What is Number Sense?

In the previous section we saw that many children have the ability to “perceive” numbers associated with small sets, without having to count. It is for this reason that numbers 1 to 5 are called Perceptual Numbers.

This can be called the starting stage of Number Sense.

Number Sense

Number Sense is defined in various ways. Some of them are given below.

1.	It is an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.

2.	It is an ability to work outside of the traditionally taught algorithms, e.g., “a well-organized conceptual framework of number information that enables a person to understand numbers and number.”

3.	Number sense refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.

Number Sense in math is the equivalent of phonemic awareness in language.

It is an idea which can be applied to all types of numbers.

Numerosity Sense

The word “number” is used in daily life in several different senses.

It could denote a “total” as in - what is the number of people in this hall?

It could denote an “order” as in – what is your number in the queue?

It could denote the “numeral” associated with a number.

The term “number sense” is used here in the sense of a countable quantity. Let us understand it as “numerosity sense”.

We need to understand that while talking of numerosity we do not take into consideration, the "size" of the items counted. A watermelon and a small berry would be "two" in terms of numerosity.

We need to clarify this to students through many examples.

Sense of Magnitude & Evolution

The sense of magnitude has been built into the brains of all living beings by the process of evolution. It is very important for their survival.

It is part of the “thinking process” of deciding whether to flee or fight when confronted by an enemy or a predator.

It is part of the “thinking process” of deciding whether we can jump over a stream or need to wade through it.

How Much & How Many

The concept of magnitude is sensed in two forms, which can be called “how many” and “how much”.

“How much” is about things we normally do not or cannot count. It includes ideas like size of a bag, depth of a river etc. We will learn them later as “measurable” quantities.

“How many” is about things we can count. It includes ideas like the number of fingers and the number of goats.

In evolutionary terms, the sense of “how much” is much older than the sense of “how many”. It must be as old as evolution of living beings, since the fight for survival must have started right from the beginning.

The idea of “how many” however must have developed only in the last 10,000 years when humans formed settlements and started acquiring property and a sense of possession.

Hence sensing of “how many” was not very important for our evolutionary survival.

The idea of a ‘measurable’ quantity (how much sugar?) is easier to grasp than ‘countable’ quantity (how many mangoes?).

We have very few words specific to the idea of “how many”. Apart from the number names (one, two etc) themselves we only have “many, few, sparse & numerous”.

Hence most of the words we have to describe magnitude are of the “how much” type - Big/ Small, Large/ Small, Tall/ Short, Thick/ Thin, More/Less etc.

Because of this lack of vocabulary, we use many “how much” words like more & less to also denote “how many”. The exact interpretation depends on the context.

This lack of “how many” vocabulary also makes the concept of a “number” more difficult to understand and even communicate.