The main objective in this paper is on learning more about younger students’ emergence of the ability to express and justify pattern generalization algebraically, particularly in relation to what aspects students need to discern to be able to express and justify pattern generalization algebraically. This forms a point of departure for discussing the meaning of making algebraic generalizations in the early grades. The findings constitute a foundation for a project on classroom teaching and learning in mathematics, carried out as a collaboration between researchers and teachers.

L'objectif principal dans ce document est d'apprendre plus sur les façons d'expérimenter la généralisation des schémas par les élèves plus jeunes et ce à propos de quels aspects les étudiants doivent discerner pour pouvoir exprimer et justifier les généralisations de formes algébriquement. Ceci comme un point de départ dans les discussions concernant la signification de faire des généralisations algébriques dans les premières années. Les résultats constituent une base pour un projet de développement de cours en collaboration entre chercheurs et enseignants.

Artikelns syfte är att beskriva och analysera vad i olika lektionssekvenser som skapar förutsättningar för att elever ska engageras i ett algebraiskt arbete och därmed urskiljer kritiska aspekter. Artikeln bygger på data från tre forskningslektioner i vilka lärandeverksamhet (learning activity) tillsammans med Radfords arbete om mönster-generaliseringar har utgjort teoretiska utgångspunkter. I analysen har didaktiska principer från lärandeverksamhet samt kritiska aspekter gällande att uttrycka och argumentera för mönstergeneraliseringar fungerat som analysredskap. Resultatet kan bidra till att fördjupa förståelsen gällande på vilka sätt principerna från lärandeverksamhet kan stödja ett etablerande och upprätthållande av ett algebraiskt arbete och därmed möjliggöra för elevers urskiljande av kritiska aspekter.

The aim of the article is to describe and analyze what in different lesson sequences that creates the conditions for students to be involved in algebraic work and thereby distinguish critical aspects. The article is based on data from three research lessons in which Learning activity together with Radford’s work on pattern generalizations were theoretical starting points. In the analysis, didactic principles of Learning activity along with a few identified critical aspects regarding the ability to express and justify algebraic generalizations served as analytical tools. The result can contribute to deepened understanding of the ways the principles can support the establishment and maintenance of algebraic work enabling students to distinguish critical aspects.

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. 

This paper aims to discuss an advance in the direction of bridging the gap between early school algebra and socially relevant issues using the idea of wicked problems. We do so by focusing on the possibilities and challenges of working with the idea of algebraic wicked in the context of planning, teaching, and reflecting on algebra lessons for young children of 7-9 years old. This endeavor is a collaboration between the researcher/teacher educator, teacher students and in-service teachers following the critical research methodology of imagining and trying to create something that does not yet exist. This paper represents partly how far we have come to formulate an algebraic wicked problem that can invite students to engage into a cultural and sociological algebraic activity and as such reports on what we have learned from trying to design and enact algebraic wicked problems.

Early algebraic thinking can be connected in significant ways to sustainability issues through algebraic wicked problems (AWP). AWP are problems that mobilize children to think algebraically while experiencing dilemmas on values at stake in sustainability. Both algebraic thinking and sustainability issues become inseparably connected. From an ongoing analysis of 10 research group meetings over a school year in a group consisting of teachers, pre-service teachers, and researchers, and based on observed lessons, we explore such dilemmas as a central characteristic of AWP. This provides details into what may be important aspects in the further design of AWPs.

This paper is an invitation to imagine new futures for mathematics education in the context of earlyalgebraic thinking in the socio-ecological. The issue at hand is to re-imagine the concerns of why,what and how to teach central areas of the school mathematics curriculum. In this paper, the researchrevolves around Jenny Fred’s current PhD work, in which a research team consisting of in-serviceteachers, pre-service teachers, teacher educators and researchers have been working on the idea ofwhat we call algebraic wicked problems (AWP) to simultaneously integrate early algebra and thesocio-ecological into students’ work (Fred et al., 2024b). We highlight five pedagogical features ofAWPs and the research team’s work in constituting a critical work zone integrating early algebraand the socio-ecological. We conclude the paper with ideas to further theorize the possibilities ofintegrating early algebra and the socio-ecological in significant ways.