<![CDATA[Differential calculus problem requires the ability to connect various mathematical ideas, making mathematical connection ability an essential skill. Research indicates that prospective mathematics teachers demonstrate varying levels of mathematical connection ability. This study aimed to describe the characteristics of prospective mathematics teachers’ mathematical connection ability when solving differential calculus problems. An exploratory qualitative approach was employed involving 61 prospective mathematics teachers enrolled in a differential calculus course at a university in Indonesia. Data were collected through a written differential calculus problem and semi-structured interviews. The written responses were analyzed using five mathematical connections indicators, each scored on a scale of 0–20, to classify participants into strong, moderate, and weak levels. Interview data were used to investigate the processes and factors underlying the emergence of different mathematical connection types. The analysis revealed four types of mathematical connections: part–whole, different representation, procedural, and implication connections. Prospective mathematics teachers with strong mathematical connection level were able to coherently integrate geometric concepts, representations, and calculus procedures by effectively connecting prior knowledge, such as right circular cone geometry and triangle similarity, with new knowledge, particularly the chain rule. In contrast, those with weak mathematical connection ability exhibited fragmented or incorrect prior knowledge, leading to inappropriate representations, flawed mathematical models, and difficulties in applying calculus concepts logically. These findings highlight that the success of differential calculus problem solving depends not only on procedural proficiency but also on the quality of mathematical connections constructed between prior and new knowledge.]]>
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