The mind's eye picture of the figures on the mental blackboard can be enlarged by practice so that the child can visualize problems of some complexity. This ability, of course, will come only after continued practice. Start with simple problems and increase their difficulty as the child progresses. You will be surprised to find how he will be able to retain the figures in his mind and soon will be able to work with them. Write on the blackboard a column of figures as illustrated below. (A small one in the house is of great value in child training. A yard of blackboard cloth can be purchased and hung on the wall.) Allow the child to look at them for a few seconds and write down the result of his addition. Do not have him write the numbers as in previous exercises, for visualization, but only the total. Now, add the first two numbers of the first example, subtract the third and add the fourth, then write the total. In the second example let him add the first two, subtract the third and multiply by the fourth, write the answer. These exercises of manipulation can be varied in many ways. The length of the columns can be accommodated to the ability of the child. 10 12 9 16 -- 15 10 14 7 -- Learning Rules All rules should be worked out in examples or illustrations and visually impressed upon the child's mind. One visual impression is equal to about twenty repetitions. Many times children get the idea that the problem cannot be worked unless the exact "Rule in the book" is followed. See to it that your children get a broader idea and that they understand the reason for doing a thing. The training in mathematics, that is of most value after school days are over, is, where we understand the reason and have worked out for ourselves the correct result, independent of any set rule for working the problem. When helping the child at home give him practical examples from every day life as well as those in the book. Fractions The first step in fractions are often confusing to children, but need not be if they have been taught to be observing and to watch for the little aids which help over the difficult places. Nominator and Denominator are two confusing terms to many. If you will show the child that most of the fractions that he has to deal with are proper fractions, and that the Nominator, upper number, is smaller than the Denominator, lower number, and that the same relationship exists between the words. Nominator De-nominator The Denominator is the denomination of the fraction, the Numerator is the number of parts. Let the D of Denominator stand for Down and remember that it is Down (lower) part of the fraction. Many scholars have difficulty in giving the correct answer to the question, What are the three kinds of fractions? The following is all that is needed to fix the answer in mind. Give the PROPER answer. If you give the IMPROPER you will be MIXED. These capitalized words are the three kinds of fractions.