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…

Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic…

The combination of modern computing power, the interactivity of web applications, and the flexibility of object-oriented programming may finally be sufficient to create computer coaches that can help students develop metacognitive problem-solving skills, an important competence in our rapidly changing technological society. However, no matter how…

We discuss collecting data simultaneously from many different instruments, including both qualitative and quantitative sources. A list of instruments used is provided, and data collection methods are described. Many practical logistical concerns are discussed, warning of potential pitfalls to be avoided. This article is intended to be a practical…

An effective way to teach the concept of image is to give students a model of human vision which incorporates a simple mechanism of depth perception. In this study two almost identical versions of a curriculum in geometrical optics were created. One used a mechanistic, interpretive eye model, and in the other the eye was modeled as a passive,…

Many high school and college students experience serious difficulties in understanding as well as applying fundamental concepts in physics. The study reported in this paper focused on the difficulties in learning about vectors in physics and strategies for making the teaching of vectors more interesting and meaningful for students. Specifically,…