Factor analysis of algebraic thinking skills: A case study on developing area model algebra worksheet based on PhET Interactive Simulation

Abstract

Algebraic thinking is a vital skill in mathematics education, enabling students to generalize patterns, decompose expressions, and apply mathematical models in real-world contexts. However, students often struggle to connect abstract algebraic concepts to practical, real-world problems, which limits their ability to apply these skills effectively. This study aims to uncover the latent structures underlying students' algebraic thinking skills through Exploratory Factor Analysis (EFA). Data were collected from 60 junior high school students in Serang, Banten, who completed worksheets assessing five indicators of algebraic thinking: X1 (Generalization – Decomposing an expression), X2 (Generalization – Using area model), X3 (Transformational – Representing multiplication problem), X4 (Transformational – Strategies for multi-digit numbers), and X5 (Meta-global level – Using area model in real-world contexts), alongside algebraic thinking ability scores (Y). Using varimax rotation, the analysis identified two significant factors. The first, "Generalization and Area Model Application Capability," explained 31.118% of the variance, with high loadings for X2 (0.701) and X3 (0.724). The second, "Transformational Strategies in Multi-digit Numbers," accounted for 20.543% of the variance, with strong loadings for X1 (0.923) and X4 (0.631). Together, these factors explained 51.661% of the total variance. These findings underscore the importance of enhancing generalization skills through area models, including their application to real-world problems and strengthening transformational strategies for multi-digit operations. Incorporating interactive tools like PhET simulations may further support these cognitive processes. Future research should explore classroom implementation and its impact on students' long-term outcomes.