Two what?
Two cubes.
One glass, and one glass, are called two glasses. One raisin, and one raisin, are called two raisins, &c. One cube, and one glass, are called what? Two things or two.
By a process of this sort, the meaning of the abstract term two may be taught. A child will perceive the word two, means the same as the words one and one; and when we say one and one are called two, unless he is prejudiced by something else that is said to him, he will understand nothing more than that there are two names for the same thing.
"One, and one, and one, are called three," is the same as saying "that three is the name for one, and one, and one." "Two and one are three," is also the same as saying "that three is the name of two and one." Three is also the name of one and two; the word three has, therefore, three meanings; it means one, and one, and one; also, two and one; also, one and two. He will see that any two of the cubes may be put together, as it were, in one parcel, and that this parcel may be called two; and he will also see that this parcel, when joined to another single cube, will make three, and that the sum will be the same, whether the single cube, or the two cubes, be named first.
In a similar manner, the combinations which form four, may be considered. One, and one, and one, and one, are four.
One and three are four.
Two and two are four.
Three and one are four.
All these assertions mean the same thing, and the term four is equally applicable to each of them; when, therefore, we say that two and two are four, the child may be easily led to perceive, and indeed to see, that it means the same thing as saying one two, and one two, which is the same thing as saying two two's, or saying the word two two times. Our pupil should be suffered to rest here, and we should not, at present, attempt to lead him further towards that compendious method of addition which we call multiplication; but the foundation is laid by giving him this view of the relation between two and two in forming four.