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This paper is a historical investigation about the relationship between concept formation and problem development in mathematics. A survey of the history of infinite series reveals different roles of concepts for generating and solving problems. Further historical considerations lead to...
In this article two kinds of error analyses are presented: (1) Error analysis using tests to describe errors and (2) cognitive error analysis in which one investigates the cognitive processes underlying the errors by thinking aloud. This method is carefully scrutinized because (1) it cannot...
In this book we report on the results of our empirical research on the process of proving and the factors which influence it. As a foundation of this research, we first give a classified analysis of didactical literature on proof and of empirical approaches to the psychology of pupils’ proving.
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