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To have stated a question clearly is often half the solution; and the teacher, who so states a high doctrine, gives a great aid to the learner's mind.

The educator's part in the enterprise of education is to furnish the environment which stimulates responses and directs the learner's course. In last analysis, all that the educator can do is modify stimuli so that response will as surely as is possible result in the formation of desirable intellectual and emotional dispositions.

The fact that classical learning acts to derange the learner's workmanlike attitudes should fall lightly upon the apprehension of those who hold workmanship of small account in comparison with the cultivation of decorous ideals: Iam fides et pax et honos pudorque Priscus et neglecta redire virtus Audet.

In a merely initiatory definition, scientific precision is not required: the object is, to insinuate into the learner's mind, it is scarcely material by what means, some general preconception of what are the uses of the pursuit, and what the series of topics through which he is about to travel.

This result is accomplished in two ways: by inspiring an habitual aversion to what is merely useful, as contrasted with what is merely honorific in learning, and so shaping the tastes of the novice that he comes in good faith to find gratification of his tastes solely, or almost solely, in such exercise of the intellect as normally results in no industrial or social gain; and by consuming the learner's time and effort in acquiring knowledge which is of no use except in so far as this learning has by convention become incorporated into the sum of learning required of the scholar, and has thereby affected the terminology and diction employed in the useful branches of knowledge.

And the little learner's face would beam with timid adoration and envy as he listened to the tales of wicked adventures so boastfully related by his teacher. Would he, could he, ever be so bold, so wise in knowledge of the world? Poor little boy in the Yesterdays who knew nothing of the value of Ignorance!

But the law to be understood and obeyed is the law of the learner's mind, and not that of the teacher's. The didactic method must be subordinated to the vital. Teaching may be developed into a very neat and orderly system, but learning is apt to be quite disorderly. It is likely to come by fits and starts, and when it does come it is very exciting.

Here experience must, in a great measure, be our guide; but some maxims may result from our consideration of the ultimate purpose to be achieved. One of the chief ends served by mathematics, when rightly taught, is to awaken the learner's belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration.

Nothing better teaches the value of money than the association in the learner's experience of hunger with an empty pocket. What slight qualification for the production of this book we possess has been obtained in a similar way. Some few things we have learned; some we have proved through our many mistakes; some, again, through our frequent failures.

Old-aged experience goeth beyond the fine- witted philosopher, but I give the experience of many ages. Lastly, if he make the songbook, I put the learner's hand to the lute; and if he be the guide, I am the light.