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The effect of explanations on mathematical reasoning tasks
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). (Att lära matematik genom imitativa och kreativa resonemang)ORCID iD: 0000-0002-7594-5602
2017 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed) Epub ahead of print
Abstract [en]

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in follow up tests than students that are given a solution method and engage in algorithmic reasoning. However, teachers and textbooks, at least occasionally, provide explanations together with an algorithmic method, and this could possibly be more efficient than creative reasoning. In this study, three matched groups practiced with either creative, algorithmic, or explained algorithmic tasks. The main finding was that students that practiced with creative tasks did, outperform the students that practiced with explained algorithmic tasks in a post-test, despite a much lower practice score. The two groups that got a solution method presented, performed similarly in both practice and post-test, even though one group got an explanation to the given solution method. Additionally, there were some differences between the groups in which variables predicted the post-test score.

Place, publisher, year, edition, pages
Abingdon: Taylor & Francis, 2017.
Keyword [en]
Mathematical reasoning, explanations, problem-solving, productive struggle, algorithmic reasoning, creative reasoning
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-137297DOI: 10.1080/0020739X.2017.1340679OAI: oai:DiVA.org:umu-137297DiVA: diva2:1117683
Projects
Att lära matematik genom imitativa och kreativa resonemang
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2017-11-30

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Norqvist, Mathias
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Department of Mathematics and Mathematical StatisticsUmeå Mathematics Education Research Centre (UMERC)
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CiteExportLink to record
Permanent link

Direct link
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
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf