Why Math is Best Suited to Develop Thinking Skills

< 2.1 Why we Learn Math in School? | Topic Index | 2.3 The Reality of Math Education in Indian Schools >

Math is a different kind of subject, compared to languages, science &amp; social science. Subjects other than math have a lot of &ldquo;information&rdquo; content which needs to be remembered.

Subjects like science &amp; social sciences are developed by observing the environment and trying to find causes for the many events which occur in it. Math has its own internal logic for development which is not related to the physical world.

If we look behind numbers &amp; shapes, math is a very abstract subject. It is full of concepts which are abstract mental ideas. The idea of a &ldquo;prime&rdquo; number is an example. The concepts are also arranged hierarchically like a pyramid built with playing cards. These concepts are connected vertically through different grade levels. The very idea of numbers changes as we go up grade levels. They are also connected horizontally across different topics &amp; even across subjects at the same grade level.

Unlike other subjects, even procedures &amp; algorithms are based on conceptual understanding. For example, understanding the algorithm of addition of multi-digit numbers depends on a good grasp of the place value system.

The concept of addition &amp; competency in it is necessary not only in various other operations but also while dealing with different kinds of numbers &amp; even non-number ideas! Math- related thinking is also necessary to understand many areas in these non-math subjects. Some of these are tabulating, graphing, representing, calculating etc.

Basic Math concepts spring from our daily human experiences. But more complex concepts are rapidly built on these basic concepts, layer by layer, like in an onion. The development of the discipline follows an internal logic of the discipline of math itself. Abstractions develop into increasing layers of complexity which after a point of time become difficult to relate to daily experiences. An example is the necessity to invent negative numbers, though they cannot be represented physically. Students cannot grasp higher-level concepts unless they have a good grounding in the concepts of the primary school.

But all children understand at least numbers up to 4 or 5, before they come to school, because they are constantly exposed to them, visually and aurally, in their surroundings. Even a small child, presented with 2 bowls of chocolates, would choose the bowl which has more chocolates. She has an understanding of &lsquo;more&amp; less&rsquo; but lacks the language to express it. All children have a rudimentary sense of numbers.

At Primary School level the concepts are closely related to the environment &amp; daily experiences of children. If they are presented to children such that they can see that they 'mirror their real-life experiences'', students would start easily grasping them and start constructing difficult concepts on them. They would also enjoy the intellectual process of constructing math. For example, the experience of collecting your belongings can be related to the process of addition.

Hence math in primary school should be used for training students to see the emergence of concepts from the environment and the evolution of complex concepts from simpler concepts. Students should also be trained to look for relations connecting various concepts both horizontally &amp; vertically. They need to realise that even the four basic operations are related to one another.

Mathematicians, educators & philosophers have identified 5 important mental & intellectual skills which can be developed through the study of math. These can together be called "Mathematical Thinking".

Let us briefly see what these skills are.

< 2.1 Why we Learn Math in School? | Topic Index | 2.3 The Reality of Math Education in Indian Schools >