THE TEACHING AND HISTORY OF MATHEMATICS IN THE UNITED STATES. I. COLONIAL TIMES. ELEMENTARY SCHOOLS. On the study of mathematics in elementary schools of the American colonies but little can be said. In early colonial days schools did not exist except in towns and in the more densely settled districts; and even where schools were kept, the study of mathematics was often not pursued at all, or consisted simply in learning to count and to perform the fundamental operations with integral numbers. Thus, in Hampstead, N. H., in 1750, it was voted "to hire a school-master for six months in ye summer season to teach ye children to read and write." Arithmetic had not yet been introduced there. As late as the beginning of this century there were schools in country districts in which arithmetic was not taught at all. Bronson Alcott, the prominent educator, born in Massachusetts in 1799, in describing the schools of his boyhood, says: "Until within a few years no studies have been permitted in the day school but spelling, reading, and writing. Arithmetic was taught by a few instructors one or two evenings in a week. But in spite of the most determined opposition arithmetic is now permitted in the day school." This was in Massachusetts at the beginning of this century. In secondary schools, "ciphering" was taught during colonial times, which consisted generally in drilling students in the manipulation of integral numbers. He was an exceptional teacher who possessed a fair knowledge of "fractions" and the "rule of three," and if some pupil of rare genius managed to master fractions, or even pass beyond the "rule of three," then he was judged a finished mathematician. The best teachers of those days were college students or college graduates who engaged in teaching as a stepping-stone to something better. An example of this class of teachers was John Adams, afterwards President of the United States. Immediately after graduating at Harvard and before entering upon the study of law, he presided, for a few years, over the grammar school at Worcester. From a letter written by him at Worcester, September 2, 1755, we clip the following description of the teacher's daily work: As a haughty monarch ascends his throne, the pedagogue mounts his awful great chair, and dispenses right justice through his whole empire. His obsequious subjects execute the imperial mandates with cheerfulness, and think it their high happiness to be employed in the service of the emperor. Sometimes paper, sometimes his penknife, now birch, now arithmetic, now a ferule, then ABC, then scolding, then flattering, then thwacking, calls for the pedagogue's attention. School appliances in those days were wholly wanting (excepting the ferule, and birch rods). Slates were entirely unknown for school use until some years after the Revolution; blackboards were introduced much later. Paper was costly in colonial days, and we are told that birch bark was sometimes used in schools in teaching children to write and figure. Thirty-six years ago a writer in one of our magazines* wrote as follows: "There are probably men now living who learned to write on birch and beech bark, with ink made out of maple bark and copperas." But more generally "ciphering" was done on paper. Dr. L. P. Brockett says that on account of its dearness and scarcity, "the backs of old letters, the blank leaves of ledgers and day-books, and even the primer books were eagerly made use of by the young arithmeticians." Since few or none of the pupils had text-books it became necessary for the teacher to dictate the "sums." As in the colleges of that time, so in elementary schools, manuscript books were used whenever printed ones were not accessible. To advanced boys the teacher would give exercises from his manuscript or "ciphering-book," in which the prob. lems and their solutions had been previously recorded. "With a book of his own the pupil solved the problems contained in it in their proper order, working hard or taking it easy as pleased him, showed the solutions to the master, and if found correct generally copied them in a blankbook provided for the purpose. * Some of these old manuscript ciphering-books, the best, one may suppose, having come down through several generations, are still preserved among old family records, bearing testimony to the fair writing and the careful copying, if not to the arithmetical knowledge, of those who prepared them. When a pupil was unable to solve a problem he had recourse to the master, who solved it for him. It sometimes happened that a dozen or twenty pupils stood at one time in a crowd around the master's desk waiting with *** problems to be solved. There were no classes in arithmetic, no explana tions of processes either by master or pupil, no demonstrations of principles either asked for or given. The problems were solved, the answers obtained, the solutions copied, and the work was considered complete. That some persons did obtain a good knowledge of arithmetic under such teaching must be admitted, but this result was clearly due rather to native talent or hard personal labor than to wise direction." Those *North Carolina University Magazine, Raleigh, 1853, Vol. II, p. 452. teachers who were the fortunate possessors of a printed arithmetic used it as a guide in place of the old "ciphering-book." In the early schools, arithmetic was hardly ever taught to girls. Rev. William Woodbridge says that in Connecticut, just before the Revolution, he has "known boys that could do something in the first four rules of arithmetic. Girls were never taught it."* In the two "charity schools" in Philadelphia, which before the Revolution were the most celebrated schools in Pennsylvania, boys were taught reading, writing, arithmetic; girls, reading, writing, sewing. Thus, sewing was made. to take the place of arithmetic. Warren Burton, in his book entitled, "The District School as it was, by one who went to it," says that, among girls, arithmetic was neglected. The female portion "generally expected to obtain husbands to perform whatever arithmetical operations they might need beyond the counting of fingers." Occasionally women. were employed in summer schools' as teachers, but they did not teach arithmetic. A school-mistress "would as soon have expected to teach the Arabic language as the numerical science." The early school-books in New England and in all other English settlements were much the same as those of Old England. John Locke, in his Thoughts concerning Education (1690), says that the method of teaching children to read in England has been to adhere to "the ordinary road of horn-book, primer, psalter, testament, and bible." This same road was followed in New England. We are told that books of this kind were sold to the people by John Pynchon, of Springfield, from 1656 to 1672 and after. Regular arithmetics were a great rarity in this country in the seventeenth century. The horn-book has been raised by some to the dignified name of a "primer" for teaching reading and imparting religious instruction. If this be permissible, then why should we not also speak of it as an arithmetical primer? For, what was the horn-book? It consisted of one sheet of paper about the size of an ordinary primer, containing a cross (called "criss-cross"), the alphabet in large and small letters, followed by a small regiment of monosyllables; then came a form of exorcism and the Lord's Prayer, and, finally, the Roman numerals. The leaf was mounted on wood, and protected with transparent horn, "To save from fingers wet the letters fair." It is on the strength of the Roman numerals that we venture to propose the horn-book as a candidate for the honor of being the first mathematical primer used in this country. Horn-books were quite common in England and in the English colonies in America down to the time of George II. They disappeared entirely in this country before the Revolution. In early days the common remark expressive of ignorance was "he does not know his horn-book." This is equivalent to the more modern saying, "he does not know his letters." * Reminiscenses of Female Education, in Barnard's Journal of Education, 1864, p. 137. + Barnard's Journal of Education, Vol. XXVII. George Fox, the founder of the Society of Friends, published in 1674, in England, a primer or spelling book, which was republished at Philadelphia in 1701, at Boston in 1743, and at Newport, R. I., in 1769.* Wickersham describes this little book as containing the alphabet, lessons in spelling and reading, explanations of scripture names, Roman nume als, lessons in the fundamental rules of arithmetic and weights and measures, a perpetual almanac, and catechism with the doctrine of the Friends. It may be imagined that a mere primer, covering such a wide range of subjects, could contain only a very few of the simplest rudiments of a subject like arithmetic. Fox's book was used little outside of the Society of Friends. Wickersham (p. 201) speaks of another book which is of interest as illustrating the book-making of those old times. It is entitled, "The American Instructor, or Young Man's Best Companion, containing Spelling, Reading, Writing, Arithmetic, in an Easier Way than any yet Pub lished, and how to Qualify any Person for Business without the Help of a Master." It was written by George Fisher, and printed in Philadelphia, in 1748, by Franklin and Hall. This work never attained any popularity. Dr. Brockett says that in New Jersey and, perhaps, also in Virginia, a book resembling the "New England Primer," but as intensely Royalist and High Church in religion as the New England Primer was Puritan and Independent, was in use in schools. It was called "A Guide for the Child and Youth, in two parts; the First for Children, the second for Youth: Teaching to write, cast accounts and read more perfectly; with several other varieties, both pleasant and profitable. By T. H., M. A., Teacher of a Private School, London, 1762." It does not appear that this book was reprinted here. Wickersham gives another book of similar stamp but of much later date. "Ludwig Höcker's Rechenbüchlein was published at Ephrata [Pennsylvania] in 1786. The Ephrata publication is an exceedingly curious compound of religious exercises and exercises in arithmetic. The creed, the Lord's Prayer, hymns, and texts of scripture, are strangely intermixed with problems and calculations in the simpler parts of arith-metic." One of the earliest purely arithmetical books used in this country was the arithmetic of James Hodder. It may possibly have fallen into the hands of as early a teacher as Ezekiel Cheever, "the father of Connecticut school-masters, the pioneer and patriarch of elementary classi cal culture in New England." In a history of schools at Salem, Mass., we are told that "among our earliest arithmetics was James Hodder's." History of Education in Pennsylvania, by James Pyle Wickersham, p. 194. After having been a faithful school-master for seventy years, he died in 1708, at the age of ninety-four, having "held his abilities in an unusual degree to the very last." |