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Self-Reliance.

satisfied himself that he is not able to solve it; the teacher may be satisfied that the pupil can perform it, but it be cal. not make the pupil think so too, it wil be difficult to bring his best energies to bear upon it and even after the pupil is persuaded that he is able to accomplish the task, it may still be necessary for the teacher to adopt special measures to set the pupil's mind at work. The pupil may have the ability to solve the problem; he may be heve that he has this ability; and he may have a willing mind; and, after all, fail entirely of doing it. And this brings to view what must be regarded as the highest gift of the teacher: namely, the ability to teach his pupils how to think and act, without doing their thinking and acting for them.

When a pupil has failed to overcome an obstacle, his mind may often be quickened to action by requesting him to explain the steps he has taken. "Great thoughts," says Dr. Channing, "are never fully possessed till he who has conceived them has given them fit utterance." So with a pupil attempting to surmount a difficulty; the very effort required to express a thought in language often aids materially in grasping the thought itself.

A scholar had become discouraged over a difficult question. He had gone through the solution again and again, but could not obtain the answer sought. The teacher availed himself of a favorable opportu nity, and requested the pupil to go through the work lowly and carefully in his presence. As the pupil

ceeded the teacher required him to explain each

Self-Reliance.

step of the process; and when he reached the point where his previous error occurred, as the teacher asked him to give his reason, the pupil's eye flashed with delight and he exclaimed, "I see my mistake!" Without further assistance he soon reached a correct esult. The teacher had not furnished the slightest nint in respect to the solution of the problem. He had only taken measures which brought the pupil's own strength to bear upon it.

There are, however, peculiar cases which no such method will reach. The pupil may be required to repeat his solution a hundred times, in the presence of the teacher or alone, with reasons or without, and all to no purpose. The result, if he reaches one, is sure to be wrong. It is not time, even now, for the teacher to give over in despair. Let him ask the pupil such questions as will call to mind the principles which he has occasion to apply, and, in a majority of cases, the pupil will need no further aid.

The same end may usually be gained by giving the pupil an example involving the difficulty over which he has stumbled, but less complicated in other respects; or by giving him several examples, leading gradually to the main obstacle to be overcome. I believe the cases are exceedingly rare in which minds properly disciplined would ever be benefited by direct assistance, in an ordinary course of mathematical study. But if it be thought best, in extreme cases, to afford this assistance, let the pupil, by all means, be required to repeat the process, after the teacher's work has been entirely

hance

erased; and thus derive, at least, the benefit of reproducing, though, he has not the power to originate.

The teacher will find it a highly useful exercise to give his pupils an occasional model of thinking. Let him take a problem to the blackboard, and think aloud as he proceeds with the solution; so that the pupils may witness the action of the teacher's wind, and observe the questions he asks himself, and The various associations and comparisons that arise, as he advances from step to step in the process.

I am aware that in many schools the teachers can Most dwell upon particular points with the same degree a thoroughness that I have recommended; but this doas hot affect the importance of the principle, which should be applied whenever the circumstances permit.

În iasi of our schools pupils indulge, to a greater al loss catant, in the practice of assisting one another 1. The solution of difficult questions. I need not say Thai We should labor most assiduously to eradicate Has Injurious practice, Pupils should be taught to regard as dishonorable, either to assist others or To Pucidi e assistance, except under the special cogniZalive and direction of the teacher.

Permit me in this connection, to allude to one of the wis kindly furnished by a large class of publishers and authors, for the special benefit of teachers; but which many pupils have thought to be quite

suited to their wants as to the wants

I refer to printed keys, containing the more difficult problems in arithbranches of mathematics.

Self-Reliance.

There are undoubtedly cases in which the time of the teacher is so limited that it is necessary for him to resort to the use of a key; but with pupils their effect is always injurious, sapping the very foundation of every thing adapted to promote manly, independent thought. Even with teachers who are compelled to resort to the use of keys for the purpose of saving time, it must be confessed that the tendency of the practice is to render instruction superficial. The very best that can be said of them is that they are necessary evils.*

The practice of introducing young children to the study of English grammar as a science, and assigning them daily lessons to be prepared from a text-book, is exceedingly injurious in its influence upon their mental habits. A thorough and intelligent analysis of the structure of language is beyond the capacity of children eight or nine years of age.

Instruction in the use of language should be commenced as soon as children enter school, and all the primary classes should have frequent oral and written exercises in cultivating this important art; but the practice of requiring pupils under ten years of age to prepare set lessons from a grammatical textbook, often accomplishes little more than to form and strengthen the habit of studying without thinking.

* I refer, in these remarks, to keys that contain the solution of difficult questions, and not to those which contain only the answers of the problems. No such evils could arise from the use of keys containing answers only.

-Reliance.

Few of us have any st conception of the latent energies of our own minds.

it was eloquently said v Prof. B. B. Edwards, that Gemus lies buried on our mountains and in our valleys:" and he might vith equal truth have added, that genius lies buried In our schools and colleges.

But

A successful teacher, of many years experience, was accustomed to say to his pupils that he did not believe their average intellectual progress was ever half so great as they were capable of making. 't would be absurd to suppose that pupils do not generally devote half so much time to study as their duty requires. Most of the pupils in our higher seminaries study to many hours in a day already. The loss is in the manner of studying. The mind is not perfectly abstracted from every thing except the anbject In wand. The mental energies are not ail aroused and concentrated on a single point.

A young nan was employed, some years ago, as an assistant teacher in a fourishing New England academy. Among the classes which he was called to instruct was one composed mostly of older pupils, in Day's Algebra. He had been over the greater part of this text-book before, but there were two or three problems which he had never been able to solve. There was one in particnlar on which he had already tried his strength a number of times without His class was now rapidly approaching

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of the book, and he must be prepared rency. He accordingly set himself at evoted several hours to the unsolved

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