Skip to main content

Abstract

This chapter describes the authors’ principal data set (PDS) for the study. This data set, which comprises 212 cyphering books, each of which was prepared between 1701 and 1861, is the largest single collection of cyphering books in the nation. In Chapter 5, questions associated with where and when the cyphering books were prepared, and by whom, are considered in the light of the author’s analyses of their PDS. It is noted that the number of students preparing cyphering books fell sharply between 1840 and 1861, and the question is raised: Why did that happen?

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • A Catechism of Arithmetic, Containing a Concise Explanation of the most Useful Rules; with a Variety of Questions and Explanatory Notes, and Exercises in each Rule (1821) (6th ed.). London, UK: W. B. Whittaker.

    Google Scholar 

  • Adams, O. F. (1903). Some famous American schools. Boston, MA: Dana Estes & Company.

    Google Scholar 

  • Brayley, A. W. (1894). Schools and schoolboys of old Boston. Boston, MA: Louis P. Hager.

    Google Scholar 

  • Broome, E. C. (1903). A historical and critical discussion of college-entrance admissions requirements. New York, NY: Columbia University.

    Google Scholar 

  • Cajori, F. (1890). The teaching and history of mathematics in the United States (Circular of Information No. 3, 1890). Washington, DC: Bureau of Education.

    Google Scholar 

  • Cajori, F. (1907). A history of elementary mathematics with hints on methods of teaching. New York, NY: The Macmillan Company.

    Google Scholar 

  • Carlo, P. W. (2005). Huguenot refugees in colonial New York: Becoming American in the Hudson Valley. Brighton, UK: Sussex Academic Press.

    Google Scholar 

  • Cohen, P. C. (1982). A calculating people: The spread of numeracy in early America. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Cohen, P. C. (2003). Numeracy in 19th-century America. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 43–76). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Coon, C. L. (1915). North Carolina schools and academies 1790–1840: A documentary history. Raleigh, NC: Edwards and Broughton Printing Co.

    Google Scholar 

  • Cubberley, E. P. (1962). Public education in the United States. Boston, MA: Houghton Mifflin Co.

    Google Scholar 

  • Davies, C. (1870). University arithmetic: Embracing the science of numbers, and general rules for their application. New York, NY: A. S. Barnes and Co.

    Google Scholar 

  • DeGarmo, C. (1896). Herbart and the Herbartians. New York, NY: Charles Scribner’s Sons.

    Google Scholar 

  • Donoghue, E. F. (2003a). Algebra and geometry textbooks in 20th-century America. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 329–398). Reston, VA: NCTM.

    Google Scholar 

  • Dyer, E. (1886). The old schools of Providence. Narragansett Historical Register, 5(1), 220–240.

    Google Scholar 

  • Eggleston, E. (1871). The Hoosier schoolmaster. New York, NY: Orange Judd.

    Google Scholar 

  • Ellerton, N. F., & Clements, M. A. (2009a). Summary of cyphering books at the Phillips Library, Salem, Massachusetts. Salem, MA: Phillips Library at the Peabody Essex Museum.

    Google Scholar 

  • Fowle, W. B. (1866). The teacher’s institute, or familiar hints to young teachers. New York, NY: Barnes & Noble.

    Google Scholar 

  • French, J. H. (1869). Common school arithmetic combining the elements of science with the practical applications to business. New York, NY: Harper & Brothers.

    Google Scholar 

  • Fuess, C. M. (1917). A history of Phillips Academy. Boston, MA: Houghton Mifflin Company.

    Google Scholar 

  • Gilman, C. (1852). Recollections of a New England bride and of a Southern matron. New York, NY: G. P. Putnam.

    Google Scholar 

  • Goodrich, S. G. (1957). Recollections of a lifetime, or men and things I have seen: In a series of familiar letters to a friend, historical, biographical, anecdotal and descriptive. New York, NY: Miller, Orton & Co.

    Google Scholar 

  • Halwas, R. (1997). American mathematics textbooks 1760–1850. London, UK: Author.

    Google Scholar 

  • Heeffer, A. (2008). Text production reproduction and appropriation within the abbaco tradition: A case study. SCIAMVS, 9, 101–145.

    Google Scholar 

  • Hornberger, T. (1968). Scientific thought in the American colleges 1638–1800. New York, NY: Octagon Books.

    Google Scholar 

  • Hoskin, K. (1994). Textbooks and the mathematization of American reality: The role of Charles Davies and the US Military Academy at West Point. Paradigm, 13, 11–41.

    Google Scholar 

  • Houser, M. L. (1943). Young Abraham Lincoln mathematician. Peoria, IL: Lester O. Shriver.

    Google Scholar 

  • Howson, G. (1982/2008). A history of mathematics education in England. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Jones, P. S., & Coxford, A. F. (1970). From discovery to an awakened concern for pedagogy, 1492–1821. In P. S. Jones & A. F. Coxford (Eds.), A history of mathematics education in the United States and Canada (pp. 11–23). Washington, DC: National Council of Teachers of mathematics.

    Google Scholar 

  • Karpinski, L. C. (1925). The history of arithmetic. Chicago, IL: Rand McNally & Company.

    Google Scholar 

  • Karpinski, L. C. (1980). Bibliography of mathematical works printed in America through 1850 (2nd ed.). Ann Arbor, MI: University of Michigan Press.

    Google Scholar 

  • Kidwell, A. K., Ackerberg-Hastings, A., & Roberts, D. L. (2008). Tools of American mathematics teaching, 1800–2000. Washington, DC: Smithsonian Institution and Baltimore, MD: The Johns Hopkins University Press.

    Google Scholar 

  • Kiely, E. R. (1947). Surveying instruments: Their history and classroom use (19th yearbook). New York, NY: Teachers College Columbia University/National Council of Teachers of Mathematics.

    Google Scholar 

  • Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics: Seventieth yearbook (pp. 3–18). Reston, VA: National Council of Teachers of mathematics.

    Google Scholar 

  • Laughlin, S. H. (1845). A diary of public events and notices of my life and family and my private transactions including travels, readings, correspondence, business, anecdotes, miscellaneous memoranda of men, literature, etc., from January 1st to August 1845, and sketch of my life from infancy. Library Search Room, Family File, Tennessee State Library and Archives. Nashville, TE.

    Google Scholar 

  • Lazenby, M. E. (1938). Lazenby; being such an account as I have been able to collect of the families in the United States bearing the name. Washington, DC: Author.

    Google Scholar 

  • Littlefield, G. E. (1904). Early schools and school-books of New England. Boston, MA: The Club of Odd Volumes.

    Google Scholar 

  • Meriwether, C. (1907). Our colonial curriculum 1607–1776. Washington, DC: Capital Publishing Co.

    Google Scholar 

  • Michalowicz, K. D., & Howard, A. C. (2003). Pedagogy in text: An analysis of mathematics texts from the 19th century. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 77–109). Reston, VA: NCTM.

    Google Scholar 

  • Middlekauff, R. (1963). Ancients and axioms. New Haven, CT: Yale University Press.

    Google Scholar 

  • Monaghan, E. J. (2007). Learning to read and write in colonial America. Amhurst, MA: University of Massachusetts Press.

    Google Scholar 

  • Monroe, W. (Walter) S. (1912). A chapter in the development of arithmetic teaching in the United States. The Elementary School Teacher, 13(1), 17–24.

    Article  Google Scholar 

  • Monroe, W. (Walter) S. (1917). Development of arithmetic as a school subject. Washington, DC: Government Printing Office.

    Google Scholar 

  • Munsell, W. W. (1882). History of Queen’s County, with illustrations, portraits and sketches of prominent families and individuals. New York, NY: Author.

    Google Scholar 

  • Overn, O. E. A. (1937). Changes in curriculum in elementary algebra since 1900 as reflected in the requirements and examinations of the College Entrance Examination Board. Journal of Experimental Education, 5, 373–468.

    Google Scholar 

  • Page, D. P. (1877). Theory and practice of teaching: The motives and methods of good school-keeping (90th ed.). New York, NY: A. S. Barnes & Company.

    Google Scholar 

  • Parker, S. C. (1912). The history of modern elementary education. Boston, MA: Ginn and Company.

    Google Scholar 

  • Parsons, W. T. (1976). The Pennsylvania Dutch: A persistent minority. Boston, MA: Twayne Publishers.

    Google Scholar 

  • Rickey, F. V., & Shell-Gellasch, A. (2010). Mathematics education at West Point: The first hundred years. Washington, DC: The Mathematical Association of America.

    Google Scholar 

  • Rogers, L. (1999). Conflict and compromise: The evolution of the mathematics curriculum in 19th century England. In P. Radelet-de Grave (Ed.), Histoire et Ă©pistĂ©mologie dans l’education mathematique – De la maternelle a l’universite (pp. 309–319). Louvain-la-Neuve, Belgium: UniversitĂ© d’Ete EuropĂ©enne sur Histoire et Epistemologie dans l’Education MathĂ©matique.

    Google Scholar 

  • Rossi, F. (2009). Michael of Rhode and his manuscript. In. P. O. Long, D. McGee, & A. M. Stahl (Eds.), The book of Michael of Rhodes: A 15th century maritime manuscript (Vol. 3, pp. 99–113). Cambridge, MA: MIT Press.

    Google Scholar 

  • Rudolph, F. (1977). Curriculum: A history of the American undergraduate course of study since 1636. San Francisco, CA: Jossey-Bass Publishers.

    Google Scholar 

  • Schubring, G. (1987). On the methodology of analyzing historical textbooks: Lacroix as textbook author. For the Learning of Mathematics, 7(3), 41–51.

    Google Scholar 

  • Seybolt, R. F. (1935). The private schools of colonial Boston. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Simons, L. G. (1924). Introduction of algebra into American schools in the 18th century. Washington, DC: Department of the Interior Bureau of Education.

    Google Scholar 

  • Simons, L. G. (1936b). Bibliography of early American textbooks on algebra published in the colonies and the United States through 1850, together with a characterization of the first edition of each work. New York, NY: Scripta Mathematics, Yeshiva College.

    Google Scholar 

  • Smith, D. E. (1900). The teaching of elementary mathematics. New York, NY: The Macmillan Company.

    Google Scholar 

  • Tolles, F. B. (1956), Philadelphia’s first scientist. Isis, 45, 20–30.

    Article  Google Scholar 

  • Van Egmond, W. (1980). Practical mathematics in the Italian Renaissance: A catalog of Italian abbacus manuscripts and printed books to 1600. Firenze, Italy: Istituto E Museo di Storia Della Scienza.

    Google Scholar 

  • Webb, S. (2008). Country school copybook. Birmingham, AL: Author.

    Google Scholar 

  • Wells, H. W. (1900). The schools and the teachers of early Peoria. Peoria, IL: Jacquin.

    Google Scholar 

  • Wickersham, J. P. (1886). A history of education in Pennsylvania. Lancaster, PA: Inquirer Publishing Company.

    Google Scholar 

  • Williamson, R. S. (1928). Grammar school arithmetic a century ago. The Mathematical Gazette, 14(194), 128–133.

    Article  Google Scholar 

  • Yeldham, F. A. (1936). The teaching of arithmetic through four hundred years (1535–1935). London, UK: Harrap.

    Google Scholar 

  • Zimmerman, J. (2009). Small wonder: The little red schoolhouse in history and memory. New Haven, CT: Yale University Press.

    Google Scholar 

  • Ackerberg-Hastings, A. (2000). Mathematics is a gentleman’s art: Analysis and synthesis in American college geometry teaching 1790–1840. PhD dissertation, Iowa State University.

    Google Scholar 

  • Ackerberg-Hastings, A. (2009, June). The relationship between mathematics and physical sciences in John Playfair’s Natural Philosophy course. Paper presented at the annual conference of the Canadian Society for History and Philosophy of Mathematics, held at St John’s, Newfoundland.

    Google Scholar 

  • Adams, D. (1801). The scholar’s arithmetic—Or Federal accountant. Leominster, MA: Adams and Wilder.

    Google Scholar 

  • Adams, D. (1827). Adams’s new arithmetic: Arithmetic in which the principles of operating by numbers are analytically explained and synthetically explained, thus combining the advantages to be derived both from the inductive and synthetic mode of instructing. Keene, NH: J. Prentiss.

    Google Scholar 

  • Bellhouse, D. (2010, May). The mathematics curriculum in the British dissenting academies in the 18th century. Paper presented at the meeting of the Canadian Society for the History and Philosophy of Mathematics, held in MontrĂ©al.

    Google Scholar 

  • Bethlehem Digital History Project. (2009). Susan Shimer cyphering book. Retrieved September 27, 2009, from http://bdhp.moravian. edu/ bethlehem/bethlehem.html

  • Bonnycastle, J. (1788). The scholar’s guide to arithmetic; Or a complete exercise-book for the use of schools, with notes containing the reason of every rule, … (5th ed.). London, UK: J. Johnson.

    Google Scholar 

  • Burke, E., & Burke, W. (1758). An account of the European settlements in America (Vol. 2). London, UK: R. and J. Dodsley.

    Google Scholar 

  • Burton, W. (1833). The district school as it was, by one who went to it. Boston, MA: Carter, Hendee and Company.

    Google Scholar 

  • Clason, R. (1968). Number ideas of arithmetic texts of the United States from 1880 to 1966 with related psychological and mathematical developments. PhD dissertation, University of Michigan.

    Google Scholar 

  • Cockburn, J. S., King, H. P. F., & McDonnell, K. G. T. (Eds.). (1969). Private education from the sixteenth century: Developments from the 16th to the early 19th century. A History of the County of Middlesex: Volume 1: Physique, archaeology, domesday, ecclesiastical organization, the Jews, religious houses, education of working classes to 1870, Private Education from Sixteenth Century (pp. 241–255). Retrieved February 10, 2011, from http://www.british-history.ac.uk/report.aspx?compid=22124

  • Cocker, E. (1678/1725). Cocker’s arithmetick: A plain and familiar method … (42nd ed.). London, UK: H. Tracy.

    Google Scholar 

  • Cocker, E. (1684/1720). Decimal arithmetic, wherein is shewed the nature and use of decimal fractions in the usual rules of arithmetic, … (5th ed.). London, UK: J. Darby for M. Wellington.

    Google Scholar 

  • Colburn, W. (1821). An arithmetic on the plan of Pestalozzi, with some improvements. Boston, MA: Cummings and Hilliard.

    Google Scholar 

  • Colburn, W. (1822). Arithmetic upon the inductive method of instruction being a sequel to intellectual arithmetic. Boston, MA: Cummings and Hilliard.

    Google Scholar 

  • Day, J. (1814). An introduction to algebra, being the first part of a course of mathematics, adapted to the method of instruction in the American colleges. New Haven, CT: Howe and DeForest.

    Google Scholar 

  • Dilworth, T. (1797). Dilworth’s arithmetic, being a compendium of arithmetic with both practical and theoretical. New London, CT: Napthali Judah.

    Google Scholar 

  • Doar, A. K. (2006). Cipher books in the Southern Historical Collection. Master of Science thesis, Wilson Library, University of North Carolina at Chapel Hill.

    Google Scholar 

  • Emerson, F. (1835). The North American arithmetic: Part third, for advanced scholars. Boston, MA: Russell, Odiorne & Metcalf.

    Google Scholar 

  • Gay, E. (1812). (Handwritten) Trigonometry and navigation cyphering book. New York, NY: Plimpton Collection, Butler Library, Columbia University. (Plimpton Manuscript MS 511, 1806).

    Google Scholar 

  • Greenwood, I. (1729). Arithmetick, vulgar and decimal, with the application thereof to a variety of cases in trade and commerce. Boston, MA: Kneeland & Green.

    Google Scholar 

  • Hodder, J. (1661). Hodder’s arithmetick, or that necessary art made most easie. London, UK: R. Davenport.

    Google Scholar 

  • Hutton, C. (1812). A course of mathematics…. New York, NY: Samuel Campbell.

    Google Scholar 

  • Jess, Z. (1799/1811). The American Tutor’s Assistant, improved: Or, a compendious system of decimal, practical arithmetic comprising the usual methods of calculation, with the addition of Federal money, and other decimals, dispersed through the several rules of that useful science adapted for the easy and regular instruction of youth in the United States. Wilmington, DE: Peter Brynberg.

    Google Scholar 

  • Kinne, W. (1831). A short system of practical arithmetic, compiled from the best authorities, to which is annexed a short plan of book-keeping, the whole designed for the use of schools (8th ed.). Hallowell, ME: Glazier, Masters & Co.

    Google Scholar 

  • Leybourn, W. (1690). Of arithmetic. London, UK: Thomas Basset, Benjamin Tooke, Thomas Sawbridge, Awnsham & John Churchill.

    Google Scholar 

  • Love, J. (1688). Geodaesia, or the art of surveying and measuring of land, made easie, showing by plain and practical rules how to survey, protract, cast up, reduce or divide any piece of land whatsoever; With new tables for the ease of the surveyor in reducing the measures of land. Moreover, a more facile and sure way of surveying by the chain than has hitherto been taught. As also, how to lay out new lands in America, or elsewhere: And how to make a perfect map of a river’s mouth or harbour, with several other things never yet published in our language. London, UK: John Taylor.

    Google Scholar 

  • Mellis, J. (1582/1658). The third part, or addition to this booke, entreateth of brief rules, called rules of practice, pleasant and commodious effects abridged into a briefer method than hitherto hath been published. In R. Record (Ed.), Record’s arithmetick: Or the ground of arts … (pp. 345–535). London, UK: I. Harrison, and H. Bynneman. [Note that Robert Recorde’s family name is spelt “Record” and not “Recorde” throughout this publication.]

    Google Scholar 

  • Morrice, D. (1801). The young midshipman’s instructor; (designed to be a companion to Hamilton Moore’s Navigation): With useful hints to parents of sea youth, and to captains and schoolmasters of the Royal Navy. London, UK: Knight and Compton.

    Google Scholar 

  • Pike, N. (1788). The new complete system of arithmetic, composed for the use of the citizens of the United States. Newburyport, MA: John Mycall.

    Google Scholar 

  • Recorde, R. (1543/1549). Grounde of the arts: Teaching the worke and practise, of arithmeticke. London, UK: R. Wolff.

    Google Scholar 

  • Slocomb, W. (1831). The American calculator, or a concise system of practical arithmetic. Philadelphia, PA: William Davis.

    Google Scholar 

  • Smith, E. B. (2005). “Let them compleately learn”: Manuscript clues about early women’s educational practices. In A manuscript miscellany, Summer 2005 Institute. Manchester, UK: Manchester University Press.

    Google Scholar 

  • Smith, R. C. (1831). Practical and mental arithmetic on a new plan, in which mental arithmetic is combined with the use of the slate. Boston, MA: Richardson, Lord & Holbrook.

    Google Scholar 

  • Sterry, C., & Sterry, J. (1795). A complete exercise book, in arithmetic: Designed for the use of schools in the United States. Norwich, CT: John Sterry & Co.

    Google Scholar 

  • Van Egmond, W. (1976). The commercial revolution and the beginnings of Western mathematics in Renaissance Florence, 1300–1500. PhD dissertation, Indiana University.

    Google Scholar 

  • Walkingame, F. (1785). The tutor’s assistant being a compendium of arithmetic and a complete question book (21st ed.). London, UK: J. Scratcherd & I. Whitaker.

    Google Scholar 

  • Ward, J. (1719). The young mathematician’s guide: Being a plain and easie introduction to the mathematicks. London, UK: Thomas Horne.

    Google Scholar 

  • Webster, W. (1740). Arithmetick in epitome: Or a compendium of all its rules, both vulgar and decimal (6th ed.). London, UK: D. Browne.

    Google Scholar 

  • Wingate, E. (1630). Arithmetique made easie. London, UK: Stephens and Meredith.

    Google Scholar 

  • Workman, B. (1789). The American accountant; or schoolmasters’ new assistant. Philadelphia, PA: John McCulloch.

    Google Scholar 

  • Ewing, A. (1799). A synopsis of practical mathematics: Containing plane trigonometry, mensuration of heights, distances, surfaces and solids, gauging, surveying of land, navigation and gunnery (4th ed.). London, UK: T. Cadlell & W. Davies.

    Google Scholar 

  • Sangster, J. H. (1865). Elements of algebra designed for the use of Canadian grammar and common schools. MontrĂ©al, Canada: John Lovell.

    Google Scholar 

  • Small, W. H. (1914). Early New England schools. Boston, MA: Ginn.

    Google Scholar 

  • Moravian Publication Office. (1876). Historical sketch of the Moravian Seminary for Young Ladies. Bethlehem, PA: Author.

    Google Scholar 

  • Bureau of Education. (1905). Report of the Commissioner of Education for the Year 1903. Washington, DC: Author.

    Google Scholar 

  • University of Michigan. (1967). Education in early America. Ann Arbor, MI: Author.

    Google Scholar 

  • Kennedy, M. F., & Harlow, A. F. (1940). Schoolmaster of yesterday: A three-generation story. New York, NY: McGraw-Hill.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nerida Ellerton .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Ellerton, N., Clements, M.K. (2012). The Principal Data Set. In: Rewriting the History of School Mathematics in North America 1607-1861. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2639-0_5

Download citation

Publish with us

Policies and ethics