Coming To Grips With Mathematics :  How does a child acquire mathematical concepts? Can any concept be presented to a child at any stage in such a manner that the child gets some idea about it? If this is so, then we adults need to be very sensitive about the level of development a learner has already reached, and present the concept accordingly. We need to gauge the "readiness" of the child for learning that particular concept.

For example, for a small child to appreciate the relation between addition and subtraction, she should be able to realise that actions are reversible. And, she can do this if she understands how conservation operates. How would you gauge this understanding?

In a typical task to check if a child can conserve number, the child is shown two rows of buttons of the same length, with the same number in each row. While the child looks on, the buttons in one row (Row A below) are spread out by the adult.

The other row (Row B) is left untouched. Then the child is asked if the two rows have the same number of buttons.

The Swiss psychologist Jean Piaget (1896 - 1980) observed the following:

Children who can conserve argue that the two rows have the same number of buttons because you have neither taken away from the untouched row nor added to the first row. They also argue that one can bring the buttons in the first row closer so that the positions of the buttons in both the rows are the same. This argument indicates the ability of the child to reverse her thought process.

In this activity the child and the adult (Piaget) were engaged in a conversation in which the adult was willing to listen to the child, tried to understand her and made her think. The adult was treating the child as an independent thinking person.