Doing the following exercise will give you and opportunity to think about this aspect of children.

E1) List some illustrations of exploration by four or five-year-olds that you know.

Let us now look at another aspect of the way a child's mind works. The other day 4-year-old Akash had gone for a walk with his father. After some time Akash said, "Father I am tired. Let us go back." The father responded, "Already tired! So soon? Let's walk some more!" The father didn't realise that, while he had walked only 75 steps, the child had walked 225 steps!

Now let's look at eight-year-old Rahul, whose teacher used to beat him regularly.

One day he decided that he had had enough. He told his mother, "I am not going to school." She said, "OK", not caring to ask why. She merely assumed that he wanted a change from the routine.

Would you agree that in both these examples the adults did not try to understand what the children were trying to communicate? They simply made assumptions, based on their own perception, about what the children felt and what they were trying to say.

While teaching mathematics, you would often come across similar situations. For example, on being asked to give half of her slice of bread, a child may give only a small piece. For her, anything less than one is half and half may just mean a piece. But how many adults bother to try and understand, the child's viewpoint?

E2) List some more examples to illustrate the difference between an adult's and a child's way of thinking.

E3) Give examples of situations where an adult imposes his logic on the child.

E4) a) In what ways does the adult-child gap show up in the primary classroom

b) List five things that you, as a teacher, can do to minimise such a gap. Now let us consider another aspect of the adult-child gap. Most preschool children of educated parents learn to recite the alphabet and numbers at home.

Some parents even boast of their children having learnt numbers up to 100 by the age of 3 or 4! But, what does this "learning" really mean? Does this mean that the child can count 100 objects? Does the child appreciate the difference between 50 objects and 100 objects?

What small children learn by constant repetition is only a string of number names, without necessarily understanding what they mean. Although knowing the number names is part of the process of learning numbers; it does not reflect the understanding of numbers. (We have discussed this in detail in Unit 5.)

When an adult assumes that a child has understood the meaning of number, just because she can recite number names, then he pushes the child to "learn" more things like addition, etc. The child hasn't been given enough time to understand the concept of number. But she wants to get appreciation from the adult. So she manages, by memorising without understanding. This is how the expectations of adults can hamper children's real learning.

Unfortunately, at present most teaching is limited to making children arrive at answers mechanically and fulfil expectations of adults by rote learning. In this way we also reduce all school knowledge to mere information rather than understanding. This is true not only for preschoolers, but also for children in higher classes. For example, we adults often reduce the concept of "area" to "length x breadth = area", or more complicated versions of the same formula.

Very few of us actually bother to help the child understand what "area" really means. I'm sure you can think of many such examples.

E5) Give one example each of a concept .that a Class 1, Class 2,........Class 5 child is made to learn by heart without really understanding the full meaning of the concept. Also list what aspects are normally missed.

So far, we have been questioning the assumptions that adults make about the way children learn. if children do not learn in this way, then how do they learn?