Why Math is Best Suited to Develop Thinking Skills

Math is Concept-Dense

All living beings have the ability to think. But when we use the term "thinking" in relation to academics, we mean thinking at a "deeper level" which can be variously called logical thinking, structured thinking, critical thinking etc.

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

Math, on the other hand has a lot of abstract concepts which need to be "understood", through a mental process which has not still been understood even by neuroscientists and psychologists.

Math is full of concepts which are abstract mental ideas. For example, even the idea of a "prime" number is an example of an abstract concept.

These concepts are also arranged hierarchically like a pyramid built with playing cards. They 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 & even across subjects at the same grade level.

A deeper understanding of the network of concepts is necessary not only in various operations but also while dealing with different kinds of numbers & 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.

Even procedures & algorithms in math 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.

Subjects like science & social sciences are developed by observing the environment and trying to find mathematical relations underlying the events which occur in it.

Mathematical Thinking

In the last few decades, math educators have grouped five higher-order thinking skills into an umbrella term called "Mathematical Thinking".

1. Represent math ideas in several modes both to demonstrate understanding as well as communicate them to others

2. Communicate math ideas using the correct vocabulary and syntax both for understanding of other points of view as well as to make others understand our view points.

3. Connect math ideas from several subtopics & real-life to "make sense."

4. Understand the process of reasoning using math concepts and the idea of a proof, which is unique to math.

5. To use all the above to solve problems in real-life.

In a later chapters, we will explore the idea of "mathematical thinking" in some detail.

Basic Math Concepts Emerge from the Environment

Basic Math concepts spring from our daily human experiences & observation of patterns in the environment. But 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 fully be represented physically. Students cannot grasp higher-level concepts unless they have a good grounding in the basic concepts learnt in the primary school.

Developmentally, abstractions are very difficult for children in the primary grades. But all children acquire a rudimentary sense of numbers, before they come to school, because they are constantly exposed to them, over a long period of time, visually and aurally, in their home & surroundings.

Children also develop a lot of non-numerical concepts in their early years, due to evolutionary reasons. Even a small child, presented with 2 bowls of chocolates, would choose the bowl which has more chocolates. She has an understanding of "more & less" but lacks the language to express it.

Math is an Effective Vehicle for developing Abstract Thinking in Schools

Building capacity for abstract thinking is an excellent training ground for developing skills of mathematical thinking. Math, even in pre-school and primary school, is an excellent vehicle for developing such thinking skills.

Luckily, at Primary School level, math concepts are closely related to the environment & 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.

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 & vertically.