NOMAD 14(2), 2009. The case of Brandon: the dual nature of key ideas in the classroom

Skapad: 2009-09-16. Ändrad: 2009-09-16  

NOMAD 14(2), 2009. The case of Brandon: the dual nature of key ideas in the classroom

The case of Brandon: the dual nature of key ideas in the classroom

MANYA RAMAN SUNDSTRÖM & MICHELLE ZANDIEH

Abstract

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

Sammanfattning

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.

MANYA RAMAN SUNDSTRÖM
Manya Sundström is Docent at Umeå University, and a member of Umeå Mathematics Education Research Centre. She comes to Sweden from the USA, where she worked as an Assistant Professor in mathematics and mathematics education at Rutgers University. Her main research area is mathematical proof.

MICHELLE ZANDIEH
Michelle Zandieh is an Associate Professor in mathematics and mathematics education at Arizona State University in the USA.  Her research focuses on student mathematical reasoning at the university level, especially the transitions students make from less formal to more formal ways of reasoning and how teachers may foster this transition.