Why are 3D Transformations in Computer Graphics Difficult? An Analysis of a Decade of Exam Questions

Three-dimensional (3D) transformations are a fundamental concept in Computer Graphics and are used for modelling, view transformations, animation, and efficient rendering. Understanding 3D transformations can be difficult, since they typically involve geometric concepts, mathematics, specific programming constructs (e.g. using graphics APIs), and visuospatial skills. While previous research investigated students’ problems with geometry in mathematics courses, we did not find any research investigating teaching and learning of 3D transformations in computer graphics. In this paper, we use historical data from eleven years of exam results to analyse the relationship between question difficulty and the dimension, representation, and complexity of a transformation. Our results suggest that the difficulty of a question is predominantly determined by the way students need to apply concepts to find a solution, rather than the concepts tested. We did not find a statistically significant difference for the spatial dimension used in a question (2D vs. 3D). However, we observed that the representation used for formulating the question did matter and many students seemed to struggle with interpreting images of 3D scenes. We suggest that many students lack spatial reasoning skills to interpret images of 3D transformations and to make suitable mental models. This is likely to impede learning and might produce inequities in the assessment. We discuss implications of our research on teaching and assessment of 3D transformations in computer graphics.