DANGER OF IMPROPER USE OF MATHEMATICAL RESULTS, FORMULAS AND SYMBOLS: ALGEBRA

Abstract

Mathematics Education has two aspects: the first deals with how to teach and the second with what to teach. The first aspect is concerned with the methodology of teaching mathematics, the “how and why” of learning process, the discussion of the objectives of learning mathematics, preparation of question bank, teachers’ guides and so on. The second aspect deals mainly with the content, i.e., the subject matter of mathematics. In actual practice, teachers are often found to be giving more attention to the first aspect. It appears that the second aspect of mathematics education has not been paid so much attention resulting in students’ getting wrong notions and concept in the content area. Since in teaching mathematics to the students, only manipulatory aspect has generally been emphasised, mathematical rules, formulas, theorems, etc., are mechanically memorised by the students without giving importance to the aspects – the language, the thought process and the logic of the subject. As a result, students sometimes get used to mathematical results, formulas, etc. without giving a thought to their validity and restrictions on them, if any, thus arriving at some fallacious results and mistakes for which they hardly find proper explanation. In a series of articles of which this is the first, these types of improper use of results, formulas, etc., from various branches of mathematics and their consequences will be discussed with the help of examples.