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CINCINNATI, Feb. 23d, 1857. Mr. John D. CALDWELL:
Dear Sir — In conformity with your request, to contribute something for the Journal, I submit an Object Lesson, which, I presume, will be interesting, inasmuch as such exercises have been introduced into all of the Cincinnati District Schools. I will, therefore, give a description of the usual manner of conducting them. The subjects for such exercises are innumerable; hence, for the sake of illustration, I have selected the subjoined lesson, which was given a few days since, by one of the Teachers in the Primary Department of one of our schools.
The Teacher, after securing the undivided attention of her pupils, writes upon the black-board, for example, Domestic Animals. All who can think of the name of one, are requested to elevate the right hand. On the first lesson of this character being commenced, the class will be covered with confusion and astonishment, but when they become acquainted with the kind of answers required, all will be eager to answer; hence, in the beginning of every succeeding lesson, every hand is very apt to be raised. The Teacher designates one to give his answer (which, we will suppose, is doy), when all who were thinking of this name, lower the hand, but are privileged to think of another immediately, and indicate the same by again elevating the hand. Another being called on, answers, cow; another, horse; a different pupil being selected every time, if possible. This process is continued until the names of all the domestic animals, with which the class is acquainted, are given; the Teacher having written the names in a column, each at the time it was given. The Teacher then writes, Mention sereral of their uses. The names, composing the list obtained as described above, are taken in their order and the best answer given for each one, is written opposite to it. Other divisions of the subject are treated in the same manner. When their knowledge on a familiar subject is found to be limited, it is thought better to defer the completion of the lesson one or more days (for them to gather what information they can), than for the Teacher to complete the list. It is generally enough for the class to know that the list is incomplete, and every facility that they can command will be brought into requisition, to enable them to complete it when the lesson is resumed.
In no department of education is so much demanded of the teacher as in mathematics. In the physical or mental sciences, or in the languages, one may “ follow the book," and have tolerable success in imparting instruction. Not so in mathematics. And this fact, since fact it is, may be accounted for by considering what are the peculiarities of mental character, the essentials to success in mathematical pursuits-quick apprehension, plodding patience, intense application, retentive memory, great powers of abstraction, a ready and clear discernment of logical sequences, a lively perception and keen appreciation of the powers, excellences and beauties of the science.
To a mental structure of such materials, mathematics presents a rich and attractive field for excursions of pleasure, and, so far as the question of education is involved, such a mind needs for its development but little of the adventi. tious aid of mathematical study. But the mind deficient, to any considerable extent, in one or more of the faculties enumerated, will meet with difficulties in the science of Quantity proportional in a very large ratio to that deficiency or, rather, want of development-and it is to the discipline induced, and consequent growth of intellectual power effected, by battling and conquering these very difficulties, that the study of mathematics owes its potency as an educational instrument.
Now, of one hundred individuals, no two will find difficulties the same in kind and degree, and yet if the teacher aim at complete success, he must see that every mind master every point-a task not to be appreciated at sight. In the first place, it must be known in what direction and to what extent assistance is required, and then that assistance must be meted out with a careful hand, too much being as worthless as none. I am equally exercised whether my burden lies upon the ground or is borne by a friend. The case of every student, then, must be understood, and though this is a great deal, yet it is but a modicum of the whole. Either you or I may understand the disease, but the surgeon alone can apply the scalpel. The sluggishness of this mind is to be enlivened to activity, and the elasticity of that is to be schooled to more prolonged and persevering action. If the memory be at fault, the teacher, by some mnemonic art, must apply the want until by that art he can develop a greater retentive power.
He must encourage closer application. With untiring industry and frequent elucidation, he must abstract the idea from the object, hold it up, turn it over, examine it in its parts, as a whole, in all its varied relations, until the pupil can comprehend it, reason upon it, and, if the term be not too glaring a misnomer, handle it as the child would a familiar toy. Right here is often found the chief obstacle to the pupil's progress. It is here the teacher must throw aside the book and substitute his own skill, his own originality ; if that fail him, then is his teaching, so far, a failure.
Again, in many minds, even though tolerably matured in other respects, there is such an inaptitude for teaching a chain of sequences from link to link, to the final conclusion, that oftentimes the step from a single antecedent to its consequent, though safe and easy, seems too great a span, and the teacher, with his own hands, must bridge the way across, and even then the timid mind must be led around by one or more circuitous paths ere it will venture upon the route direct. Here, again, is an obstacle, often amounting to an effectual and final barrier to farther advance. It is at this point that the teacher's patience pays the heaviest tax, and yet at this very point is impatience most to be deprecated. It might be well to dwell here, more fully, but as it is the present design to point out rather than remove obstructions, one or two more remarks will bring our article to a close.
To but few minds does the science present attractions. Generally regarded with indifference, often with decided aversion, it fails to elicit the interest indispensable to its successful pursuit. Here again is the burden thrown upon the teacher. He must conquer prejudice. He must convince of utility. He must frequently apply, copiously illustrate, clearly exemplify, ably defend, and so bring out in bold relief, the ideal beauty, power and extent of the science, as it can only be done by the faithful, earnest, able educator.
Doubtless the former correspondents and readers of the Mathematical Depart. ment will "hail with gladness” its reäppearance in the Journal. And may we not hope that still others, in view of a promise we are about to make, will turn their attention a little more closely to its pages? We have endeavored above, in a few words, to point out some of the difficulties of the practical teacher of mathematics. Hints, from time to time, setting forth the best and easiest methods of removing or overcoming those difficulties cannot fail to be of great utility and general interest. Such hints we promise to offer, relying upon the friends of this department to make good our pledge. Come up, then, to the work, and let us have the benefit of your experience.
But in the meantime, do not give up the problems. Continue them by all means. None are published in this issue because none have been furnished, and the Editor prefers that correspondents should choose for themselves what questions they would have solved. Solutions will, as heretofore, appear in the second number after that in which the problems are published. Remember, to be mathematical, is to be accurate, clear, brief.
* Address of Editor of Mathematical Department, W. H. YOUNG, Athens, O.
The Western News Boy, published at Malta, Morgan Co., has an interesting historical notice of schools in olden time in that county, and compares them with their improved condition now. The Institutes are well attended; Teachers are well paid, and liberally support the "Journal.”
aƐ INTRODUKSON OV FONETIK SPELITS. dar egzists wun real and veri serius impediment in de wa ov a · spedi introdukson ov a fonetik sistem ov erdografi, hwig haz bin jenerali overlukt; it konsists in de grat and prevaliŋ ignorans ov te sjens ov fonoloji, de natyur ov speg sondz, đạr varjetiz, đạr analisis, and đąr sintesis. It iz rąr tu met wiđ a singl elementari wurk hwig kontanz evn a tolerabli korekt akont ov dis important subjekt, and evn skolarz and profest tegerz ov pronunsiafon and elokuson qr jenerali veri ignorant ov te later. Na, mor, de veri tecerz and best investigatorz ov de subjekt ar at varians. Let eni wun peroz de wurks ov de gratest etoriti we pozes, doz ov Aman, Johanez Muler, Wilis, Hwetston, Lepsius, Maks. Muler, Latam, ets., and he wil se diferensez on fundamental ponts hwig ar irekonsilabl. If he turn tu wurks ov mịnor pretens, az Bel, Smart, Weker, Wuster, and te nųmerus wurks on elokuson, he wil fjnd konfuzon arizin partli from ignorans, and partli from a parsal vų ov de subjekt. Hwil in komon gramarz, and in de komon tretizez ov travelerz, and pronensiy vokabyylariz and diksonariz, he wil find dat wun person haz kopid from anuder witst understandiy him, til wurdz qr repeted and sens iz entirli lost.
No it iz absolutli nesesári dat dis kunfuzon sud, tu a serten ekstent, be removd,—&at spekerz ov de Inglis laygwaj at larj, hwąrever liviŋ, ma be duroli akwanted wid an aproksimatli akyyrat fonetik analisis ov dạr laŋgwaj and familyar wiđ its yus, befor we kan hop tu fjnd dem sufisentli prepard tu aksept fonetik speliŋ, not merli az a sjentifik instroment, but az a praktikal wurkiy tol. And ho iz dis rezult, dis nesesari preliminári, tu be gand. Bį introdysiŋ a fonetik alfabet and de proper instrukfonz in yuziy it, intu everi skol, so dat de yuygest gildren sud bekum yuzd tu analiz wurdz intu đạr elementari søndz, and tu kombịn đạr elementari sgndz intu wurdz, and dus obtán a praktikal nolej and feliz ov de fonetik konstituson ov sr laŋg waj. But 3 bị hwot menu kan we efekt is. Bį de veri sam menz bị hwiç we propoz tu overkum de konservativ objekson arīzip from de egzistens ov a previus unfonetik ertografibį maky fonetik rediŋ an introdukson tu romanik, on de grond dat it iz praktikali de best metod ov akwiriŋ fasiliti in ordinari rediŋ. In dis respekt, den, elso, a rediŋ reform iz a nesesári antesedent tu a speliŋ reform. Tu kari it st properli rekwirz, ferst, de produkson ov a number ov buks in fonetik spelig ; and, sekondli, de yys ov sug buks in skolz and elshwar for akwjriy a nolej ov gud spekiŋ and ov romanik rediŋ. dez eforts wil be advanst, ov kors, bį periodikal publikasonz in a fonetik karakter, suç az de ‘Tip ov te Timz,' and 'Fonetik Jurnal,' tu so its aplikabiliti tu everi
purpus for hwig de ordinari spelin iz yuzd, and tu meni purpusez fer hwig erdinári romanik spelig haz provd entịrli inefisent.
ONE BY ONE....(From Household Words.)
One by one the sands are flowing
One by one the moments fall;
Do not strive to grasp them all.
Let thy whole strength go to each;
Learn thou first what these can teach.
One by one, (bright gifts of heaven,)
Joys are sent thee here below;
Ready too to let them go.
Do not fear an armed band;
Shadows passing through the land.
See how small each moment's pain;
Every day begin again.
Has its task to do or bear ;
If thou set each gem with care.
Or for pending hours despond !
Look too eagerly beyond !
Reaching heaven; but one by one,
Ere the pilgrimage be done.
The Dayton Journal publishes the following letter from a school master in Shelby Co., V., to his pupils, who had " barred ” him out:
“ JANUARY, 1rst, '57. Belovid students as you have shut me oute there are thre things you may concider while I retire for a few moments : namely first what authority have you for clozing the door in my face ; 2ond doe you think you can be gustified in the act ; 3rd doe you act on a principle of Honor. when you concider These I will return when you can either let me in or By keeping the door shut allow Me to spend the day in visiting my friends.
R. C. The boys concluded to let him visit his friends.