# Mathematics Pedagogy PDF

### Pedagogy Of Mathematics

Mathematics is a subject that finds application in every walk of our life.

Knowingly or unknowingly, people use concepts of Mathematics in their daily life. Considering the relevance of Mathematics, it is treated as one of the basic and compulsory subjects in school curriculum.

In the elementary school curriculum, learning basic concepts of Mathematics is emphasised.

As and when children reach higher classes, the complexity of mathematical concepts gets widened.

It is commonly observed that many children have a belief that Mathematics is, in a way, difficult to learn and understand.

In this context, teachers have a great role to play.

A successful teacher of Mathematics should have profound knowledge of nature and theoretical concepts in Mathematics so as to help children in effective learning.

The nature of Mathematics includes mathematical ideas progress from concrete to abstract; grow from particular to general and its knowledge is conceptual as well as procedural.

Similarly, in Mathematics we come across ‘definitions’ that describe concepts; ‘examples’ to illustrate procedures; ‘theorems’ to state valid results; ‘conjecture’ that talks about mathematical statements for which proofs are to be worked out but which seem plausible, and ‘counter example’ to disprove statements.

A teacher who has adequate knowledge on these aspects of Mathematics would be able to organise learning activities in a more effective way.

This unit will elaborate on these concepts in an extensive manner.

DISCIPLINE OF MATHEMATICS

The development of the discipline of Mathematics dates back in thousands years.

Starting from the prehistoric period to the twentyfirst century, much development has taken place in the field of Mathematics.

The Babylonian, Egyptian, Greek, Chineese and Indian mathematicians have contributed remarkably to the field of mathematics.

To name a few, Pythagoras, Fibonaaci, Aryabhata, Euclid, Archimedes and Rene Descartes have contributed significant inputs to the field of Mathematics in ancient times.

During the sixth century B.C. Pythagoreans (Pythagoras and his followers) coined the term Mathematics.

Mathematics is derived from the Greek word ‘Ganita’ which means ‘inclined to learn’. ‘Mathematics’ is a broad term that encompasses many branches and components.

It is this view that makes the word ‘Mathematics’ hard to define. Even then, we would say.

Mathematics is a science that involves dealing with numbers, different kinds of calculations, measurement of shapes and structures, organisation and interpretation of data and establishing relationship among variables, etc.

Despite of such broadness, a few definitions of Mathematics are given below:

“Mathematics should be visualised as the vehicle to train a child to think, reason, analyse, and articulate logically.

Apart from being a specific subject, it should be treated as a concomitant to any subject involving analysis and meaning” (National Policy on Education, 1986).

• “We cannot overstress the importance of Mathematics in relation to science, education and research.

This has always been so, but at no time has the significance of Mathematics been greater than what it is today-it is important that deliberate efforts are made to place India on the world map of Mathematics within the next two decades or so” (National Education Commission or Kothari Commission, 1964-66).

• “Mathematics, as an expression of the human mind, reflects the active will, the contemplative reason, and the desire for aesthetic perfection.

Its basic elements are logic and intuition, analysis and construction, generality and individuality” (Courant and Robbins, 1996)

The definitions given above will enable one to conclude that; Mathematics is a study of patterns, numbers, geometrical objects, data and chance.

It is a diverse discipline that deals with data analysis, integration of various fields of knowledge, involves proofs, deductive and inductive reasoning and generalisations, gives explanation of natural phenomena and human behaviour.

Mathematics also helps to understand the world around us by exploring the hidden patterns in a systematic and organised manner; and it has universal applicability.

Mathematics is considered as a formally organised subject of study, and hence, it is treated as a discipline.

In Mathematics, we deal with various branches such as arithmetic, algebra, geometry, trigonometry, etc. The branches of Mathematics find application in our daily life.

Keeping these views, it is said that Mathematics has gained relevance and popularity as a useful subject. Mathematics is classified broadly into two types, which are given below:

Pure Mathematics: A study of the basic concepts and structures for the purpose of a deeper understanding of the subject.

Pure Mathematics deals with the basic information/facts of Mathematics where various concepts, proofs and theories, etc. are discussed.

For example, the theoretical knowledge concerning arithmetical operations such as addition, subtraction, multiplication and division are part of it.

Applied Mathematics: Applied mathematics is an abstract science of numbers, quantity and space as applied to other disciplines such as Physics and Engineering.

The Pure Mathematics when utilized to solve different problems either mathematical or life is termed as applied Mathematics.

For example, children study the concept of ‘addition’ which is explored while buying food items from a grocery shop’ the concept of ‘interest’ is used to calculate the interest on money deposited in banks, etc.

Concept and Nature of Mathematics

People started using the concepts of Mathematics long back, and it is the backbone of modern civilisation.

Nowadays, Mathematics is used by every individual.

Consider an example of a boy who buys groceries from a shop. The boy may ask, “Uncle! Can you please give me 1 kg sugar?”

Then the salesman would use his weighing balance to weigh the sugar.

For that, he will put 1 kg weight in one pan of the balance, and in the other, he will put 1 kg sugar.

He will put sugar until it gets balanced with the 1 kg weight.

Then, he will hand over the sugar to the boy, and in return, the boy pays the price for 1 kg sugar.

What did you understand from this example? Did you find any Mathematics here? Definitely! in the given example, Mathematics is involved at many places.

For instance, the boy asks 1 kg sugar. Mathematics is involved in it.

The quantity ‘1kg’ sugar is a kind of measurement.

When the salesman weighs, he makes use of the principle of balance (in a way, balancing equations, equal to symbol etc.).

Similarly, the payment of price of sugar also involves Mathematics.