<![CDATA[This research aims to develop a Local Instructional Theory (LIT) for teaching the concept of derivatives through internalization using the real-life context of climate change. It employed a three-phase design strategy: (1) the development of a Hypothetical Learning Trajectory (HLT); (2) teaching experiments conducted with 5 students in pilot experiments and 37 Grade 11 students in final experiment; and (3) a retrospective analysis. Data was collected through observations of classroom interactions, student worksheets, tests, interviews, and field notes. The retrospective analysis involved comparing the actual learning processes to the HLT. The results indicate that students' perceptions of the derivative developed through three fundamental activities: (1) amount of change and instantaneous rate; (2) rates of change, where the derivative was introduced as a tool for understanding instantaneous changes; and (3) prediction, in which students used derivatives to forecast future climatic patterns. These exercises helped students to conceptually understand the derivative as a measure of instantaneous rate of change, while also promoting mathematical modeling and environmental awareness. The resulting LIT offers a pragmatically based approach to conveying the concept of calculus in contextualized and provides practical implications for the construction of curricula and the teaching of mathematics at the secondary school level.]]>
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