Involving Students in Original Research with Primary Sources

A Graduate Course in the History of Mathematics Education
  • Patricia Baggett
  • Andrzej Ehrenfeucht
Part of the ICME-13 Monographs book series (ICME13Mo)


We describe the structure and content of a graduate mathematics course, History and Theories of Mathematics Education, which focuses mostly on the history of mathematics education in colonial America and the US, including different authors’ opinions about the purpose/methods of mathematics education. Students study original antiquarian books and read articles by writers who have influenced the development of mathematics education, preparing a major final project that they present at a conference at the course’s end, open to faculty, students and guests. Our aim in designing and implementing this course is to use original sources in the history of mathematics education (rather than the history of mathematics) to allow each student to carry out his/her own individual research in the history of the issues described in these sources, and to report publicly on these results. We give details on the actual implementation of this course and its evaluation by the students enrolled in it.


Undergraduate and graduate mathematics Student research History of mathematics education Original sources 


  1. Beecher, C. (1832). Arithmetic simplified. Hartford, CT: D. F. Robinson & Co.Google Scholar
  2. Burstyn, J. (1947). Catherine Beecher and the education of American women. New England Quarterly, 47, 386–403.CrossRefGoogle Scholar
  3. Cajori, F. (1890). The teaching and history of mathematics in the United States. Washington, DC: Government Printing Office.Google Scholar
  4. Clark, I. A. (1846). Prussian calculator. Rochester, NY: Power Press of E. Shepard.Google Scholar
  5. Cocker, E. (1715). Edward Cocker’s arithmetick. London: A. Bettesworth & C. Hitch.Google Scholar
  6. Colburn, W. (1825). First lessons in arithmetic on the plan of Pestalozzi. Boston, MA: Cummings, Hilliard, & Co.Google Scholar
  7. Common Core Standards Initiative (CCSSI). (2010). Common core state standards for mathematics. Accessed August 7, 2017.
  8. Day, J. (1834). An introduction to algebra. New Haven, CT: Howe & Spalding.Google Scholar
  9. Dewey, J. (1938). Experience and education. New York: Collier Books.Google Scholar
  10. Dodgson, C. (1885). Euclid and his modern rivals. London: McMillan & Co.Google Scholar
  11. Ellerton, N. F., & Clements, M. A. K. (2014). Abraham Lincoln’s cyphering book and ten other extraordinary cyphering books. New York: Springer.CrossRefGoogle Scholar
  12. Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics, 12(2), 133–150.CrossRefGoogle Scholar
  13. Hawney, W., & Keith, T. (1813). Hawney’s complete measurer. Baltimore, MD: F. Lucas, Jr.Google Scholar
  14. Hillway, T. (Ed.). (1964). American education: An introduction through readings. Boston: Houghton Mifflin.Google Scholar
  15. Jones, J. B. (1870). Elementary arithmetic in Cherokee and English. Tahlequah, OK: Cherokee National Press.Google Scholar
  16. Kangshen, S., Crossley, J. N., & Lun, A. W.-C. (1999). The nine chapters on the mathematical art. Oxford: Oxford University Press.Google Scholar
  17. Kline, M. (1974). Why Johnny can’t add: The failure of the new math. New York: Random House.Google Scholar
  18. Leifeste, K. (2015). A forgotten contrivance: A study of the diagonal scale and its appearance in mathematics texts from 1714 to the present. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 30(1), 50–66.CrossRefGoogle Scholar
  19. Lester, T. (2009, December). Putting America on the map. Smithsonian Magazine. Accessed August 7, 2016.
  20. Levey, M., & Petruck, M. (1965). Principles of Hindu reckoning (Kushyar Ibn Labban). A translation with introduction and notes. Madison, WI: University of Wisconsin Press.Google Scholar
  21. Pike, N. (1788). A new and complete system of arithmetic composed for the citizens of the United States. Newbury-port, MA: John Mycall.Google Scholar
  22. Pike, S. (1811). The teacher’s assistant or a system of practical arithmetic. Philadelphia: Johnson and Warner.Google Scholar
  23. Recorde, R. (1632/2012). The Grounde of Artes. First imprinted by Reynold Wolf in 1543. A 16th century treatise on arithmetic. Derby, UK: TGR Renascent Books.Google Scholar
  24. Riese, A. (1550/1991). Rechenung nach der Lenge, auff den Linihen und Feder. Derby, UK: TGR Renascent Books.Google Scholar
  25. Sfard, A. (2012). Why mathematics? What mathematics? The Mathematics Educator, 22(1), 3–26.Google Scholar
  26. Skinner, B. F. (1984). The shame of American education. American Psychologist, 39(9), 947–954.CrossRefGoogle Scholar
  27. Smith, D. E. (1921). The Sumario Compendioso of Brother Juan Diez. Boston & London: Ginn & Co.Google Scholar
  28. Stanic, G. (1986). Mental discipline theory and mathematics education. For the Learning of Mathematics, 6(1), 39–47.Google Scholar
  29. Swetz, F. (1987). Capitalism and arithmetic (The Treviso arithmetic arte dell’Abbaco, 1478). LaSalle, IL: Open Court.Google Scholar
  30. The Public School (1897). Euclid and algebra. Toronto: G. M. Rose & Sons.Google Scholar
  31. Ward, J. (1734). Young mathematician’s guide. London: A. Bettesworth & C. Hitch.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Computer Science DepartmentUniversity of ColoradoBoulderUSA

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