Systems Modelling of Multidimensional Mathematical Resilience in Educational Assessment: A Type-1 Mamdani Fuzzy Inference and Adaptive Measurement-Weighting Framework

Source abstract

Multidimensional educational constructs are often summarised using additive scores, although such summaries may obscure how component states co-occur within individuals. To address this problem, this model-development and calibration study develops a systems-modelling framework for representing mathematical resilience in educational assessment. Mathematical resilience is specified as an individual-level, cross-sectional configuration of three measured components—Value, Struggle, and Growth—together with explicit transformation and contextualisation layers. The framework represents component configurations, system boundaries, and aggregation rules rather than temporal dynamics, feedback, emergence, or causal interaction. A type-1 Mamdani fuzzy inference system (FIS), comprising overlapping Low, Medium, and High input membership functions and a complete 27-rule base, produces a continuous centroid-defuzzified score. Descriptive linguistic categories are assigned through consequent-specific rule activation. An independently computed adaptive measurement-weighted (AMW) score combines graded response model-referenced heuristic baseline weights with prespecified ceiling-sensitive attenuation. Record-based indicators of academic difficulty provide a separate descriptive contextual layer. The framework was applied to data from 395 preservice teachers who completed the 23-item Mathematical Resilience Scale. Defuzzified FIS scores ranged from 1.50 to 6.67 (M = 4.41, SD = 1.18). The AMW score correlated strongly with conventional mean-based scoring (r = 0.994); the overall mean absolute difference was 0.048, and the higher-dispersion mean absolute difference was approximately 1.89 times the lower-dispersion value (0.063 vs. 0.034). The framework makes its components, boundaries, rule structure, and aggregation assumptions explicit and auditable. The findings demonstrate the internal computational behaviour of a constructed scoring architecture within one development sample drawn from three universities rather than generalisable validity, predictive accuracy, or diagnostic utility.