Nature of Mathematics: The nature of Mathematics can be made explicit by analyzing the chief characteristics of Mathematics. (i) Mathematics is a science of Discovery: E.E.Biggs states that, "Mathematics is the discovery of relationships and the expression of those relationships in symbolic form – in words, in numbers, in letters, by diagrams (or) by graphs."
Problem solving – a sort of healthy mental exercise. (iii)Mathematics deals with the art of drawing conclusions: One of the important functions of the school is to familiarize children with a mode of thought which helps them in drawing right conclusions and inferences. According to Benjamin Pierce, "Mathematic is the science that draws necessary conclusions." In Mathematics, the conclusions are certain and definite. Hence, the learner can check whether (or) not he has drawn the correct conclusions, permit the learner to begin with simple and very easy conclusions, and gradually move over to more difficult and complex ones.
Mathematics is a tool subject: Mathematics has its integrity, its beauty, its structure and many other features that relate to Mathematics as an end in it. However, many conceive Mathematics as a very useful means to other ends, a powerful and incisive tool of wide applicability. In the article "Mathematics & the Teaching Sciences", John. J. Bowem pointed out that, "Not all students are captivated by the internal consistency of Mathematics and for everyone who makes it a career; there will be dozens to whom it is only an elegant tool." As Howard. J. Fehr says, "If Mathematics had not been useful, it would long ago have disappeared from our school curriculum as required study."
Mathematics involves an intuitive method: The first step in the learning of any mathematical subject is the development of intuition. This must come before rules are stated (or) formal operations are introduced. The teacher has to foster intuition in our young children, by following the right strategies of teaching. Intuition when applied to Mathematics involves the concretization of an idea not get started in the form of some sort of operations (or) examples. Intuition is to anticipate what will happen next and what to do about it. It implies the act of grasping the meaning (or) significance (or) structure of a problem without explicit reliance on the analytic mode of thought. It is a form of mathematical activity which depends on the confidence in the applicability of the process rather than upon the importance of right answers all the time. It is up to the teacher to allow the child to use his natural and intuition way of thinking, by encouraging him to do so and honoring him when he does.
Mathematics as a science of Logical Reasoning:
Mathematics is the science of precision & accuracy: Mathematics is known as an exact science because of its precision. It is perhaps the only subject which can claim certainty of results. In Mathematics, the results are either right (or) wrong, accepted (or) rejected. There is no midway possible between right and wrong. Mathematics can decide whether (or) not its conclusions are right. Even when there is a new emphasis on approximation, mathematical results can have any degree of accuracy required. It is the teacher's job to help the students in making decisions regarding the degree of accuracy which is most appropriate for a measurement (or) calculation. (vii)Mathematics is the subject of logical sequence: The study of Mathematics begins with few well – known uncomplicated definitions and postulates and proceeds step by step to quite elaborate steps. Mathematics learning always proceeds from simple to complex and from concrete to abstract. It is a subject in which the dependence on earlier knowledge is particularly great. Algebra depends on Arithmetic, Calculus depends on Algebra, Dynamic depends on Calculus, Analytical Geometry depends on Algebra and Elementary Geometry and so on. Thus gradation and sequence can be observed among topics in any selected branch of Mathematics. (viii)Mathematics requires the application of rules and concepts to new situations: The study of Mathematics requires the learners to apply the skill acquired to new situations. The students can always verify the validity of mathematical rules and relationships by applying them to novel situations. Concept and principle become more functional and meaningful only when they are related to actual practical applications. Such a practice will make the learning of Mathematics more meaningful and significant.
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