Enhancing Students' Combinatorial Thinking for Graceful Coloring Problem: A STEM-Based, Research-Informed Approach in ATM Placement

Combinatorial generalization thinking, a component of higher-order thinking skills, encompasses perception (pattern identification), expressions (pattern illustration), symbolic expressions (pattern formulation), and manipulation (combinatorial results application). Implementing a research-based learning (RBL) model with a Science, Technology, Engineering, and Mathematics (STEM) approach can effectively transform students' learning processes, promoting experiential learning through the integration of STEM elements. This study employs a mixed-method research design, combining quantitative and qualitative methodologies, to evaluate the impact of this RBL-STEM model on students' ability to solve graceful coloring problems, hence developing their combinatorial thinking skills. Two distinct classes, one experimental and one control, were analyzed for statistical homogeneity, normality, and independent t-test comparisons. Results indicated a significant post-test t-score difference between the two groups. Consequently, we conclude that the RBL model with a STEM approach significantly enhances students' combinatorial generalization thinking skills in solving graceful coloring problems. As this research provides empirical evidence of the effectiveness of a STEM-based RBL model, educators, and curriculum developers are encouraged to incorporate this approach into their instructional strategies for enhancing combinatorial thinking skills. Future research should consider various contexts and diverse student populations to further validate and generalize these findings