MODELING CHESS THROUGH COMBINATORICS AND PROBABILITY: AN APPLIED STUDY IN A PUBLIC SCHOOL IN MARANHÃO

Abstract

This article presents the results of a didactic–pedagogical intervention that connected concepts from Combinatorics and Probability to the game of chess, aiming to promote logical reasoning and problem-solving performance in a 2nd-year high school class at a public school in Maranhão, Brazil. The study adopted a mixed-methods approach, with an emphasis on action research, and was organized into 12 sessions: a diagnostic assessment; workshops to produce the instructional materials (3D-printed pieces and an 8×8 board made from a reused banner with Velcro); a chess workshop delivered over three sessions (history, rules, notation, strategy, and tactics); implementation of contextualized mathematical activities; and a final assessment. Data were collected through performance instruments (activities and questionnaires) and qualitative records (field notes and students’ statements). In the diagnostic assessment, performance was heterogeneous: 30% of students answered only 1 out of 8 content questions correctly, while 12.5% achieved 8 correct answers. After the intervention, accuracy rates in the mathematical activities were predominantly high in counting and basic probability items (≥80%), with difficulties concentrated in items requiring greater formalization (e.g., the binomial model and expected value). In the final questionnaire, content items showed percentages mostly above 65%, including one item with 100% correct answers, and perception items indicated high acceptance of the proposal (92.5% reported having enjoyed the activities). The findings suggest that chess, as a context for decision-making and situation modeling, is a promising pedagogical resource for making counting and probability more meaningful, provided it is accompanied by didactic mediation to support the transition from intuitive to formal reasoning.