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Matematik som teoretiskt arbete - utveckling av matematiska modeller för rationella tal i åk 4
Stockholm University, Faculty of Humanities, Department of Humanities and Social Sciences Education.ORCID iD: 0000-0003-0764-5728
2016 (Swedish)In: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 4, no 1, p. 6-24Article in journal (Refereed) Published
Abstract [en]

The teaching of rational numbers to young students (grade 4-6) is known to be difficult. It is for instance difficult for students to understand that fractions and decimal numbers may represent the same value, or that fraction has a specific place on the number line, i.e. that it is a number among other numbers. The purpose of this article is to discuss and exemplify how students can be involved in a theoretical exploration of fractions as numbers. The basis of the students’ exploration was a designed situation where they were to make measurements of wooden rods where the measurements did not make an equal, i.e. “a little bit” was missing. With these measurements students in joint discussions were able to design a general model for fractions. Such a model could be used as a tool in discussions of “the whole” and “its parts” in fractions. The article is based on data from a series of Learning studies conducted in a grade 4 in an intercultural school in 2012-2013.

Abstract [sv]

Undervisning om rationella tal på mellanstadiet är ett erkänt svårt område. Eleverna har till exempel svårt att förstå att tal i bråkform och decimaltal kan representera samma värde eller att tal i bråkform har en bestämd plats på tallinjen, det vill säga att de är tal. I den här artikeln diskuteras och exemplifieras hur elever kan engageras i ett teoretiskt utforskande av tal i blandad form. Grunden för elevernas utforskande bestod i situationer där eleverna fick göra jämförelser av trästavar som inte gick jämt upp - det saknades ”en liten bit”. Utifrån dessa jämförelser kunde eleverna i gemensamma diskussioner skapa en generell modell för tal i blandad form, det vill säga en modell som också kunde beskriva mätningar som inte gick jämnt upp. Analysen visar bland annat att arbetet med modellen gjorde det möjligt för eleverna att diskutera heltalsdelar i förhållande till bråkdelar i tal i blandad form. Artikeln bygger på data från en serie Learning studies som genomfördes i en årskurs 4 på en interkulturell skola under 2012 – 2013.

Place, publisher, year, edition, pages
2016. Vol. 4, no 1, p. 6-24
Keywords [en]
Davydov’s mathematical program, rational numbers, learning activity, mathematical models
Keywords [sv]
rationella tal, matematiska modeller, lärandeverksamhet/Learning activity, Davydovs matematiska program
National Category
Didactics
Research subject
Didactics
Identifiers
URN: urn:nbn:se:su:diva-137152OAI: oai:DiVA.org:su-137152DiVA, id: diva2:1060517
Available from: 2016-12-28 Created: 2016-12-28 Last updated: 2017-09-01Bibliographically approved

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