Download 144 problems of the Austrian-Polish Mathematics Competition, by Kuczma M.E. (ed.) PDF

By Kuczma M.E. (ed.)

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INTRODUCTION The breadth of research in mathematics education has expanded relatively rapidly. From one area of specialization within psychometrics in the 1950s, it has grown into a field of inquiry that draws eclectically on the theories and methodologies of a broad span of science, social science and the humanities. As this field of inquiry has become more diffuse, both its rationale and its scope of potential utility have become less clear, both for educational practitioners and for those potential customers who fund the activity; in particular, those in central or local government or educational charities.

A theory for 'realistic mathematics education'. That is why we speak of theoryguided bricolage. At the beginning of the innovation of mathematics education in The Netherlands, this theory was more a global philosophy of mathematics education than a theory. Gradually. however. a domain-specific instructional 280 KOENO GRA VEMEIJER theory evolved. This theory serves as a guide not only for the construction of the provisional design, but also for the further elaboration of the course which is executed in an iterative process of experimentation and adaptation.

Luckily, however, there is considerable evidence that there are many features in common to the different 'countries' inhabited by different pupils and teachers. The act of identifying common features in different groups of individuals and using these to describe a number of 'ideal types' is a form of psychological modeling akin to mathematical modeling. In each case, the model presents a general way of thinking about the behavior of specifics (objects or people). This act of identifying common features means that other more idiosyncratic features have been ignored.

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