Lectures on Teaching

It must not be set down as a fault if at first he counts with his fingers. Let him do so by all means if he likes. The faculty of abstracting numbers, and of learning to do without visible and tangible illustrations comes more slowly to some children than others. So long as they get the answer right, let them have what help they want till this power comes. It is sure to come ere long. At first, too, the little questions and problems which are given to children may fitly refer to marbles or apples, or to things which are familiar to them. But the mistake made by many teachers is to continue using these artifices too long; to go on shewing an abacus, or talking about nuts and oranges after the children have fully grasped the meaning of 6 + 5 in the abstract, and are well able to do without visible help. It is a sure test of a good teacher that he knows when and how far to employ such artifices, and when to dispense with them. The moment that concrete illustrations have served their purpose, they should be discarded.