Development and Validation of a Multiple Representation-Based Concept Test on Algebra Topics for Form Four Mathematics

This study developed and validated the Algebra Concept Understanding Test (ACUT), a multiple representation-based concept for Form Four mathematics, specifically targeting the conceptual understanding of Variables, Algebraic Formulas, and Algebraic Expressions. Grounded in the Revised Bloom’s Taxonomy (2001) and aligned with a Table of Test Specifications (TTS), the ACUT was designed to assess algebraic comprehension across six distinct modalities of representation. Utilizing a quantitative survey approach, a pilot study (n = 32) and a main study (n = 135) were conducted among Form Four students in Selangor, Malaysia selected via a two-stage stratified cluster random sampling method. Psychometric evaluation using Winsteps software version 3.64.2 revealed high item reliability indices, yielding 0.88 in the pilot study and 0.98 in the main study. Item fit and construct validity were confirmed through point-measure correlation (PT-MEA CORR), Infit/Outfit MNSQ, and Z-STD values. Additionally, content validity was verified by three mathematics education experts, achieving a Content Validity Index (CVI) of 0.92. These findings demonstrate that the ACUT is a highly reliable and valid instrument for diagnosing student comprehension and systematically identifying conceptual weaknesses in algebra. Ultimately, this diagnostic tool enables targeted instructional interventions and offers broader implications for developing multi-representational assessments in other mathematical and scientific domains.

Algebra Comprehension, Form Four Mathematics, Educational Assessment, Test Validation, Multiple Representations

1. Amir, M., Ahmad, S., Kebangsaan, S., Baharu, P., Kebangsaan, S., & Geruntum, U. (2016). Analisis Kesalahan Newman Dalam Penyelesaian Masalah Kurikulum Untuk Mata Pelajaran Matematik Berubah Seiring Dengan Perkembangan Kurikulum Yang Berlaku. Lampiran Peraturan Menteri Pendidikan Nasional. 6(2), 69–84. [Google Scholar] [Crossref]

2. Arefaine, N., Michael, K., & Assefa, S. (2022). Effect of Multiple Representations on Students’ Performance on Interpretations and Techniques of Representation in Calculus. Mathematics Education Journal, 16(3), 351–372. https://doi.org/10.22342/jpm.16.3.18291.351-372 [Google Scholar] [Crossref]

3. Avcu, A. (2025). The Contribution of Rasch Modeling on Measuring Attitudes for Better Classroom Assessment. International Journal of Psychology and Educational Studies, 12(3), 169–179. https://doi.org/10.52380/ijpes.2025.12.3.1432 [Google Scholar] [Crossref]

4. Azizi Yahaya, & Elanggovan AL M Savarimuthu. (2010). Kepentingan Kefahaman Konsep Dalam Matematik. 1989. [Google Scholar] [Crossref]

5. Azrillah Abdul Aziz, Mohd Saidfudin Masodi, & Azami Zaharim, ... (2017). Asas Model Pengukuran Rasch (Third edit). Penerbit UKM. [Google Scholar] [Crossref]

6. Bond Trevor, & Christine, M. F. (2015). Applying the Rasch Model: Fundamental Measurement in the Human Sciences (Third Edit). Routledge Taylor & Francis Group. [Google Scholar] [Crossref]

7. Creswell, J. W., & Guetterman, T. C. (2024). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research (7th ed.). Pearson Education, Inc. [Google Scholar] [Crossref]

8. Dahiana, W. O., Herman, T., Nurlaelah, E., & Pereira, J. (2023). Student Semiotic Representation Skills in Solving Mathematics Problems. Jurnal Didaktik Matematika, 10(1), 34–47. https://doi.org/10.24815/jdm.v10i1.30770 [Google Scholar] [Crossref]

9. Erbilgin, E., & Gningue, S. M. (2023). Using The Onto-Semiotic Approach to Analyze Novice Algebra Learners’ Meaning-Making Processes with Different Representations. Educational Studies in Mathematics, 114(2), 337–357. https://doi.org/10.1007/s10649-023-10247-8 [Google Scholar] [Crossref]

10. Flores, R., Koontz, E., Inan, F. A., & Alagic, M. (2015). Multiple Representation Instruction First Versus Traditional Algorithmic Instruction First: Impact in Middle School Mathematics Classrooms. Educational Studies in Mathematics, 89(2), 267–281. https://doi.org/10.1007/s10649-015-9597-z [Google Scholar] [Crossref]

11. Gitonga, I. (2016). Utilizing Semiotic Perspective to Investigate Algebra II Students’ Exposure to and Use of Multiple Representations In Understanding Algebraic Concepts. Georgia State University. [Google Scholar] [Crossref]

12. Kusumaningsih, W., Darhim, Herman, T., & Turmudi. (2018). Improvement algebraic thinking ability using multiple representation strategy on realistic mathematics education. Journal on Mathematics Education, 9(2), 281–290. https://doi.org/10.22342/jme.9.2.5404.281-290 [Google Scholar] [Crossref]

13. Linacre, J. M. (1994). Sample Size and Item Calibration Stability. Rasch Measurement Transactions, 7(4), 328. [Google Scholar] [Crossref]

14. Luki Luqmanul Hakim, B. Y. (2021). Conceptual and Procedural Knowledge in Mathematics Education. Design Engineering, 9/pages:1271-1280, 1–10. https://doi.org/10.4324/9780203063538 [Google Scholar] [Crossref]

15. Marlina Ali, & Aziz, N. H. A. (2008). Tahap Kefahaman Dalam Tajuk Ungkapan Algebra Pelajar Tingkatan Dua. [Google Scholar] [Crossref]

16. Miller, L.A., Lovler, R. L., & McIntire, S. A. (2019). Foundations of Psychological Testing: A Practical Approach (6th edition). In Personnel Psychology (Sixth edit, Vol. 60, Issue 3). Thousand Oak: SAGE Publications Inc. https://doi.org/10.1111/j.1744-6570.2007.00091_11.x [Google Scholar] [Crossref]

17. Nur Afiqah Athirah Mohd Rushdi, & Asbulah, L. H. (2022). Kesahan Dan Kebolehpercayaan Instrumen Sikap Pelajar Terhadap Pembelajaran Bahasa Arab (I-SPPBA) Menggunakan Model Pengukuran Rasch. 98–110. [Google Scholar] [Crossref]

18. Panasuk, R. M., & Beyranevand, M. L. (2010). Algebra Students’ Ability to Recognize Multiple Representations and Achievement. International Journal for Mathematics Teaching and Learning. [Google Scholar] [Crossref]

19. Sarimah Baco. (2022). Domain Kognitif dan Pencapaian Ungkapan Algebra dalam kalangan Pelajar Tingkatan Dua. Borneo International Journal of Education (BIJE), 2, 55–68. https://doi.org/10.51200/bije.v2i.4112 [Google Scholar] [Crossref]

20. Sarimah Baco, & Mohd Zaki Ishak. (2021). Kesahan Dan Kebolehpercayaan Instrumen Penilaian Kendiri Pembelajaran Ungkapan Algebra Tingkatan Dua. [The Validity and Reliability of The Form Two Algebraic Expression Self- Assessment Learning Instrument]. Malaysian Journal of Social Sciences and Humanities (MJSSH), 6(11), 127–137. [Google Scholar] [Crossref]

21. Shamsina Shamsuddin. (2013). Pengubalan Item Ujian (First edit). Freemind Horizons Sdn. Bhd. [Google Scholar] [Crossref]

22. Sumintono, B. (2017). Aplikasi Pemodelan Rasch pada Asesmen Pendidikan: Implementasi Penilaian Formatif (assessment for learning). 1–19. [Google Scholar] [Crossref]

23. Sumintono Bambang. (2017). Rasch Model Measurement as Tools in Assessment for Learnig. International Conference on Education Innovation. [Google Scholar] [Crossref]

24. Tularam, G. A., & Hassan, O. M. (2025). Persistent Misconceptions in Algebra: A Critical Analysis of Errors with Implications for Teaching and Further Research. Journal of Social Sciences, 21(1), 38–50. https://doi.org/10.3844/jssp.2025.38.50 [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples