The field of geometrical optics features a broad knowledge base concerning conceptual learning difficulties and student conceptions. However, in contrast to other areas of physics, no widely used standard test instrument exists to assess middle school students' conceptual knowledge of geometrical optics. This is even more true for other areas of…

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux…

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…

Students should learn mathematics with understanding. This is one of the ideas in the literature on mathematics education that everyone supports, from educational politicians to curriculum developers, from researchers to teachers, and from parents to students. In order to decide whether or not students understand mathematics we should first…