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Critical features of formal and informal reasoning in the case of the concept 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.
2011 (English)In: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education: Vol. 4: developing mathematical thinking / [ed] Ubuz, Behiye, 2011, 305-312 p.Conference paper, Published paper (Refereed)
Abstract [en]

Mathematical reasoning can be categorised into formal and informal ones on the basis of the type of used arguments. Both types of reasoning are needed in mathematics, but students usually tend to restrict their reasoning either to formal or informal mode only. Three examples collected and re-analysed from earlier studies reveal some critical features of this kind of restricted reasoning: A formal reasoning may easily become dependent on memory or authoritative references or it may become superficial imitation of algorithms. Informal reasoning, for one, may easily be based on intuitive conceptions, and its validity may be difficult to evaluate.

Place, publisher, year, edition, pages
2011. 305-312 p.
Series
PME Conference Proceedings, ISSN 0771-100X
Keyword [en]
argument, derivative, formal and informal reasoning, mathematical reasoning, visual reasoning
National Category
Didactics Mathematics
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-45679ISI: 000343399800039ISBN: 978-975-429-298-5 (print)OAI: oai:DiVA.org:umu-45679DiVA: diva2:433641
Conference
35th Annual Conference of the International-Group-for-the-Psychology-of-Mathematics-Education (PME), Ankara, Turkey, July 10-15, 2011
Available from: 2011-08-12 Created: 2011-08-10 Last updated: 2017-01-16Bibliographically approved

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Viholainen, Antti
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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