Writing Mathematical Theorems: Towards an Innovative Pedagogy

Abstract

Objectives: Teaching mathematical theorems in Indian classroom settings usually focuses on explaining the statement of the theorem followed by methods of giving its proof. This hardly enables students to learn how to write a new theorem. Even teachers, at times, express their inability to write a new theorem. The objective of this article is to present a situational casestudy explaining the general processes involved to facilitate writing a new mathematical theorem. Methods: The methodology followed for coming up with a new mathematical theorem is based on careful observation of events around and recognizing patterns thereof. The emphasis is on summing up facts at different levels of observations, in order to evolve a concise theorem. Findings: From a small observation of the arrangements of the numbers on the keypads of a mobile phone or a calculator, a general mathematical theorem is evolved. This is an example for the pedagogy to be followed for writing a mathematical theorem, which can be useful both for the teachers and the students to self-educate themselves in new situations and casestudies. Novelty: This article formulates an innovative pedagogy using the mathematical concepts of subtraction, addition, divisibility, pattern recognition and generalization & randomization of event to evolve a mathematical theorem. The transformation in statement of the theorem with addition of more and more facts leading to its newer versions is the main feature of this article. Keywords: Mathematics Education; Mathematical Theorem; Innovative Pedagogy; Pattern recognition; Teaching Methods