STUDYING MATHEMATICS
Children learn to count by using objects, in the school room they count the desks, the children, the number of cards, or blocks. The first lessons are object-lessons dealing with objects which can be handled and formed into groups. Digits are symbols which represent objects, 7+3=10, is an abbreviated form for 7 (Apples) and 3 (Apples) are 10 (Apples).
It is easier to teach addition and subtraction by the use of the objects to add and to take away from. The realization of the process comes by seeing the objects and the result of the change. The digits become symbols for the objects that the child has been working with. Counting boards are helpful in teaching children, for they enable you to continue the visual process. All methods of teaching through the visual processes should be continued as long as possible.
The child's interest in the problem will be stimulated if he deals with objects, or things, and not with meaningless groups of figures. The problem 127+323+417= , is a meaningless one and uninteresting, but if you encourage him to think that this is the number of soldiers with which a general is going out to meet an army of two thousand, then he has some interest in finding out how many men the general really has to meet the two thousand with. This makes the problem read thus, in his mind.
127 (soldiers) + 323 (soldiers) + 417 (soldiers) = How large an army?
Figuring a page of problems will be uninteresting, but if you can encourage the child to introduce the imaginary objects, it will increase his interest.
Fractions are usually explained by the division of an apple or some easily divided object. Division, as a process of dividing a group of objects among a smaller group of children, is easily understood and interesting to them. Encourage your child to continue to think of the objects when dealing with fractions.
Visualization Always Aids
All mental processes should take form in pictures. The adding of 4 and 7 should be seen in the mind's eye, if the problem is not written down. A parent tells the story of his difficulty with his son and this simple problem. The child got the idea fixed in his mind that 4 and 7 were 12. The father had told the boy that the answer was 11, and had the child repeat, 4 and 7 are 11, several times. But the original impression was still the stronger, and the next day, when asked by the father, "How many are 4 and 7?" the child's answer was 12. In some way this impression had become a very strong one and was recalled before the weaker one of the correct answer, 11. The idea of visualization was brought to the father's attention during the day by his having attended a lesson in Memory Training given by the author. That evening he called the boy to him and said, "Son, how many are 4 and 7 tonight?" He received the same incorrect answer, 12. Then he took a piece of paper and wrote upon it the figures in exaggerated size, as illustrated on the right. He had the boy look at the problem for a moment and then look away and see it in his mind's eye, then look at the problem again. Thus he placed a visual impression of the correct answer in the child's mind and this became the stronger of the two impressions and was never forgotten. The next morning the father asked the boy the same question, "How many are 4 and 7?" and the answer was promptly given, "Eleven." "Why, I can just see those figures in my mind and I never will forget that."