Formal Concept Analysis of Students’ Solutions on Computational Thinking Game

Contribution: We present a framework for teachers to investigate the relationships between attributes of students’ solutions in the process of problem solving or computational thinking. We provide visualization and evaluation techniques to find hidden patterns in the students’ solutions which allow teachers to predict the specific behavior of students or to prevent some student mistakes or misconceptions in advance or further pedagogical intervention. Background: Formal concept analysis is a method of unsupervised Machine Learning that applies mathematical lattice theory to organize data based on objects and their shared attributes. Several fuzzy extensions of formal concept analysis have a great potential to visualize and evaluate students’ solutions, to categorize the solutions into overlapping biclusters (formal concepts) or to generate the attribute implications between extracted attributes. Research Question: Does formal concept analysis describe the various solutions and the relationships between the extracted attributes of students’ solutions in the educational and computational thinking game Light-Bot? Methodology: Targeting the evaluation of 64 students’ solutions in the Light-Bot game, we construct the formal contexts of the extracted attributes. We apply formal concept analysis to construct the concept lattices from two binary formal contexts and to generate attribute implications and their fuzzy counterparts to find the dependencies between the extracted attributes. Findings: The results of our paper provide a description of various students’ solutions which are visualized in the concept lattices. 1) Regarding the concept lattice of binary formal contexts, we obtained the characterization of the largest biclusters which includes a description of the largest group of similar solutions. 2) The attribute implications mainly reveal the characterization of similar solutions, e.g., with a higher count of executed commands in solutions. 3) Using fuzzy attribute implications, we obtained the characterization of solutions with unnecessary commands, going out of the game area, or using indirect recursion.