Investigating mathematical proficiency of elementary school students: A foundation for effective learning models

Mathematical proficiency is a critical mathematical competency and a primary goal in mathematics education. However, previous studies have often examined each aspect of mathematical proficiency in isolation, without comprehensively exploring the interrelationships among these aspects. This study investigates the relationships among the five aspects of mathematical proficiency, namely conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition in elementary school students. Using a descriptive design with a correlational approach, data were collected from 220 fifth-grade students in elementary schools. Mathematical proficiency was measured using a combination of tests and questionnaires, with the data analyzed through descriptive statistics, correlation analysis, and factor analysis. The results reveal significant relationships among the aspects of mathematical proficiency. Factor analysis grouped conceptual understanding and procedural fluency into one factor, while strategic competence and adaptive reasoning formed another factor. Productive disposition was found to be an independent aspect, not directly related to the other factors. These findings provide a foundation for developing effective instructional models that integrate all aspects of students' mathematical proficiency.