Over a sixteen-week term, the study dove into how chess could enhance math skills for eleventh graders at three public schools in Cartagena, Colombia. It assumed that chess would sharpen their minds and problem-solving prowess. Seventy-one pupils took part, trying out a chess-centric way of learning. Researchers used multiple statistical approaches such as multivariate regression and cluster analysis - to measure effects on various academic fronts. The analysis encompasses students' chess-play performance, strategic thinking, and problem-solving approaches, employing graph theory to gain a comprehensive understanding. The findings reveal distinct clusters of strategic approaches adopted by students, elucidating intricate relationships and patterns in their gameplay. Additionally, the study examines the correlation between chess-based learning and academic performance over the duration of the intervention. The identified clusters through graph theory shed light on diverse problem-solving strategies, offering insights into the dynamic nature of chess gameplay. The results affirm the research hypothesis, highlighting the significant relationships and patterns revealed through the application of graph theory. By employing various statistical procedures, it contributes to a deeper understanding of the impact of chess-based pedagogy on students' strategic thinking development skills. Furthermore, this research provides valuable insights for educators seeking innovative approaches to enhance mathematical proficiency and strategic thinking in secondary education.