Project-based learning as a catalyst for 21st-Century skills and student engagement in the math classroom.

Along with traditional academic knowledge, 21st-century skills are crucial for equipping students with a competitive future. Project-based learning (PBL) cultivates these competencies among learners as an instructional approach. This research aimed to construct and analyze a PBL framework designed to weave 21st-century skills into high school education. Data collection involved a survey questionnaire based on an extensive literature review administered to students from ten government-run girls' high schools, where mathematics was taught using the PBL approach. Employing Confirmatory Factor Analysis (CFA) and Structural Equation Modeling (SEM) via the Analysis of Moment Structures (AMOS) software, the study meticulously calculated chi-square values, modification indices, and standardized estimates to validate the framework's effectiveness. The results showed a significant enhancement in collaborative learning, problem-solving, critical thinking, and positive attitudes toward mathematics among students, mediated by the PBL approach. The Heterotrait-Monotrait Ratio (HTMT) values were below the threshold of 1, confirming discriminant validity and ensuring that each construct was unique. The observed substantial correlations between PBL and educational outcomes, ranging from moderate to significant, attest to these variables' interconnectedness and mutual reinforcement. Overall, the structural model and subsequent analyses underscore PBL's pivotal role in promoting active learning and student engagement. This approach advocates its adoption as a forward-thinking educational strategy.