DESIGNING A LEARNING ENVIRONMENT WITH SOME SOPHISMS: RECOMMENDATIONS FOR TEACHERS TO PIQUE STUDENTS' INTEREST AND IMPROVE THEIR ENGAGEMENT IN MATHS SESSIONS

Abstract

The exploration of mathematics often involves encountering extraordinary challenges, intricate puzzles, sophisticated mental games, paradoxes, and thought-provoking sophisms. Delving into captivating examples has the potential to engage, enlighten, and inspire students, fostering a drive for discovery. This research paper aims to elucidate some intriguing mathematical sophisms and their implications within the realm of mathematics education. Several factors impact the establishment of an evolving educational setting for teaching mathematics from a humanistic viewpoint. The methodology adopted in this paper is a multi-case study that involves showcasing specific examples, highlighting these characteristics, and implementing mathematical concepts without strictly adhering to their assumptions, which can lead to logical inconsistencies. Students frequently need help with topics such as dividing an equation by zero or extracting a nonnegative square root. The tactics and stages of erroneous thinking that give rise to sophisms are intricately linked to various mathematical principles, including square roots, trigonometry, equations, differentiation, logarithms, geometry, binomial expansion, and integration. The requirements for developing a healthy learning environment with cheerful sensations are undoubtedly expressed. As a result, these emotions will stimulate students' thinking, link with their cognitive interests, and aid them in their future undertakings. This exploration delves into sophisms associated with each of these mathematical notions. It is our aspiration that those with an interest in mathematics will perceive the concepts presented in this article as a catalyst for future mathematical research.

Keywords

• Critical thinking
• engagement
• learning-environment
• misconception
• sophisms
• STEM education

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