OF ARITHMETIC. By A. SONNENSCHEIN AND H. A. NESBITT, M. A. Part I. Integral. Parts II. & III. Fractional & Approximate Calculations. OPINIONS OF THE PRESS. "Mr. Sonnenschein is a pupil, and a thoroughly taught pupil, of Mr. De Morgan's, and it is scarcely necessary to say more in order to convince all who know Mr. De Morgan's works that there is nothing like half-digested work in this arithmetic. This first part of Mr. Sonnenschein's book is admirable of its kind, aul better fitted for ordinary school use than Mr. De Morgan's Arithmetic, which is more suitable to students and teachers. Brevity and lucidity in the exposition of principle are its main characteristics as a scientific book; and great care in the explanation of simple practical rules for shortening or verifying calculations is its main characteristic in reference to the art of computation. It gives a clear proof of all the rules,-insisting on the exact meaning of the various operations and their interpretation,—and contains a remarkably good chapter on the general properties of numbers, so far as they can be explained to beginners who have only mastere 1 the arithmetic of integers. It is hardly possible to speak too well of this little book, which we have examined very carefully."-Spectator. "... Nor should we notice this lucid and clever work, except with a word of commendation in our short notices, but for the chapter on the ready decimalization of our weights and measures, which is worth the attention of all calculators. . . . Still, it is an ingenious suggestion to decimalize all the different tables of weights and measures by observing the analogies between the relations of those tables and those of the money table, and so making one rule do for all alike. . . . We should add, as we have noticed a particular chapter in this excellent arithmetic, that the book is throughout good, though some portions of it are better adapted for the use of teachers than for the use of pupils. These portions, however, can easily be omitted by the pupil until he is sufficiently advanced. The thoroughness of the methods of proof is exceedingly praiseworthy."-Spectator. "Forty years have elapsed since the appearance of Prof. De Morgan's 'Elements of Arithmetic,' at a time when perhaps few teachers, as they submitted the rules of the science to their pupils, cared to establish them upon reason and demonstration. The effect of this work was that a rational arithmetic began to be taught generally, and the mere committing of rules to memory took its due subordinate position in the course of instruction. Such a method of treatment will go far to develop and exercise the reasoning powers, and in the case of many pupils, there is hardly any other subject which can so well be made a groundwork for the exercise of the reasoning faculty. The book before us is avowedly drawn up in agreement with the principles of Mr. De Morgan's work, and the aim of the authors is to lead the student 'to the discovery of the several rules by some path such as an original discoverer might have travelled.' In this first part, which treats of Integral Arithmetic, we consider that they have carried out their principles successfully, and hope they will succeed as well with the remaining two parts, which are to embrace respectively Vulgar Fractions and Approximate Calculations. The rules enunciated are few and tersely given; there is a great store of illustration; elementary difficulties are well stated and honestly grappled with, and cleared up in a way that brings the subject to the level of the capacities of junior students; at the same time advanced as well as young teachers may gather much that is useful from the book. A reader who has carefully gone through the work, can hardly fail to master the early details of the science; if he fail, it will not be the fault of the authors. The subjects treated of are numeration, modes of computation, the so-called first four rules, contracted operations, scales of notation, and properties of numbers. Under this last division we have much valuable matter grouped under the several heads of Divisibility of Numbers, Casting out Nines, Resolution into Prime Factors, Greatest Common Measure, and Least Common Multiple. Throughout and at the end of the work occur numerous examples, very varied, all of which are carefully arranged, and many fully worked out in two or more ways. With this short analysis of the contents, we heartily cominend the work to teachers generally, assuming, of course, that they will regulate their use of it in proportion to the requirements of age and ability of their pupils. The work is neatly got up, and we have detected hardly any errata."-Nature. ... "The authors of this excellent school arithmetic are to be congratulated on having brought their work to a successful termination. . . . The same good arrangement, ample store of illustration, and copious examples for practice, are to be found in this volume as had place in the first. . . . In this volume we have more advanced subjects treated in like manner. But an analysis of the contents will give a good idea of the work. Under Part II. we have the subject of Vulgar Fractions clearly treated, with applications to Practice, and a chapter which treats of Proportion, the Chain Rule, Compound Proportion, and Proportional Parts. In Part III. are chapters on Converging Fractions, Decimals with their properties, and several applications to Money, Weights, Measures, &c., the Metric System, Progressions, Interest, Discount, Stocks, Evolution, and a good chapter on Arithmetical CompleThere is also a chapter in which we have Continued Product to a given limit, Compound Interest, Equation of Payments, Complex Decimals, Duodecimals, and International Calculations. At the end of the work are given 250 Miscellaneous Exercises. There is enough here to satisfy any youthful arithmetician, and the methods employed are the latest out.' The complete work gives ample evidence that it is the composition of men who have given much time and thought to the subject, and have had much tuitional experience."-Nature. ments. "Decidedly the clearest, most useful, and easiest method we have seen of teaching the principles and practices of arithmetic. It combines the excellences of Colenso, De Morgan, and Barnard Smith, with excellences peculiar to itself."-The Rock. "It is a very original and well-reasoned system of educating the mind by means of numbers. The authors, working upon the principle that the student must be led to the discovery of the several rules by some path such as an original discoverer might have travelled,' have really begun at the beginning and logically deduced one step from another, making all so clear as they proceed, that the merest beginner should understand not merely the 'how' but the 'why.' It is perfectly true that more time and space than some may judge necessary are occupied in presenting what is merely one and the same fact under different aspects, and that what appears to be a complete system of arithmetic may be, and often is, packed into less space than the volume before us, which is but the first of three parts. Those, however, who have any experience in teaching, or perhaps remember their own difficulties in working by rule of thumb, will entirely agree with the authors that progress is not mere advance from rule to rule. Any process once properly realized can never be quite forgotten, and to impart to students what our authors term 'a thorough and all but visual realization of each process,' should be the aim of every teacher. They can scarcely have a more efficient book to work with than that of Messrs. Sonnenschein and Nesbitt."-Standard. "Some little time ago we drew attention to Part I. of Messrs. Sonnenschein and Nesbitt's Science and Art of Arithmetic. We have now Parts II. and III., dealing with vulgar fractions and approximate calculations, in which again we notice an independence of thought and originality of treatment which go far to shew how little the educational value of arithmetic has hitherto been understood."-Standard. "If we mistake not, Messrs. Sonnenschein and Nesbitt's volume will altogether evolutionize the old methods of teaching what has hitherto been supposed a dry study. It is divided into three parts, viz., 'Integral, Vulgar Fractions, and Approximate Calculations.' New methods are given for very rapid, and in most cases, mental,' decimalization of money, weights and measures to any assigned degree of accuracy, and for the ready intro-conversion of the coins, weights, and measures of different nations. The volume must supersede the old-fashioned methods, and will be invaluable to young teachers, as well as learners, and will rapidly make its way as 'the' text-book of arithmetic."-Naval and Military Gazette. "This is a work on Arithmetic of a peculiar, and in some respects an original character. Following in the steps of Professor De Morgan, the chief aim of the authors in explaining the rationale of the various arithmetical processes is not to give logical demonstrations of the several rules which a student is required to learn, but to carry him along some such path of reasoning as must have been travelled by an original discoverer; the present concise and conventional processes being unravelled, so to speak, and traced up to their first principles. . . . . There is much to recommend in this view of teaching arithmetic; for, as the authors remark in the preface, no subject is so well fitted as this for the early training of the reasoning powers, principally because the student is enabled, without apparatus of any kind, steadily to test all his à priori conclusions by the light of experience.'"-Educational Times. "This is the second part of a treatise on Arithmetic, the first of which has been already favourably noticed in these columns. The subject of Fractions is here taken up and treated with the fulness and completeness due to the important place it occupies as the Key-stone of Arithmetic. . . . In dealing with Decimals the authors have introduced the principle of 'Approximate Calculations,' by means of which much trouble is saved in working out results. . . . It is here that the great utility and simplicity of Decimals is seen, and the book before us does good service in giving prominence to this feature. . . . We are disposed altogether to entertain a high opinion of the merits of this work. The way in which it leads up to the various rules, by mental calculations and other preparatory steps, which serve to break the difficulty felt by the young learner, and its general adherence throughout to the best principles and methods of teaching, distinguish it as a work out of the common run on treatises of School Arithmetic."-Educational Times. We are "We have no hesitation in saying that the right note has been struck by the authors of the little book, a second edition of which lies before us. happy to conclude with an assurance that, take it as it is, the work of Messrs. Sonnenschein and Nesbitt is the best in the language on the subject of which it treats."-Inquirer. London: WHITTAKER & Co., Ave Maria Lane. i Sonnenschein & Allen's Educational Publications. Arithmetical Books by A. Sonnenschein and H. A. Nesbitt, M.A. SCIENCE AND ART OF ARITHMETIC, crown 8vo, cloth, Part I. Fourth Edition, 2s. 6d. ; Parts II.-III., Second Edition, 3s. 6d. ; Parts I.-III. in One Vol., Fourth Edition, 5s. 6d. ;.Exercises to Part I., Is. ; Exercises to Parts II.-III., Is. 3d. Answers to Exercises complete, Is. 6d. ABC OF ARITHMETIC, New Edition, crown 8vo, boards, Teacher's Book, Part I., Is. ; Teacher's Book, Part II., IS.; Pupil's Book (Exercises), Part I., 4d. ; Pupil's Book, Part II., 4d. Sonnenschein's Books on Arithmetic have been adopted by numerous School Boards. Price, per set of 14 sheets on a roller, 7s. 6d. ; In portfolio, 8s. 6d. Mounted on varnished canvas, with rollers, 16s.; on boards, and varnished, 16s. Descriptive Pamphlet, 6d. To these Pictures was awarded the Silver Medal, Paris Exhibition, 1878 (Highest Award in the British Educational Section). TABLES FOR PRACTISING SHORT DIVISION, for the use of Pupil Teachers and Monitors, by A. SONNENSCHEIN. All the Tables from I to 12 printed on Carbonized Slate, Is. Ditto, in Polished Rosewood Frame, IS. 6d. 12mo On Carbonized Slate-paper, as Pocket-book of 8 pp., 2s. "An ingenious attempt to minimise the pupil's efforts in learning Short Division, and to utilise to the utmost the labours of monitors and teachers.'-Educational Guide. CIPHERING BOOK. Being an Arithmetical Exercise-book, each righthand page being ruled in faint blue ink in chequers, for the Pupil's Use, the facing page being reserved "for Teacher's Remarks and Pupil's Corrections." 40 pp., in wrapper, post 4to, 3s. per dozen. EXERCISE-BOOK, for Dictation, Composition, &c., on the principle of the 'Ciphering Book (one page for Pupil and the facing one for Teacher), 48 pp., oblong 4to, 2s. 6d. per dozen. Sonnenschein's (A.) Patent Arithmometer. Designed to render Visible and Tangible all the operations in Arithmetic from Numeration to the Extraction of the Roots (SILVER MEDAL AT THE PARIS EXHIBITION, 1878), consisting of A Box (No. 1) containing A Box (No. 2) containing 10 rigid "plates." A long Box (No. 3) containing (a) 1 "large stave," being a framework 1 metre long and I decimetre broad and deep; (b) I "large plate," being a framework 1 metre long and broad, and I decimetre deep. . (c) I large box," being a cubic metre (framework). The large plate and the large box can fold up, so as to occupy but little space when not in use. 4s. 6d.; Long Box, 20s.; Complete Set, 30s. Applications sent Post Free. ALLEN, PATERNOSTER SQUARE. THE KINDERGARTEN. Child and Child-Nature, Contributions to the Understanding of Froebel's Educational Theories. By the Baroness MARENHOLTZ BÜLOW. Translated by ALICE M. CHRISTIE. Second (stereotyped) edition, with 10 woodcuts, crown 8vo, cloth extra, 38. "An admirable and very readable translation the book will be of special value to those who desire a more exact knowledge of Froebel and his work."-Academy. "We may at once say that it is the most readable contribution we have to what may be called Kindergarten literature; it is beautifully translated. For all teachers there are passages on nearly every page full of suggestion and often of beauty."--The Teacher. "The clearest and most compact exposition of Froebel's theories. . . . full of suggestiveness for parents."-Scotsman. FROEBEL SOCIETY'S SERIES OF KINDERGARTEN 12mo. in Wrappers. PAPERS. No. 1. Shirreff (Miss) On the Connection between the Kindergarten and the School. 16 pp., 3d. No. 2. Buckland (Miss) On the Use of Stories in the Kindergarten. 20 pp., 3d. No. 3. Hoggan (Frances E., M.D.) On the Physical Education of Giris. 28 pp., 4d. No. 4. Sonnenschein (A.) A Visit to a Belgian Training College. 16 pp., 3d. ***The Series to be rapidly continued. The Paradise of Childhood. A Complete Guide to the Kindergarten. By EDWARD WIEBE. Third edition, illustrated by 75 plates, 4to, extra cloth, 6s. then follow the beautifully-lithographed plates, showing the almost endless variety of combinations that may be obtained by a skilful use of the gifts. To the Kindergartner this book will prove very serviceable."-School Guardian. "The clear and simple instructions are illustrated by a large number of well-executed diagrams, which will be found invaluable."-Journal of Educational Union. Manual of Drawing for the Kindergarten. By N. MOORE. plates, 4to, extra cloth, 3s. 6d. Uniform with "The Paradise of Childhood. With 17 Synoptical Table, Showing the Connection between the Kindergarten and the School. By A. DE PORTUGALL. Folio, mounted on canvas, rollers, and varnished, 25., or to fold on canvas as book, 2s. 6d. "Its purpose is to show visibly the essential unity of the system, not merely of the Kin dergarten system, but of Froebel's entire views of education. No Kindergarten should be without it."-Journal of Educational Union. .... Slate Images for Infant Drawing Copies. Two parts, 12mo, each with sixteen pages of figures in white outline on black ground, paper covers, each 2d. "For training a child. . . . they are excellent; they will certainly create a longing for the drawing lesson."-The Teacher. A. Sonnenschein's Kindergarten Box of Letters, with "Nursery W. SWAN SONNENSCHEIN & ALLEN, PATERNOSTER SQUARE. |