Swedish high school students’understanding of functions : The role of digital tools

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.