object of research: empirical studies within theoretical
perspectives”. An essential object of mathematics education research is the analysis of interactive teaching and learning
processes in which mathematical knowledge is mediated and communicated. Such a research perspective on processes of mathematical interaction has to take care of the difficult relationship between mathematics education theory and everyday mathematics teaching practice.
In this regard, the paper tries to relate the development in mathematics education research within the theory of didactical situations to developments in interaction theory and in the epistemological analysis of mathematical communication. 相似文献
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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. 相似文献
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Heinz Steinbring 《Educational Studies in Mathematics》2006,61(1-2):133-162
Mathematical signs and symbols have a decisive role for coding, constructing and communicating mathematical knowledge. Nevertheless
these mathematical signs do not already contain mathematical meaning and conceptual ideas themselves. The contribution will
present basic elements of an epistemology of mathematical knowledge and then apply these theoretical ideas for analyzing case
studies of two teaching episodes from elementary mathematics teaching. In this way different roles of mathematical signs as
means of communication (oral function), of indicating (deictic function) and of writing (symbolic function) will be elaborated. 相似文献
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Heinz Steinbring 《Educational Studies in Mathematics》1991,22(6):503-522
The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deduced from more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on the concept of chance illustrates this conflict. The interaction between teacher and students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the concept of chance is conceived of as a concrete generalization, which takes chance as a fixed and universalised pattern of explanation instead of unfolding potential and variable conceptual relations of chance or randomness and developing the theoretical nature of this concept in an appropriate way for students' comprehension. 相似文献
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Educational Studies in Mathematics - 相似文献
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Heinz Steinbring 《Educational Studies in Mathematics》1997,32(1):49-92
In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during the course of ritualized formats of communication, such as the funnel pattern, and is replaced by social conventions. Problems of understanding occurring during the interactively organized elaboration of the new knowledge require an analysis of the interplay between the social constraints of the communicative process and the epistemological structure of the mathematical knowledge. Specific aspects of the problem of meaning development are investigated in the course of two exemplary second-grade teaching episodes. These are then used to develop and discuss decisive requirements for the maintenance of an interactive constitution of meaning for mathematical knowledge. 相似文献
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Elements of Epistemological Knowledge for Mathematics Teachers 总被引:1,自引:1,他引:0
Heinz Steinbring 《Journal of Mathematics Teacher Education》1998,1(2):157-189
Epistemological knowledge of mathematics in social learning settings is an important type of professional knowledge for mathematics
teachers because it refers to social and interactive processes of communication. This article focuses on one central aspect
of epistemological mathematical knowledge, namely on the problematique of how mathematical signs and symbols gain meaning
in the interactive social processes of teaching and learning. A teaching episode is presented and analyzed from an epistemological
perspective. This analysis leads to the identification of three important components of epistemological knowledge that could
be introduced into the education of mathematics teachers: the developmental nature of mathematical knowledge; interactive
social processes of mathematical communication as autonomous systems; and the interdependence of social and epistemological
constraints in mathematical communication.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献