Assessing the Psychometric Properties of an Instrument Measuring Instructional Strategies, Algebraic Thinking and Flexible Mathematical Thinking: A Pilot Study

Abstract

This paper reports on the results of a pilot study conducted at the International Islamic University Malaysia (IIUM), Kuantan Campus to examine the clarity, reliability, and internal consistency of a survey instrument measuring instructional strategies, algebraic thinking, and flexible mathematical thinking among undergraduate students. The sample comprised 33 students of Mathematics who responded to a 47-item Likert scale on the three constructs. Data were analyzed using SPSS version 30 and Partial Least Squares Structural Equation Modeling (PLS-SEM) with SmartPLS version 4. The reliability analysis revealed strong internal consistency for each construct: instructor-based instruction (5 items, α = 0.78), learner-focused instruction (9 items, α = 0.85), generalized arithmetic (9 items, α = 0.90), functions (9 items, α = 0.93), modelling (5 items, α = 0.90), and flexible mathematical thinking (10 items, α = 0.90). Convergent validity was supported, with most factor loadings above 0.50 and Average Variance Extracted (AVE) values ranging from 0.52 to 0.72, demonstrating that the items adequately captured the intended constructs. Discriminant validity was confirmed through cross-loadings, the Fornell–Larcker criterion, and HTMT ratios below 0.85. Full collinearity VIF values were examined to assess potential common method bias, with all VIFs below the recommended threshold of 3.3 (ranging 1.00–2.47), indicating minimal risk of CMV. Three items were removed due to low loadings, further improving model validity. The results suggest that the instrument can be effectively used to assess instructional strategies, algebraic thinking and mathematical thinking among undergraduates, providing insights for curriculum design and pedagogical practices. Further studies are necessary to examine the predictive validity of this instrument, particularly within mathematics classrooms.