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Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis
Örebro University, School of Science and Technology. (Matematikdidaktik)ORCID iD: 0000-0001-9530-4151
International Conference on Industrial Engineering and Engineering Management (IEEM), Technische Universität Dortmund, Dortmund, Germany.
Örebro University, School of Science and Technology. (Matematikdidaktik)
Freudenthal Institute, Utrecht University, Utrecht, Netherlands.
2017 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 29, no 4, p. 471-492Article in journal (Refereed) Published
Abstract [en]

Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these experiences. This article presents results from an empirical study investigating sixth-grade students’ reasoning and inferring from school-based and out-of-school experiences. In particular, it addresses the order relation, which deals with students’ very first encounters with negative numbers. Here, students can reason in different ways, depending on the experiences they draw on. We study how students reason before a lesson series and how their reasoning is influenced through this lesson series where the number line and the context debts-and-assets are predominant. For grasping the reasoning’s inferential and social nature and conducting in-depth analyses of two students’ reasoning, we use an epistemological framework that is based on the philosophical theory of inferentialism. The results illustrate how the students infer their reasoning from out-of-school and from school-based experiences both before and after the lesson series. They reveal interesting phenomena not previously analyzed in the research on the order relation for integers. 

Place, publisher, year, edition, pages
Springer, 2017. Vol. 29, no 4, p. 471-492
Keywords [en]
Negative numbers; Negative integers; Reasoning; Prior experiences; Contexts; Inferentialism
National Category
Didactics
Identifiers
URN: urn:nbn:se:oru:diva-60735DOI: 10.1007/s13394-017-0202-xISI: 000417402300006Scopus ID: 2-s2.0-85037051473OAI: oai:DiVA.org:oru-60735DiVA, id: diva2:1139965
Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2018-08-06Bibliographically approved

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Schindler, MaikeNilsson, Per

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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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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