Part 1: Maths by Ruth Merttens
There is unequivocal evidence that the skills children possess on entry to school make a difference. Their skill level predicts later success or failure in education.
We know that children who can count to 10, who know their letters, who can write their own name, and who are familiar with the practices involved in reading books and telling stories, are most likely to succeed at seven, 11, and later.
Therefore many in education have given a cautious welcome to the government's "desirable outcomes" for children's learning on leaving nursery education, feeling that these may help schools, play groups and parents to focus attention where it counts. However, there is also a great deal of anxiety, lest this approach should engender a narrow, over-formalised and pressurised curriculum for these very young children.
As far as the maths is concerned, there seems to be no contradiction between expecting that children can perform such feats as counting to 10 and recognising simple shapes, and the desire to ensure that their learning is exploratory, creative and enjoyable. The crucial point here lies in the relation between learning and teaching. In maths, at least, right from the start, there has to be a constant dialogue between those aspects of maths which we "teach" and those aspects which the children "discover".
To take an example, it is certainly the case that children are taught to count. Parents and teachers "teach" them by chanting the numbers in order, encouraging repetition and imitation, by showing children how to match numbers to quantities, and by demonstrating the number order. However, children need to make this knowledge their own through exploring number-use in a variety of contexts. They make sense of what they have been taught by using numbers in many different situations and by trying out ways to make them work effectively. Thus, if encouraged, they will discover that adding one to one end of a line of objects and taking one off the other end, leaves the quantity unaltered.
Counting is probably both the most basic and the most important skill that we teach children in these years. Almost all parents count with their children. Teachers, play group leaders and nursery nurses can encourage this as much as possible. Make a "counting card" for children as they enter a nursery or play group.
Encourage the children to count to their age, since this is often the first number that they recognise. Three-year-olds can count "one, two, three!" as they jump down the slide or start a race. They can be asked to make three biscuits, and shown how to match the numbers to the count. The essential piece of equipment in progressing from "one, two, three" to counting to six or 10 is the washing-line of numbers. Every day the children can chant the numbers in order as one child moves along the line pointing to each number in turn. This bit of daily "teaching" will not, in and of itself, ensure that children can use these numbers to count a set, nor that they understand that five is less than seven. It provides the necessary, though not the sufficient, condition for these things to happen.
The best way of allowing children to explore number-size as it relates to order is to use "bags". You will need several cloth bags (the ones they use in the Post Office for money are ideal). In front of a group of children, count three or four wooden bricks into the bag. Allow each child to shake the bag. How many bricks are there in it? Add another brick. How many bricks now? Take a brick out - how many now? Start again with an empty bag per pair of children. They throw the dice and collect that number of bricks and put them in their bag. Each pair adds one. How many have each pair got now? Without looking, can they tell you? Use the number line to help. Add two more, or take one out. The great advantage of doing arithmetic using the cloth bags and bricks like this is that the children cannot see the quantities - they have to imagine them. And yet it is a situation which makes perfect sense to them. It is surprising how very young children can cope with arithmetic, including counting on one or two more, (a concept normally regarded as very abstract and difficult) in these circumstances.
Since counting is such a primary skill, it is difficult to exaggerate the extent to which it makes a difference that children count - either along the number line, or on their fingers or small piles of bricks. Number the children's fingers to help them remember which number name goes with which numeral.
Once children of four become confident counters, even just as far as six, they can start counting on one or two. Make a track of pieces of numbered paper along the floor. They take it in turns to stand on one. Spin a coin. Heads, jump on two spaces, tails, jump on one. But, before they jump, all the children must guess what number they will land on next.
With shape, as with number, the mixture of teaching and facilitating activities is a crucial one. The children need to handle and play with different shapes, both flat and three dimensional, in a variety of contexts. They also need to be taught the names of the common shapes, and shown how many sides and corners each has, to enable them to differentiate one shape from another. Using cardboard shapes cut out of old cereal packets, and then placing a sheet of thin paper over the shapes and wax-crayoning over the top, produces some very nice prints and certainly attracts children's attention to the specific characteristics of each shape - curved or straight sides, how many corners, and so on. This makes an excellent activity for children to do at home.
As we can see from each of these activities, helping children to become confident in maths at this early age involves a skilled mixture of proactive teaching and reactive facilitating. We teach children by showing them how to do things, by demonstrating techniques, such as counting on our fingers, and by asking questions designed to lead them to the next stage. We set up activities which allow them to explore and use numbers in contexts where they will make sense. And we require a certain amount of routine practice. This practice gives children confidence and provides a backdrop against which they can "play with" mathematical ideas. The children often draw upon a mechanically-acquired skill later on in a different situation. Thus, they will often count as they jump into the paddling pool or run round the playground, as well as using their counting skills to establish just how many biscuits they have.
The "desirable outcomes" do not give any hint as to how they are to be achieved. As with the national curriculum, the most important questions are left for teachers to answer.
Ruth Merttens is joint author of the Abacus maths scheme published by Ginn
SCAA's MATHS TARGETS FOR CHILDREN TURNING FIVE
Children use mathematical language, such as circle, in front of, bigger than and more, to des-cribe shape, position, size and quantity. They recognise and recreate patterns. They are familiar with number rhymes, songs, stories, counting games and activities. They compare, sort, match, order, put in sequence and count using everyday objects. They recognise and use numbers up to 10 and are familiar with larger numbers from their everyday lives. They begin to use their developing mathematical understanding to solve practical problems. Through practical activities, children understand and record numbers, begin to show awareness of number operations, such as addition and subtraction, and begin to use the language involved.