The growth of arithmetic as a school subject.—In 1789 the teaching of reading, writing, and arithmetic was made obligatory in both Massachusetts and New Hampshire. It is not unreasonable to suppose that these laws simply represent the legalizing of a practice which was already prevalent. Whether this is the case or not, the enactment of these laws shows that arithmetic was then considered necessary to an elementary education and was given a place coordinate with reading and writing. The following records of attendance in the Boston schools indicate the increasing popularity of the writing school, the special school for giving instruction in arithmetic and writing:

In 1745 Yale required arithmetic for entrance. In 1760 Princeton required the candidates "to understand the principal rules of vulgar arithmetic." In 1807 Harvard required

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Candidates for admission into Harvard College shall be examined by the President, Professors and Tutors. No one shall be admitted, unless he be thoroughly acquainted with the Grammar of the Greek and Latin languages, in the various parts thereof, including Prosody, can properly construe and parse Greek and Latin authors, * be well instructed in the following rules of arithmetic, namely, Notation, simple and compound Addition, Subtraction, Multiplication, and Division, together with Reduction and the single Rule of Three, a Compendium of Geography, *

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* have well studied can translate English into Latin correctly,

* * * and have a good moral character, certified in writing by the Preceptor of the Candidate, or some other suitable person.2

By 1814, the reference to arithmetic was changed to "and be well instructed in Arithmetic through the Single Rule of Three," and in and after the year 1816, "the whole of Arithmetic."

This recognition of arithmetic in the college entrance requirements necessitated the teaching of arithmetic in the grammar schools.

The establishment of a new type of school, the academy, which included arithmetic in its curriculum from the first, and the subsequent rapid rise of the academy evidences the growing appreciation of arithmetic and other forms of elementary mathematics. In the first academy, established at Philadelphia as the result of the labors of Benjamin Franklin, there were three departments or schools, the Latin, the English, and the mathematical.

The production of arithmetic texts by American authors and the numerous editions of texts by English authors which were published in this country in the latter part of this period also indicate the

1 D. C. Colesworthy: John Tileston's School, p. 15.

2 E. E. Brown: The Making of Our Middle Schools, p. 249.

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increasing interest in the subject. American arithmetics may be said to date from 1788, the year in which Nicolas Pike published A New and Complete System of Arithmetic composed for the use of the citizens of the United States. The publishing of Pike's book seems to have been the signal for the appearance of texts by American authors. By 1800, at least 20 arithmetics by American authors had been published, besides several of not purely arithmetical nature, such as, Instructor, 1794; The Traders Best Companion, 1795; and an American adaptation of John Gough's Treatise of Arithmetic, 1788.

1

In the 21 years which elapsed between 1800 and the close of this period, arithmetics by American authors appeared with increasing frequency. The Scholar's Arithmetic, by Daniel Adams (first published in 1801) had passed through nine editions by 1815. Daboll's Schoolmaster's Assistant (first published in 1799) was even more popular. Other American texts had an extended circulation. Numerous editions of Dilworth's Schoolmaster's Assistant (first published in England in 1743) were reprinted in this country. A revision of this popular text, by Daniel Hawley, was published in 1803. In his American Journal of Education, Henry Barnard gives reminiscences by a number of persons who attended school in the last quarter of the eighteenth century. One writing from rural Connecticut says that "arithmetic was hardly taught in day school." but adds that it was taught in evening schools. Only two say that arithmetic was not taught, but they were prepared for college in academies about 1780 and presumably never attended an elementary school. Ten who attended school in rural districts, including the States of Massachusetts, Connecticut, Pennsylvania, New Jersey, and North Carolina, say that arithmetic was taught. Most of them mention it coordinately with reading and writing. Three make no mention of arithmetic, and four studied arithmetic in cities. The appearance of arithmetic in the college entrance requirements, the activity of American euthors in writing texts, and the direct tes

1 This number includes arithmetics by the following authors: Isaac Greenwood (1729), Benjamin Dearborn (1782), Alexander McDonald (1785), Nicolas Pike (1788), Thomas Sarjeant (1788), Consider and John Sterry (1790), John Vinall (1792), Benjamin Workman (1793), Joseph Chaplin (1795), Daniel Fenning (1795), Erastus Root (1796), James Noyes (1797), Chauncey. Lee (1797), William Milns (1797) David Kendall (1797), Peter Tharp (1798), Zachariah Jess (1798), Ezekiel Little (1799), Nathan Daboll (1799), David Cook (1800). In his American Bibliography, Evans accredits a text to Jonathan Burnham in 1748. It has not been possible to verify this. 2 The names, the States in which they attended school, and the years attended are given in the Analytical Index to Barnard's American Journal of Education as follows (the figures following the dates refer to the volume and page on which the reminiscence is given): Allen, Mrs. L. L., Massachusetts, 1795-1808, 30:581; Buckingham, J. T., Connecticut, 1783, 13:129; Bushnell, Rev. H., Connecticut, 1800, 13:142; Caldwell, C., North Carolina, 1790, 16:109; Channing, Rev. W. E., Rhode Island, 1780, 17:189; Darlington, W., Pennsylvania, 1795, 13:741; Davis, John, Virginia, 1800, 13:748; Day, Rev. J., Connecticut, 1780, 16:126; Everett, E., Massachusetts, 1800, 13:747; Goodrich, S. G., Connecticut, 1800, 13:134; Hall, W., Massachusetts, 1785, 16:127; Hedges, N., New Jersey, 1800, 16:738; Humphrey, Rev. H., Connecticut, 1790, 13:125; Nott, Rev. E., Connecticut, 1780, 13:132; Oliver, H. K., Massachusetts, 1805, 26:209; Quincy, J., Massachusetts, 1778, 13:740; Seton, S. W., New York, 1795, 17:555; Town, S., Massachusetts, 1785, 13:737; Webster, D., New Hampshire, 1790, 27:282; Webster, M., Connecticut, 1770, 26:197, 13:123.

timony of these persons show that, by 1800, arithmetic was generally taught in the schools, even in the country districts.

The increasing recognition of arithmetic as an essential school subject is but one element of a larger change which culminated in the nineteenth century in the complete secularization of public schools in this country. The control of education passed from the church to the state, and instead of education primarily for teaching the catechism and church doctrines the purpose of education came to be a preparation of children for the secular activities of life. In the period from the close of the Revolution to 1821 arithmetic grew rapidly in importance as a school subject, and in later chapters it will be shown that it was given a place of prime importance in the secularized concept of education.

The aim of instruction in arithmetic.-The aim of arithmetical instruction in this period was not well defined. In a general way the practical needs of trade and commerce were to be satisfied, and this was the principal aim. The authors of the texts used clearly thought of arithmetic primarily as a commercial subject. James Hodder says in the preface to his arithmetic, or, That Necessary Art Made Easy (first published 1661 and widely used in the colonies): "And now for the better compleating of youth, as to clerkship and trades, I am induc'd to publish this small treatise of Arithmetic." The title of Greenwood's book, Arithmetick Vulgar and Decimal: with the Application thereof, to a variety of Cases in Trade, and Commerce, indicates a similar recognition of the practical aim. Daboll says in the preface to Daboll's Schoolmaster's Assistant (first published 1799): "The design of this work is to furnish the schools of the United States with a methodical and comprehensive system of Practical Arithmetic." A ciphering book prepared in Boston, in 1809, has the following title: Practical Arithmetic composing all the Rules necessary for transacting Business.

The immediate end sought, which also represents the standard of instruction, was a knowledge of the rules and their application. We shall show in another place that the pupil was expected to learn the rule and then to apply it to a very few examples or problems. No opportunity was given for drill upon the application of the rule, even in the case of the fundamental operations. Skill and facility were not expected nor attempted.

Dilworth's Schoolmaster's Assistant contains only 9 examples for drill on addition, a like number on subtraction, and a somewhat greater number on multiplication and division. Pike's arithmetic, which is an elaborate text of 512 pages,1 contains only 9 examples for drill on addition and 9 in subtraction. Subtraction is disposed of

1 Only 408 pages are devoted to arithmetic. See Appendix for table of contents.

within a single page. Adams's Scholar's Arithmetic contains 10 examples for drill on addition and 9 on subtraction.

Reminiscences and records of the schools of this period indicate that the pupil actually solved even a less number of drill examples than were given in the texts. The compiler of this report has in his possession a copy of Adams's Scholar's Arithmetic in which blank places are left for the solution of the problems. Only 5 of the 10 problems in addition are solved and only 2 of the 9 in subtraction. The examination of other texts and of ciphering books written in this period reveals about the same amount of drill work.

William B. Fowle relates the following which is probably typical:

No boy had a printed arithmetic, but every other day a sum or two was set in each manuscript, to be ciphered on the slate, shown up, and if right, copied into the manuscript. Two sums were all that were allowed in subtraction, and this number was probably as many as the good man could set for each boy. This ciphering occupied two hours, or rather consumed two, and the other hour was employed in writing one page in a copy book. Once, when I had done my two sums in subtraction, and set them in my book, and been idle an hour, I ventured to go to the master's desk and ask him to be so good as to set me another sum. His amazement at my audacity was equal to that of the almshouse steward when the half-starved Oliver Twist "asked for more." He looked at me, twitched my manuscript toward him, and said, gutturally: "Eh, you gnarly wretch, you are never satisfied." I had never made such a request before, nor did I ever make another afterwards.1

Furthermore, there was very little attempt made to develop ability to apply the rules except to problems explicitly falling under given rules. If a problem appeared which could not be readily classified as coming under some known rule, both pupil and teacher were usually at a loss to know how to proceed. Occasionally there was a pupil who developed some real ability to reason out problems and to control unfamiliar arithmetical situations. However, this was the exception and happened not in response to a conscious attempt on the part of the teachers, but rather in spite of the system.

1 The Teacher's Institute, or Familiar Hints to Young Teachers, p. 61.

Chapter II.

THE SUBJECT MATTER OF ARITHMETIC BEFORE 1821.

With few exceptions the texts in use in the United States before 1800 were of English authorship. Copies of these texts were imported, and editions of the popular ones were printed in this country. The "first purely arithmetical work published in the United States" was an edition of Hodder's arithmetic, printed in Boston in 1719 by J. Franklin.' Editions of the texts by Cocker, Wingate, Bonnycastle, Gough, and Dilworth were printed in this country. In settlements other than English, notably New York and Pennsylvania, arithmetics written by their countrymen were used.

The Schoolmaster's Assistant, by Thomas Dilworth, originally published in 1743, was used very extensively in this country, almost exclusively prior to 1800. Numerous editions were printed in this country, and after the adoption of a Federal money it was revised to meet the commercial needs. A revised edition was published by Daniel Hawley in 1802 with the title of Federal Calculator. This revision had passed through five editions by 1817. Revised editions of this revision, by William Stoddard, were published in 1817 and in 1832.

On page 14 there is printed a list of the American authors of arithmetics published by 1800. Few of these texts were used extensively. The first arithmetic by an American author, Arithmetick, Vulgar and Decimal: with the applications thereof, to a Variety of Cases in Trade and Commerce, by Isaac Greenwood, 1729, found no place in the schools and was soon forgotten. In fact all of the texts prior to the one by Nicolas Pike in 1788 were so little known that his text was considered by some to be the first by an American author. Pike seems to have held this opinion himself, Although not the first text, this book, which was entitled A New and Complete System of Arithmetic, marked the beginning of arithmetic adapted to the needs of the United States. It comprised 512 pages, of which the first 408 are devoted to arithmetic and closely related topics and problems. There follow 4 pages of "plain" geometry, 11 pages of "plain" trigonometry, 45 pages of mensuration of superficies and solids, 33 pages of "an introduction to algebra, designed for the use of academies," and 10 pages of an introduction to conic sections."

1 Evans's American Bibliography, Vol. I, p. 272.

The complete table of contents is given in the Appendix, p. 152.