Uncovering Influencing Mechanisms and Practical Strategies for Teaching Effectiveness of College Mathematics General Education Courses: Evidence from SEM-fsQCA Hybrid Analysis

As a core foundational course in higher education, college mathematics general education courses play a crucial role in fostering students' logical thinking and supporting their subsequent professional learning. However, current teaching practices face challenges such as insufficient student engagement and significant disparities in learning outcomes. Traditional evaluation methods struggle to reveal implicit correlations among multiple variables, making it difficult to provide targeted optimization strategies. This study adopted a mixed method approach combining Structural Equation Modeling (SEM) and fuzzy set Qualitative Comparative Analysis (fsQCA) to evaluate and optimize the teaching effectiveness of college mathematics general education courses at University A. A total of 572 valid samples were collected from freshmen of Grade 2025 using a structured questionnaire. SEM results indicated that teaching methods had the strongest direct effect on learning outcomes (standardized coefficient = 0.362, p < 0.001). Meanwhile, teachers’ literacy and teaching resources exerted indirect effects on learning outcomes through teaching methods, with mediating effect ratios of 81.8% and 55.7%, respectively. For three groups of majors with different mathematical needs (high, moderate, and low), fsQCA identified three distinct configurational paths leading to high learning outcomes: (1) For majors with high mathematical needs, the optimal path was “teaching resources + high school mathematics foundation + teaching methods”; (2) For majors with moderate mathematical needs, the effective path was “teaching content + teaching methods + teachers’ literacy”; (3) For majors with low mathematical needs, the key path was “teachers’ literacy + teaching methods”. This study addresses the limitations of single quantitative or qualitative research by integrating SEM and fsQCA. The proposed optimization strategies, including hierarchical teacher training, diversified collaborative teaching teams, and targeted student support, provide practical references for improving the teaching quality of college mathematics general education courses and realizing personalized teaching in similar universities.