authors stated explicitly, either in the preface or the title, that the text was based upon Pestalozzian principles. William B. Fowle, The Child's Arithmetic or the Elements of Calculation in the Spirit of Pestalozzi's Method, for the Use of Children between the ages of Three and Seven Years, 1826. Roswell C. Smith, Practical and Mental Arithmetic on a New Plan, in which Mental Arithmetic is combined with the use of the slate; containing a complete system for all practical purposes; being in dollars and cents; 1827. Martin Ruter, The Juvenile Arithmetic and Scholar's Guide; wherein Theory and Practice are combined and adapted to the Capacities of Young Beginners; containing a due proportion of examples in Federal Money; and the whole being illustrated by Numerous Questions similar to those of Pestalozzi, 1827. James Ryan, The Pestalozzian System of Arithmetic, 1829. Adams's New Arithmetic, by Daniel Adams, author of the Scholar's Arithmetic, was published in 1827. It is described on the title page as being a text "in which the principles of operating by numbers are analytically explained and synthetically applied; thus combining the advantages to be derived from both the inductive and synthetic modes of instructing." The New Federal Calculator, by Thomas T. Smiley, 1828, is described as being "in appearance a twin to Daboll's Arithmetic." It passed through several editions and was still printed in 1899 by J. P. Lippincott & Co. The extended use of this text shows an element of conservatism. Elementary Lessons in Intellectual Arithmetic, by James Robinson, 1830, was designed as an "introduction to Colburn's First Lessons and other arithmetics." The number facts are presented objectively. Peter Parley's Method of Teaching Arithmetic, by S. G. Goodrich, 1833, is an interesting primary arithmetic. George Perkins published Higher Arithmetic, 1841; Primary Arithmetic, 1850; and Practical Arithmetic, 1851. George P. Quackenbos builded upon the texts by Perkins in 1863 and following. Many of the problems in the Practical Arithmetic are made up of important statistics and valuable facts in history and philosophy. A series of arithmetics was published by Horace Mann and Pliney E. Chase: Elements of Arithmetic, Part First and Part Second, 1850; and Arithmetic Practically Applied, 1850. In addition Mr. Chase published the following under his own name: The Good Scholars Easy Lessons in Arithmetic, 1845; the Elements of Arithmetic, 1844; and Common School Arithmetic, 1848. The last two of these are specified as being "on the plan of Pestalozzi," and the series is sometimes called a Pestalozzian series. George A. Walton, assisted by Electa N. L. Walton, published a series of arithmetics in the sixties. Later in 1878 and 1884 George A. Walton with Edwin P. Seaver wrote the Franklin Arithmetics, which embody Pestalozzian ideas. A feature of both these series of arithmetics is the provision for drill. A separate book, Arithmetical Problems, 1872, by George A. Walton, contains over 12,000 problems for drill. A series by S. A. Felter was first published in the years from 1862 to 1877. A prominent feature is the provision for drill. The content and organization of the texts.-The series of arithmetics by Joseph Ray has probably been the most popular and the most extensively used texts of this period. The series is also the most representative of the content and organization of the texts of this period. In the following description we shall follow Ray's arithmetics, quoting from others only to emphasize a trait or to show the presence of a tendency which later modified the subject. Primary arithmetic.-Warren Colburn intended his First Lessons to be a first text for a pupil, but it seems that, despite the very simple beginning, pupils found the book very difficult.1 The Child's Arithmetic, by W. B. Fowle, 1826, is a little volume of 104 pages. He states in the preface "that this manual is prepared in the spirit of Pestalozzi's method, and is intended as an introduction to the more advanced work of Colburn, which has wrought such a revolution in our own schools." The book is in three parts. The first has to do with numbers from 1 to 10, the second with numbers 10 to 20, and the third from 20 to 100. The first lessons contain explicit instructions for teaching children to count by using objects. They are taught to count out many of the number facts before they are given any practical examples. The practical examples are very similar to the simpler ones in Colburn's First Lessons. The book is a teacher's manual rather than a pupil's text. The plan is for the teacher to take the initiative; the pupil is to do what he is told to do. On the whole the book possesses no distinctive merit. Emerson's North American Arithmetic, Part First, 1829, was a text in which "illustrations by the use of cuts" is made a very conspicuous feature in an attempt to exemplify the object teaching of Pestalozzi. Pictures of various objects are used-apples, cherries, trees, pears, hats, lamps, houses, horses, chairs, fishhooks, pins, etc. In many cases simply marks or stars are used. All concrete problems in the book, except miscellaneous problems, are graphically represented. Not all of the number facts are developed in this way, but such as are, always precede the formal statement and drill. This makes the form of the book inductive, although it is not noticeably so in spirit. The Hindu numerals are introduced in the very beginning and are used in stating the problems. The pages of the book are attractive in appearance and doubtless appealed to the child. On the whole it is a primary arithmetic of considerable merit. 1 Clifton Johnson, Old Time Schools and School Books, p. 37. The relation of this text to Pestalozzi is given by Emerson in the preface. He says: The plan of the lessons accords with the method of instruction practiced in the school at Stanz, by the celebrated Pestalozzi. The method of illustration, by the use of cuts, and the location of unit marks under the question, it is hoped, will be found to be an improvement. The book was evidently designed to be used before a pupil commenced such a book as Colburn's First Lessons, since it was introduced immediately into the Boston schools, apparently without displacing the First Lessons which was then in use. Peter Parley's Arithmetic is a quaint little volume. Its lessons are "About dogs," "About soldiers," "About money," "About a baker's shop," etc. Each lesson is headed by an appropriate picture. The following lesson, "About a cat and her kittens," is typical: Here is a cat with four kittens. She has been out in the field where she has caught a bird; this she has brought home and given to the kittens. She has also caught a mouse, and one of the kittens is playing with it. Puss is a sly creature, and she kills a great many little birds and mice. Her foot is so soft that she can walk without noise, and her eye is so formed that she can see as well in the night as in the day. When all my little readers are asleep, she steals forth into the meadow or the wood, and woe to the mouse or bird that falls in her way. 1. If 1 cat kills 2 birds in a day, how many will 3 cats kill? 4? 5? 6? 2. If 5 kittens eat 2 mice in a day, how many will 10 kittens eat? 3. If a cat divides 4 birds between 2 kittens, how many will each kitten have? 4. If a cat kills 3 birds in a week, how many will she kill in 2 weeks? 3 weeks? 5 weeks? 5 weeks? &c. 5. If a cat kills 7 birds and mice in a week, how many will she kill in 14 days? 4 days? 4 days? &c. 6. If one cat kills 5 mice in a week, another 3, another 7, another 4, and another 2, how many do they all kill? 7. If 4 kittens have devoured 16 mice and 12 birds in a month, how many has each devoured? 8. If there are 21 mice in a house, and a cat kills 17 of them, how many are left? 9. If there are 18 mice in a barn, out of which a weasel kills 7 and a cat 11, how many are left? In Elementary Lessons in Intellectual Arithmetic, by James Robinson, 1830, the illustrations consist of a figure 1 placed in small squares. These are designed to be used as counters, in performing practical questions." Every fundamental number fact is illustrated in this manner. A little later the primary texts came to conform to a rather fixed type which embodied many of Colburn's ideas. The problems were very simple and about things from the pupil's life. They were to be solved by means of objects and in the mind. There were no rules or definitions. Usually the texts were illustrated by means of cuts. Ray's Arithmetic, Part First, was advertised in 1843 as containing "very simple lessons for little learners, illustrated with amusing pictures, as cats, dogs, rabbits, boys, girls, etc." In another place reference is made to it being "illustrated with about 1,000 pleasing pictorial counters." The content of these primary texts sometimes included some of the more common and simple tables of denominate numbers. During the latter part of this period their content was increased, and they were made more formal. Illustration by cuts disappeared. In Ray's New Primary Arithmetic, 1877, there are only four pictures to illustrate the problems of the text, and all the tables of denominate numbers are given except those obsolete. Piece-meal treatment of the fundamental number facts was the characteristic feature of the general organization. For instance, in multiplication an entire "lesson" was devoted to the table of two's, another to the three's, etc. Mental arithmetic.-Colburn's First Lessons was the pioneer in this field. The mental, or intellectual, arithmetics by other authors were patterned closely after this prototype. The oral arithmetic of Part Second of Emerson's North American Arithmetics is commensurate with the First Lessons and we find much similarity. The main differences are: Hindu numerals are used from the beginning, the traditional order of topics is followed, and some use is made of pictured objects for illustration, especially in the presentation of fractions. The book is inductive in form as well as in spirit, being very similar to Colburn's in this respect. As in the case of the First Lessons, a number relation is given first in a practical problem and is followed by the same combination in abstracted form. For example: 1. A lady divided 15 peaches among some little girls, giving 3 to each girl. How many girls were there? Solution. As many times as 3 peaches are contained in 15 peaches, so many girls were there. 2. If you had 16 cents to lay out in pencils, and the price of the pencils was 4 cents apiece, how many could you buy for all the money? 3. How many times is 4 contained in 16? 4. If 4 horses are required to draw one wagon, how many wagons might be drawn by 20 horses? 5. How many times 4 in 20? How many are 5 times 4? What became Ray's Arithmetic, Part Second, was first published in 1834 under the title, The Little Arithmetic; Elementary Lessons in Intellectual Arithmetic on the Analytic and Inductive Method of Instruction. In the preface, dated March 1, 1834, he acknowledges his indebtedness to Pestalozzian influences by saying: So far as the plan of the work is concerned, we make few pretensions to originality; we tread in the footsteps of Pestalozzi, and shall rejoice if this work should be the means of making more extensively known the principles of the analytic and inductive method of instruction. The book begins with numeration, and the numbers 1 to 10 are represented pictorially by means of apples. The Hindu numerals are given, along with their names. The numbers up to 100 are given before addition, but it is suggested that the numbers from 51 to 100 "may be omitted until the pupil has made some progress in addition." A table of 100 stars arranged in the form of a square is used in teaching the pupils to count. They "may also be used as counters, though the fingers are generally to be preferred." Addition is begun with such examples as: James had one apple and his brother gave him one more. James had two apples and his brother gave him one more. How many had he? How many had he? There are 25 more questions of this type, and the suggestion is made that the teacher make up many more. The addition tables are then given and are followed by 5 pages of abstract drill and 14 practical problems. The section is closed with a statement of the definition of addition in question and answer form. Subtraction, multiplication, and division are presented in the same general way. Fractions are introduced with the suggestion that "for illustration, the teacher should be provided with a number of apples." Halves and fourths are pictured as parts of apples, and the first problems are concerning apples. In the following lessons the teacher is advised to use other illustrative materials. The first lesson on fractions is made up of questions such as, "If you divide an apple into four equal parts, what is one part called? What are two parts called? How many fourths in one apple? In two apples? In three apples?" "How many fourths in one apple and one-fourth of an apple?" The next lesson takes up in order the fractions from halves to tenths in this manner. If an apple be worth 3 cents, what is one-third of it worth? What is 2-thirds of it worth? What is one-third of 3? What is 2-thirds of 3? If an orange is worth 3 cents, what part of the orange will 1 cent buy? What part will 2 cents buy? 1 is what part of 3? 2 is what part of 3? of 3. Ans. 1 is the 1-third of 3. Ans. 2 is the 2-thirds of 3; that is, 2 is 2 times the one-third If a yard of cloth cost 3 dollars, how much can you buy for 4 dollars? How much for 5 dollars? 4 are how many times 3? 5 are how many times 3? 6 are how many times 3? 8 are how many times 3? 10 are how many times 3? Ans. Once 3 and the third of 3. Following this there are problems of division like "57 are how many times 5? 6 ? 7 ? 8? 9 ? 10?" and problems of multiplication such as "8 times 6 and 2-sixths of 6 are how many?" These two questions are then combined in one exercise and in later lessons there are examples which call for operations of the following types: "7 is one |