Between Local Perspectives and Theories: A Study of Derivative Teaching Practices in Secondary Schools in Palestine

Abstract

This study aimed to explore the teaching practices of three mathematics teachers in teaching the concept of derivatives in classrooms in Palestine, with a focus on how to activate the local perspective in the teaching process. The study included three main phases: interviews with three teachers in secondary schools in Palestine, observing their practices while teaching derivatives, and analyzing the data using a theoretical framework. The teachers' practices were analyzed in the context of teaching the tangent line equation and the derivative function using video recordings and direct observations. The study showed how semiotic resources such as graphs and symbols contribute to the development of the local perspective of 45 students, distributed across three classrooms, regarding the mathematical concept during the didactic transposition process. It also led to identifying two different teaching methods related to derivatives, based on different conceptual images of the tangent line: the secant line limit and the best linear approximation. These methods were discussed by illustrating the different levels of intervention of the perspective used in working on functions, where its presence was observed to be weak and ambiguous. Therefore, the study recommended the development of the curriculum by working on improving the scientific composition in teaching derivatives and emphasizing the necessity of activating the local perspective on functions, not only in the topic of derivatives but also in the entire Palestinian mathematics curriculum.