<![CDATA[Functional fixedness constitutes a pervasive cognitive bottleneck in geometry, yet educational interventions rarely target the representational mechanisms underlying this rigidity. Addressing this critical gap, this study challenges the view of fixedness as an immutable trait by experimentally testing the efficacy of analogical mapping and dynamic representational shifts. Through a rigorous randomized controlled trial, the investigation demonstrates that integrating analogical reasoning with dynamic geometry environments significantly outperforms conventional procedural instruction in fostering creativity. Crucially, mediation analysis reveals that representational flexibility rather than mere software usage serves as the primary mechanism driving this cognitive breakthrough. These findings validate the proposed Analogical Representational Shift Model (ARSM), offering a theoretical advancement in creative cognition. Practically, the study provides a definitive blueprint for developing next-generation AI tutoring systems capable of detecting and dismantling cognitive rigidity, marking a pivotal shift from routine drill-based learning to the cultivation of adaptive mathematical insight.]]>
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