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Arithmetic Books (1658 – 1882)

Adams, D. (1808). *The scholar’s arithmetic or federal accountant* (5th ed.). Troy, NY: John Prentiss.

Adams, D. (1830). *Adam’s new arithmetic*. Keene, NH: J. & J.W. Prentiss.

Adams, D. (1848). *Adam’s new arithmetic: Revised edition*. Keene, NH: J. & J.W. Prentiss.

Ayres, J. (1711). *Arithmetick: A treatise defined for the use and benefit of trades-men* (11th ed.). London, UK: Tho. Norris at Looking Glass on London Bridge.

Barreme, N. (1747).* L’Arithmetique du Sr Barreme ou le livre facile pour apprendre l’arithmetique. *Paris, France: Gandouin.

Botham, P.E. (1835). *Botham’s common school arithmetic: The common school arithmetic. *Hartford, CT: Henry Benton.

Braune, A. (1882). *Vollständige Kaufmännische Arithmetik für Handels-, Real- und Gewerbescheulen sowie zum Selbstunterrichte für Angehende Geschäftsleute.* Leipzig: Verlag von Ferdinand Hirt & Sohn.

Brookes, J. (1776). *A treatise on arithmetic.* New Castle, UK: J. Smith.

Cocker, E. (1702). *Cocker’s arithmetick*. London, UK: W. Richardson.

Colburn, W. (1824). *First lessons in arithmetic *(2nd ed.)*. *Boston, MA: Hilliard & Metcalf.

Colburn, D. P. (1855). *Arithmetic and its applications: Designed as a text book for common schools, high* *schools, and academies.* Philadelphia, PA: H. Cowperthwait & Co.

Colburn, D .P. (1858). *The common-school arithmetic: A practical treatise on the science of numbers.* Philadelphia, PA: H. Cowperthwait & Co.

Daboll, N. (1829). *Daboll’s schoolmaster’s assistant, a plain practical system of arithmetic*. Utica, NY: Hastings & Tracy.

Dilworth, T. (1802). *The schoolmaster’s assistant: Being a compendium of arithmetic, both practical and theoretical.* New York, NY: Lewis Nichols.

Dilworth, T. (1810). *The schoolmaster’s assistant: Being a compendium of arithmetic, both practical and theoretical*. New York, NY: E. Duyckinck & R. McDermott.

Farrar, J. (1818). *Arithmetic taken primarily from the arithmetic of S.F. Lacroix*. Cambridge, MA: Hilliard & Metcalf.

Fish, D.W. (1874). *Robinson’s shorter course: The complete arithmetic oral and written.* New York, NY: Ivison, Blakeman, & Co.

Fisher, G. (1785). *The instructor*. Edinburgh, Scotland: J. Dickson.

Gough, J. (1803). *Practical arithmetick*. Dublin, Ireland: Author.

Greenleaf, B. (1866). *The national arithmetic, on the inductive system, combining the analytic and synthetic methods; forming a complete course of higher arithmetic*. Boston, MA: Robert S. Davis & Co.

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

Lee, C. (1797). *The American accomptant: Being a plain, practical and systematic compendium of federal arithmetic. *Lansingburgh, NY: William W. Wands.

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

Pinnock, William (1823).* Pinnock’s catechism of arithmetic containing the most useful rules with exercises upon each *(6th ed.)*. *London, UK: G. & W.B. Whittaker.

Ray, J. (1856). *Ray’s higher arithmetic: The principles of arithmetic.* Cincinnati, OH: Winthrop B. Smith & Co.

Ray, J. (1877). *Eclectic educational series: Ray’s new practical arithmetic.* Cincinnati, OH: Van Antwerp, Bragg & Co.

Record[e], R. (1658). *Record’s arithmetick or the ground of arts.* London, England: James Mether.

[Spence, David] (1721). *Arithmetick compendiz’d or, a short treatise of arithmetick.* Edinburgh, Scotland: William Monro.

Walsh, M. (1828). *The mercantile arithmetic*. Boston, MA: Richardson & Lord.

Wentworth, G.A. (1897). *A practical arithmetic*. Boston, MA: Ginn & Company.

Weston, T. (1729). *A treatise of arithmetic in whole numbers and fractions. *London, UK: J. Hooke.

Wingate, W. H. (1865). *The parallel arithmetic: A collection of examples composed and arranged on a new plan. *London, UK: Longman, Green, Longman, Roberts, & Green.

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Some Cyphering Books from the Clements-Ellerton Collection (1702 – 1834)

Bigelow, G. (c. 1820). NY: Unpublished manuscript.

Brayton, O. (1792). Unpublished manuscript.

Burlingame, T. (1779 –1784). Burlingame, RI: Unpublished manuscript.

Butlar, J. (1785). Bucks County, PA: Unpublished manuscript.

Cuming, M. (c. 1820). RI: Unpublished manuscript.

Green, W. (1795-1800). Connecticut: Unpublished manuscript.

Hall, E. (1780). Unpublished manuscript.

Johnson, L. (1798-1801). MA: Unpublished manuscript.

Prust, T. (1702). Unpublished manuscript.

Steiner, M. (1801). Germany: Unpublished manuscript.

Senter, W. (1795-1801). Portsmouth, NH: Unpublished manuscript.

Thompson, J. (1820-1834). ME: Unpublished manuscript.

Townsend, W. (1824-1830). NY: Unpublished manuscript.

Unknown author (c. 1820). RI: Unpublished manuscript.

Wilson, U. (1823-1827). PA: Unpublished manuscript.

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References (1905 – 2012)

Ellerton, N. F. & Clements, M. A. (2012). *Rewriting the history of school mathematics in North* *America 1607*-*1861*. New York, NY: Springer.

Johnson, J. T. (1938). *The relative merits of three methods of subtraction: An experimental comparison of the decomposition method of subtraction with the equal additions and the Austrian method.* New York, NY: Teachers College, Columbia University.

National Governors Association Center for Best Practices. Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington DC: Author. Retrieved from http://www.corestandards.org/the-standards

Osburn, W. J. (1927). How shall we subtract? *Journal of Educational Research, *16(4): 237 -246.

Ross, S., & Pratt-Cotter, M. (2000). Subtraction in the United States: An historical perspective. *Mathematics Educator, *8(1), 49-56.

Smith, D. E. (1905). *Handbook to Smith’s arithmetic. *Boston, MA: Ginn & Co.

Smith, D. E. (1925). *History of mathematics: Special topics of elementary mathematics* (Vol. 2). Boston, MA: Ginn & Co.

Smith, D. E. (1909). *The teaching of arithmetic. *Boston, MA: Ginn & Co.

Swetz, F. J. (1987). *Capitalism and arithmetic*. La Salle, IL: Open Court.