This study aims to identify the factors that influence students’ competence in using tools and means for learning mathematics in secondary schools. Survey data were collected from 252 mathematics teachers across various localities and analyzed using Exploratory Factor Analysis (EFA). The results revealed a data structure comprising five latent factors that explained 72.84% of the total variance. These factors include: (1) Effectiveness of competence in using tools and means for learning mathematics; (2) Student characteristics; (3) Teacher characteristics; (4) Facilities and learning resources; and (5) Educational policy and management. The novelty of the study lies in constructing and validating a five-factor model that affects students’ competence in using tools and means for learning mathematics. This approach has received limited attention in the context of Vietnamese general education. The findings provide both theoretical and practical foundations for innovating teaching methods, developing teacher training programs, and designing learning environments oriented toward students’ competence development.