Decoding cognitive transitions in undergraduate mathematics: An integrated APOS AND SOLO+ framework for formal epsilon-delta limit proofs - Nugroho, Khathibul Umam Zaid; Sukasno, Sukasno; Widada, Wahyu; Alias, Norma; Herawaty, Dewi; Anggoro, Shadaqnas Dewarif Tri (Al-Jabar: Jurnal Pendidikan Matematika, 2026)
Purpose: This study examines cognitive transitions and epistemological obstacles in undergraduate mathematics education by testing an integrated APOS and SOLO+ framework within formal ε-δ limit proofs. Method: Using an explanatory sequential mixed-methods design, CB-SEM analyzed data from 278 undergraduates to test theoretical structural relationships. Qualitatively, a "diagnostic task analysis" employing the Constant Comparative Method examined task-based interviews from 8 key informants to dissect transitional cognitive anomalies. Findings: CB-SEM confirmed that Structural Complexity (SOLO+) significantly partially mediates the effect of Cognitive Mechanisms (APOS) on Proof Proficiency, explaining 62.4% of the variance. Qualitative autopsies identified two specific transitional traps: Interiorization Instability (Semi-Relational level), marked by universal quantifier failures and reversed logic in linear tasks; and Encapsulation Rigidity (Semi-Extended level), marked by intuitive blockages during bounding strategies in non-linear tasks. Consequently, a grounded taxonomy was generated to distinguish superficial syntactic "slips" from deep-seated epistemological "errors." Significance: This framework shifts pedagogical evaluation from outcome-based syntax to transitional cognitive diagnosis, providing a powerful blueprint for addressing learning barriers and laying the theoretical foundation for future diagnostic tools.