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Finnish mathematics teacher students' skills and tendencies to use informal and formal reasoning in the case of derivative
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Ajankohtaista matemaattisten aineiden opetuksen ja oppimisen tutkimuksessa (About the actual research in teaching and learning of mathematical subjects): Matematiikan ja luonnontieteiden opetuksen tutkimuspäivät Joensuussa 22.-23.10.2009 (Symposium of the Finnish Mathematics and Science Education Research Association, Joensuu, October 22-23, 2009) / [ed] M. Asikainen, P. Hirvonen & K. Sormunen, Joensuu: University of Eastern Finland , 2010, 87-102 p.Conference paper, Published paper (Refereed)
Abstract [en]

The arguments constructed in mathematical reasoning may be either formal or informal: They may be based either on definitions, axioms and previously proven theorems or on concrete interpretations of mathematical concepts and situations. In addition, arguments may be superficial or deep. Results shared in this paper are from three different studies in which both students’ skills to produce informal and formal arguments and their tendencies to choose between informal and formal reasoning in problem solving situations were studied. The students in all these studies were Finnish high school pre-service mathematics teachers, and the data was collected by using a written test and videotaped interviews. The tasks used were about the concept of derivative. Results of the studies indicated that the students’ skills to produce informal and formal arguments were dependent on each other. The difference between the levels of these skills was not significant, but several students had a tendency to avoid the use of the formal definition of derivative, which led to difficulties in problem solving situations. However, this tendency could not be explained by the students’ inadequate skills to handle the definition of derivative

Place, publisher, year, edition, pages
Joensuu: University of Eastern Finland , 2010. 87-102 p.
Series
Publications of the University of Eastern Finland: Reports and Studies in Education, Humanities and Theology, ISSN 1798-5641
Keyword [en]
argumentation, definition, derivative, informal and formal, mathematical reasoning, problem solving
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-38776ISBN: 978-952-61-0265-8 (print)OAI: oai:DiVA.org:umu-38776DiVA: diva2:381915
Conference
The Annual Symposium of the Finnish Mathematics and Science Education Research Association, Joensuu, October 22-23, 2009
Available from: 2011-01-03 Created: 2010-12-29 Last updated: 2011-01-05Bibliographically approved

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Viholainen, Antti
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CiteExportLink to record
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Citation style
  • apa
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Output format
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