“I could say it, only you put me out.”

“Well, now try to say the Alphabet, and let me see if I can put you out there.”

As might have been expected, the teacher failed.  The boy went regularly onward to the end.

“You see, now,” said the teacher to the class who had witnessed the experiment, “that this boy knows his Alphabet in a different sense from that in which he knows his Multiplication Table.  In the latter, his knowledge is only imperfectly his own; he can make use of it only under favorable circumstances.  In the former it is entirely his own; circumstances have no control over him.”

A child has a lesson in Latin Grammar to recite.  She hesitates and stammers, miscalls the cases, and then corrects herself, and, if she gets through at last, she considers herself as having recited well, and very many teachers would consider it well too.  If she hesitates a little longer than usual in trying to summon to her recollection a particular word, she says, perhaps, “Don’t tell me,” and if she happens at last to guess right, she takes her book with a countenance beaming with satisfaction.

“Suppose you had the care of an infant school,” might the instructor say to such a scholar, “and were endeavoring to teach a little child to count, and she should recite her lesson to you in this way, ’One, two, four—­no, three—­one, two, three——­stop, don’t tell me—­five—­no, four--four--five--------I shall think in a minute--six--is that right? five, six,’ &c.  Should you call that reciting well?”

Nothing is more common than for pupils to say, when they fail of reciting their lesson, that they could say it at their seats, but that they can not now say it before the class.  When such a thing is said for the first time it should not be severely reproved, because nine children in ten honestly think that if the lesson were learned so that it could be recited any where, their duty is discharged.  But it should be kindly, though distinctly explained to them, that in the business of life they must have their knowledge so much at command that they can use it at all times and in all circumstances, or it will do them little good.

One of the most common cases of difficulty in pursuing mathematical studies, or studies of any kind where the succeeding lessons depend upon those which precede, is the fact that the pupil, though he may understand what precedes, is not familiar with it.  This is very strikingly the case with Geometry.  The class study the definitions, and the teacher supposes they fully understand them; in fact, they do understand them, but the name and the thing are so feebly connected in their minds that a direct effort and a short pause are necessary to recall the idea when they hear or see the word.  When they come on, therefore, to the demonstrations, which in themselves would be difficult enough, they have double duty to perform.  The words used do not readily suggest the idea, and the connection of the ideas requires careful study.  Under this double burden many a young geometrician sinks discouraged.