These are the four principal modes of calculating which occur to me. Pupils do not generally practice any one of them exclusively, but occasionally resort to each, according to the circumstances of the particular case."
The teacher here stopped to inquire how many of the class were accustomed to add by calculating in either of these ways; or in any simpler ways.
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, then 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."