Abstract:

Students taking a calculus course for the very first time have generally had an intuitive approach to infinity, which has likely had to do with “real life” events, such as the infinite nature of the Universe. The students have not usually reflected upon any of the mathematics aspects of infinity and to a certain extent this hampers their understanding within a mathematical context. When learning about the concept of limit (essential in order to adequately build calculus concepts) knowledge of infinite processes is required. Moreover if the task of teaching calculus is restricted to its algebraic aspects without paying attention to the use of non-algebraic representations, it is very difficult for students to arrive at a deep understanding of calculus. It is even difficult to conceive of a student being able to comprehend calculus without having first developed visual skills tied in to building calculus concepts, for example.

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