Jenny Fred’s Doctoral Thesis: The Wicked World of Algebra

What is your thesis mainly about?

– Algebra teaching in the early years of schooling is about helping students discover patterns, relationships, and structures—the foundations of algebraic thinking. In my thesis, I investigate how this type of teaching can be developed beyond the traditional tasks found in mathematics textbooks and connected to complex issues related to sustainability and other social and ecological challenges.

– Through the concept of Algebraic Wicked Problems, I explore how students in Years 1–3 can develop both mathematical reasoning and an understanding of issues that affect society. The thesis highlights that mathematics is not only a school subject but also a way of understanding and navigating a complex world.

What led you to focus on this particular topic?

– My interest in early algebra began during my licentiate research, where I explored what algebraic work can mean for students in the early years of schooling. When I later started my doctoral studies, I wanted to deepen that research and broaden the perspective on what algebra teaching can be.

– A significant shift came when I took a course in critical mathematics education. It made me reflect on how mathematical ideas can do more than help students identify patterns and relationships—they can also provide tools for understanding and reasoning about issues that affect their everyday lives and futures.

– This led to the idea of Algebraic Wicked Problems—a way of bringing together algebraic thinking and complex societal issues.

Can you tell us something about your findings?

– One of the key findings is that students as young as Years 1–3 can engage with complex societal issues while simultaneously developing their algebraic thinking. The study shows that younger students are more capable of reasoning about relationships, connections, and future consequences than is often assumed.

– Another important finding is that societal issues do not merely serve as a backdrop for mathematics. When integrated into teaching, they can actually deepen students’ reasoning about patterns, relationships, and change. The results therefore suggest that mathematical learning and engagement with societal issues can reinforce one another.

– As part of the study, I also developed the concept of Algebraic Wicked Problems itself and identified five pedagogical dimensions that can support teachers who wish to design similar forms of instruction.

What was the most enjoyable part of conducting your study?

– The most rewarding aspect was collaborating with student teachers, practicing teachers, and researchers to rethink what algebra teaching for younger students can be. It was exciting to explore ideas that do not yet have an established place in contemporary mathematics education.

– What was particularly interesting was how the collaboration evolved over time. Initially, many participants looked to me to provide direction, but gradually it became a shared and exploratory process in which everyone’s experiences and perspectives were valued. Many of the most interesting ideas emerged through these collective discussions.

What do you hope your thesis will contribute?

– I hope my thesis will contribute to a broader understanding of early algebra as something that belongs not only in the mathematics classroom but also in how we understand and relate to the world around us.

– I also hope it highlights the importance of critical engagement—the ability to understand, examine, and reflect on the models, patterns, and abstractions used to describe and address societal issues. In this way, mathematics education can contribute both to students’ subject knowledge and to their ability to participate actively and thoughtfully in society.

What are your plans going forward? Has your thesis influenced your future direction?

– Going forward, I would like to continue developing and exploring Algebraic Wicked Problems, preferably in close collaboration with teachers, student teachers, and fellow researchers. I also see opportunities to initiate new research projects that build on the questions raised by the thesis.

– The doctoral process has definitely influenced me. It has strengthened my conviction that algebra can be connected more closely to the issues and challenges students encounter in their everyday lives, and that this is an area with significant potential for both research and teaching.

– My ambition is therefore to continue developing and disseminating knowledge in this field, establish this line of research more firmly, and build on the international collaborations that the thesis has opened up.

Download and Read Jenny’s Thesis

The Wicked World of Algebra: Re-imagining the practices of teaching and learning early algebra in the socio-ecological