Pre-Number Concepts 1

Pre-Number Concepts & Skills

Children come to school with some elementary math-related concepts & skills which they learn at home.

Among these are identifying small quantities perceptually, which we call perceptual numbers. In the previous chapter we talked about strengthening their understanding and ability of perceptual numbers in pre-school.

This skill is part of a set of skills called "pre-number skills", which build the foundation for children to understand the abstract concept of a number.

The basic idea of pre-number skills is to enable children understand the idea of sets, of numerosity/ cardinality of sets and how numbers can represent numerosity in a very precise manner.

Acquiring Pre-Number Skills

In this and the next two chapters we will deal with various aspects of pre-number concepts and activities to enable children to understand as well as acquire them.

Some of the most basic pre-number concepts are

1. Compare & Contrast

2. Belong/ Does not belong

3. Pairing

4. Grouping/ Sorting by physical attributes like colour, shape, texture, size etc

5. Seriation

These activities enable children to observe various physical characteristics of items in a collection and learn to form other kinds of collections or sets based on some of these.

An important lesson is that the membership of a set is not fixed but dependent on the selected criteria. The same item, say a green triangle, can belong to a set of green items and also a set of triangles.

Seeing things grouped in sets also leads to the idea of numerical quantity and then to numbers.

Compare & Contrast

Compare & contrast objects using properties, some of which are given below.

Ideas like - Tall/ Short, Big Small, Sweet/ Sour, Loud/ Soft, Heavy/ Light. Tall/ Short, Big/ Small, Rough/ Smooth, Soft/ Hard, Sweet/ Sour, Hot/ Cold, Loud/ Soft, Heavy/ Light, Blue/ Green, Bright/ Dull.

Example - Ram & Lakshmi are siblings. Lakshmi is tall and compared to her Ram is short.

Initially these qualities cannot be quantified using numbers.

Later, as children start understanding the concept of numbers, they can compare and contrast sets of things using their respective quantities or cardinalities.

Belong/ Does Not Belong

Children need to play with things which have a variety of characteristics like colour, shape, texture, taste, smell etc. This helps them to identify different characteristics of items in a collection.

One of the basic skills is to look at a collection and decide which items can belong to a particular group and which items do not belong to that group. For example, there could be a green piece in a collection of red pieces. Or there could be a triangular piece in a collection of rectangular pieces.

Children should be allowed to make independent decisions on these but explain the reason behind their decision. This gives them a sense of autonomy, improves both their critical thinking but also their ability to use language to explain their decisions.

Pairing

This is to locate 2 objects which are connected in some familiar way. For example they could need to be used as a pair. They can be of 2 kinds; like and unlike.

Like items are a pair of shoes (left & right), palms (right & left). Or it could be arranging pairs of roses in a number of flower vases.

Unlike items which can be paired are shoe & socks, eyes & spectacles, pencil & eraser etc. The items look totally different from each other but still connected by the way they are used together.

These exercises with things familiar to the child would develop its mental ability.

Sorting

Sorting is one of the most basic and important activities. It is an extension of the "Belong/ Do Not Belong" idea.

Children play with different materials and group them in different ways as per the any of the physical properties. The child sees a green triangle piece in a group sometimes with green things of different shapes and sometimes with triangles of different colours. By repeatedly seeing things as part of different collections, they form an idea of a set of objects.

By seeing sets of containing various quantities they also get a sense of the cardinality of sets.

Sorting is a Fundamental Learning Skill

Sorting also involves critical thinking which is very necessary in any learning activity. Any definition in sciences basically says which set a particular thing belongs to and at the same time identifies in what way it is different from other things in that set.

For example, consider the definition "a plant is a living being which makes its own food". It is first clarified that the plant belongs to a set of "living things". Then it is clarified as to how it is different from other living beings in that set by saying "they make their own food" whereas other living beings do not make their own food.

We have seen in Chapter 4.3 the rough stages by which sorting activities enable children to observe collections with varying numbers of items and slowly develop an idea of different quantities and strengthen number sense.

Seriation of Individual Objects

A set of objects sharing the same property, say size, can be arranged in increasing or decreasing order of that property. Blocks can be arranged in increasing order of height.

This activity also leads to the idea of "order" and that the same arrangement can be seen as increasing or decreasing in order depending on the direction of our perception.