A little delicate management of this sort will often have more influence over young persons than the most vehement scolding, or the most watchful and jealous precautions.  The Tabu was always most scrupulously regarded, after this, whenever employed.

20.  MENTAL ANALYSIS.—­Scene, a class in Arithmetic at recitation.  The teacher gives them an example in addition, requesting them, when they have performed it, to rise.  Some finish it very soon, others are very slow in accomplishing the work.

“I should like to ascertain,” says the teacher, “how great is the difference of rapidity with which different members of the class work in addition.  I will give you another example, and then notice by my watch the shortest and longest time required to do it.”

The result of the experiment was that some members of the class were two or three times as long in doing it as others.

“Perhaps you think,” said the teacher, “that this difference is altogether owing to difference of skill; but it is not.  It is mainly owing to the different methods adopted by various individuals.  I am going to describe some of these, and, as I describe them, I wish you would notice them carefully, and tell me which you practice.”

There are, then, three modes of adding up a column of figures, which I shall describe.

1.  I shall call the first counting.  You take the first figure, and then add the next to it by counting up regularly.  There are three distinct ways of doing this.

(a.) “Counting by your fingers.” ("Yes, sir.”) “You take the first figure—­suppose it is seven—­and the one above it, eight.  Now you recollect that to add eight, you must count all the fingers of one hand, and all but two again.  So you say ’seven—­eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.’”

“Yes, sir, yes, sir,” said the scholars.

(b.) The next mode of counting is to do it mentally, without using your fingers at all; but, as it is necessary for you to have some plan to secure your adding the right number, you divide the units into sets of two each.  Thus you remember that eight consists of four twos, and you accordingly say, when adding eight to seven, ’Seven; eight, nine; ten, eleven; twelve, thirteen,’ &c.

(c.) “The third mode is to add by threes in the same way.  You recollect that eight consists of two threes and a two; so you say, ’Seven; eight, nine, ten; eleven, twelve, thirteen; fourteen, fifteen.’”

The teacher here stops to ascertain how many of the class are accustomed to add in either of these modes.  It is a majority.

2.  The next general method is calculating; that is, you do not unite one number to another by the dull and tedious method of applying the units, one by one, as in the ways described under the preceding head, but you come to a result more rapidly by some mode of calculating.  These modes are several.