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 person’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 through the prism of numbers.

Number Sense in math is "in a limited way" the equivalent of phonemic awareness in language.

Though number sense starts with understanding small whole numbers, it is equally applicable 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 initially in the sense of the "countable quantity". We start understanding it as “numerosity sense”.

Numerosity is Independent of Individual Size

We need to understand that while talking of numerosity we do not take into consideration, the "size" of the individual items counted. A large 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 many” is about things we can count. It includes ideas like the number of fingers and the number of goats.

“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.

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 of life.

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

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.

How Much is Easier to grasp than How Many

The idea of a ‘measurable’ quantity (how much sugar?) is easier to grasp than ‘countable’ quantity (how many mangoes?). Hence we use many words related to the idea of "How Much?"

Limited Vocabulary to Describe "How Many"

Hence we have evolved many words to describe & compare the idea of “how much” - Big/ Small, Large/ Small, Tall/ Short, Thick/ Thin, More/Less etc.

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

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.

When asked about the capacity of a hall, we interpret it as question asking "how many" can be accommodated in the hall.

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