Decision trees have a long history in artificial intelligence and have been successful in several applications. Numerous studies have utilized educational games as learning environments to aid in teaching introductory programming courses and fostering the development of computational thinking. An example of such an educational game is Light-Bot, which is an educational game focused on developing computational thinking, where the objective is to create an algorithm to direct a robot's movements to illuminate all the blue tiles in a level. In our paper, we propose the method of generalized decision-directed acyclic graphs to find the dependencies between the extracted attributes for evaluating students’ solutions in the Light-Bot educational game. Moreover, the Formal concept analysis of these solutions is performed and visualized.

In particular, we generate datasets based on the extracted attributes from sixty-four solutions created by university students aged 22-24 from Teacher Training programs and teachers aged 30-50 who aim to enhance their qualifications in teaching Computer Science. Data spanning four years, 2019 to 2022, was utilized. The study was incorporated into the mandatory courses Teaching of Computer Science or Teaching of Programming. The solutions were evaluated as a component of the overall course grade. Our main findings depict student solutions visualized within concept lattices and decision-directed acyclic graphs. The attribute implications primarily highlight the characterization of similar solutions, such as those with more executed commands in the game. The example of such attribute implication can be understood as the assertion that any correct solution with the number of calls of function one from the main function greater than the median value of distances for all solutions will have a count of executed commands exceeding the median value. Concerning the concept lattice of binary formal contexts, we identified the characteristics of the largest biclusters, which describe the largest grouping of similar solutions.

The practical implications of this study for researchers, educators, and professionals are as follows: Results from data analysis can assist educators (or researchers) in identifying the diversity among students' solutions; can identify (or validate) exceptional students based on extracted attributes; they may appear as small clusters (e.g., containing one or two elements). Moreover, educators can foster students' computational thinking and creativity by assigning multiple solution tasks identified through data analysis of their solutions.

Keywords: Computational thinking, educational game, directed acyclic graph, formal concept analysis.