Survey data of Student Learning Experience with Embedded Mathematical Competency Development in a Design Thinking Course: A Three-Factor Model and Structural Pathways

Developing mathematical reasoning is critical in engineering education, yet traditional approaches often fail to engage students in authentic application of mathematics. Project-based learning (PBL) offers an alternative emphasizing real-world problem solving, but little is known about how students experience mathematics learning in PBL contexts—specifically their perceptions of the learning environment, emotional experiences, and learning outcomes—or how these dimensions interrelate. This study examines learning experiences in a design thinking-based engineering course (N=273) where students develop mathematical competency through authentic problem-solving and first principles of thinking. Using structural equation modeling, we validated a three-factor measurement model (Learning Environment, Emotional Experience, Perceived Learning Outcomes) while controlling method effects, then tested direct and mediated pathways. Students reported substantial perceived learning outcomes, including gains in mathematical competency (M=3.90, SD=0.66). A strong direct pathway from learning environment to perceived learning outcomes emerged (β=.84, R²=.67), while emotional experience did not mediate this relationship (indirect effect β=-.02, 95% CI [-.08, .04]). Emotional experience, though associated with environmental quality (r=.42), did not independently predict outcomes. Findings challenge simple mediation assumptions, suggesting well-structured environments directly support perceived learning outcomes in PBL contexts.