En modell som stöd för att utforska ekvationer

Charlotta Andersson; Jane Tuominen

doi:10.31129/LUMAT.10.1.1581

Authors

Charlotta Andersson Institutionen för ämnesdidaktik, Stockholms universitet, Sverige https://orcid.org/0000-0003-4383-0613
Jane Tuominen Institutionen för ämnesdidaktik, Stockholms universitet, Sverige https://orcid.org/0000-0003-2340-3374

DOI:

https://doi.org/10.31129/LUMAT.10.1.1581

Keywords:

lärandemodell, ekvation, del-helhetsstruktur, lärandeverksamhet, tematisk analys, learning model, equation, part-whole structure, learning activity, thematic analysis

Abstract

Syftet med artikeln är att lyfta fram om, och i sådant fall på vilka sätt, en specifik strukturell modell kan utgöra stöd när elever utforskar matematiska strukturer i ekvationer. Artikeln bygger på en empirisk forskningsstudie där elever utforskade matematiska strukturer med stöd av modellen, vilken är avsedd att visualisera strukturer. Lärare och forskare arbetade i en kollaborativ och intervenerande studie i iterativa processer. Sammantaget 149 elever från grundskolans årskurser 3, 8 och 9 deltog i filmade forskningslektioner utifrån forskningsansatsen learning study. Lektionerna designades med inspiration från ramverket lärandeverksamhet och eleverna utmanades i ett teoretiskt arbete. Analysen utfördes utifrån tematisk ansats och två kvalitativt skilda kärnteman identifierades: Formulär respektive Lärandemodell. I analysen framträdde att undervisningen behöver vara tillräckligt utmanande för att eleverna ska finna modellen meningsfull. Undervisningen behöver möjliggöra för eleverna att urskilja relationer mellan alla tal i en ekvation, där relationerna kan beskrivas som en del-helhetsstruktur.

A model to support exploring equations

The aim of the article is to highlight whether, and if so in what ways, a selected model can constitute support when students explore mathematical structures in equations. The article is based on an empirical research study where students explored mathematical structures with support by the model, which is intended to visualize structures. Teachers and researchers worked in a collaborative and interventional study in iterative processes. A total of 149 students from compulsory school grades 3, 8 and 9 participated in video recorded research lessons based on the research approach learning study. The lessons were designed with inspiration from the framework of learning activity and the students were challenged in a theoretical work. The analysis was performed on the basis of a thematic approach and two qualitatively different core themes were identified: Template respectively Learning model. In the analysis, it emerged that the teaching has to be challenging enough for the students to find the model meaningful. The teaching needs to enable students to discern relationships between all numbers in an equation, where the relationships can be described as a part-whole structure.

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