EconPapers    
Economics at your fingertips  
 

Teaching and Learning Mathematical Philosophy Through Infinity

Mr. Lam Kai Shun
Additional contact information
Mr. Lam Kai Shun: Alumni of the University of Hong Kong, Faculty of Science, Department of Mathematics, Hong Kong

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 2, 94-105

Abstract: Lam [1], 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 way to teach mathematical philosophy through infinity. These alternatives are as follows: 1. Teach the concept of a limit in formalism through story telling, 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. 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 [2]. One can analyze these changed beliefs against the background of con-ceptual change. According to Davis [3], “this change implies conceiving of teaching as facili-tating, 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.

Keywords: Cosmology and universe; Quantum mechanics; Human cognition and philosophy (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
https://www.arpgweb.com/pdf-files/ajams7(2)94-105.pdf (application/pdf)
https://www.arpgweb.com/journal/17/archive/04-2021/2/7 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arp:ajoams:2021:p:94-105

Access Statistics for this article

Academic Journal of Applied Mathematical Sciences is currently edited by Dr. Diana Bílková

More articles in Academic Journal of Applied Mathematical Sciences from Academic Research Publishing Group Rahim Yar Khan 64200, Punjab, Pakistan.
Bibliographic data for series maintained by Managing Editor ().

 
Page updated 2021-02-18
Handle: RePEc:arp:ajoams:2021:p:94-105