Factor analysis of algebraic thinking skills: A case study on developing area model algebra worksheet based on phet interactive simulation

Giyanti Giyanti; Adika Artasari; Rina Oktaviyanthi; Sharifah Kartini Said Husain

doi:10.21831/jitp.v11i4.79362

Factor analysis of algebraic thinking skills: A case study on developing area model algebra worksheet based on phet interactive simulation

Giyanti Giyanti, Universitas Serang Raya, Indonesia
Adika Artasari, Universitas Serang Raya, Indonesia
Rina Oktaviyanthi, Universitas Serang Raya, Indonesia
Sharifah Kartini Said Husain, Universiti Putra Malaysia, Malaysia

10.21831/jitp.v11i4.79362

Abstract

This study aims to identify the latent structures underlying students' algebraic thinking skills using factor analysis. Algebraic thinking is a crucial skill in mathematics education, enabling students to generalize patterns, decompose expressions, and apply mathematical models in real-world contexts. The research analyzes data from 60 students 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), along with scores on algebraic thinking ability (Y). The data were standardized, and factor analysis was performed using varimax rotation. The analysis revealed two significant factors. The first factor, termed "Generalization and Area Model Application Capability," showed high loadings for X2 (0.701) and X3 (0.724) and explained 31.118% of the variance. The second factor, "Transformational Strategies in Multi-digit Numbers," exhibited strong loadings for X1 (0.923) and X4 (0.631), accounting for 20.543% of the variance. Together, these two factors explain 51.661% of the total variance in students' responses. These findings provide deep insights into the underlying cognitive structures of students' algebraic thinking. The results suggest that educational strategies should focus on improving generalization skills through the use of area models, and strengthening transformational strategies in multi-digit number operations. Such targeted interventions could lead to significant improvements in students' algebraic thinking abilities. Additionally, this study underscores the potential of interactive and dynamic learning environments, such as PhET simulations, to enhance students' conceptual understanding. Future research should explore the practical implementation of these findings in classroom settings and further investigate their impact on students' long-term learning outcomes.

Keywords

Algebraic thinking skills; area model algebra; factor analysis; latent structure; phet-based interactive simulation

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DOI: https://doi.org/10.21831/jitp.v11i4.79362