Abstract
Throughout the period 1607–1865 most families had very few books other than a Bible in their homes, and most people did not know much mathematics beyond reading, writing, and counting with Hindu-Arabic numerals. Between 1636 and 1865 only a tiny proportion of the residents of that part of North America which is now mainland United States of America attended college and, of those who did, most had not previously studied mathematics beyond low-level abbaco arithmetic, elementary algebra, and the first few books of Euclid’s Elements. It is not surprising, therefore, that the period did not produce more than three or four scholars who, by European standards, might be considered to have been “outstanding” mathematicians. The U.S. college curriculum had its origin in the classical curriculum traditions of the medieval universities of Europe and especially of Cambridge and Oxford Universities. However, many of those who attended North American colleges did study what we have called “applied mathematics”—embracing fields like astronomy, surveying, mensuration and navigation— while they were at college, and we argue that this aspect of the implemented curriculum had been successfully translated mainly from Great Britain.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ackerberg-Hastings, A. (2014). Mathematics teaching practices. In A. Karp & G. Schubring (Eds.), Handbook on the history of mathematics education (pp. 525–540). New York, NY: Springer. https://doi.org/10.1007/978-1-4614-9155-2_26
Adams, C., Russell, T. et al. (Ed.). (1965). The West Point Thayer papers 1808–1872. West Point, NY: Association of Graduates.
Albree, J. (2002). Nicolas Pike’s Arithmetic (1788) as the American Liber Abbaci. In D. J. Curtin, D. E. Kullman, & D. E. Otero (Eds.), Proceedings of the Ninth Midwest History of Mathematics Conference (pp. 53–71). Miami, FL: Miami University.
Anderson, C. (1962). Technology in American education: 1650–1900 (Report No. OE-34018). Washington, DC: Office of Education, U.S. Department of Health, Education, and Welfare.
Archibald, R. C. (Ed.). (1925). Benjamin Peirce. Oberlin, OH: The Mathematical Association of America. https://doi.org/10.1080/00029890.1925.11986401
Association of Masters of the Boston Public Schools. (1844). Remarks on the Seventh Annual Report of the Hon. Horace Mann, Secretary of the Massachusetts Board of Education. Boston, MA: Charles C. Little & James Brown.
Barnard, F. A. P. (1875–1876). Progress of the exact sciences. Harper’s New Monthly Magazine, 52, 82–100.
Beadie, N. (2010). Education, social capital and state formation in comparative historical perspectives: Preliminary investigations. Paedagogica Historica, 46(1–2), 15–32. https://doi.org/10.1080/00309230903528439
Blinderman, A. (1976). Three early champions of education: Benjamin Franklin, Benjamin Rush, and Noah Webster. Bloomington, IA: Phi Delta Kappa Educational Foundation.
Brasch, F. E. (1939, October). The Newtonian epoch in the American colonies (1680–1783). Paper presented to the American Antiquarian Society.
Broome, E. C. (1903). A historical and critical discussion of college admission requirements. New York, NY: Columbia University.
Brown, C. (1721). The geography of the ancients so far described as it is contain’d in the Greek and Latin classicks. London, England: Author.
Buzbee, L. (2014). A personal history of the classroom. Minneapolis, MN: Gray Wolf Press.
Cajori, F. (1890). The teaching and history of mathematics in the United States (Circular of Information No. 3, 1890). Washington, DC: Bureau of Education.
Cajori, F. (1907). A history of elementary mathematics with hints on methods of teaching. New York, NY: Macmillan.
Cajori, F. (1928). A history of mathematical notations. La Salle, IL: Open Court Publishing Company.
Cajori, F. (1980). The chequered career of Ferdinand Rudolph Hassler. New York, NY: Arno Press.
Campbell, F. (1968). Latin and the elite tradition in education. The British Journal of Sociology, 19(3), 308–325. https://doi.org/10.2307/588835
Chateauneuf, A. O. (1930). Changes in the content of elementary algebra since the beginning of the high school movement as revealed by the textbooks of the period. PhD dissertation, The University of Pennsylvania.
Clements, M. A., & Ellerton, N. F. (2015). Thomas Jefferson and his decimals 1775–1810: Neglected years in the history of U.S. school mathematics. New York, NY: Springer. https://doi.org/10.1007/978-3-319-02505-6
Cocker, E. (1720). Decimal arithmetic, wherein is shewed the nature and use of decimal fractions in the usual rules of arithmetic, … (5th ed.). London, England: J. Darby for M. Wellington.
Cohen, A. M. (1998). The shaping of American higher education. San Francisco, CA: Jossey-Bass.
Cohen, P. C. (1982). A calculating people: The spread of numeracy in early America. Chicago, IL: The University of Chicago Press.
Cohen, P. C. (2003). Numeracy in nineteenth-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.
Cowley, W. H., & Williams, D. (1991). International and historical roots of American higher education. New York, NY: Garland Publishing, Inc.
Cremin, L.A. (1977). Traditions of American education. New York, NY: Basic Books.
Crilly, T. (2008). Arthur Cayley and mathematics education. HPM Newsletter, 68,1–4.
Crozet, C. (1821). A treatise on projective geometry, for the use of the cadets of the United States Military Academy. Part 1. New York, NY: A. T. Goodrich and Co.
Darwin, G. H. (1913). Opening address. In E. W. Hobson & A. E. H. Love (Eds.), Proceedings of the Fifth International Congress of Mathematicians (pp. 33–36). Cambridge, England: Cambridge University Press.
Dauben, J. W., & K. H. Parshall (2014). Mathematics education in North America to 1800. In A. Karp & G. Schubring (Eds), Handbook on the history of mathematics education (pp. 175–185). New York, NY: Springer.
Davies, C. (1826). Elements of descriptive geometry, with their application to spherical trigonometry, spherical projections, and warped surfaces. Philadelphia, PA: H. C. Carey and I. Lea.
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 & Deforest.
Day, J. (1815). A treatise of plane trigonometry … being the second part of a course of mathematics, adopted to the method of instruction in the American colleges. New Haven, CT: Yale College.
Day, J. (1817). The mathematical principles of navigation and surveying, with the mensuration of heights and distances. New Haven, CT: Yale College.
Day, J. (1836). The teacher’s assistant in the “course of mathematics.” New Haven, CT: Yale College.
Deming, C. (1904). Yale wars of the conic sections. The Independent, 56, 667–669.
Dexter, F. B. (1887). Estimates of population in American colonies. Proceedings of the American Antiquarian Society (pp. 22–50). Boston, MA. American Antiquarian Society.
Draper, J. (1772). The young student’s pocket companion. Newcastle-Upon-Tyne, England: Newcastle Literary and Philosophical Society.
Ellerton, N. F., & Clements, M. A. (2012). Rewriting the history of mathematics education in North America, 1607–1861. New York, NY: Springer. https://doi.org/10.1007/978-94-007-2639-0
Ellerton, N. F., & Clements, M. A. (2014). Abraham Lincoln’s cyphering book, and ten other extraordinary cyphering books. New York, NY: Springer. https://doi.org/10.1007/978-3-319-02502-5
Ellerton, N. F., & Clements, M. A. (2017). Samuel Pepys, Isaac Newton, James Hodgson and the beginnings of secondary school mathematics: A history of the Royal Mathematical School at Christ’s Hospital 1673–1868. New York, NY: Springer. https://doi.org/10.1007/978-3-319-46657-6
Else-Quest, N., Hyde, J. S., & Linn, M. (2010). Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 136(1), 103. https://doi.org/10.1037/a0018053
Farrar, J. (1818). Introduction to Farrar’s translation of Lacroix, S. F., An elementary treatise on arithmetic and an introduction to the elements of algebra. Cambridge, MA: Hilliard & Metcalf.
Fauvel, J. (1999, April 15). Thomas Jefferson and mathematics. Lecture given at the University of Virginia.
F. D. B. (1911). Blackboards. In P. Monroe (Ed.), A cyclopedia of education (Vol. 1, pp. 390–394). New York, NY: The Macmillan Company.
Fletcher, R. S. (1943). A history of Oberlin College from its foundation through the Civil War. Oberlin, OH: Oberlin College.
Franklin, B. (1749). Proposals relating to the education of youth in Pensilvania. Philadelphia, PA: Author.
Franklin, B. (1793). The private life of the late Benjamin Franklin, LL.D. London, England: J. Parsons.
Fuess, C. M. (1917). An old New England school: A history of Phillips Academy Andover. Boston, MA: Houghton Mifflin Company.
Geiger, R. L. (2016). The history of American higher education. Princeton, NJ: Princeton University Press.
George Washington to Nicolas Pike, 20 June 1786. Founders Online, National Archives, accessed December 29, 2019 https://founders.archives.gov/documents/Washington/04-04-02-0119.
Goldsmith, O. (1837). The Grecian history, from the earliest state to the death of Alexander the Great. Hartford, CT: Judd, Loomis & Co.
Goodchild, L. F., & Wechsler, H. S. (1989). The history of higher education (2nd ed.). Boston, MA: Pearson Custom Publishing.
Green, A. (2015, September 15). The Yale chalkboard rebellion of 1830. From https://www.mentalfloss.com/article/68749/yale-chalkboard-rebellion-1830, viewed on April 9, 2020.
Greenwood, I. (1729). Arithmetick, vulgar and decimal, with the application thereof to a variety of cases in trade and commerce. Boston, MA: Kneeland & Green.
Grew, T (1853). The description and use of the globes, celestial and terrestrial, with variety of examples for the learner’s exercise: Intended for the use of such persons who would attain to the knowledge of those instruments: but chiefly designed for the instruction of young gentlemen at the Academy of Philadelphia. To which is added rules for working all the cases in plain and spherical triangles without a scheme. Germantown, PA: Christopher Sower.
Gwynne-Thomas, E. H. (1981). A concise history of education to 1900 A.D. Washington, DC: University Press of America, Inc.
Halwas, R. (1990). American mathematics textbooks 1760–1850. London, England: Author.
Herbst, J. (2004). The Yale Report of 1828, International Journal of the Classical Tradition, 11(2), 213–231. https://doi.org/10.1007/BF02720033
Hertel, J. (2016) Investigating the implemented mathematics curriculum of New England navigation cyphering books. For the Learning of Mathematics, 36(3), 4–10.
Hill, T. (1880). Benjamin Peirce. The Harvard Register, 6(1), 91–92.
Hirsch, D., & Van Haften, D. (2019). The tyranny of public discourse. El Dorado Hills, CA: Savas Beatie.
Hobson, E. W., & Love, A. E. H. (Eds.). (1913). Proceedings of the Fifth International Congress of Mathematicians. Cambridge, England: Cambridge University Press.
Hu, J. C. (2016, November 4). Why are there so few women mathematicians? The Atlantic.
Hurd, D. H. (1890). History of Middlesex County, Massachusetts, with biographical sketches of many of its pioneers and prominent men. Philadelphia, PA: J. W. Lewis & Co.
Iliffe, R. (1997). Mathematical characters: Flamsteed and Christ’s Hospital Royal Mathematical School. In F. Willmoth (Ed.). Flamsteed’s stars: New perspectives on the life and work of the first Astronomer Royal (1646–1719) (pp. 115–144). Woodbridge, England: The Boydell Press.
Jackson, A. (2002). Teaching math in America: An exhibit at the Smithsonian. Notices of the American Mathematical Society, 49(9), 1082–1083.
Johnston, S. (1996). The identity of mathematical practitioners in 16th-century England. In I Hantsche (Ed.), Der “mathematicus”: Zur entwicklung und beturdung einer neuen berufsgruppe in der zeit Gerhard Mercators (pp. 93 –120). Bochum, Germany: Brockmeyer.
Karpinski, L. C. (1980). Bibliography of mathematical works printed in America through 1850 (2nd ed.). New York, NY: Arno Press.
Kidwell, P. A., Ackerberg-Hastings, A., & Roberts, D. L. (2008). Tools of American mathematics teaching, 1800–2000. Baltimore, MD: Johns Hopkins University Press.
Kraus, J. W. (1961). The development of the curriculum in the early American colleges. History of Education Quarterly, 1(2), 64–76. https://doi.org/10.2307/367641
Krause, D. A. (2000). “Among the greatest benefactors of mankind”: What the success of the chalkboard tells us about the future of computers in the classroom. Computers and the Future of the Humanities, 33(2), 6–16. https://doi.org/10.2307/1315198
Lacroix, S. F. (1818). An elementary treatise of arithmetic, and an introduction to the elements of algebra, comprehending the mathematics required for admission to the University of Cambridge, New England. Cambridge, MA: Hilliard and Metcalf.
Leacock, S (1970). Feast of Stephen. Toronto, Canada: McClelland & Stewart, Inc.
Lemprière, J. (1834). Lemprière’s classical dictionary for schools and academies. Boston, MA: Carter, Hender & Co.
Lial, M. L., Miller, C. D., & Hornsby, E. J. (1992). Beginning algebra. Boston, MA: Addison Wesley.
Looby, C. (1984). Phonetics and politics: Franklin’s alphabet as a political design. Eighteenth-Century Studies, 18(10), 1–34. https://doi.org/10.2307/2738304
Lucas, C. J. (1994). American higher education: A history. New York, NY: St. Martin's Griffin.
Macintyre, S., & Clark, A. (2004). The history wars. Melbourne, Australia: Melbourne University Press.
Martin, G. H. (1897). The evolution of the Massachusetts public school system: A historical sketch. New York, NY: D. Appleton and Company.
Martines, L. (1979). Power and imagination: City states in renaissance Italy. New York, NY: Alfred A. Knopf.
Matz, F. P. (1895). B. O. Peirce: Biography American Mathematical Monthly, 2, 173–179. https://doi.org/10.1080/00029890.1895.11998647
McDonald, A. (1785). The youth’s assistant … Norwich, CT. John Trumbull.
Meyer R. (1968). Opponents of classical learning in America during the revolutionary period. Proceedings of the American Philosophical Society, 112, 221–234.
Minto, W. (1788). An inaugural oration, on the progress and importance of the mathematical sciences. Manuscript, held in the Clements Library, The University of Michigan.
Molloy, P. M. (1975). Technical education and the young Republic: West Point as America’s ́Ecole Polytechnique, 1802–1833. PhD dissertation, Brown University.
Monge, G. (1811). Géométrie descriptive (New edition). Paris, France. J. Klostermann.
Monroe, W. S. (1917). Development of arithmetic as a school subject. Washington, DC: Government Printing Office.
Morison, S. E. (1956). The intellectual life of colonial New England. Ithaca, NY: Great Seal Books.
Muttappallymyalil, J, Mendis S, John L. J., Shanthakumari N., Sreedharan J, & Shaikh R. B. (2016). Evolution of technology in teaching: Blackboard and beyond in medical education. Nepal Journal of Epidemiology, 6(3), 588–592. https://doi.org/10.3126/nje.v6i3.15870
Ogg, F. A. (1927). Builders of the Republic. New Haven, CT: Yale University Press.
Peirce, B. (1837). An elementary treatise on algebra; to which are added elementary equations and logarithms. Boston, MA: James Munroe and Company.
Peirce, B. (1841). An elementary treatise on curves, functions, and forces (Volume First): Analytic geometry and the differerential calculus. Boston, MA: James Munroe and Company.
Peirce, B. (1846). An elementary treatise on curves, functions, and forces (Volume Second): Calculus and imaginary quantities, residual calculus, and integral calculus. Boston, MA: James Munroe and Company.
Peirce, B. (2019, May 13). Wikiquote, Retrieved July 5, 2021 from https://en.wikiquote.org/w/index.php?title=Benjamin_Peirce&oldid =2596188.
Phalen, H. R. (1946). The first professorship of mathematics in the colonies. The American Mathematical Monthly, 53(10), 579–582. https://doi.org/10.1080/00029890.1946.11991755
Peterson, S. R. (1955). Benjamin Peirce: Mathematician and philosopher. Journal of the History of Ideas, 16, 89–112. https://doi.org/10.2307/2707529
Phillips, C. J. (2015). An officer and a scholar: Nineteenth-century West Point and the invention of the blackboard. History of Education Quarterly, 55(1), 82–108. https://doi.org/10.1111/hoeq.12093
Pike, N. (1788). The new and complete system of arithmetic, composed for the use of the citizens of the United States. Newbury-Port, MA: John Mycall.
Pike, N. (1793). Abridgement of the new and complete system of arithmetick composed for the use, and adapted to the commerce of the citizens of the United States. Newbury-Port, MA: John Mycall, Isaiah Thomas.
Pillans, J. (1856). First steps in the physical and classical geography of the ancient world. London, England: Longman, Brown, Green & Longmans.
Pioariu, R. (2011). Cross-cultural issues in teaching English to Romanian students. In T. Popescu, R. Pioariu, & C. Herteg (Eds.), Cross-disciplinary approaches to the English language: Theory and practice (pp. 150–160). Newcastle-on-Tyne, England: Cambridge Scholars Publishing.
Plimpton, G. A. (1916). The hornbook and its use in America. Worcester, MA: American Antiquarian Society. https://doi.org/10.5479/sil.258315.39088004241238
Preveraud, T. (2015). American mathematics journals and the transmission of French textbooks to the United States. In K. Bjarnadottir, F. Furinghetti, J. Prytz, & G. Schubring (Eds.), “Dig where you stand 3” (pp. 309–325). Uppsala, Sweden: Uppsala, Universitet
Quincy, J. (1860). The history of Harvard University. Boston, MA: Crosby, Nicholls, Lee & Co.
Richard, C. J. (1994). The founders and the classics: Greece, Rome, and the American enlightenment. Cambridge, MA: Harvard University Press.
Rickey, V. F., & Shell-Gellasch, A. (2010, July). Mathematics education at West Point: The first hundred years—Teaching at the Academy. Convergence (Publication of the Mathematical Association of America).
Roberts, D. L. (2014). History of tools and technologies in mathematics education. In A. Karp & G. Schubring (Eds), Handbook on the history of mathematics education (pp. 565–578). New York, NY: Springer. https://doi.org/10.1007/978-1-4614-9155-2_28
Robinson, H. (1870). The progressive higher arithmetic for schools, academies, and mercantile colleges. New York, NY: Ivison, Blakeman, Taylor & Co.
Rudolph, F. (1990). The American college and university: A history. Athens, GA: The University of Georgia Press.
Rush, B. (1806), Essays, literary, moral and philosophical (2nd ed.). Philadelphia, PA: Thomas and William Bradford.
Schlesinger, A. M. (Ed.). (1983). The almanac of American history. New York, NY: G. P. Putnam.
Seybolt, R. F. (1969).The public schools of colonial Boston 1635–1775. New York, NY: Arno Press.
Simons, L. G. (1924). Introduction of algebra into American schools in the 18th century. Washington, DC: Department of the Interior Bureau of Education.
Smith, D. E., & Ginsburg, J. (1934). A history of mathematics in America before 1900. Chicago, IL: The Mathematical Association of America.
Stamper, A. W. (1909). A history of the teaching of elementary geometry, with reference to present-day problems. PhD dissertation, Columbia University. https://doi.org/10.1017/S0007087499003556
Stewart, L. (1999). Other centres of calculation, or where the Royal Society didn’t count: Commerce, coffee-houses and natural philosophy in early modern London. British Journal of the History of Science, 32, 132–153.
Stedall, J. (2012). The history of mathematics: A very short introduction. New York, NY: Oxford University Press.
Stoeckel, A. (1976). Presidents, professors, and politics: The colonial colleges and the American revolution. Conspectus of History, 1(3), 45–56.
Sylvester, J. J. (1870, January 6). A plea for the mathematician II. Nature, 1, 261–263.
Tebbel, J. (1972). A history of book publishing in the United States. New York, NY: R. R. Bowke.
“Thomas Jefferson to John Farrar, 10 November 1818,” Founders Online, National Archives, https://founders.archives.gov/documents/Jefferson/03-13-02-0343
Todhunter, I. (Ed.). (1955). Euclid’s elements. London, England: J. M, Dent and Sons.
Tyler, L. G. (1897). Education in colonial Virginia. Part II, private schools and tutors. William and Mary Quarterly, 6, 1–6. https://doi.org/10.2307/1914792
Varcoe, K. E. (2002). A historical review of curriculum in American higher education: 1636–1900. PhD course paper, Nova Southeastern University.
University of Michigan (1967). Education in early America. Ann Arbor, MI: The University of Michigan Library.
Wallis, P., Wallis, R., Ransom, P., & Fauvel, J. (1991). Mathematical tradition in the north of England. Newcastle-Upon-Tyne, England: University of Newcastle.
Ward, J. (1719). The young mathematician’s guide: Being a plain and easie introduction to the mathematicks. London, England: Thomas Horne.
Ward, J. (1758). The young mathematician’s guide: Being a plain and easy introduction to the mathematicks. London, England: C. Hitch and L. Hawes.
Webster, N. (1787). The American speller. Boston, MA: Isaiah Thomas.
Wilson, N. G. (Ed.). (2006). Encyclopedia of ancient Greece. New York, NY: Routledge
Windschuttle, K. (1996). The killing of history: How literary critics and social theorists are murdering our past. San Francisco, CA: Encounter Books.
Wylie, C. D. (2012). Teaching manuals and the blackboard: Accessing historical classroom practices. History of Education, 41(2), 257–272. https://doi.org/10.1080/0046760X.2011.584573
Yale College. (1828). Reports on the course of instruction in Yale College by a committee of the Corporation, and the academical faculty. New Haven, CT: Author.
Zitarelli, D. A. (2019). A history of mathematics in the United States and Canada. Volume 1: 1492–1900. Washington, DC: American Mathematical Society. https://doi.org/10.1090/spec/094
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ellerton, N., Clements, M.A.K. (2022). College Mathematics, 1607–1865. In: Toward Mathematics for All. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-85724-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-85724-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-85723-3
Online ISBN: 978-3-030-85724-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)