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Powerful algebraic ideas: Early algebraic thinking andactive citizenship
Stockholm University, Faculty of Humanities, Department of Teaching and Learning.ORCID iD: 0000-0002-0252-7223
Stockholm University, Faculty of Humanities, Department of Teaching and Learning.ORCID iD: 0000-0002-5736-7562
Stockholm University, Faculty of Humanities, Department of Teaching and Learning.ORCID iD: 0000-0003-1975-7778
2022 (English)In: Proceedings from the 12th Congress of the European Society for Research in Mathematics Education (CERME12), 2022Conference paper, Published paper (Refereed)
Abstract [en]

How can powerful algebraic ideas be understood for the combined purpose of developing students’ emergent algebraic thinking and fostering future active citizens? To address this question, we have examined two major research review books on early algebra to investigate the interpretations of “powerful algebraic ideas” that are present in the books as a whole. Skovsmose and Valero’s (2008) four interpretations of powerful mathematical ideas (which focus on the logical, psychological, cultural, and sociological power of mathematics) were used. We show that in the books and book chapters there is a dominance of the logical and psychological interpretations of the power ofalgebraic. Furthermore, the cultural and sociological interpretations appear connected to algebraic thinking as a resource or tool for action in “society”. Advancing new possibilities of expanding the ways in which early algebraic thinking is made powerful for students is a challenge to research. 

Place, publisher, year, edition, pages
2022.
Keywords [en]
Early algebra, algebraic thinking, powerful algebraic ideas, socio-political perspective
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-207894OAI: oai:DiVA.org:su-207894DiVA, id: diva2:1687551
Conference
Twelfth Congress of the European Society for Research in MathematicsEducation (CERME12),Bozen-Bolzano, Italy, February 2022
Available from: 2022-08-16 Created: 2022-08-16 Last updated: 2026-04-16Bibliographically approved
In thesis
1. The Wicked World of Algebra: Re-imagining the practices of teaching and learning early algebra in the socio-ecological
Open this publication in new window or tab >>The Wicked World of Algebra: Re-imagining the practices of teaching and learning early algebra in the socio-ecological
2026 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis reimagines the teaching and learning of early algebra for students in grades K-3 in light of current socio-ecological crises. While early algebra has primarily been justified as preparation for later mathematical studies, I argue that algebraic thinking is also a key component of critical citizenship: it can help young students recognize, question, and act on the relationships, models, and values that shape their life-worlds.

The overarching aim is to examine how to create conditions that enable students in the early grades to participate in algebraic activity, first focusing on algebraic development and then expanding to citizenship within a socio-ecological context. Across three phases of work, the thesis brings together Learning Activity Theory (LAT) and Critical Mathematics Education (CME) and uses them in complementary ways. This theoretical combination broadens prevailing definitions of algebraic activity and reveals its educational possibilities.

Part 1 (my licentiate thesis) explores aspects of teaching that create conditions for students in grades K–3 to engage in algebraic work. Part 2 critically examines influential overview literature in early algebra to analyze which “powerful algebraic ideas” are foregrounded, revealing a predominance of logical and psychological framings and a relative scarcity of cultural and sociological framings connected to citizenship. Part 3 explores critical problem situations for early algebra within the socio-ecological. In this third part, a research team consisting of in-service teachers, pre-service teachers, teacher educators, and researchers has been developing the concept of Algebraic Wicked Problems (AWPs) to integrate early algebra and the socio-ecological into students’ work.

The main contribution of this thesis is a conceptualization of AWPs as five interrelated features. Another contribution highlights the powerful complementarity between LAT and CME. These results suggest directions for curricula and pedagogy that position early algebra as both a form of mathematical development and preparation for critical citizenship in uncertain socio-ecological times.

Place, publisher, year, edition, pages
Stockholm: Department of Teaching and Learning, Stockholm University, 2026. p. 179
Keywords
algebraic wicked problems, early algebra, critical mathematics education, learning activity theory, socio-ecological
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-254253 (URN)978-91-8107-622-6 (ISBN)978-91-8107-623-3 (ISBN)
Public defence
2026-06-05, Hörsal 9, hus D, Universitetsvägen 10 D and online via Zoom, public link is available at the department website, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2026-05-11 Created: 2026-04-16 Last updated: 2026-05-28Bibliographically approved

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Fred, JennyValero, PaolaVan Steenbrugge, Hendrik

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