3. "There is one more mode which I shall describe: it is by memory. Before I explain this mode, I wish to ask you some questions, which I should like to have you answer as quick as you can.
"How much is four times five? Four and five?
"How much is seven times nine? Seven and nine?
"Eight times six? Eight and six?
"Nine times seven? Nine and seven?"
After asking a few questions of this kind, it was perceived that the pupils could tell much more readily what was the result when the numbers were to be multiplied than when they were to be added.
"The reason is," said the teacher, "because you committed the multiplication table to memory, and have not committed the addition table. Now many persons have committed the addition table, so that it is perfectly familiar to them, and when they see any two numbers, the amount which is produced when they are added together comes to mind in an instant. Adding in this way is the last of the three modes I was to describe.
"Now of these three methods the last is undoubtedly the best. If you once commit the addition table thoroughly, you have it fixed for life; whereas if you do not, you have to make the calculation over again every time, and thus lose a vast amount of labor. I have no doubt that there are some in this class who are in the habit of counting, who have ascertained that seven and eight, for instance, make fifteen, by counting up from seven to fifteen hundreds of times. Now how much better it would be to spend a little time in fixing the fact in the mind once for all, and then, when you come to the case, seven and eight are—say at once 'Fifteen,' instead of mumbling over and over again, hundreds of times, 'Seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.'
"The reason, then, that some of the class add so slowly, is not, probably, because they want skill and rapidity of execution, but because they work to a great disadvantage by working in the wrong way. I have often been surprised at the dexterity and speed with which some scholars can count with their fingers when adding, and yet they could not get through the sum very quick—at least they would have done it in half the time if the same effort had been made in traveling on a shorter road. We will therefore study the addition table now, in the class, before we go any farther."
21. TARDINESS.—When only a few scholars in a school are tardy, it may be their fault; but if a great many are so, it is the fault of the teacher or of the school. If a school is prosperous, and the children are going on well and happily in their studies, they will like their work in it; but we all come reluctantly to work which we are conscious we are not successfully performing.