Abstract
In this paper we analyze our own practice with the focus on the noticed disparity in students’ use of different representations of a curve in a space and their theoretical underpinnings given by the Implicit Function Theorem. We designed two tasks with the aim to scaffold students’ learning in the way that supports linking of procedures and theory, and thus possibly leads to formation of a more comprehensive and coherent students’ knowledge. Tasks that required students’ use of different representations of curves in space referred to determining the tangent line of a curve given by the implicit equation(s). In the design and analysis of students’ interaction with the tasks, we used the adaptation of Theory of Didactic Situations to university mathematics and analysis of features of a task regarding its adidactic, linking and deepening potential. In this paper we discuss the affordances of the designed task sequence and also observed students’ difficulties related to the notion of curve in space that could be related to similar difficulties observed with linear objects - straight lines and planes in space.
Published Version
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