What are the most essential methods of Teaching Mathematics?

In recent times, Perry in England and Moor in America called attention to the growing need for recognizing Secondary and College Curricula. The use of method, laboratory models and experiments was advocated. Important view points crept into the minds of the mathematicians with regard to not only “what to teach” but also “how to teach”. This movement is popularly, known as Perry movement.

What to teach relates to content of the subject as to how much matter to be taught at a certain level of education. This is certainly important. But “how to teach” is really a difficult problem for the teacher. Teaching, it is said, is an art.

Methods are the ways to understand and practice art; and this goes for the “how” aspect of teaching of Mathematics “How to impart mathematical knowledge?” and “How to enable the child to learn it?” are the two most important questions before the teachers of mathematics to do the job of teaching.

The main methods are the inductive and the deductive: the analytic and the synthetic, the dogmatic, the heuristic and the laboratory.

Long ago, the individuality of students was scarcely considered. The method of deduction was responsible for the dullness and monotony in the class and taxed the brain too much. Nowadays learning by doing predominates.

Opportunity is provided for practical work a greater responsibility is thrown on the pupils. Accordingly’ methods have undergone radical changes. Analytic rather than synthetic, inductive rather than deductive, practical rather than theoretical methods are preferred. Let us now look into these methods of teaching Mathematics in Secondary Schools.

Inductive and Deductive Methods of Teaching Mathematics

It is a combination of two methods. In order to understand this combination, one shall have to understand them separately.

Inductive

All new teaching should be started with inductive method and should end in deductive method. Inductive method is laborious and lengthy, but it leads to knowledge and discovery. We proceed from concrete to abstract; and from known to unknown.

To speak it more meaningfully, inductive method is based on induction. Induction in Physics means production of electric current by magnetic changes in the neighborhood without contact. Induction is proving a universal truth or theorem by showing that if it is true to any particular case, it is further true to the next case in the same serial order.

In this method we proceed from particular to general, from concrete to abstract, from known to unknown and from special example to general formulae. It is a method of constructing formulae with the help of sufficient number of concrete examples. After a number of concrete cases have been understood, the student successfully attempts the generalization as given below:-

Squares of (a+b), (x+y), (1+m), (p+q) can be generalized as (1st term +2nd term)² = 1st term² + 2nd term² + 2) (1st term), (2nd term)

Average = Generalization by calculation of a number of averages can be made as,

Sum of the terms Number of terms

Deductive Method

It is opposite of inductive method. Here the learner proceeds from general to particular from abstract to concrete, and from formulae to examples. In this method, the students are asked to solve the relevant problems with the help of pre-established formulae.

And as such, the pupils have to memories a large number of formulae and rules. After forgetting these formulae the student feels helpless as he cannot explore into the problems. So deduction places memory at a premium and intelligence at a discount.

The deductions arrived at through induction must be applied to particular cases. It is deductive method that gives speed, skill, efficiency in the solution of problems. There is no deduction without induction. In this method, the teacher explains the application of the formulae to problems; he solves a number of such problems on the black-board. The students come to learn as to how the formulae can be used to apply. As for example:—

(1) Area of a rectangle = Length x breadth

(2) Simple Interest =Principal x Rate x Time/100.

(3) Profit or loss is always calculated on the cost price.

The students are required to memories these formula and apply them to solve the problems in the lines of those formula.