1. The teacher must keep in the line of ideas followed by the book. Something more or less may be allowed at times, but in no case anything different. That is a bad state of affairs when the class say, "The book says so, but the teacher so." By opposing himself to the book the teacher commits two mistakes: he destroys the pupil's confidence in the book, and so his interest in it; and he engenders confusion and weakness.

2. The teacher should follow the methods of presentation employed by the book, otherwise his train of thought will collide with the book's train. 3. The teacher will study to make the first presentation of the subject successful. This is important for a double reason, or at least a reason that may be stated in two forms.

The mental power expended by a pupil on the unsuccessful presentation is wasted, and more than wasted; the debris of this presentation "litters up" the mind, and so stands in the way of a second one. This is the reason why it is often more difficult to teach a subject to a pupil to whom it has been imperfectly taught than to one who knows nothing about it.

4. The wise teacher will not present a subject in more than one way, provided his presentation has been successful. It is folly to explain the division of a fraction by a fraction in a second way, if the first has been understood. It is well enough, perhaps, for the author of an arithmetic to give two or more methods for finding interest, but the teacher should use only one with the pupils the first time over the work. Never give, at the stage of the teaching now supposed, more than one definition or rule. Again, superfluous illustrations not only do no good, but they do harm, begetting confusion worse confounded.

5. If the subject-matter of a lesson is radically bad, or if the method of the book is decidedly faulty, the capable teacher will do well not to assign the lesson from the book at all, but to teach it himself de novo.

It should be observed that the end of teaching is the matter taught and the habits of mind thus created; methods of teaching are simply ways or modes of reaching that end, and the teacher who has come to think more of the method than of the end, as some do, needs to orient himself. The superiority of the traditionary "Man of One Book," finds its explanation in the considerations now presented.

The criteria thus explicated exclude all "broad" teaching from the earlier stages of education. But the pupil will be able, progressively, to get out of his "one single line of thought." He will be able to deal with more subjects and with more ideas about the same subject. He will at last be able to consider with advantage different definitions of the same thing, divergent views, conflicting processes, and a variety of methods. He may now consult several text-books. In the essay already quoted from, Dr. Bain thus presents the pupil's march of progress:

"Our first maxim is, 'Select a text-book in chief.'

The meaning is,

that when a large subject is to be overtaken by book-study alone, some one work should be chosen to apply to, in the first instance, which work should be conned and mastered before any other is taken up. There being in most subjects a variety of good books, the thorough student will not be satisfied in the long run without consulting several, and, perhaps, making a study of them all; yet it is unwise to distract the attention with more than one while the elements are to be learned. In geometry the pupil begins upon Euclid, or some other compendium, and is not allowed to deviate from the single line of his author. If he is once thoroughly at home on the main ideas and the leading propositions in geometry, he is safe in dipping into other manuals, in comparing the differences of treatment and in widening his knowledge by additional theorems and by various modes of demonstration."

Dogmatism and authority will now recede into the background and the teacher will play a new part. He will contribute more freely than before of his own stores of knowledge, and will more and more discuss subjects with his pupils. Varying views and conflicting arguments will receive due attention. Education has at last entered upon its critical stage. If the student continue to advance, he will become able to follow a wide treatment of subjects from the time he takes them up, handling divergent definitions, conflicting principles, contradictory facts, and complicated lines of reasoning from the very first. But such ability as this comes as the result of much study and of long training.

Broad training is the true goal of education. But the road leading up to it, particularly in its earlier stages, is narrow teaching. Broad teaching in the beginning will defeat broad teaching in the end. Just enough knowledge well presented will make a lodgment in the mind and will create discipline; a flood of knowledge poured over the young student will make no lasting impression. Teaching everything is teaching nothing. The "inundating" teacher, the teacher who lets the knowledge down like a shower bath, defeats his own end in a lower-grade school. A hosepipe is not the best instrument to use in filling a wine-glass. Fine scholars sometimes fail as teachers because they make their work too broad and discursive, while very ordinary scholars often succeed, particularly in lower grades, if they are clear in their thoughts and statements. The first are hindered by their breadth, the second are helped by their narrowness.

The terms "narrow" and "broad" are here used in a relative sense. To give them quantitative content is impossible. I must depend upon the good sense of the reader, taking them in connection with the subjectmatter and their contents, to assign to them their proper meaning.— Moderator.

The Treatment of the Pupil During the Formative Period of the Growth of Reason.

BY O. W. WEYER, PRINCIPAL GRAMMAR SCHOOL, KEOKUK, IOWA.

Reasoning is defined to be the process of comparing two objects of thought through their relation to a third. It is also defined as the process of deriving one judgment from two other judgments.

We are wont to consider reason our highest intellectual faculty, and the exercise of reason as the highest employment of our intellectual being. Teachers are often confronted with the question "At what age ought I to expect my pupils to begin to reason?" meaning usually by the question "At what time in a pupil's school-life should I demand of him a clearly worded explanation of the work which he is able to do?" Reason undoubtedly begins to develop very early in the child's life, yet not in the same ratio as the other mental faculties. The activities of the mind that end in knowledge are called cognitions, and the cognitive or knowing faculties, develop in the following order: 1. The acquisitive, comprised of perception and self-consciousness. 2. Memory, including recollection. 3. Imagination. 4. Judgment. 5. Reason.

With children from five to ten years of age, perception, memory and imagination are very active. During this period of school-life, Wickersham, in his Methods of Instruction, says that the child should be taught reading, spelling, language and the operations of addition, subtraction, multiplication and division; that he cannot make much progress in reasoning about the properties of numbers; that before the age of ten a child is not prepared to appreciate generalizations, abstractions, theories or systems, and that it is folly to attempt to teach them to him.

And yet it is not argued that during this period there is, and should be, no exercise of the reason; but that the culture of reason should be subordinate to the activities of perception, memory and imagination, and that these activities should be employed in making the child skillful with the instruments to be used in the culture of reason to the extent that their use shall have become a habit so fixed as not to distract from the higher thought processes. In other words, by the time the culture of reason becomes a special aim in school work, the child should read readily, express his ideas with a fair degree of clearness, and perform number work accurately and rapidly.

In the school-life of the pupil I recognize two stages, or periods, in the growth of reason. In the first, or informal period, we ask the pupil what? In the second, or formal period, we ask why? in addition to what?

During the earlier period the pupil will, from given premises, arrive at

correct conclusions by proper methods and yet be unable to give, with any clearness, the reasons for the several steps in the process. Here it may be observed that, when such work is done by the pupil without similar questions having first been solved for him by the teacher, the questions are such as he has met with in his own experience, and are all concrete in their nature. In this stage of the pupil's growth the questions upon which he is expected to reason should be such as are wholly in the domain of childish experience, and results should be expected without the teacher's first paving the way by the solution of an exactly similar example. We are very apt at this time to allow the pupil to fall into the habit of solving his questions by means of comparison and memory. Comparison lies at the basis of reasoning and enters into the solutions of all problems. But when a pupil makes a comparison of a new question as a whole with some previous question, the solution of which he remembers, the comparison is made—not for the purpose of establishing the condition of the new question, but for the purpose of applying memoriter the processes of the old one. The comparison should be made between the questions and the child's experience, thereby forming the habit of considering a question upon its own conditions without depending for its processes upon its similarity or dissimilarity to some other problem.

During this period in the growth of reason, which I think is covered by the first five or six years in school, the most I should ask in mathematical work would be the results and the statement of the processes by which they were attained. With most children I question very much if the force of an "if" or a "since" is at all understood before ten or twelve years of age. In the subjects of reading and language, much may be done by skillful questioning, which will at the same time aid in a better mastery of the subject. But the questioning must have method and purpose in it. Every question should be based upon some discrimination which the child is capable of making. Essential points should be dwelt upon, minor ones passed lightly over. A great advance has been made by that teacher who has learned what to teach and what not to teach.

As our graded schools are arranged, I consider the fifth and the sixth grades the transition period between the informal and the formal periods. In these years he is passing from that period in which he can give no formal explanation of results correctly obtained to that second period in which he should be asked for an orderly statement of the reasons which induced him to follow certain processes to obtain a required result. At this time a pupil should be guided by an unyielding hand. The teacher must, here more than at any other time, exercise patience and firmness continuously.

Mental activity increases in difficulty as it departs from the activity of

the senses. Any of us are conscious of less difficulty in recalling what we have learned than in reasoning upon it; and we reason more easily upon the concrete-upon that of which the senses take cognizance-than upon the abstract. Then it follows that reasoning is a difficult mental activity; and it has not been my experience that children take to difficult work very eagerly-many educational enthusiasts to the contrary, notwithstanding. Hence, as we enter upon difficult work, any disinclination on the part of the pupil to second us heartily in the subject need not surprise us; but there should be no yielding of the teacher's judgment to the ignorance of the pupil as to what is for his own good. In this transition period there should be a most careful and thorough sifting of the classes; there should be more failure "to pass" than at any other period of the school course. The child should no longer be carried by the teacher; the aid which heretofore was so freely given must be gradually withdrawn, and independent effort on the part of the pupil insisted upon unceasingly. His responsibility for the preparation of his lessons should be impressed both upon him and upon his parents, and the idea "that the teacher will not allow him to fail" should be most effectually done away with. To change the wording of a somewhat trite saying, “he should learn to think by thinking."

In the first part of this transition period the ability of the pupil to solve questions in the fundamental operations-addition, subtraction, multiplication and division-and problems combining two or more of these processes, should be carefully noted by the teacher. The class should be resolved into two divisions; one division being composed of those pupils whose daily work indicates that the reasoning faculty, and not imitation or memory, is employed in the solution of the problems; the other division being composed of those who seldom solve any question until the solution of a similar one has been explained to them. In any of our classes we do not expect to find all the pupils having an equal degree of development; and yet, in many cases, a "test" will show about the same average strength. It is the experience of nearly every teacher that in any class there are some pupils whose daily work is not at all good, and who depend very largely upon the recitation for what they learn about the lesson. This failure in daily work may be because of a lazy habit, or because the mental strength is not equal to the work. whatever be the trouble the pupil should not be allowed to enter upon the advanced line of work until there is good evidence of his being ready. With such pupils, a test on the work gone over is not a very trustworthy basis for promotion. The range of work for this period is somewhat limited, and the active memory soon holds in grasp a limited number of model solutions, and a set of test questions is rather a test of memory than of thinking ability. If the teacher is at all fitted for the work of this period, her personal judgment, based upon each pupil's ability to

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