What is Mathematics 1

A Section for the Math Teacher

In this book, we have, till now, covered the math curriculum in grades k-8 with a focus on understanding the concepts & procedures. We have followed the development of different types of numbers, shapes, operations and the inter-relations between them.

We have also seen that math has developed into a very precise language capable of expressing the core idea of a situation using numbers & symbols, cutting out any unnecessary information.

We now devote an entire section to understand what the discipline of mathematics itself is. This is for the understanding of most teachers of mathematics.

Many of the issues touched upon in this article briefly, would be taken up for a more detailed treatment in subsequent chapters of this section.

Early Development of Math & Science

Most scientific & mathematical concepts & theories started in ancient times as “stories” for explaining the universe. Stories preserve memories of old “observations” from the hoary past.

Slowly these theories took shape toned by observations over a long period of time.

Development of Math

Ideas of math have been built into our minds by the process of evolution. We have seen this in Chapter 3.1. Math educators have also identified Number Sense as a skill critical for learning math, which emanates from our brain.

We also see ideas of math expressed in the world around us in terms of the spirals of a galaxy, curves of a shell and arrangements of petals in a plant & seeds in a flower.

We have also explored the reasons why we learn math in Chapter 2.1. Math is a compulsory part of the school curriculum in all countries.

However, a peculiar aspect of math is that, both students and teachers find it difficult to explain what is it that they are learning in math.

For entirely different reasons, even mathematicians, working on areas of math, find it difficult to explain what they are working on to non-mathematicians.

There are a lot of wrong or partial perceptions about math among students & teachers. Most think that math is mainly about numbers & shapes and that it has a lot of rules to be memorised.

The Indian school math curriculum does not help matters since it focusses mainly on procedural aspects without making any mention about critical issues like Number Sense.

The fundamental reason for such wrong perceptions is that the “nature” of math and how it is different from other subjects, have not been clarified in the curriculum. Hence teachers are unaware of this aspect.

Like any other topic to be learnt, math also consists of 4 kinds of knowledge – Conceptual, Procedural, Factual & Values.

And each of these kinds of knowledge needs a different kind of approach to learning & teaching. Concepts are particularly a difficult idea for children in the Primary School to understand. Teaching of concepts needs to be different.

The important thing about math is that it has a preponderance of concepts, even in pre-school and primary school. Even the procedures in math are based on underlying concepts. Hence math needs a different kind of pedagogy as compared to other subjects.

Wrong pedagogy is the major reason for math being known as a difficult subject both by teachers and students. This has also given rise to a perception in society that only certain “math persons” can learn math. Competence in math is correlated with intelligence.

Wrong pedagogy leads to issues like math avoidance, math anxiety and even math phobia among students.

Changes in Perception of Math

At the same time, as the discipline of math developed, perception about it has been changing through the centuries.

Even within the school curriculum, the changing nature of math is visible starting with the topic of integers. Math starts loosening its ties with physical reality and takes off into an abstract realm where the main guiding principle is the internal logic of math.

Teachers are mostly unaware of this shift and are not able to explain it. The end result is strengthening of the belief that math is only for a few persons.

In the last few decades, the world is moving towards increasing digitization and a knowledge-based economy. In such a society, knowledge of ideas & skills related to math are essential for survival and individual prosperity.

Another carpet is also being pulled from under our feet. Computers & software have made traditional computational skills totally redundant. The emphasis in math education, in developed economies, is shifting towards development of critical and logical thinking.

The math curriculum being taught in Indian schools is becoming irrelevant to the needs of the society. The objectives of math education need to be revisited and the curriculum and pedagogy of math education reviewed.