Swedish high school students’understanding of functions

Abstract

 This thesis explores Swedish high school students’ learning experiences with the

concept of functions, focusing on the challenges they encounter and the role of

digital tools in deepening their understanding. Despite its central role in mathematics,

the concept of functions remains one of the most challenging topics for many

students. As a foundation for mathematical modelling, logical reasoning, and

problem-solving, addressing these learning difficulties is essential for long-term

mathematical development. With the growing integration of technology in education,

digital tools have become increasingly significant in mathematics instruction. This

thesis examines how such tools enhance conceptual understanding by analysing how

students use them to solve function-related tasks. It draws on four interconnected

papers that together provide a comprehensive perspective on students’ learning of

functions and the pedagogical effects of digital tool usage. Paper I presents a

qualitative analysis based on observations of two high school students solving

function problems. It identifies misconceptions and highlights how strong graphical

knowledge and visual reasoning reduce learning difficulties. Paper II is a quasi-

experimental comparison between students using a digital tool and those employing

traditional methods. Results show that students using digital tools performed

significantly better. Paper III investigates how students independently use a digital

tool when solving mathematical tasks, identifying four key strategies: using it as the

primary solving method, for verification, as a support tool, or variably depending on

the task. Paper IV examines the digital tool usage of teachers and students, as well as

their respective perspectives. It further explores teaching strategies, teachers’

perspectives on student usage, and the instructions students receive about digital

tools. Findings across the studies indicate that visualisation through digital tools

enhances conceptual understanding by providing dynamic, interactive learning

experiences. Students can autonomously use these tools in diverse ways, influencing

their learning outcomes and engagement. The research underscores the importance of

teacher facilitation in guiding meaningful tool use and offers practical insights for

integrating technology into mathematics education. Overall, this thesis contributes to

the growing field of technology-enhanced mathematics education and provides

recommendations for improving students’ understanding of functions through digital 

means. Collectively, the studies demonstrate that digital visualisation makes abstract

concepts more tangible, enables multiple solution pathways, and supports student

understanding. However, they also emphasise that the realisation of the potential of

digital tools depends on their use and on intentional pedagogical integration.

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