What is a number?

In my previous blog post I explored some of the reasons why you might consider having a tutor for your child. One reason was to develop a child’s skills and confidence in maths: this can be achieved by giving them a better understanding of mathematical concepts, numbers and problem-solving. In this blog post I will look at ways of building on a child’s numeracy skills, which will equip them with strategies to handle the number problems which are found in all areas of mathematics, from addition and subtraction to data handling and measurement.

For a child to be comfortable with numeracy he or she needs to understand three concepts of number: a number as a symbol; a number as an amount; a number as a position. Let’s look at each of these in turn.

Number as a symbol – this is simply the recognition of the shape of a number, which distinguishes it from the shape of another number. For example, a 4 looks different from an 8. This nominal aspect of number is used purely to label objects or to identify that one thing is different from another. For example, in a block of flats, flat 3 is different from flat 7 – a footballer wearing shirt number 21 is different from a player wearing shirt number 13.

Number as an amount – this cardinal aspect of number helps a child to visually recognise the size of a number when compared to another. In other words the amount 9 is more than the amount 7. This aspect of number allows a child to see the size of each number and how it compares to the size of other numbers. There are a range of strategies to develop a child’s understanding of a number as an amount; these strategies will help build mental connections between numbers and their values. Pictures or images can be used to show objects, such as 6 sheep in a field or 2 pigs in a pen. Counters or cubes can be used to give a child a concrete experience of handling a given number and how it looks and feels when compared to another number. The recognition of a number as an amount is vital if a child is to understand place value, which requires a child to realise that the digit 2 in the number 21 represents twenty and not two.

Number as a position – the ordinal aspect of number enables a child to understand where a number value is positioned in relation to other numbers. This helps a child develop skills in sequencing numbers and recognising patterns in numbers, which are essential skills in many assessments, including Secondary School Selection Tests and Common Entrance Exams. Simply counting orally will help a young child develop awareness of the order of numbers and this can be extended by the use of number lines and number squares as a child becomes confident with larger numbers.

For a child to become confident across a range of mathematical concepts it is vital he or she understands the order of numbers and the amounts they represent. Through the use of

language, symbols, images and practical exercises a child can develop mathematical confidence and make mental connections between experiences with numbers.