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Mathematics Education in America in the Premodern Period

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  • Mathematics Education
  • Eighteenth Century
  • Sixteenth Century
  • Religious Order
  • Mathematical Curriculum

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Fig. 9.1
Fig. 9.2
Fig. 9.3

Notes

  1. 1.

    For an analysis that highlights the role of different religions in the transmission of mathematics to the Americas, see Schubring (2002).

  2. 2.

    This date is not without controversy, but, if accepted, places the founding of the Collegiate School at a date slightly earlier than that of either the Boston Latin School (founded in 1635) or Roxbury Latin School (founded in 1645). It is based on the premise that, in this period, schools were not so much founded as they founded themselves. See Cremin 1970, p. 197, and Frost 1991, p. 183.

  3. 3.

    The Ursulines founded a convent and the first school for girls in North America in Québec in 1639. By the early eighteenth century, the order had succeeded in establishing schools across Canada and as far south as New Orleans on the Gulf of Mexico. Apparently, the assumption was that boys needed to study a trade, whereas girls would ultimately civilize the colony by teaching their children. An exception to the usual rule, the Ursulines taught basic reading, writing, and mathematics along with religious instruction and such domestic skills as sewing and knitting (Robenstein 1992). Girls also studied ciphering in at least four schools in Bruton Parish, Virginia, in 1724 (Ellerton and Clements 2012, p. 38).

  4. 4.

    The first arithmetic to appear in French Canada was Jean-Antoine Bouthillier’s 1809 Traité d’arithmétique pour l’usage des écoles. See Karpinski (1940, p. 174) and compare Archibald and Charbonneau (2005, pp. 150–151).

  5. 5.

    Also printed in 1729 was Pieter Venema’s Dutch Arithmetica of Cyffer-konst, volgens de munten en gewigten, to Nieu-York, gebruykelyk als mede een kort ontwerp van de algebra (Arithmetic or the Art of Ciphering, According to the Coins, Measures, and Weights Used at New York, Together with a Short Treatise on Algebra). Printed in New York, it would have served mainly as a text in private schools emphasizing commerce (see below) (Mutchler and Craig 1912, p. 226).

  6. 6.

    For these details on Winthrop’s life and work, see Shipton 1963, pp. 349–373.

  7. 7.

    The Jesuits and Franciscans also established educational outposts in what would only much later become the state of California. The Jesuits founded the first permanent mission in Baja, California, in 1697 and some seventeen additional missions over the course of the next seventy years along the so-called Camino Real. The Franciscans followed beginning in 1769 and took over the work of the Jesuits when that order was suppressed in 1773 (Butler 2000, pp. 36–41).

  8. 8.

    Some 40,000 loyalists to the British crown left the lower British colonies for Nova Scotia, New Brunswick, and Québec following the outbreak of the American Revolution in 1776. They transplanted their Anglican educational ideals to new institutions such as King’s College founded in Windsor, Nova Scotia, in 1789 and the College of New Brunswick established in Fredericton in 1800 (Axelrod 1997, p. 6).

  9. 9.

    The Collège de Saint-Raphaël (now the Collège de Montréal, a private secondary school), founded in Montréal in 1767, initiated a humanities curriculum in 1773 as well. It only rounded that curriculum out with “philosophy,” ultimately including arithmetic and other basic mathematics, in the early 1790s.

  10. 10.

    This essay is based on my paper D’Ambrosio (2006). I recently published a book that, although focusing Brazil, has references to the transmission, acquisition and diffusion of mathematics in Latin America: D’Ambrosio (2008).

  11. 11.

    See a discussion on these issues in D’Ambrosio (2000).

  12. 12.

    See D’Ambrosio (1995, 1996).

  13. 13.

    For a brief introduction to this theme, see D’Ambrosio (1977).

  14. 14.

    An important survey of pre-Columbian Mathematics of extant cultures is the book by Closs (1986).

  15. 15.

    See the chapter on premodern times in Europe. Due to the Jesuits’ strong interest in astronomy, several works and publications were written by Jesuits in Latin America on astronomical issues, particularly comets.

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D’Ambrosio, U., Dauben, J.W., Parshall, K.H. (2014). Mathematics Education in America in the Premodern Period. In: Karp, A., Schubring, G. (eds) Handbook on the History of Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9155-2_9

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