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18. Is this a correct rule for finding the volume of the frustum of a pyramid ? If not, why not?
Find the area of the mean base by taking half the sum of the areas of the upper and lower bases. Muluply the area of the mean base thus found by the height.
YOUNG TEACHER. Litchfield, O.
19. At the Summit County Institute last summer, Superintendent Hartzler, one of the instructors, was asked to explain the following problem : “What is the time when f of the time past noon equals 34 of the time to midnight ?” The explanation was deferred for want of time, and Mr. Hartzler promised to give, the next day, a new and better method of solving such problems. When the next day came time was still wanting, and we failed to get the instruction.
Will not Mr. Hartzler be so kind as to give us a brief explanation of the above question through the Monthly, and oblige a number of his admiring teacher-pupils at the institute last August. COUNTRY TEACHER.
20. Why has Rhode Island two capitals ? W. A. MORTON. Sherman, O.
21. In the sentence, “In mother goose, the cow jumped clear over the moon,” is the phrase "in mother goose” adjective or adverbial? or, does it modify the subject or predicate ?
C. F. Southington, O.
“PROCEED FROM THE KNOWN TO THE
W. H. PAINE, UNIVERSITY OF MICHIGAN.
I have selected for examination one of the most plausible of the socalled "Pestalozzian Principles.” Many teachers have accepted this as a simple axiom. Such will think it absurd to attempt a critical examination of it. If this were an axiom, it would certainly be absurd to discuss its truth; and so I will begin by asserting that this well worn "principle” is a bit of educational cant that passes current to save the labor of thinking. Axioms that are not axiomatic arrest thought. They foster the delusion that a method has received its final justification when it has been shown to be consistent with one of these assumed principles. The mischief lies in the fact that these maxims are partly true and partly false. In some cases they lead us to the truth, and in others they betray us into error.
This maxim is often employed to justify the constructive or synthetic method of teaching geography, according to which the pupil proceeds from school-yard to township, from township to county, from county to state, from state to nation, from nation to continent, from continent to hemisphere, and finally to the globe. But if an undoubted psychological law can be. trusted, this specious method is false, is absolutely without scientific justification. My faith in a psychological law is much stronger than my faith in this educational axiom. Therefore I suspect that we have to do with an axiom that is not absolutely axiomatic. From my point of view, then, this examination is not absurd.
The "genesis of knowledge in the race" has been a favorite starting point with the educational philosophers who make a liberal use of this axiom. Now it must be apparent that with the race, the genesis of knowledge must have been from the unknown to the known; for each individual of the race had nothing in the line of knowledge to begin with, and so must have proceeded from the unknown to the known. This primal experience is typical of the experiences that follow in the life of the child; for a considerable time passes before the old is implicated in the new to a degree sufficient to fall within the compass of this rule. The child is ever encountering new sensations; but as these are simple, he derives no help from previous sensations. In his knowledge of objects, the general process is still the same.
Each new object is a new unknown It may be composed of parts that are really contained in objects previously known; but as first impressions are always confused, these parts are as yet not discriminated, and so cannot be used to analyze the new unknown.
Again, in this course of unconscious tuition, the learning of elements or parts is always subsequent to the learning of aggregates or wholes. Definitude, as Hamilton has observed, is not the first, but the last term of our cognitions. It is only in a mature period of culture that the knowledge of elements is sufficient to permit a prompt resolution of the new into the old. Childhood is well over before the resolution of the confused into the definite is well begun. One half of thinking is mental disintegration,—the reaction of the mind in the way of analysis upon complex presentations; so that, if before the presentation is made, its elements are already in the mind, the tension of thought is low. To think vigorously, there must be some resistance ; but resistance becomes less as analysis becomes easier ; and analysis grows easy in proportion as elements admit of quick discernment.
If, then, the dogma, "proceed from the known to the unknown"
means that the pupil should master the elements of a complex notion before the notion itself has been presented, it is unsound from two points of view;
1. It is in direct conflict with a normal law of mental growth-a law that is stated by Hamilton as follows: “The first procedure of
“ the mind in the elaboration of its knowledge is always analytical. It descends from the whole to its parts, from the vague to the definite.”
2. In consequence of a violation of this law, this dogma, interpreted as above, absolves from the necessity of thinking. Indeed, when I think on the possible consequences of such a doctrine, I feel glad that this dogma can neither be interpreted nor applied. How happily hopeless the case is, we may judge from Mr. Bain's fruitless struggle with this "favorite maxim of the teaching art."-(Education as a Science, p. 128.)— Educational Weekly.
HINTS TO YOUNG TEACHERS.
Be punctual. You cannot enforce punctuality on others unless you set an example of it yourself.
Keep a cheerful countenance; your face is a looking-glass, and should give only pleasant reflections. It costs no more to look goodhumored than to look glum, and it will add seven years to your life. If you must put on a sour face, and wrinkle your brows, and let down the corners of your mouth, let it be in the dark, where no one will suffer from it but yourself.
Avoid forming the habit of fault-finding and scolding. Never withhold approbation when you can give it conscientiously. Never find fault, unless compelled to do so. The withholding of praise will soon be regarded as an expression of displeasure. So you will save time
Give but few orders; see that they are obeyed promptly and fully. Give directions to a class in a firm and decided tone, loud enough (and only loud enough) to be heard by all concerned, the tone being that of command; disobedience will be a breach of discipline. Directions to an individual are better given in the form of a request, the tone being that of courtesy ; disobedience will be a breach of good manners.
"Attention! class; close books; take up slates; John, have the goodness to raise the window next you.”
Keep your class well in hand; stir up the indolent; restrain the restless; give your instructions to the class, not to an individual. The class is the teacher's unit. The point to be gained is that every member of it shall be occupied by the same thoughts at the same time. Call occasionally for a general answer from the class by way of keeping them awake. Let the class answer by a show of hands, and call on one to answer orally. Never let iwo speak at once (except in concert recitations), nor one unless he has received permission,
Give short lessons. Try to have them well recited. If you fail, and find that the majority of the class are badly prepared, inflict the usual penaly at once ; drop the form of recitation, and teach the subjectmatter of the lesson viva voce. You only waste time and temper by pumping a dry well.
If, owing to the weather, or your headache, or the weariness of the pupils, or any other "circumstances beyond your control," you cannot fix the attention of the class on the lesson, stop; change the subject; take five minutes for calisthenics, if the weather is cool, or a song, if it is warm; give them a conundrum, or tell them a story; do something, anything, that will bring the thoughts of all the class into one channel, and then resume your lesson. Never allow yourself to talk to a restless or inattentive class; and, remember, the restlessness and inattention may be as much your fault as theirs.
Order is essential; but it should not be your primary object. Order is to teaching what the shadow is to the substance--an accompaniment, a sign, an effect-not a cause. If a school is well taught, good order necessarily follows. But a teacher, well armed, may have good external order, and do no good teaching. Such order is not "Heaven's first law." The more perfect the order in a badly taught school, the worse it is for the scholars. Perfect silence, unbroken stillness, are not in themselves desirable for young children, however necessary they may be for good school work. A good teacher will rather seek to produce them as the results of good teaching than to enforce them as conditions precedent to teaching. Maintain no more and no less order than is necessary to enable teachers and pupils to do their work efficiently. The mind cannot work to advantage unless free from external constraint and internal anxiety. Be careful, therefore, to make your pupil's feel at home. Do not drive, habitually, with a tight rein, but be ready to pull up at a moment's warning. - The Teacher.
THE CLEVELAND SCHOOLS,
Since our last issue, we spent a part of two days in the Cleveland schools, with a view of giving our readers some account of the work which Superintendent Hinsdale and his five hundred teachers are doiny. The pleasure of visiting friends, however, interfered with the business of inspecting school work, so that we are able to give, at this time, but a general outline of what is going on in these schools, hoping to get, at no distant day, a nearer and more complete view.
We were constantly impressed with the marvelous growth of the system. It is about twenty years since we were called to the principalslip of the Brownell Street School. At that time, there were about cighiy tracers, under the superintendence of Rev. Anson Sinyth. Now, the numresereds five hundred.
The first buildings erected, after the adoption of the graded system, were two-story structures containing three rooms. There were two rooms on the first floor, the one intended for the primary department, and the other for the intermediate, with one teacher for each. The upper story was intended for the grammar school, in which two teachers were usually employed. It will be readily seen that the classification of these schools could have been little, if any, better than the best country schools of to-day.
A few years later, three-story buildings were crected, containing five rooms, The classification was not improved, however, as it might have been; for instead of dividing the pupils below the grammar school into four grades, corresponding to the four rooms, the sexes were separated, and a primary and an intermediate school was established for each sex.
In the course of time, the need of better classification led to the erection of seven-room buildings and the establishment of three departmants below the grammar school, with a school of each department for each sex. These departments were called primary, secondary and intermediate. This classification was not by any means a rigid one. No very detinite amount of work was laid out for each department, and no time was absolutely fixed for passing through it. The same school would often contain four or five classes, with intervals varying from three or four months to a year. The classification was sufficiently loose to satisfy the most ardent aclmirer of a flexible school system.
This was about the condition of the Cleveland schools, as far as classification and consse of study are concerned, at the time of Mr. Rickoff's accession to the superintendenog in 1807. The first important measure of his administration was the adoption of a definite course of study and the reclassification of the schools in accordance with it. This course of study provided for three departments (primary, grammar and high) of four grades each, the work of fach grade requiring one year for its completion. Under this course, the Kchools were classified without regard to sex,tach seo containing but one,