ArticleOpen Access http://dx.doi.org/10.26855/er.2026.03.005
An Exploration to Introduce the Formal System in Teaching Class
Feng Zhang
School of Integrated Circuits and Electronics, Beijing Institute of Technology, Beijing 100081, China.
*Corresponding author: Feng Zhang
Published: March 18,2026
Abstract
Formal systems are a central issue in mathematical logic and mathematics. The student who has never encountered it before may feel that it is very abstract and difficult to understand. To overcome it, a more natural approach to introducing the formal system in teaching classes is presented. Also, this approach has been tested in the author’s teaching class several times and received high evaluations. In this approach, several visual examples related to the mathematical logic and the formal system make the important effect on the understanding of the formal system. First, a simple and intuitive example about logic is presented, which can give students an initial feeling that the inference is not associated with the meaning of the sentences. Then, non-Euclidean geometry and Russell’s paradox in set theory have enhanced this feeling in students again. After this groundwork, the introduction of the formal system becomes more understandable for students in the author’s teaching class.
Keywords
Formal system; set theory; non-Euclidean geometry; mathematical logic; metamathematics
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Copyright
© 2026 by the author(s).
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How to cite this paper
An Exploration to Introduce the Formal System in Teaching Class
How to cite this paper: Feng Zhang. (2026). An Exploration to Introduce the Formal System in Teaching Class. The Educational Review, USA, 10(3), 141-147.
DOI: http://dx.doi.org/10.26855/er.2026.03.005