American tutor's assistant or a compendious system of practical arithmetic. 3d ed. 1797.

"Arithmetic is the art of computing by numbers."

Cocker, Edward. Cocker's vulgar arithmetic. 1677.

An American edition of this English text was published in Philadelphia in 1779. It has been said that this text "may be considered the father of modern arithmetic, as it furnished the plan all of them have copied."

Daboll, Nathan. Daboll's schoolmaster's assistant. 1799.

This became a very popular text.

Dilworth, Thomas. The schoolmaster's assistant: Being a compendium of arithmetic, both practical and theoretical. 1743.

Numerous editions of this English text were printed in this country. A revision by William Hawley was published in 1802 which passed through five editions by 1817. Robert Patterson edited an edition in 1805 and William Stoddard another in 1817.

Federal ready reckoner; or trader's valuable guide in purchasing and selling all kinds of articles by wholesale and retail. Printed by Leonard Worcester, 1795. A book of tables for computating the cost of articles and interest.

Fisher, George. The instructor; or, American young man's best companion. 30th ed. 1785.

See page 40 for complete title which indicates the nature of the book.

Greenwood, Isaac. Arithmetic vulgar and decimal: with application thereof to a variety of cases in trade and commerce.

1729.

This is the first arithmetic by an American author. There are copies in the Harvard College Library, the Boston Public Library, and the Library of Congress.

Hodder, James. Hodder's arithmetic: or that necessary art made most easy. 1661. The 25th edition of this English text was printed in Boston in 1719. This was the "first purely arithmetical work published in the United States."

Kendal, David. The young lady's arithmetic.

1797.

"Arithmetic is the art of computing by figures." Directs the student to "learn well by heart" rules and definitions. It is simply a condensed form of the arithmetics of this period.

Kimber, Emmor. Arithmetic made easy to children: Being a collection of useful and familiar examples, methodically arranged and under their respective heads. 2d ed.

1805.

A traditional text.

Leavitt, Dudley. Elements of arithmetic made easy by an original introduction to that science. 1813.

Lee, Chauncey. The American accomptant.

1797.

This is the first arithmetic in which a dollar mark is used and it is also interesting because of an attempt by the author to decimalize all weights and measures.

M'Donald, Alexander. The youth's assistant; being a plain easy, and comprehensive guide to practical arithmetic. 1785, 1789.

The practical reasons for teaching arithmetic are emphasized.

Pike, Nicolas. A new and complete system of arithmetic, composed for the use of the citizens of the United States. 1788.

This is commonly supposed to be the second arithmetic by an American author but probably was the fifth. It is the first arithmetic in which the Federal money is given.

Pike, Stephen. The teacher's assistant. 1811.

It was revised in 1845 and 1852.

Root, Erastus. Introduction to arithmetic, for the use of common schools. 1795. Sarjeant, Thomas. Elementary principles of arithmetic; with their application to the trade and commerce of the United States. 1788.

Temple, Samuel. An arithmetical primer for young masters and misses; containing simply, the first principles of that most useful art. 1809. 48 pp.

It is intended to be followed by a more advanced book. Blank spaces are left for the solution of examples.

Vinall, John. Preceptor's assistant. 1792.

Vyse, Charles. A key, or the arithmetician's repository. 9th ed. 1806.

A key to the tutor's guide.

Walkingame, Francis. The tutor's assistant; being a compendium of arithmetic and a complete question book.

A text by an English author reprinted in this country.

Walsh, Michael. A new system of mercantile arithmetic; adapted to the commerce of the United States, in its domestic and foreign relations; with forms of accounts, and other writings usually occurring in trade. 1801.

Watt, Alexander. A new plain and systematic compendium of arithmetic adapted to the commerce of the United States. 1806, 1814.

Welch, Oliver. American arithmetic. 1814.

White, John. A practical system of mental arithmetic, or a new method of making calculations by the action of the mind without pen, ink, pencil, or paper. 1818.

Rules and facts were to be memorized. Many short-cuts are given but there are no analyses and the book is not a "mental" arithmetic in the sense the term is generally used. Wingate, Edmond. Artificial arithmetic. 1629.

The 15th edition of this English text was published in 1726. Littlefield states: "A copy of the first edition is now in existence which was used in the Winslow family of Massachusetts for over one hundred years."

Workman, Benjamin. A treatise of arithmetic in theory and practice; containing everything important in the study of abstract and applicate numbers. 1788.

This is an edition of an English text by John Gough. It was revised by R. Patterson in 1796. The youth's instructor in the English tongue, 1760.

OTHER SOURCES.

Barnard, Henry. American journal of education.

For articles bearing upon this period see Analytical Index to Barnard's American Journal of Education under "Reminiscences of schools and teachers."

Burton, Warren. The district school as it was.

A very interesting description of schools in the period from 1810 to 1830.

Cajori, F. The teaching and history of mathematics in the United States. Washington, Government Printing Office, 1890. (U. S. Bureau of Education. Circular of information, No. 3, 1890.)

A general account devoted mostly to mathematics beyond arithmetic.

Clews, Elsie W. Educational legislation and administration of Colonial govern

ments.

Colesworthy, D. C. John Tileston's school.

Cornell, William Mason. The history of Pennsylvania.

Cyphering books.

Only a few of these manuscripts are available in libraries. Two were found in the library of the American Antiquarian Society and two in the library of the Worcester Society of Antiquity. In addition, a manuscript by Miss Catherine G. Willard, now in possession of Prof. W. C. Gore, of the University of Chicago, was examined.

Evans, Charles. Evans' American bibliography.

A complete bibliography of all books and pamphlets published in America beginning with the first book printed in America in 1639.

Jackson, L. L. The educational significance of sixteenth century arithmetic. 1906. Johnson, Clifton. Old-time schools and school-books.

A very interesting account.

Kilpatrick, William H. The Dutch schools of New Netherland and Colonial New York. Washington, Government Printing Office, 1912. (U. S. Bureau of Education. Bulletin, No. 12, 1912.)

A carefully prepared account of an intensive study.

Littlefield, G. E. Early New England schools, club of old volumes. Boston, 1904. Meriwether, Colyer. Our Colonial curriculum, 1607–1776.

Murry, David. History of education in New Jersey. Washington, Government Printing office, 1899. (U. S. Bureau of Education. Circular of Information, No. 1, 1899.)

Powell, Lyman C. The history of education in Delaware. Washington, Government Printing Office, 1893. (U.S. Bureau of Education. Circular of Information, No. 3, 1893.)

Steiner, B. C. History of education in Maryland. Washington, Government Printing
Office, 1894. (U. S. Bureau of Education. Circular of Information, No. 2, 1894.)
Tolman, William H. History of higher education in Rhode Island. Washington,
Government Printing Office, 1894. (U. S. Bureau of Education. Circular of
Information, No. 1, 1894.)

Watson, F. The beginnings of the teaching of modern subjects in England.
The English grammar schools to 1660, their curriculum and practice.

This and the above book by the same author give a good account of contemporary practice in England.

Wickersham, J. P. History of education in Pennsylvania.

Worcester Society of Antiquity. Collections, vol. 9, Proceedings, 1888-1890.

THE BEGINNING OF THE PESTALOZZIAN MOVEMENT IN AMERICA AS APPLIED TO ARITHMETIC.

Barnard's American Journal of Education, vol. 2, p. 294.

This appears to be the most complete biographical account of Colburn available. Biber, E. Henry Pestalozzi and his plan of education.

Colburn, Warren. First lessons in arithmetic on the plan of Pestalozzi; with some improvements. 1821.

An edition of 1826 has the title, "Colburn's first lessons. Intellectual arithmetic upon the induc. tive method of instruction." This title has been retained. A copy of the first edition is in the library of the American Antiquarian Society, Worcester.

Arithmetic; being a sequel to first lessons in arithmetic.

1822.

The teaching of arithmetic. An address delivered before the American Institute of Instruction in Boston, August, 1830.

It was published in the proceedings of that society and was reprinted in the Elementary School Teacher, June, 1912.

Krüsi, Herman. Pestalozzi: His life, work, and influence.

One section of the book is devoted to the "Principles and method of Pestalozzi." A chapter on "Special application of Pestalozzi's method" gives Pestalozzi's ideas on number.

Monroe, Will S. History of the Pestalozzian movement in the United States.

This account deals only with general features. No mention is made of Warren Colburn and very little is said concerning the influence of Pestalozzian principles upon school subjects and the method of teaching.

Pestalozzi, J. H. Anschauungslehre der Zahlenverhältnisse, Part I.

This contains a list of exercises upon Pestalozzi's unit's table. Parts II and III contain those on the fraction tables. Herman Krüsi assisted in preparing the exercises.

Leonard and Gertrude. Trans. by Eva Channing. Boston, D. C. Heath & Co.

A narrative account of Pestalozzi's theory of education before 1781.

How Gertrude teaches her children. Trans. by Lucy E. Holland and Frances

C. Turner. Syracuse, N. Y., C. W. Bardeen.

An excellent account of Pestalozzi's educational theory.

Ünger, Fredrich. Die Methodik der Praktischen Arithmetik.

A reliable account of the development of arithmetic as a school subject in Germany.

FROM 1821 TO 1892.

GENERAL SOURCES.

American Journal of Education, vol. 1, 1826.
Connecticut school document, Nos. 7 and 16.

These contain reports of surveys of Connecticut schools.

Davies, Charles. The logic and utility of mathematics. 1850.

"A full analysis of the science of mathematics."

DeGraff. The schoolroom guide. 1877.

Fowle, William B. The teacher's institute; or familiar hints to young teachers. 1866.

A book on the teaching of the common branches.

Greenwood, J. M. Principles of education practically applied. 1887.

Key to Ray's practical arithmetic. 1845.

The teaching of arithmetic is discussed briefly.

Page, David P. Theory and practice of teaching. 1847.

Stoddard, John F. Methods of teaching arithmetic and key to Stoddard's American mental arithmetic.

ARITHMETIC TEXTS.

Some of the more important series of arithmetics have been described in Chapter VIII. The authors of these series are included in this list and a page reference is given to Chapter VIII. No attempt has been made to give a complete list of the arithmetic texts published during the period. Those interested in such a list are referred to the bibliography by J. M. Greenwood and Artemas Martin. Adams, Daniel. Adams's new arithmetic. 1827. See p. 103.

Adams, Frederick A. Common and high school arithmetic, 1846.

Belfield, H. H. The revised model elementary arithmetic. 1887.

"Oral exercises will be found on the left-hand page and written on the right, with a few exceptions."

Brooks, Edward. See p. 102.

Chase, Pliney E., and Mann, Horace. See p. 103.

Cobb, Lyman. Arithmetic. 1832.

Colburn, Dana P. The child's book of arithmetic, 1859; Intellectual arithmetic, 1859; Common school arithmetic, 1858; Arithmetic and its applications, 1855. Crozet, Claudius. An arithmetic for colleges and schools. 1848.

Davies, Charles. See p. 95.

Dean, Philotus. Primary arithmetic, 1860; Intellectual arithmetic, 1861; Elementary arithmetic, 1868; Intermediate arithmetic, 1865.

Eaton, James Stewart. See p. 99.

Emerson, Fredrick. See p. 94.

Ernst, Henry. Arithmetic. 1857.

Felter, S. A. Primary arithmetic, 1863; New primary, 1880; First lessons, 1865, 1880; Intermediate arithmetic, 1862, 1866; New intermediate, 1875; New practical, 1872; Complete arithmetic, 1877; Advanced arithmetic, 1877.

Fowle, William B. The child's arithmetic, or the elements of calculation, in the spirit of Pestalozzi's method. 1826.

For the use of children between the years of three and six.

French, John H. First lessons in numbers, 1866; Mental arithmetic, 1870; Elementary arithmetic, 1867; Common school arithmetic, 1869.

Goff, M. B. First book in arithmetic, 1876; Arithmetical problems, 1877; Elementary arithmetic, 1888.

Goodrich, S. G. Peter Parley's method of teaching arithmetic to children. 1833. See p. 103.

Greenleaf, Benjamin. See p. 97.

Groesbeck, John. Commercial arithmetic. 1868.

Hagar, Daniel B. Primary lessons in numbers, 1871; Elementary arithmetic, 1871; Dictation problems and reviews in arithmetic, 1874.

Hanna, J. S. Complete ready reckoner. 1871.

Harper and Bros. Two-book series. 1882.

Hill, Thomas. An elementary arithmetic. 1845.

"It is not the design of this treatise to make arithmetic easy nor to give such practical skill as may be useful in business."

Hoose, James H. Arithmetic. 1882.

The author attempted to follow Pestalozzi's plan.

Jameson, Richard S. The basis of arithmetic. 1867.

Kirk, Alfred. Model elementary arithmetic, 1876; Model complete arithmetic, 1875. Leach, Daniel, and Swan, Robert. Elementary intellectual arithmetic. 1853. Leonard, George, Jr. A practical treatise on arithmetic. 1839.

Loomis, Elias. The elements of arithmetic. 1863.

Mecutchen, Samuel. Graded problems in arithmetic and mensuration. 1880.

and Sayre, George M. New American practical arithmetic, 1877.

Milne, W. J. First lessons, 1878; Practical arithmetic, 1878; Elementary arithmetic, 1882.

Olney, Edward. Primary arithmetic, 1874; Elements of arithmetic, 1875; Practical arithmetic, 1879; First lessons in arithmetic, 1881; Teacher's handbook of arithmetical exercises, 1875.

Olney, Jesse. An improved system of arithmetic. 1839.

Orton, Hoy D. Lightning calculator. 1866.

Parke, Uriah. Farmers', merchants', and mechanics' practical arithmetic. 3d ed., 1839; 20th ed., 1847.

Payson, John P. Practical arithmetic. 1887.

Peck, William G. Complete arithmetic. 1874.

Perkins, George Robert, and Quackenbos, George P. Builded on the texts of Perkins. See p. 103.

Raub, Albert N. Elementary arithmetic, 1877; Complete arithmetic, 1877.

Ray, Joseph. See p. 96.

Robinson, James, Jr. The American arithmetic, 1825; Elementary lessons in intellectual arithmetic, 1830.

Robinson, H. N., also Fish, D. W., who was associated with Robinson. See p. 101. Rodgers, M. H. A notebook of arithmetical rules and definitions. 1862.

Ruger, William. A new system of arithmetic. 1829.

Sadler, W. H., and Will, W. R. Inductive arithmetic. 1885.

Sanford, Shelton Palmer. The intermediate arithmetic, 1871; The common-school arithmetic, 1872.

Seymour, George E. Elementary arithmetic, 1880; Practical arithmetic, 1880. Singer, Edgar A. Elementary arithmetic, 1876; The model mental arithmetic, 1876. Smiley, Thomas T. The new federal calculator. 1828.

"In appearance is a twin to Daboll's arithmetic." It was still printed in 1899 by J. B. Lippin cott & Co. It seems to have been revised by L. Talbot and printed in 1841 under the title, "The Western practical arithmetic."

Smith, Roswell C. The little federal calculator. 1832. (It starts, "How many little fingers have you on your right hand? How many on both?"); Practical and mental arithmetic, designed principally to accompany Daboll's system of arithmetic, 1826; Practical and mental arithmetic on a new plan, 1827; The productive arithmetic, 1841.

Stewart, Charles. An analytical arithmetic for the use of schools and colleges. 1856, 1863, 1874.

Stoddard, John F. See p. 99.

Talbot, John L. The Western practical arithmetic. 1841.

Thomson, James B. See p. 98.

Ticknor, Almon. Columbian calculator. 1846.

Towne, Paul Allen. Mental arithmetic. 1870.

Townsend, Julius L. Primary arithmetic, 1885; Intermediate arithmetic, 1885;

Grammar-school department, 1885.