After a lot of effort, 8-year-old Hari worked out 2 x 88 = 176. When asked to say what 2 x 89 was, after a lot of hard work, he produced the answer 178. How would you help him to realise that there is a simpler way of getting to the answer?
Most children are like Hari. They have not been trained to observe, explore, recognise connections and generalise patterns that they find. For them 2 x 88 is as much a piece of information or 'fact' to be retrieved, as 2 x 89 is. This is in spite of the fact that children perceive patterns in their environment and see links between things that they relate to. How can we correct this situation?
Much of mathematics teaching is actually about encouraging children to become more aware about the patterns they find, to articulate the rules and to use them in their thinking. So, to start with, let us consider some ways in which we can help children find patterns in mathematics. A good way is to provide them with exercises involving play with sequences of objects. When children place object after object in a sequence, they begin to learn to express and develop a sense of pattern, a sense of generality. Slowly, they can be shifted from games dealing with objects to games that involve sequences of pictures of objects that they are familiar with. Gradually, children will be able to find patterns in number as well. Once children begin to. Identify, understand and create patterns, they can use them to do operations in arithmetic also.
A word of caution! It is not enough to just show children a pattern, as in multiplication, say, and then move on to another topic. Children need time to explore for themselves, and get a feel of what they are just finding out. Thus, while doing the following exercise, you need to also think about how long the tasks will take.