from the Jen. No. for 1828 of the Journal or Education, * A careful examination of this valuable work will show that its ambor hus compiled it, all woks for school use ought to be compiled, from the resulte of setual experiment and observation in the school-room. It is antirely practical work, combining the merius of Colburn's system with copious practice ca the ulate. To * Two circumstances enhanco very much the value of this book. It is very cocaprebensivo, containing twice the Qgual quartity of matter is works of this olage; whilo, by judicious attention to arrangement and printing, it is renJerod, perhaps, the cheapest book in this department of education. The brief oystern or Book-Kooping, attached to the Arithmetic, will be a valuable aid to moro completo instruction in common schools, to which the work is, in other rospects, to peculiarly adapted. si There are several vory valuable peculiarities in this work, for which we annot, in a notice, find sufficient space. We would recommend carefuler. Kraination of the book to all teacluers who me demrous of combining goud theory with copious and rigid practice." from the Report of the SCHOOL-COMMITTEE or PROVIDENCR. u Tho buoks at present used in the schools are, in the opinion of your Comaittee, altogether above the range of thought of tho pupils. Works of a nulnative character would be better understuod, would be more interesting, and would, of course, teach the pupil to read with more taste and judgment. The boy who yotes, in utter disgust, over the book which he reads in schools, will bagten home to read with avidity his story-book. The true wisdom would then be, to introduce the story-book into school, aud thus render his place of when he, to introduce this amusement. in which time and jade $ “Nevertheless, as this subject is one in which time and judgment are necer ary for a selection, and as a change of this sort, through all the schools, would be. Troductivo of 'considerable additional expense, your Committee would jecoiamend that no change, at prosent, bo mado in books, excepting only tho Arithmetic. Ifa.school, by way of experiment, be established on the monitoria plan, various school-books can be tried there, and, after a fair opportunity of testing the merits of several, those can be selected which seem best adapted to accomplish the purposes of education. Your Committee are, however, of opinion, that it would be expedient to introduce the system of Arithmetic published by Mr. Smith subsequently adopted) into all the Public Grammar Schools : and, also, that all the scholars in arithmotic be taught by classes, and not individually, as is now the provalent modo." The above Report was signed by the following named gentlemen. Rev. F. WAILAND, Jr., D. D., Pres. Brown Univ., (Chairman.) 1. Rev. THON AS T, WATERMAN. WILLIAM T. GRINNELL, Esq. x Dated April 24, 1828. This work is recommonded by the State Commissioners of Vermont to be adopted throughout that state. It is likewise introduced into the public and private schools of Hartford, Conn.. by the concurrence both of committees and teachers, and in like manner in various other places. : . WH:CH ACCOMPANIES THIS ARITHMETIC. * * The utility, and even necessity of a work of this description, will scarcely be questioned by those who have had any experience in teaching Arithmetic. Most young persore after having bero pero snacted, again and again, to review a long anthmetical process, feel, or, affect to feel, certain that they have performed it correctly, althongh the result, by the book, is erronevus. They then apply to their in structer; and, unless he points out their mistake, or performs the opera tion for them, they become discouraged, think it useless to try' linger, and the foundation for a habit of idlencss is thus imperceptibly estab lished. Now, in a large school, it is always inconvenient, and some. times impossible, for the instructer to devote the time necessary to overlook or perform a very simple, much more a complex, question In Arithmetic. This is at once obviated by having at hand a Key, 10 , which reference can be easily and speedily made. The time of the deacher will thus be saved, and the pupil will not have his ardor damped ! by being told that his süm is wrong,' without learning where or how. - « This work is not designed for, and can scarcely become, a help to laziness: its object is to lighten the burden of teachers, and facilitate the progress of scholars. To promote, both of these important purpower to is now presented to the public. M. January, 1834" 10 TIE THIRD EDITION. PT WHEN a new work is offered to the puhlic, expecially on a sntifra alsounding with treatisex like this, the inquiry is very naturally niade, u Dore this work contain any thing new?" "Are there not a hundred otners as good as this?" "To the first inquiry it is replied, that there are many things which are believed to be new ; and, as to the securid, a cantdid public, after a careful examination of its contents, and not till then, it is hoped, must decide. Another inquiry may still be made : "Is this editivy ditferent from the precedirgi" Tire answer is, Yes, in many respects. The present malition professes to low sttirily on the Pestalozzian, or inductive, plan of teaching. Thuis, howeyer, is not claimed as a novelty. In ibis respect, it resembles many other systems. The novelty of this work wiil be found to consist in alhering more closely to the trile spirit of the Pestalozzian plant ; consequently, in ditlering from other systems, it ditler less from the l'eslaloz. 2130. Tois sinuiiarity will now be sbown. 1. The Pestalozzian professos lo unite a coinplete system of Mental with Wrillen Arithmetic. Su, does this. 2. That rejects no rules, but simply illustrates them by inental questions. So does this. 3. Thai commences with examples for children as simple as this, is as extensive, and ends with questions adapted to inindo as mature. . . Here it may be azked. “In what respect, then, is this different from that?" To this question it is allowered, in the execution of our cottQuin plan. The following are a few of the prominent characteristics of this work, in whico it is t ight to differ from all others, J. The interrogative systein is generally adopted throughout this work. 2. The common rules of Arithinetic are exhibited so as to cor. respund with the occurrences in actual business. Under this head is reckoned the application of Rutio to practical purposes Hellowship, &c: 3. There is a constant recapitulation of the s'ibject attended to, styled “ Qurstions on the foregoiny." . 4 The mode of giving the individual results without points, then the aggregate of these results, with points, for an answer by which the relative value of the whole is determined, tnus furnishing a complete test of the knowledge of the pupil. This A editions." then generalized; thematical principles. o satisfy hinsell of us stem in a characteristic difference between this and the forume 6 A new rule for calculating interest for days with month.. 6. The niode of introducing and conducting the subject of Proportion. 7. The adoption of the Federal Coin, to the exclusion of Stere ling Money, except by itself. 8. The Arithmetical Tables. are practically illustrated, previ. ously and subsequently to their insertion. 4. As this mode of teaching recognizes no anthority but that of reason, it was found necessary to illustrate the rule for the extraction of the Cube Ruot, by means of blocks, which accom pany this work. These are some of the predominant traits of this work. Others might be mentioned, but, by the exainination of these, the reader will be qualified to decide on their comparative value. * As, in this work, the common rules of Arithmetic are retained, perhape the reader is ready to propose a question frequently asked, “What is the use of so many rules?" "Why not proscribe then ?" The reader must nere be reininded, 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 inathematical principles. These deductions, or truths, are then generalized; that is, brietly samined in the forın of a rule, which for convenience' sake, is named. Is there any impropriety in this? On the contrary, is there not a great convenience in it should the pupil le left to form his own rules, it is more than probable he might mistake ihe most concise and practical one. Besides, different minds view things different. ly, and draw different conclusions. Is there no henetit, then, in helping the pupil to the most concise and practical method of solving the various problems incident to a business life? Some ha'.e even gone so far as it condemn the Role of Threr, or Proportion, and almost all the successive rules growing olit of it. With more reason, they might condenın Long Division, and even Short Division : and. in fact, all the common and fundamental rules of Arithmetic, except Addi' tion ; 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 convenienco requires. As the Rule of Three is generally taught, it must be confessed, that alinust any thing rise, provided the mind of the popil be exercised, would be a good substitute. But when tauglit as it should be, and the scholar is led on in the same train of thoitglie that originated 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 combined, its ne. cessity miav be advocated with as much renson as any fundamental rule. As taught in this work, it actually wil ves more figures than short, compared with long Division. Here, then, on the ground of convenience, it would be reasonable to infer. that its retention was more necessary than either. But, waiving its utility in this respect, there is another view to be taken of this subject. and that not the least ill importance, viz. the ideas of beauty arising from flowing the harnionious relations of numbers. Here is a delightful field for an inquisitive mind It here inoljbex truths as lasting as life. When the utility and convenience of this rule are. Ance conceded, all the other rules gruwing onlt of this will demand a place, aud fur the same reason. It may, perhaps, he asked by many, " Why not take the principle with. ortit the name?". To this it is again replied, convenience forbids. The nanie, che pupil will see, is only an aggregate Term. given to a process im. tudying ne verul dintre principles. And is there to convenience in this |