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By far the most useful thing for young children to have when starting to learn maths is confidence. Confidence is key.
The usual process when young children begin to learn maths is for them to start with hands-on, practical work, such as counting coloured blocks or physically sorting toys into different groups. The child learns that a digit written on a paper corresponds to a certain number of objects.
When, and only when, the child is ready they move on to visual representations of those objects. An addition sum might be displayed as three pictures of bananas and four pictures of apples, with the question 'how many pieces of fruit are there altogether?'.
After this, dots might be used instead of pictures (known as an array) and, at around the same time, the child will begin to use number lines to help with calculations. Four multiplied by three might be shown as an array of three parallel rows of four dots, or as three 'jumps' of four along a number line.
Number lines will accompany the child's mathematical journey for several years, until they are confident with more formal 'written methods'. These are processes such as grid multiplication which tend to be the methods parents remember from the own school days.
The important thing to remember is that your child will move through these stages when it is right for them to do so. Forcing them to move on before they are ready is counter-productive. Very few adults perform addition by lining up the right number of teddies and then counting them; your child WILL move through the stages when they are ready to. To help your child, encourage them to enjoy the method of calculation they are comfortable with. Praise them when they apply what they know and take an interest in any maths knowledge they want to share with you.
A child who is confident in their maths will automatically begin to look for more efficient ways to work things out, as and when they are ready. In this way, they will progress through the stages of calculation at their own pace and with confidence.
