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The case of Brandon: the dual nature of key ideas in the classroom
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). (UMERC)
Arizona State University.
2009 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 14, no 2, 29-47 p.Article in journal (Refereed) Published
Abstract [en]

This paper looks at proof production in the midst of classroom interaction. The setting is a collegelevel geometry course in which students are working on the following task: Prove that two paralleltransported lines in the plane are parallel in the sense that they do not intersect. A proof of this statement istraced from a student's idea, through a small group discussion, to a large class discussion moderated by ateacher. As the proof emerges through a series of increasingly public settings we see ways in which the keyidea of the proof serves to both open and close class discussion. We look at several examples of openingand closing, showing how not only the key idea, but the warrants and justifications connected to it, play animportant role in the proof development.

Abstract [sv]

Artikeln beskriver en studie av hur bevis konstrueras i interaktion mellan elever. Under en geometrilektion på ett amerikanskt college arbetar eleverna med följande uppgift: Bevisa att två parallellförskjutna linjer i planet är parallella i meningen att de inte skär varandra. Formuleringen av beviset följs från en idé från en av eleverna, via diskussion i en mindre grupp till en lärarledd diskussion i helklass. Allteftersom beviset utvecklas genom en följd av diskussioner i allt större grupper finner vi olika sätt varpå bevisets "key idea" bidrar till att både öppna och sluta diskussionen. Vi beskriver flera exempel på öppnande och slutande, och visar hur inte bara nyckelidén, utan även de rättfärdiganden och motiveringar som är knutna till den, spelar en viktig roll i utvecklingen av beviset.

Place, publisher, year, edition, pages
2009. Vol. 14, no 2, 29-47 p.
Keyword [en]
Proof, Tertiary level, Case study
National Category
Educational Sciences Other Mathematics
Research subject
didactics of mathematics
URN: urn:nbn:se:umu:diva-46763OAI: diva2:440617
Available from: 2011-09-13 Created: 2011-09-13 Last updated: 2015-01-27Bibliographically approved

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Raman Sundström, Manya
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