Methodological Competence Development in Mathematics Teachers Using Fuzzy Driven Computational Learning Under Uncertainty

Mathematics teachers make instructional decisions under uncertainty, yet professional development models rarely represent imprecision in teachers' competence assessments or mathematical procedures. This study develops and evaluates a framework combining triangular fuzzy numbers (TFNs) for representing self-assessed methodological competence with alpha-cut fuzzy arithmetic for modelling uncertainty propagation in numerical procedures. Sixty mathematics teachers (30 in-service and 30 pre-service) were randomly assigned to experimental (n = 30) and control (n = 30) groups in a pre-test/post-test design. A 30-item instrument assessed Mathematical Content Knowledge (MCK), Pedagogical Strategy Knowledge (PSK), Computational Technology Skills (CTS), and Reflective Teaching Practice (RTP). Responses were represented and aggregated using TFNs. Intervention effects were evaluated using mixed ANOVA and ANCOVA, supported by sensitivity analyses across four defuzzification methods and possibility/necessity comparisons. Significant Group × Time interactions were observed for all dimensions (MCK: F(1,58) = 56.72; PSK: F(1,58) = 45.26; CTS: F(1,58) = 45.40; RTP: F(1,58) = 30.50; all p < 0.001), with partial eta-squared ranging from 0.345 to 0.494. Adjusted post-test differences ranged from 0.93 to 1.33 points, with all 95 \% confidence intervals excluding zero. Results remained stable across defuzzification methods. The alpha-cut fuzzy Newton scheme reproduced the exact fuzzy-root alpha-cuts to machine precision, yielding an asymmetric support width of 0.1109, compared with 0.2 under a symmetric midpoint construction. The framework provides a reproducible approach to assessing competence development while explicitly representing measurement imprecision and uncertainty propagation.