Adapting Knowledge Inference Algorithms to Measure Geometry Competencies through a Puzzle Game

The rapid technological evolution of the last years has motivated students to develop capabilities that will prepare them for an unknown future in the 21st century. In this context, many teachers intend to optimise the learning process, making it more dynamic and exciting through the introduction of gamification. Thus, this article focuses on a data-driven assessment of geometry competencies, which are essential for developing problem-solving and higher-order thinking skills. Our main goal is to adapt, evaluate and compare Bayesian Knowledge Tracing (BKT), Performance Factor Analysis (PFA), Elo, and Deep Knowledge Tracing (DKT) algorithms applied to the data of a geometry game named Shadowspect, in order to predict students' performance by means of several classifier metrics. We analysed two algorithmic configurations, with and without prioritisation of Knowledge Components (KCs) - the skills needed to complete a puzzle successfully, and we found Elo to be the algorithm with the best prediction power with the ability to model the real knowledge of students. However, the best results are achieved without KCs because it is a challenging task to differentiate between KCs effectively in game environments. Our results prove that the above-mentioned algorithms can be applied in formal education to improve teaching, learning, and organisational efficiency.