Nature of School Math

Before we look at effective ways of learning math, we need to understand the nature of math as a subject to be learnt.

Like any other subject learnt in school, the knowledge in math can be classified into 4 kinds.

1.	Factual Knowledge – that needs to be “remembered & recalled”

2.	Procedural Knowledge – that needs to be “practiced”

3.	Conceptual Knowledge – that needs to be “understood”

4.	Habits & Attitudes to be developed – that needs to be “internalised”.

These have also been arranged in ascending order of difficulty – both in learning & teaching. Let us look at each of them in brief. We will look at each of them in detail in subsequent articles.

Concepts are abstract ideas which cannot be sensed by our 5 senses. They have to be grasped by a 6th sense using our thinking skills, a process which we call understanding. An example is the idea of a prime number. We cannot observe this just by seeing a number.

Understanding itself is a difficult idea. There is no clear understanding of what is understanding.

Math is a subject which contains a preponderance of concepts. Children in primary school do not have the mental capacity to directly "understand" concepts.

Math also has an equal amount of procedures & computations to be mastered. Many procedures themselves are based on understanding of certain concepts. FOr example, the procedure for adding two 2-digit numbers is based on a concept called "regrouping" or "carry over". Hence procedures need to be practiced many times, with an understanding of the underlying concept to attain mastery

Factual knowledge consists of statements, definitions & conventions. The statements may be mathematically & factually correct or incorrect. Their correctness however can be verified.