Identifying the Factor Structure of Students' Algebraic Thinking Through an Area Model Supported by PhET Interactive Simulation
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Abstract
This study aims to identify the factor structure of students’ algebraic thinking skills within an area model learning context supported by PhET Interactive Simulation. A quantitative approach using exploratory factor analysis was applied to data from 128 students based on 16 indicators representing four aspects of algebraic thinking: generalization, representation, transformation, and conceptual meaning. The analysis involved the Kaiser-Meyer-Olkin (KMO) test, Bartlett’s test of sphericity, measures of sampling adequacy (MSA), principal component analysis, eigenvalue criteria, and Varimax rotation. The initial analysis produced a KMO value of .631, while four variables (G1, G3, G4, and R1) were removed because their MSA values were below .50. The analysis of the remaining 12 variables produced a KMO value of .689 and a significant Bartlett’s test (p < .001). Four components with eigenvalues greater than 1 were retained and accounted for 62.06% of the total variance before rotation. The rotated solution revealed three interpretable dimensions: a visual-representational factor integrating generalization and representation, a procedural-transformational factor, and a conceptual-meaning factor. The fourth component had no clearly dominant group of indicators and was therefore interpreted cautiously as a residual component. These findings indicate that students’ algebraic thinking in the examined instructional context is multidimensional, with visual-representational, procedural-transformational, and conceptual dimensions showing distinct patterns.
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