REMARKS FOR THE TEACHER.

Ir is the leading feature of the method of instruction developed in this book, to teach the pupil to combine figures by the eye alone.

The common language must first be used to indicate the relation between the figures. After that relation becomes known, the figures themselves should suggest the combination. For example, after having taught the first ten combinations in the usual way, as 1 and 1 are two, 1 and 2 are 3, &c., let the table be written on the blackboard as below, in lesson first, and in each of the following lessons. Let the teacher then take a pointer, and point to the figures 1 and 1, and let the whole class answer 2. Let him then point to the figures 1 and 2, and let the class answer 3, and so on for the entire table.

The drill of the class should be continued until the combinations can be read by the eye. This reading will save the use of four words in each combination. Thus, instead of saying one and six are seven, the eye glances at 1 and 6, and seven is uttered immediately. This method of operating on numbers by the combined process of sight and thought, will train the mind to the most rapid and exact methods of computation. Each of the ten lessons should be taught in the same manner—and

REMARKS FOR THE TEACHER.

Having written the column of 1's on the blackboard, let the pupils add them when pointed, beginning with the lower figure. The column of 2's being written, let them also be added, the class repeating the words four, six, eight, ten, &c., and none others. Let the 3's and each of the following columns be added in the same manner. Let the same method be pursued through the entire tables