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nate numbers or fractions, or in the exact statement of a rule not yet sufficiently illuminated by examples. Generally such careful, exhaustive analyses are suited only to advanced pupils who have already acquired a clear knowledge of their subjects. In beginning any important topic in arithmetic, children should first become familiar with a process by repeated oral and written problems. If they can work these problems and give short, intelligent answers as to the reasons, it is enough. By such simple questions and answers, the teacher can tell if a child understands a problem, and more than this is often mere vexation of spirit. The recitation period is often wasted and the children vexed and confused by such long-winded analyses and statement of rules.

Over-exactness in defining the meaning of words in the reading lesson leads also to a waste of time and a wearisome routine. Such excess of verbal precision may give a little clearer insight, but it is often gained at the expense of interest and enthusiasm for the subject. It is very depressing.

Summing up: inability to state the generalization reached is due primarily to vagueness of thought; such a statement, then, is an essential part of instruction. The wording for the same should come from the child himself, being an immediate outgrowth from the data that he has at hand; this is especially important, since any rule is likely to be forgotten, and unless it can be recalled without help, the utility of the knowledge is greatly diminished. The book's statement may be memorized, but not unless it seems to voice the child's own feeling. If possible, a classical form of expression should be found for the generalization. If the precaution here advised in approaching the generalization is in place, it is apparent how ridiculous it is to place the general before children, even before the individual facts have been presented, as is often done.

CHAPTER IX

HOW SHOULD GENERAL NOTIONS BE APPLIED ?

WHAT worth have these general truths which have When shall

the applicabeen gained at such expense of labor on the part of

tion of prinboth teachers and pupils ? We may stop a moment ciples be

acquired? to take account of our work done, and of the task that still lies before us. In the previous chapters we have dealt somewhat in detail with the series of steps necessary to the construction of those general notions which, properly fitted together, constitute the chief framework of a study. When the children have worked their way to a clear grasp of these general notions, by a self-active, inductive process of thinking, have they not reached the end sought by instruction ? If so, the goal set up is a clear view of important principles. To those who look upon the school as a place of preparation in contrast with later life as a field of application, this is the goal of school studies. But this leaves unsolved the child's most difficult problem; namely, the acquisition of skill in the ready use of principles. It has been said over and over again by the best teachers and writers on education that principles and rules are never safely mastered

till they have settled into the usual practice and conduct of a child. “For from repeated cautions and rules, never so often inculcated, you are not to expect anything either in this or any other case further than practice has established them into habits.” (Locke, par. 10, “Thoughtson Education.") If children are to know how to apply important principles in later life, when shall they acquire the extremely difficult art of application? There may be a whole series of abortive efforts in education due to this disposition to call a halt in the mental movement before the final result

in the form of useful application is reached. Errors on the The first of these errors was seen above in the road to appli- verbal mastery of rules and principles without clear

insight. No matter how fluently and trippingly a child in the schoolroom may run off such formulæ, the whole process of learning may be empty and farcical. At the other extreme, the most complete theoretical mastery of principles will not give proficiency in their practical use. One may master the grammar of the German language and still cut a most blundering figure in German conversation. Between the extremes of rote-learning and of clear insight into principles there may be an entire series of miscarriages. But even beyond the step of clear insight there may be the greatest miscarriage of all in the failure to turn clearly recognized rules into use. The end of instruction has not been reached until skill in the actual application has been developed.

We deceive ourselves again and again by stopping at halfway stations on the highway of learning. We are not simply sight-seers, to be satisfied with fine views, not caring to reach any destined point. One who has worked his way up to the clear grasp The breadth

and variety of some important principle stands at a high point of applicaand gets a broad survey. A survey of what? Of the tions. road he has already travelled, and in part also of that which he is still to traverse. That is, he has a double task to perform : first, to look backward and see the extent to which the principle operates in what he already knows; and, second, to look forward and apply it to the new problems which he is about to meet. Both these things are difficult. But they are difficulties which lie of necessity in the path of knowledge. As when travellers ascend some broad mountain range, till they reach at last the summit of the highest ridge, from which they look back over the slopes behind and forward on their journey through mountains and plains, so the student, as he rises to the grasp of some large principle, looks back over the steps already traversed and forward to those which follow. The discovery of a great principle is no doubt a long forward step, but it may take all the rest of one's life to find out the breadth and variety of its applications. The first grasp of such a principle, be it never so clear, is only a foretaste of the richer fruitage it will still bear. When Columbus first landed on the shores of the Bahamas, he had

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