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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Jyväskylä
Univ.
2008
|
| Schriftenreihe: | Report / University of Jyväskylä, Department of Mathematics and Statistics
115 |
| Schlagworte: | |
| 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. |
| Beschreibung: | Zsfassung in finn. und engl. Sprache. - Enth. 5 Veröff. des Verf. aus den Jahren 2006 - 08 |
| Beschreibung: | Getr. Zählung graph. Darst. |
| ISBN: | 9789513932770 |
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| 245 | 1 | 0 | |a Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability |c Antti Viholainen |
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| 520 | 3 | |a 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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| spelling | Viholainen, Antti Verfasser aut Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability Antti Viholainen Jyväskylä Univ. 2008 Getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Report / University of Jyväskylä, Department of Mathematics and Statistics 115 Zsfassung in finn. und engl. Sprache. - Enth. 5 Veröff. des Verf. aus den Jahren 2006 - 08 Jyväskylä, Univ., Diss., 2008 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. Mathematik Calculus Study and teaching Concept learning Mathematics Study and teaching Reasoning Differentiation Mathematik (DE-588)4149787-9 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)4113937-9 Hochschulschrift gnd-content Mathematikunterricht (DE-588)4037949-8 s Differentiation Mathematik (DE-588)4149787-9 s DE-604 University of Jyväskylä, Department of Mathematics and Statistics Report 115 (DE-604)BV016506109 115 |
| spellingShingle | Viholainen, Antti Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability Mathematik Calculus Study and teaching Concept learning Mathematics Study and teaching Reasoning Differentiation Mathematik (DE-588)4149787-9 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4149787-9 (DE-588)4037949-8 (DE-588)4143413-4 (DE-588)4113937-9 |
| title | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability |
| title_auth | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability |
| title_exact_search | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability |
| title_full | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability Antti Viholainen |
| title_fullStr | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability Antti Viholainen |
| title_full_unstemmed | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability Antti Viholainen |
| title_short | Prospective mathematics teachers' informal and formal reasoning about the concepts of derivative and differentiability |
| title_sort | prospective mathematics teachers informal and formal reasoning about the concepts of derivative and differentiability |
| topic | Mathematik Calculus Study and teaching Concept learning Mathematics Study and teaching Reasoning Differentiation Mathematik (DE-588)4149787-9 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathematik Calculus Study and teaching Concept learning Mathematics Study and teaching Reasoning Differentiation Mathematik Mathematikunterricht Aufsatzsammlung Hochschulschrift |
| volume_link | (DE-604)BV016506109 |
| work_keys_str_mv | AT viholainenantti prospectivemathematicsteachersinformalandformalreasoningabouttheconceptsofderivativeanddifferentiability |