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.
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References
Allison, R. J. (Ed.). (1997). American eras: The Reform era and eastern United States development, 1815–1850 (Vol. 5). Detroit, MI: Gale.
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.
Cajori, F. (1890). The teaching and history of mathematics in the United States (Circular of Information No. 3, 1890). Washington, DC: Bureau of Education.
Carpenter, C. (1963). History of American schoolbooks. Philadelphia, PA: University of Pennsylvania Press.
Cornell, E. (1860). Cyphering book prepared in 1823 and 1824, with later comments inserted by Ezra Cornell. Ithaca, NY: Cornell University Archives.
De Morgan, A. (1853). The elements of arithmetic. London, UK: J. Walton.
Dickens, C. (1850). David Copperfield. London, UK: Bradbury & Evans.
Dossey, J, Halvorsen, K., & McCrone, S. (2008). Mathematics education in the United States 2008. Reston, VA: NCTM.
Earle, A. M. (1899). Child-life in colonial days. New York, NY: The Macmillan Company.
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.
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.
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.
Heeffer, A. (2008). Text production reproduction and appropriation within the abbaco tradition: A case study. SCIAMVS, 9, 101–145.
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.
Karpinski, L. C. (1925). The history of arithmetic. Chicago, IL: Rand McNally & Company.
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.
Littlefield, G. E. (1904). Early schools and school-books of New England. Boston, MA: The Club of Odd Volumes.
Monaghan, E. J. (2007). Learning to read and write in colonial America. Amhurst, MA: University of Massachusetts Press.
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.
Plimpton, G. A. (1916). The hornbook and its use in America. Proceedings of the American Antiquarian Society, 26, 264–272.
Richeson, A. W. (1935). Warren Colburn and his influence on arithmetic in the United States. National Mathematics Magazine, 10(3), 73–79.
Smith, D. E. (1925). History of mathematics: Volume II, Special topics of elementary mathematics. Boston, MA: Ginn and Company.
Smith, W. (1973). Theories of education in early America, 1655–1819. Indianapolis, IA: Bobbs-Merrill.
Thayer, V. T. (1928). The passing of the recitation. Boston, MA: D. C. Heath and Company.
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.
White, E. (1886). The elements of pedagogy. New York, NY: American Book Company.
Wright, P. W. D., Wright, P. D., & Heath, W. H. (2008). Wrightslaw: No Child Left Behind. Hartsfield, VA: Harbor House Law Press.
Yeldham, F. A. (1936). The teaching of arithmetic through four hundred years (1535–1935). London, UK: Harrap.
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.
Butler, W. (1788). An introduction to arithmetic designed for the use of young ladies. London, UK: S. Couchman.
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.
Chambers, R. (1835). Cyphering book. Bethania, PA: Author.
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.
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.
Doar, A. K. (2006). Cipher books in the Southern Historical Collection. Master of Science thesis, Wilson Library, University of North Carolina at Chapel Hill.
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.
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.
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.
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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
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