Learning the integral concept by constructing knowledge about accumulation

AbstractWe propose an approach to the integral concept for advanced high school students and provide evidence for the potential of this approach to support students in acquiring an in-depth proceptual view of the integral. The approach is based on the mathematical idea of accumulation. A ten-lesson unit has been implemented with four pairs of students. The students’ learning processes were micro-analysed using the methodological–theoretical framework of Abstraction in Context. In this paper, we focus on the lessons in which the notions of approximation and accumulation are introduced. The work of one student pair is analysed in detail, and the work of the other pairs is summarized. Our results show that most of the students reached a proceptual understanding of the integral that prepared them for the next step in the curriculum, namely the Fundamental Theorem of Calculus.

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