Development and Validation of Questionnaire on Difficulties Encountered in Operating Rational Numbers: Exploratory and Confirmatory Factor Analyses

This study developed and validated the Difficulties Encountered in Operating Rational Numbers (DEORN) questionnaire to identify learners’ challenges in fractions, decimals, and negative numbers. Using a research and development design, 40 initial items derived from literature were refined through Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA). A total of 85 mathematics teachers participated in both EFA and CFA, with 20 teachers for pilot testing and 6 experts for validation. Initial sampling adequacy was low (KMO = 0.427), but after item reduction to 17 indicators, adequacy improved (KMO = 0.795), and Bartlett’s test was significant (χ² = 475.97, df = 136, p < 0.001), confirming suitability for factor analysis. EFA revealed four dimensions explaining learners’ difficulties: misconceptions in arithmetic operations, conceptual confusions, misapplication of natural number concepts, and errors in operations and interpretation. Factor loadings ranged from 0.459 to 0.873. Reliability analysis showed excellent internal consistency (Cronbach’s α = 0.924; 95% CI: 0.883–0.953). Content validity ratings were very high across criteria, with overall means of 4.77 (usability), 4.63 (content), 4.67 (appropriateness), 4.77 (relevance), and 4.87 (acceptability). CFA results indicated good model fit (χ² = 11.292, df = 9, p = 0.256; CFI = 0.984; TLI = 0.974; NFI = 0.930). These findings confirm that the DEORN questionnaire is a valid and reliable diagnostic tool for identifying learners’ difficulties in rational numbers.