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

Abstract

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.