COMMUNICATING THE MEANING OF ADDITION : One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and one?" The child replied, "A bigger one." This response is unusual. But, isn't it valid in several situations where 'and' means 'join', for example, when two rivers come together and then flow on as one bigger, wider river?
Isn't it usually take that when we add two quantities we get a larger quantity? Even at for me you can think of several instances of this. In all these examples, didn't you put two or more sets together and make a larger set? For instance, adding 2 oranges and 5 oranges, or adding water to flour gives a larger quantity. In this unit, however, we shall limit ourselves to adding those sets which can be counted, i.e., which are numerable; like oranges or chapatis. We will not talk of examples like the rivers or dough.
Over here we are going to discuss ways of helping children learn that adding the objects of different sets means finding the total number of objects that are being considered. We would like them to understand the concepts and language involved. How can we achieve this teaching objective?
Young children need to place addition in a context. They need to be given plenty of concrete experiences to start with. For example, a child could be given a set of three pebbles, and another of two pebbles, saying that 'These are three stones, and here are two more stones. Now how many stones are there in all?'. Then she could be given three twigs and two twigs, three buttons and two buttons, three marbles and two marbles, three biscuits and two biscuits, and each time asked to do the same. Each time she should be encouraged to describe what she is doing, for example, to say, "These are two marbles, and these are 3 marbles. I put them together. Now they are 5 marbles (counting them)." Initially, you may need to prompt her by asking questions like: How many pebbles did you have? .And how many more did I give you? How many in all?
Slowly, as she builds up her ability to describe what she is doing, you could introduce the word 'add', and relate it to the action she is performing. Gradually, she would include the word in her vocabulary, and associate it with the action of grouping. You could similarly help her to understand and absorb terms like 'altogether' and 'plus'.
Now, as she loudly speaks out, say, "2 marbles and 3 marbles make 5 marbles", you can write 2 + 3 = 5 on the board or on paper. When she says "2 pencils and 3 pencils make 5 pencils", you could again write 2 + 3 = 5, and so on. This will introduce her to the symbolic representation of the addition statements. As she gets used to seeing this representation, she can begin to write it herself. With practice, she will become comfortable with the symbols.
It is also with a lot of exposure to joining sets of objects that children would be able to realise that 3+2 is the same as 1+4, and so on. Similarly, many concrete experiences would be needed to realise the reversibility of the operation of addition, that is, if 3+2 = 5, then 5 = 3+2.