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The paper deals with the problem of changing mathematics teaching within the framework of teachers’ beliefs. Firstly, the concept of belief is discussed briefly, e.g. distinctions between knowledge and beliefs are explained. Also, the central role of beliefs for teaching mathematics is...
The starting-point for research on “mathematical world views” („mathematische Weltbilder”) is the thesis that these “mathematical world views” play a central and significant rôle in the individual learning and doing of mathematics.
My reflections about the research on women and mathematics have led me to the thesis that this research is in a paradigmatic state, although there have been empirical and theoretical analyses not being in accordance with the paradigm in some respect. To a large extent the research is based on a...
When introducing negative numbers mathematics teaching is confronted with the following developmental problem: the students interpret natural numbers within the frame of concrete, empirical conditions of counting, adding and taking away etc. Negative numbers are no longer immediately applicable...
The paper relates to one of the topics raised in [RE], the issue of tests in teacher training. The nature of common tests and their negative impact on the quality of learning is discussed. It is recommended to include in tests questions which enforce students to experience higher thought levels...
Three variants of constructivist learning theory for mathematics are contrasted. These are information processing, radical, and social constructivism. Each position is sketched, and the underlying metaphors of mind and models of the world (with their links to epistemology and ontology) are...
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