All parents, whether home educating or not, have the opportunity to introduce their toddlers to many subjects and activities. But some shy right away from the idea of maths for toddlers or small children.
Some people teach extensive counting by rote at an early stage, but I believe this is unhelpful. The first thing a child needs to know is what numbers are, not what order they come in. This should come naturally into conversation from the early years, perhaps as you are getting your baby dressed. ‘Here’s one sock, here’s the other sock. That’s two socks!’ Or when you’re having meals: ‘Here are two apples. One for me, and one for you’.
As your child is learning language, introduce the lower numbers naturally and in context, and your child will get to know the relevant concepts as easily as he learns about animals or food. A useful site with activities to help your child understand basic number concepts is Numberline Lane.
Shapes and patterns
Understanding about shapes and patterns is a useful exercise with small children too, who often see the world in different ways from adults. If you’re not sure of the correct names for basic flat shapes such as circles or triangles, the page Simple geometrical shapes gives a quick overview.
To provide a good background for arithmetic ideas, introduce your children early on to Duplo and then Lego. Building walls, they quickly discover simple addition facts: for instance that two ‘two-bricks’ go together to make a ‘four-brick’.
Talk to your children about these concepts as part of everyday speech: ‘There are four of us, and Grandma is coming to tea so we need five plates’…. ‘We have ten little cakes here – how many will we each have?’ Counting aloud, showing practical adding and dividing provides the background a child needs to make sense of numbers when he comes to see them on paper. If your child is interested in the abstract concept of adding and subtracting, you might like to take this further, as explained on my page Introducing number bonds.
Simple fractions
You can begin talking about simple fractions at around the same stage, in the same relaxed manner. Cut an apple into four, then show how two quarters are the same as a half. A child who has difficulty understanding fractions at the age of 8 probably never saw how they worked intuitively at the age of three or four.
Lego, too, can be used to demonstrate simply how fractions work: don’t deliberately set out to teach a maths lesson, but take the opportunity to point out how you can divide an 8-brick into four twos, or a 12-brick into three fours. For further ideas on developing this, see my article Fractions for four-year-olds? or explore the maths games at the PBS site, some of which are suitable for very young children just beginning to understand number concepts.
Take it slowly
There is no need hurry maths skills for a child learning at home. Gone are the days – even in schools – when children learnt a concept and did weeks of drill in the same topic, then moved on to something else. Mathematics is a gradual discovery and awakening, and your child will understand and enjoy it more if he works entirely at his own pace.
Whenever you can relate something in real life to his maths topics, do so. Count aloud when you set the table, or collect library books for returning. Count the number of stairs when you go up and down. Talk about the clock face, and the numbers on it, and what the hands mean, as you discuss the time of day and when certain activities will take place. Bake cakes and biscuits together, and explain what the measurements mean, giving further explanations of weight and measure only if your child asks.
If you want to ensure your child covers basic maths skills, including arithmetic, in a fairly formal manner, you can still do this without drill or boredom, so long as you teach concepts rather than ‘facts’. Numbers are all inter-related, and a child who understands this will always be able to work out ways of doing arithmetic, even if not at the rapid speed of a ‘drilled’ child. But he is far more likely to find interesting ways of solving problems, and to enjoy maths all his life, whereas a child taught by drilling and factual memorisation is likely to find the topic tedious and painful.
More basic maths for young children:
Beginning multiplication
Number bonds – beginning addition
Introducing place value
Prime numbers and factors