The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers |
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| Authors: | Pessia Tsamir |
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| Institution: | (1) School of Education, Tel Aviv University, 69978 Tel Aviv, Israel;(2) Mathematics Education, Kibbutzim Teachers College, 62507 Tel Aviv, Israel |
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| Abstract: | Research in mathematics education indicates that in the transition from given systems to wider ones prospective teachers tend to attribute all the properties that hold for the former also to the latter. In particular, it has been found that, in the context of Cantorian Set Theory, prospective teachers have been found to erroneously attribute properties of finite sets to infinite ones — using different methods to compare the number of elements in infinite sets. These methods which are acceptable for finite sets, lead to contradictions with infinite ones. This paper describes a course in Cantorian Set Theory that relates to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. The findings clearly indicate that when comparing the number of elements in infinite sets the prospective teachers who took the course were more successful and were also more consistent in their use of a single method than those who studied the traditional, formally-based Cantorian Set Theory course.This revised version was published online in September 2005 with corrections to the Cover Date. |
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