Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability
The scientific nature of mathematics is extremely exact, detailed and abstract. However, holistic and concrete interpretations are very important in creative mathematical thinking. They are as well important in mathematical understanding, because mathematical knowledge presented in a formal form is...
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| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Jyväskylä
Univ.
2008
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| Schriftenreihe: | Report / University of Jyväskylä, Department of Mathematics and Statistics
115 |
| Schlagworte: | |
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| Zusammenfassung: | The scientific nature of mathematics is extremely exact, detailed and abstract. However, holistic and concrete interpretations are very important in creative mathematical thinking. They are as well important in mathematical understanding, because mathematical knowledge presented in a formal form is usually not very explanatory and thus does not underpin understanding. The classification of mathematical reasoning into informal and formal types used in this work is based on this dichotomy. The formal reasoning means exact reasoning based on axioms, definitions and previously proven theorems, as against the informal reasoning is based on visual or physical interpretations of mathematical concepts. This study examined informal and formal understanding of the concepts of derivative and differentiability and the use of informal and formal reasoning in problem solving situation where these concepts were needed. The subjects of the study were mathematics education students in the middle or in the final phase of their studies. The data are based on a written test given at six Finnish universities and on some oral interviews. The study showed that connecting informal and formal reasoning was often difficult for the students. |
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| Beschreibung: | Zsfassung in finn. und engl. Sprache. - Enth. 5 Veröff. des Verf. aus den Jahren 2006 - 08 |
| Beschreibung: | Getr. Zählung graph. Darst. |
| ISBN: | 9789513932770 |