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Publications (4 of 4) Show all publications
Andersson, C. & Tuominen, J. (2022). En modell som stöd för att utforska ekvationer: [A model to support exploring equations]. LUMAT: International Journal on Math, Science and Technology Education, 10(1), 182-209
Open this publication in new window or tab >>En modell som stöd för att utforska ekvationer: [A model to support exploring equations]
2022 (Swedish)In: LUMAT: International Journal on Math, Science and Technology Education, E-ISSN 2323-7112, Vol. 10, no 1, p. 182-209Article in journal (Refereed) Published
Abstract [sv]

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.

Abstract [en]

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.

Keywords
learning model, equation, part-whole structure, learning activity, thematic analysis, lärandemodell, ekvation, del-helhetsstruktur, lärandeverksamhet, tematisk analys
National Category
Educational Sciences
Research subject
Didactic Science for Teachers and Teaching Professions; Didactics
Identifiers
urn:nbn:se:su:diva-207120 (URN)10.31129/LUMAT.10.1.1581 (DOI)2-s2.0-85140719544 (Scopus ID)
Available from: 2022-07-06 Created: 2022-07-06 Last updated: 2023-09-12Bibliographically approved
Tuominen, J., Andersson, C. & Björklund Boistrup, L. (2020). Critical aspects of equations when explored as a part-whole structure. In: Yvonne Liljekvist, Lisa Björklund Boistrup, Johan Häggström, Linda Mattsson, Oduor Olande, Hanna Palmér (Ed.), Sustainable mathematics education in a digitalized world: Proceedings of MADIF 12 The twelfth research seminar oft he Swedish Society for Research in Mathematics Education Växjö, January 14–15, 2020. Paper presented at The twelfth research seminar oft he Swedish Society for Research in Mathematics Education (MADIF 12), Växjö, Sweden, 14-15 January, 2020 (pp. 223-233). Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF
Open this publication in new window or tab >>Critical aspects of equations when explored as a part-whole structure
2020 (English)In: Sustainable mathematics education in a digitalized world: Proceedings of MADIF 12 The twelfth research seminar oft he Swedish Society for Research in Mathematics Education Växjö, January 14–15, 2020 / [ed] Yvonne Liljekvist, Lisa Björklund Boistrup, Johan Häggström, Linda Mattsson, Oduor Olande, Hanna Palmér, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2020, p. 223-233Conference paper, Published paper (Refereed)
Abstract [en]

The aim of this paper is to present critical aspects that were identified when students explored equations as a part-whole structure with negative numbers included. Students in grades 3, 8 and 9 participated in a ”theoretical work”. Learning study was used as a research approach and learning activity theory constituted a guiding principle when designing research lessons. According to the analysis, five critical aspects were identified, regardless of grade. The critical aspects are: there is a relationship between all the numbers in an equation; two parts together equals a whole with the same value; what constitutes the parts and the whole, respectively; the same relationship can be formulated in four different ways; the whole can assume a lower value than the parts.

Place, publisher, year, edition, pages
Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2020
Series
Skrifter från Svensk Förening för MatematikDidaktisk Forskning, ISSN 1651-3274 ; 15
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-207121 (URN)978-91-984024-4-5 (ISBN)
Conference
The twelfth research seminar oft he Swedish Society for Research in Mathematics Education (MADIF 12), Växjö, Sweden, 14-15 January, 2020
Available from: 2022-07-06 Created: 2022-07-06 Last updated: 2022-12-14Bibliographically approved
Andersson, C., Andrén, S., Eriksson, H. & Tuominen, J. (2020). Skapa behov av multiplikation. Nämnaren : tidskrift för matematikundervisning (4), 11-15
Open this publication in new window or tab >>Skapa behov av multiplikation
2020 (Swedish)In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 4, p. 11-15Article in journal (Other (popular science, discussion, etc.)) Published
Abstract [sv]

Kan multiplikation förstås på något annat sätt än som upprepad addition? Här prövar författarna ett nytt sätt att undervisa om multiplikation. Genom att atbeta med indirekt mätning skapas ett behov av multiplikation.

National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-187440 (URN)
Available from: 2020-12-10 Created: 2020-12-10 Last updated: 2022-02-25Bibliographically approved
Tuominen, J., Andersson, C., Björklund Boistrup, L. & Eriksson, I. (2018). Relate before calculate: Students’ ways of experiencing relationships between quantities. Didactica Mathematicae, 40, 5-33
Open this publication in new window or tab >>Relate before calculate: Students’ ways of experiencing relationships between quantities
2018 (English)In: Didactica Mathematicae, ISSN 0208-8916, Vol. 40, p. 5-33Article in journal (Refereed) Published
Abstract [en]

The aim of this article is to contribute with findings concerning students’ ways of experiencing general mathematical structures and, in particular, relationships in additive structures.When students discern relationships in additive structures, it may lead to positive consequences for students’ future ability to perform calculations in addition and subtraction tasks. In the study, semi-structured interviews were conducted with students in grades 3, 8, and 9. An illustration showing a set of different quantities was the starting point during the interviews, together with an opening question regarding how the diverse quantities could be equalised. After the students’ discussions, they were asked if this could be described mathematically using written symbols. The students’ expressions concerning the phenomenon “relationships between quantities” were analyzed using phenomenography as an analytical tool. According to phenomenography, there are a limited number of ways in which a phenomenon can be experienced. Further, it is not about exploring how many individuals hold a specific experience that is of interest. In the case of this article, it is about capturing qualitatively different ways of experiencing the phenomenon relationships between quantities. Despite no specific numbers being presented, many students attributed specific numbers and values when expressing relationships between quantities. The students expressed general mathematical structures only to a limited extent and, in those cases, mostly only after encouragement from the interviewer. Following the phenomenographical analysis, the students’ ways of experiencing “relationships between quantities” are: as something that has to be calculated, or as something that has to be related. The first of these was most common in all grades. In this study, one critical aspect was identified, namely, that quantities are related to each other, additively. Instead of introducing mathematics with a focus on answer-oriented tasks, it is essential to introduce mathematics based on general structures such as additive structures. Even if the students are not familiar with such a mathematical “culture”, it is worth it. This was confirmed in our study.

Keywords
general mathematical structures, relationships, part-whole, additive structures, quantities, phenomenography, ways of experiencing, critical aspect
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-163382 (URN)10.14708/dm.v40i0.6431 (DOI)
Funder
Swedish Research Council
Available from: 2018-12-29 Created: 2018-12-29 Last updated: 2022-11-29Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-2340-3374

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