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From thc Jan. No. for 1828 of the JOURNAL OF EDỰCATION
“A carcful examination of this valuable work will show that its author has rompiled it, as all books for school uso ought to be coinpiled, from the resulta of actual experiinent and observatiou in the schocl-room. It is entirely a practical work, combining the merits of Colburn's systein with copious practico on the glate.
“Two circumstances enhance very much the value of this book. It is very comprehensivo, containing twice the usual quantity of matter in works of this class; whilo, by julicious attention to arrangement and printing, it is sendered, perhaps, the cheapest book in this department of education. The brief system of Book-keeping, attached w the Aritlimetic, will be a valuable aid to more compiele instruction in common schools, to which the work is, in other respects, so poculiarly adapted.
There are several very valuablo peculiarities in this work, for which we cannot, in a notice, find sufficient spuce. We would recoininend a careful examination of the book to all teachers who are desirous of combining good thico. ry with copious and rigid pructice.”
0 12-5-35 heu
From the Report of the School-COMMITTEE OF PROVIDENCE.
“The books at present usod in tlic schools are, in the opinion of youut Com mitloe, altogether above the range of thought of thio pupila. Works of a nar. rative character would be better understood, would be more interesting, and would, of course, tcach the pupil to read with more taste and jur?gment. The boy who pores, in uttor disgust, over the book which he reads in schools, will hasten home to read with avidity, his story-hook. The true wisdom would then be, to introduce the story-book into school, and thus rendur his place of education the place of his amniscinent.
“Nevertheless, as this subject is one in which time and judgment are neces sary for a selection, and as a chango of this sort, through all the schools, would bo productive or considerable additional expense, your Committce would reciommend that no change, at present, be niado in books, excepting only the Arithmetic. If a school, by way o experiment, be established on the mor.ito rinl plan, various school-books can be tried there, and, after a fair opportunity ol testing the merits of several, those can be selected which scom besi adapled to accomplish the purposes of cducation. Your Committee are, however, of opinion, ihat it would be expedient lo introduce the system of Arithnielic pu! Jished by Mr. Smith (subsequently adopted into all the Public Graminur Schools ; and, also, that all the scholars in arithmctic be tauglit by classcs, and pot individually, as is now the prevalent mode."
The above Report was signed by the following named gen flemcn:
Rev. F. WA FLAND, Jr., D.D. Pres. Brown Unio., (Chairman.)
Dated April 24, 1828.
This work is recommended by the State-Commissioners di Vermont to be adopted throughout that State. It is likewise in. troduced into the public and private schools of Hartford, Conn. by the concurrence both of committees and teachers, and in ike manner in various other places.
SUGGESTIONS TO TEACHERS
ON TIIE METHOD OF USING THIS WORK,
For a course of mental arithmetic, adapted to the capacities of very young pupils, they may take the mental exercises in each rule, as far as the first exampie for the slate. This course is not meant to include any of the exercises styled “ Questions on the foregoing."
This course embraces the whole of the first 20 pages, together with the arith metical tables, extending to the Appendis. The necessity of impressing these tabins on the minds of pupils at an early age is sufficiently obvious. Where the pupil is perfect master of this course, as will, most probably, be the case after one or two reviews, the teacher will find no difficulty in making him understand the operations by slute. lle may then take the whole in course.
In every school, it would be well to institute classes ; and as there are seldom any answers given to the metal questions, the pupils may be allowed to read in their turns the questions from the book, thus giving the teacher no further trouble than occasional corrections By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editions have been In large schools these corrections may be made by an advanced scholar, instcad of the teacher. Whenever an advanced scholor takes up the book with a view of profiting from it, he should omit nothing as he pio greases, but make it his practico to quality himself to answer any question, is the mental exorcises, rules, or respecting the roason of the operations.
Teachers will find it to be a useful occupation for their scholars, to assign them a morning lesson, tu be recited as soon as they come into school. With little oxertion on the part of teachors, pupils in this way may be made assidu our and ambitious, very much to their advantago, and to the credit of their teachers. The mental questions, under the head of “Quostions on the foregoing," will
, inteiligenitoy answered, furnish to committees an adonirable test of the pupil's knowledge of this subject.
The Appendix is designed for those who have time and opportunity to Jevote to the study of the noro abstruse parts of mathematics.
Nole. Lest some may mistake the object of the figures in tho parentheses, it may hero ha remarked, that these figures are separato answers, les without assigning any value to them, reserving this particular for the discretion of the pupil, which he inust necessarily exercise, in order to obtain the answer which follows, that the aggregate of tho whole.
The above directions are those which seem the best to the authur ; but n every intelligent teacher has a way of his own, which, though nut intrinsically the heat, is, parlaps, the best for him, the subject is respoctfully subrnitros to his own choice.
TO THE THIRD EDITION.
WHEN a new work is offered to the public, especially on & gulject aboundIng with treatises, like this, tho jaquiry is very naturally made, “ Docs this work centain any thing now?" “ Are there not a hundrel others as good as this?"
To the first inquiry it is replied, that thero re many things which aro belicved to bo new ; and, as to the second, a candid public, after a careful examination of its contents, and not till then, it is hoped, must decide. Another inquiry may still be made : “Jo this edition different from the preceding?” The answer is, Yes, in many respects. The present alition professes to be strictly on the Pestalozzian, or inductivo plan of teaching. This, however, is not claimed as a novelty. In this respect, it resembles many other systéms. 'l'he novelty of this work will be found to consist in adhering more closely to the true spirit of the Pestalozzian plan ; consequently, in differing from other systems, it differs less from the l'estulozzian. This similarity will now be shown.
1. The Pestalozzian professes to unite a complete system of mental with written arithmetic. So does this.
2. That rejects no rules, out simply illustrates them by mental questions. So does this.
3. That commences with examples for children as simple as this, is as extensite, and ends with questions adapted to minus as matrere.
Here it may bo asked, “In what respect, then, is this different from that? To this question it is answered, In the execution of our common plan.
The following are a few of the prominent characteristics of ihis work, in which it is thought to differ from all others.
1. The interrogatitc system is generally adopted throughout this world.
2. The common rules of arithmetic are exhibited so as to correspond with the occurrences in actual lusincss. Under this head is reckoned the application of Ratio to practical purposes, Fellowship, &.c.
3. There is a constant recapitulation of the subject attended 10, styled “ Questions on the foregoing"
4. The mode of giving the individual results without poin's then the aggregate of these results, with points, for an ansl.net by chich the relative value of the whole is determined, thus tur nishing a complete test of the knowledge of the pupil. This is e characteristic difference between this and the former editior:9. 5. À nero rule for calculating interest for days with or onths
6. The mode of introducing and conducting the subjuct of Proportion.
7. The adoption of the federal coin, to the exclusion of ster ling money, except by itself.
8. The arithmetical tables are practically illustrated, predi. ously and subsequently to their insertion.
9. As this mode of teaching recognises no authority but that of reasm, it was found necessary to illustrate the rule for the extraction of the cube root, by means of blocks, which accompany this work. These are some of the produminant traits of this work. Oth
might be mentioned, but, by the examination of these, the reader will bo qualified to de ciile on their comparative valuc.
As, in this work, the common rules of arithmetic are retained, perhaps the reador is ready to propose a question frequently asked, " What is the use of so ma ny rules?" ( Why ont proscribe them?”. The reader must here be reminded, that these rules are taught differently, in this system, from the common method. The pupil is first to satisfy himself of the truth of several distinct mathematicul principles. These deductions, or truths, are then generalized ; that is, briefly summed in the form of a rulé, which, for convenience' sako, is named. Le there any impropriety in this?. On the contrary, is there not a great conve nionce in it? Should the pupil be left to form his own rules, it is more than prubablo he might mistake the most concise and practical one. Besicles, dilicrent ininds view things differently, and draw different conclusions. Is thoro no benefit, then, in helping the pupil to the most concise and practical method of solving the various problems incident to a business life?
Some have even gone so far as to condemn the Rule of Three, or Proportion, and almost all the successive rules growing out of it. With more reason, they might condemn Long Division, and even Short Division ; and, in fact, all the common and fundamental rules of arithmetic, except Addition"; for these may all be traced to that. The only question then is, “To what extent shall we go To this it is replied, As far as convenience requires. As the Rule of Thrce is generally taught, it must he confessed, that alingst any thing else, provided the mind or the pupil be exercised, would be a goud substitute. But when taught as it should be, and the scholar is led on in the saine train of thought that origi. nated the rule, and thus effectually made to see, that it is simply a convenient method of arriving at the result of both Multiplication and Division Cuinbinod, its necessity may be advocated with as much reason as any fundamental rulo. As taught in this work, it actually saves moro figures than Short, compared with Long Division. Here, then, on the ground of convenience, it would be rousonable to infor, that its rctention was moro necessary tilan oither.. But, waiving its utility in this respect, there is another view to be taken of this sub ject, and that not the least in importance, viz. the ideas of beauty arising from viewing the harmonious relations of numbers. Pare is a dolightful field for an inquisitive mind. It hero imbibcs truths as lasting as life When the utility and convenicnce of this rule are once conceded, all the other rules glowing out of this will demand a placo, and for the same reason.
It may, perhaps, be asked by many, "Why not take tio principle withɔut the name ?" To this it is again replied, Convenience forbids. The name, the pupil will see, is only an aggregate term, given to a process imbodying several distinct principles. And is there no convenience in this ? Shall the pupil, when in actual business, he obliged to call off his mind from all other pursuits, to trace a train of deductions arising from abstract reasoning, when his atten. tion is most needed on other subjects? With as much propriety the name of captain may be dispensed with; for, although the general, by merely summon. ing his captain, inay summon 100 men, still he might call each ou separately, although not quite so conveniently. With these remarks the subjoct will be
fismissed, merely adding, by way of request, tha, the reader will defer his decision till he has examined the doctrine of Proportion, Fellowship, &c., us thyght in this work.
The A-PENDIX contains many useful rules, although a knowledyo of these le not absolutely essential to the more common purposes of life. Under this kend aro reckoned Alligution, Roots, Progression, Permutation, Annuitics, &c. l'he propriety of scholars becoming acquaiotod, some time or other, with these rules, has long since been settled; the only question is, with regard to the expodioncy of introducing them into our arithmetics, and not reserving them for our algebras. In reply to this, the writer would ask, whether it can be supposed, the dovelopement of these truths, by figures, will invigorate, strongthen, and expand the mind less than by letters? Is not a more extersive knowledge of the power of figures desirable, aside from the improvement of the mind, and the practical utility which these rules afford? Besides, there always will, in sono nook or other, spring up some poor boy of mathematical genius, who will be desirous of extending his resnarches to more abstrusc subjecis. Must lo, as well as all others, be taxed with an additional expense to procure a system, tontaining the same principles, only for the sake of discovering them by letters?
Position, perhaps, may be said to be entirely useless. The same may be said of the doctrine of Eluations by algebra. If the former be taught ra. ionally, what great superiority can be claimed for tho ono over the other? Is it not obvious, then, that it is as beneficial to the pupil to discipline his nind by the acquisition of useful and practical knowledge, which may bo in the possession of alınost every learner, as to reserve this interesting portion of mathematics for a favoured few, and, in the mean time, to divort the atten tion of the pupil to less useful subjects?
'The blucks, illustrative of the rule for the Cube Root, will satisfactorily account for many results in other rules ; as, for instance, in Decimals, Mensura. tion, &c., which the pupil, by any other means, might fuil to perceive. By observing these, he will see the reason why his product, in decimals, should be ess than either facto: ; as, for instance, why the solid contents of a half un inch tube should be less than half as much as an inch cube. In this case, the faccors are each half an inch, but the solid contents are much loss than half a solid inch.
In this work, the author has endeavoured to makc overy part conform to His maxim, viz. THAT NAMES SHOULD SUCCEED IDEAS. This method of túlounicating knowledge is diametrically opposed to that which obtains, in many places, at the present day. The former, by first giving ideas, allures the pupil into a luminous comp-ehension of the subject, whilo tho latter astounds him, at first, with a pompous nams, to which he seldcm affixes any definite ideas, and it is exceedingly problematical whether ho ever will. In addition to this is the fact, that, by the last mentioned method, when the name is given and tho process shown, not a single reason of any operation is adduced ; bat the pupil is dogmatically told he must proceed tius and so, and he will come out go and so. This modo of teaching is very much as if a merchant of this city shou direct his clerk, without intrusting him with any business first to go to South Boston, then to the stato-housc, afterwards to the market, and then to return, leaving him to surmise, if he can, the cause of all this peregrination. Many are fools envagh to take this jaunt pleasantly; others are rostiff, and some fractious. This sentiment is fully sustained by an article in Miss Edgoworth's works, from which the following extract is made: “A child's secming stupidity, in learning arithmetic, may, perhaps, be a proof of intelligence and good sense. It is casy to make a boy, who does not reason, repent, by rote, any tochnical rules, which a common writing master, with magisterial solemni!y, may lay down for him; but a child who reasous will not be thus casily managel; he stops, frowns, hesitatcs, questions his diuster, is wretched and refractory, until he can discover why he is to proceed in such and such a manner; he is i'ot content with secing his proceptor muko figures and lines on the slate, and perform wondrous operations with the self-com placopt dexterity of a conju ar ; be is not content to be led to the ti casaron of