Integrating Computational Thinking into Signal Processing Mathematics Through Analytical and MATLAB-Based Verification

Computational thinking has been increasingly recognised as a core component of mathematics education, particularly in areas where analytical reasoning and computational practices intersect. However, limited empirical research has examined how computational verification supports mathematical reasoning in postgraduate mathematics education, where teaching often emphasises either analytical derivations or software implementation without explicitly connecting the two. This study investigates the integration of computational thinking within a postgraduate Mathematics of Signal Processing module through a structured coursework design combining analytical problem solving with computational verification. Over three academic years, students solved discrete-time signal and convolution problems analytically and then verified their solutions computationally. Performance data were analysed using descriptive and non-parametric statistical methods to examine differences between analytical and computational performance. Across cohorts, computational verification resulted in statistically significant performance improvements, with mean gains ranging from +1.20 to +2.00 marks (Wilcoxon signed-rank test, p < 0.05) and moderate-to-strong effect sizes (r = 0.56–0.59). Strong positive correlations were also observed between analytical and computational marks (0.61 ≤ r ≤ 0.96), indicating alignment between mathematical understanding and computational validation. The findings suggest that verification-driven learning can improve solution accuracy, reduce conceptual errors and strengthen computational thinking practices in advanced mathematics education. This study contributes empirical evidence from postgraduate mathematics education and highlights the value of integrating analytical reasoning with computational validation in technical modules.