Traditional methods of teaching differentiation calculus usually involve lectures. Nevertheless, this process impedes students' thorough comprehension of concepts and their practical application by promoting dependence on memorisation and procedural learning. Numerous studies have also denoted that teaching experiments and technology can enhance mathematics learning concerning differentiation topics. Therefore, this study proposed a teaching experiment to examine the pre-university students' understanding of curve property-related derivative problems. The proposed strategy grounded in mathematics-related education presented two primary outcomes: (a) data regarding student understanding and (b) adoption of student-centred instruction. This strategy also involved the Action, Process, Object, and Schema (APOS) theory in assessing the interview and worksheet-based data. Consequently, the students held two misconceptions about positive derivative functions: (a) the positive derivative functions were erroneously correlated with an increasing interval on the derivative function, and (b) misinterpretation of negative value derivative functions as decreasing intervals on the derivative functions. These students also encountered difficulties in aligning cubic graphs with their corresponding derivatives. The instructional practices for the subsequent cycle were then improved based on the results of this analysis. Overall, improved mathematical understanding and practical instructional strategies could be realised by employing teaching experiments as an effective strategy to address these issues.