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…

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…