Research and Suggestions in Learning Mathematical Philosophy through Infinity

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Carson Lam Kai Shun

Abstract

Lam, May 2016, explained how mathematics is not only a technical subject but also a cultural one. As such, mathematical proofs and definitions, instead of simply numerical calculations, are essential for students when learning the subject. Hence, there must be a change in Hong Kong’s local teachers’ pedagogies. This author suggests three alternative ways to teach mathematical philosophy through infinity. These alternatives are as follows: (1) Teach the concept of a limit in formalism through storytelling, (2) use geometry to intuitively learn infinity through constructivism, and (3) implement schematic stages for proof by contradiction. Simultaneously, teachers should also be aware of the difficulties among students in understanding different abstract concepts. These challenges include the following: (1) Struggles with the concept of a limit, (2) mistakes in intuitively computing infinity, and (3) challenges in handling the method of proof by contradiction. By adopting these, alternative approaches can provide the necessary support to pupils trying to comprehend the above mentioned difficult mathematical ideas and ultimately transform students’ beliefs (Rolka et al., 2007). One can analyze these changed beliefs against the background of conceptual change. According to Davis (2001), “this change implies conceiving of teaching as facilitating, rather than managing learning and changing roles from the sage on the stage to a guide on the side.” As a result, Hong Kong’s academic results in mathematics should hopefully improve.

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Research Article

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