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One of the main goals of the Complex Mathematics Education Experiment set by Tamás Varga was the following: “That is, the knowledge we provide fits the closest developmental zone and developmental level of the children; and yet is mathematically correct and forward-thinking. We do not tell stork tales.” (Varga, 1974, p. 1984.) We give some examples from the topic of number theory, where we cannot avoid telling “stork tales”, no matter how hard we try. In section 1.3 we describe some of the sources of disturbance. In section 2 we deal with the conflict of the different interpretations of some concepts occurring in primary/secondary school and university education, such as: “divisibility”, “divisor”, “common divisor”, “greatest common divisor”, “division with remainder”, the perceived or real special properties of zero, and “prime number”. We believe that it is important to make prospective teachers aware what facts they hide and why when teaching. In section 3 we present problems that can be discussed with children of different ages and different abstraction levels. Classification: D70, E40, F60, U60. Keywords: misconceptions and student errors, concept formation, treatment of mathematical concepts and definitions in mathematics education, number theory, educational games. |
