Conceptual Thinking Processes of Students in Partial Differentiation: Examining the Gap Between Practice and Evaluation

Abstract

This study aims to evaluate students’ conceptual thinking processes when solving partial differential problems and to investigate differences in performance between new evaluations and routine exercises. This study employed a qualitative case study approach involving four students from the Mathematics Education Program at Bosowa University to explore in depth students’ conceptual thinking processes in solving partial differential problems. Purposive sampling was used to select the participants, and data were collected through semi-structured interviews and written responses regarding problem-solving approaches and conceptual difficulties. Error patterns, thinking strategies, and concept transfer abilities were identified through thematic data analysis using triangulation. The findings revealed that students experienced significant challenges when dealing with new problems. These challenges were mainly caused by dependence on mechanical exercise patterns, limited strategic flexibility, and difficulties in integrating partial differential concepts. Students’ adaptive abilities remained limited even though some students employed reflective thinking strategies. These findings indicate that procedural mastery does not always represent conceptual understanding. The novelty of this study lies in identifying students’ error patterns and thinking strategies in the context of partial differentials, which has rarely been discussed in previous studies. The practical implications suggest that adaptive learning approaches are needed to improve conceptual understanding and cognitive flexibility. This includes providing various types of problems before assessment to enhance students’ concept transfer abilities.