What is a Number?

Number is an abstract idea. In the previous section we saw that before children can understand the idea of numbers, they should be prepared through pre-number concepts & activities.

Let us explore the idea of a number in some detail.

Multiple Meanings of the word Number

We need to remember that the word “number” has several meanings – the numeral, number representation and the quantity. In many cases, the meaning of the term "number" has to be figured out from the context in which it has been used.

It is a good idea to use the word numerosity to indicate the idea of quantity.

How Much Vs How Many

Neuroscience research is showing that the part of the brain which is related to math, actually has two parts; one which judges “how much” and the other which judges “how many”.

Dr B Butterworth, author of “The Mathematical Brain” suggests that there seems to be a “numerosity module” or the "how many" area in our brain specialised for dealing with numerical representations of quantity.

A feel for number emerges from the “how many” area. In evolutionary terms, the sensing “how much” has been more important than sensing “how many.” Hence, the sense of “how many” has developed very slowly.

In daily language, there are only very few words, like many & few, to describe or compare the idea of numerical quantity. We mostly end up using number words like three or four. We use the word ‘number’ to indicate a number by itself (as a noun) as well as the related quantity (as an adjective).

There is no other way of accurately describing a collection of mangoes except by using the word like “five.”

In contrast a quantity of rice can be described using various phrases as “a cup full” or “two handfuls” etc. Words like “less” and “more” are used in both counting and measuring situations.

“How Much” is more prevalent that “How Many”

In their daily experiences, children are more likely to hear words like big, large & long more frequently than words like four or five. Hence the idea of a ‘measurable’ quantity (how much sugar?) is easier for them to grasp than ‘countable’ quantity (how many mangoes?).

They can easily perceive the difference in quantity between 2 bags of rice. But the difference between 2 collections, particularly if they are not sufficiently different (basket of 5 apples vs basket of 6 apples), is difficult.

Hence, at early ages, it is not easy for children to mentally connect a small numerical quantity (a collection of pencils) with a number (say Three). It is a skill which has to be practiced.

So it is more difficult for humans to acquire a sense of “how many” or a sense of number.

In the last few decades, anthropologists, have come across remote tribes, (like Piraha in the Amazon basin & Walpiri in Australia) who do not have a sense of numerical quantity beyond two. Their social & economic life seems to find the ideas one, two & many sufficient for their needs.

Dyscalculia is a recently discovered learning disability which makes it difficult for children to understand numbers and numerical processes. Research is indicating that one of the primary reasons for this is the weakness of the “numerosity module” which results in an inability to develop a strong sense of number at an early age.

“How Much” also interferes with “How Many”

In real life both “how much” and “how many” situations often occur together.

Consider the difficulties when viewing a collection of say fruits. Piaget has shown that the same number of fruits when spread over a larger area is mistaken by children as “more.” A collection of five mangoes appears more than a collection of berries.

Colour (a green fruit) or shape (round fruits) or size (which is bigger) is easy for children to directly perceive. But, numerical quantity is not a concrete quality like colour of shape which can be perceived or pointed out directly.

Other Number Concepts

Numbers have several properties & relations which need to be understood. Some of them are;

1. Number represents countable quantity

2. The Number sequence is built on the logic of "one more" in one direction and "one less" in the reverse direction.

3. There is no "biggest" number. The sequence of numbers does not have an end.

4. Numbers are related to one another in a variety of ways.

5. Numbers have many properties

Hence the idea of a number is an abstract one and it requires a lot of practice & experience to acquire it.