Cognitive Decoupling and Compensatory Gains: An AI‐Enhanced Pedagogy for Bridging the Mathematical Gap in Signals and Systems

The heavy mathematical requirements in Signals and Systems frequently prevent students from developing physical intuition. This study evaluates an Outcome‐Based Education framework implemented through a novel dual‐component architecture. This architecture pairs a RAG‐enabled Socratic Pedagogical Agent (SPA) with a dynamic visual platform to provide a safe‐failure environment for parameter exploration across four instructional stages: Perception, Exploration, Synthesis, and Transfer. A quasi‐experimental study with 192 students assessed this approach. The final evaluation isolated Procedural Fluency (55%), Analytical Derivation (25%), and Conceptual Mastery (20%). Despite entering with a statistically lower math baseline ( p < 0.001), the experimental group achieved statistical parity with the historical control in overall grades ( p = 0.724), Procedural Fluency ( p = 0.312), and Analytical Derivation ( p = 0.362). Crucially, the experimental cohort scored significantly higher in Conceptual Mastery ( p = 0.004, d = 0.42). The findings provide preliminary support for the compensatory hypothesis: pairing visual cognitive offloading with AI‐guided inquiry is associated with enhanced mastery of complex system dynamics for learners with weaker prior mathematical preparation, without degrading procedural skills. Finally, subjective evaluations revealed high student acceptance, with learners specifically valuing the safe‐failure environment over direct computational shortcuts.