Skip to main content

Abstract

The five research questions identified in Chapter 4 are answered in this chapter. It is argued that the cyphering tradition inculcated among students an “ownership” of the mathematics they studied, and that many students who prepared cyphering books proudly used these as reference books for the rest of their lives. The chapter closes with a list of researchable questions, associated with the cyphering tradition, for future investigation.

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

Access this chapter

eBook
USD 16.99
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

  • Allison, R. J. (Ed.). (1997). American eras: The Reform era and eastern United States development, 1815–1850 (Vol. 5). Detroit, MI: Gale.

    Google Scholar 

  • Babu, D. S. (2007). Memory and mathematics in the Tamil Tinnai schools of South India in the 18th and 19th centuries. International Journal for the History of Mathematics Education, 2(1), 15–37.

    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 

  • Carpenter, C. (1963). History of American schoolbooks. Philadelphia, PA: University of Pennsylvania Press.

    Google Scholar 

  • Cornell, E. (1860). Cyphering book prepared in 1823 and 1824, with later comments inserted by Ezra Cornell. Ithaca, NY: Cornell University Archives.

    Google Scholar 

  • De Morgan, A. (1853). The elements of arithmetic. London, UK: J. Walton.

    Google Scholar 

  • Dickens, C. (1850). David Copperfield. London, UK: Bradbury & Evans.

    Google Scholar 

  • Dossey, J, Halvorsen, K., & McCrone, S. (2008). Mathematics education in the United States 2008. Reston, VA: NCTM.

    Google Scholar 

  • Earle, A. M. (1899). Child-life in colonial days. New York, NY: The Macmillan Company.

    Google Scholar 

  • Ellerton, N. F., & Clements, M. A. (2009b). Theoretical bases implicit in the abbaci and cyphering-book traditions. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9–16). Thessaloniki, Greece: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Gaydos, T., & Kampas, B. (2010). American and Canadian cyphering books, n.d., 1727–1864 (2nd ed.). Salem, MA: Phillips Library at the Peabody Essex Museum.

    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 

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

    Google Scholar 

  • Isoda, M., (2007). A brief history of mathematics lesson study in Japan. In M. Isoda, M. Stephens, Y. Ohara, & T. Miyakawa (Eds.), Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement (pp. 8–15). Singapore: World Scientific Publishing.

    Chapter  Google Scholar 

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

    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 

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

    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 

  • Plimpton, G. A. (1916). The hornbook and its use in America. Proceedings of the American Antiquarian Society, 26, 264–272.

    Google Scholar 

  • Richeson, A. W. (1935). Warren Colburn and his influence on arithmetic in the United States. National Mathematics Magazine, 10(3), 73–79.

    Article  Google Scholar 

  • Smith, D. E. (1925). History of mathematics: Volume II, Special topics of elementary mathematics. Boston, MA: Ginn and Company.

    Google Scholar 

  • Smith, W. (1973). Theories of education in early America, 1655–1819. Indianapolis, IA: Bobbs-Merrill.

    Google Scholar 

  • Thayer, V. T. (1928). The passing of the recitation. Boston, MA: D. C. Heath and Company.

    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 

  • White, E. (1886). The elements of pedagogy. New York, NY: American Book Company.

    Google Scholar 

  • Wright, P. W. D., Wright, P. D., & Heath, W. H. (2008). Wrightslaw: No Child Left Behind. Hartsfield, VA: Harbor House Law Press.

    Google Scholar 

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

    Google Scholar 

  • Beckers, D. J. (1999). “Come children!” Some changes in Dutch arithmetic books 1750–1850. Report 9902 of the Department of Mathematics, the University of Nijmegen.

    Google Scholar 

  • Butler, W. (1788). An introduction to arithmetic designed for the use of young ladies. London, UK: S. Couchman.

    Google Scholar 

  • Butler, W. (1788/1806). Arithmetical questions, on a new plan, intended to answer the double purpose of arithmetical instruction and miscellaneous information, to which are subjoined, a collection of arithmetical tables, questions for practical examination and a copious index of persons, places and things, occasionally treated of, or mentioned in the work, designed for the use of young ladies (4th ed.). London, UK: S. Couchman.

    Google Scholar 

  • Chambers, R. (1835). Cyphering book. Bethania, PA: Author.

    Google Scholar 

  • Cobb, L. (1835). Cobb’s cyphering book, No. 1, containing all the sums and questions for theoretical and practical exercises in Cobb’s Explanatory Arithmetic No 1. Elmira, NY: Birdsall & Huntley.

    Google Scholar 

  • Colburn, W. (1830/1970). Teaching of arithmetic. In J. K. Bidwell & R. G. Clason (Eds.), Readings in the history of mathematics education (pp. 24–37). Washington, DC: National Council of Teachers of Mathematics.

    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 

  • Dowling, D. (1829). New and improved system of calculation in which a universal rule of proportion is, by new arrangement, applied to questions relating to military affairs, mensuration, natural philosophy, and mercantile operations. London, UK: Author.

    Google Scholar 

  • Hutton, C. (1766). The schoolmaster’s guide: Or a complete system of practical arithmetic, adapted to the use of schools, to which is added, a promiscuous collections of questions, and a course of retail book-keeping (2nd ed.). Newcastle-upon-Tyne, UK: J. White & T. Saint.

    Google Scholar 

  • Reynolds, G. H. (1818). The first elements of arithmetic, or the teacher’s and scholar’s assistant. London, UK: Longman, Hurst, Rees, Orme and Brown.

    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). Conclusions, and Some Final Comments. In: Rewriting the History of School Mathematics in North America 1607-1861. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2639-0_7

Download citation

Publish with us

Policies and ethics