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Algorithmic contexts and learning potentiality: A case study of students' understanding of calculus
University of Skövde, School of Life Sciences.
(English)Manuscript (Other academic)
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:his:diva-2756OAI: oai:DiVA.org:his-2756DiVA: diva2:173973
Available from: 2009-02-18 Created: 2009-02-18 Last updated: 2010-01-14
In thesis
1. Algoritmiska, intuitiva och formella aspekter av matematiken i dynamiskt samspel: en studie av hur studenter nyttjar sina begreppsuppfattningar inom matematisk analys
Open this publication in new window or tab >>Algoritmiska, intuitiva och formella aspekter av matematiken i dynamiskt samspel: en studie av hur studenter nyttjar sina begreppsuppfattningar inom matematisk analys
2008 (Swedish)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Focusing on the potentiality of students’ ways of treating a mathematicalmaterial this thesis aims to investigate how students use their conceptualunderstanding when working with mathematical tasks in calculus. Two casestudies were carried out to explore students’ understanding of thresholdconcepts. The first study, an interview study, explored engineering students’understanding of limit and integral. The second study, a problem solvingstudy, involved students within a mathematics programme, working on achallenging task including the concepts function and derivative, requiringproof by induction. Drawing on a theory of contextualisation data wereanalysed within a constructivist research framework following the principlesof intentional analysis. The results reveal that the students in themathematics programme expressed their understanding in a formal contextin which also intuitive ideas played an important role. They used intuitiveideas and formal reasoning in a dynamic interplay with several functions:to control intuitive ideas, to offer a new basis of reasoning, to reduce thecomplexity of the problem and to push the problem solving process forward.The engineering students expressed their conceptions in an algorithmiccontext, in which procedural knowledge was predominant and the operationsof the concepts were seen as defining features and a basis for understanding.However, faced with probing questions, the students appeared to shift to acontextualisation foregrounding ideas relating to conceptual dimensions ofcalculus. These contextual shifts display the transformative aspect ofthreshold concepts allowing the development of conceptions and students’awareness of ways of thinking and practising in mathematics.

Place, publisher, year, edition, pages
Göteborg University, 2008. 88 p.
Series
Doktorsavhandlingar vid Chalmers tekniska högskola, ISSN 0346-718X
Keyword
Algorithmic context, Calculus, Conceptual understanding, Contextualisation, Higher education, Intentional analysis, Learning potentiality, Procedural knowledge
National Category
Didactics
Research subject
Humanities and Social sciences
Identifiers
urn:nbn:se:his:diva-2758 (URN)978-91-628-7379-0 (ISBN)
Public defence
(English)
Available from: 2009-04-03 Created: 2009-02-18 Last updated: 2010-04-15Bibliographically approved

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Citation style
  • apa
  • harvard1
  • 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
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  • asciidoc
  • rtf