Problems of Abstraction: Defining an American Standard for Mathematics Education at the Turn of the Twentieth Century

Abstract

Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university officials found clear outlets in the reform movement concerning secondary school offerings and college entrance requirements. This article therefore focuses on these debates and also the attempts to achieve compromises through standardized curricula in the recommendations of the Committee of Ten. In discussing the interplay between university and secondary education, it exposes a feature of the history of science education that has been neglected.

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

References

  1. Anonymous. (1918). Dr. Arthur H. Cutler, school founder, dies. New York Times, 22 June.

  2. Archibald, R. C. (1924). Simon Newcomb, 1835–1909: Bibliography of his life and work. Memoirs of the National Academy of Sciences, 17, 19–69.

    Google Scholar 

  3. Archibald, R. C. (1938). A semicentennial history of the American Mathematical Society, 1888–1938. New York: American Mathematical Society.

    Google Scholar 

  4. Butler, N. M. (1900). Uniform college entrance requirements with a common board of examiners. In Proceedings of the 13th annual convention of the Association of Colleges and Preparatory Schools of the Middle States and Maryland (pp. 43–49). Held at State Normal School, Trenton N.J., Friday and Saturday Dec 1–2, 1899, University of the State of New York, Albany, NY.

  5. Butler, N. M. (1939). Across the busy years. New York NY: Charles Scribner’s Sons.

    Google Scholar 

  6. Cajori, F. (1890). The teaching and history of mathematics in the United States. Washington, DC: Government Printing Office.

    Google Scholar 

  7. Calkins, N. A. (1894). Prefatory note. In National educational association, report of the committee of ten on secondary school studies, with the reports of the conferences arranged by the committee (pp. iii–iv). New York, NY: American Book Company.

  8. Coffin, S. J. (1890). The men of Lafayette, 1826–1893: Lafayette College, its history, its men, their record. Easton, PA: George W. West.

    Google Scholar 

  9. Collar, W. C. (1891). The action of the colleges upon the schools. Educational Review, 2, 422–441.

    Google Scholar 

  10. College Entrance Examination Board of the Middle States and Maryland. (1901). First annual report of the secretary. New York, NY: The Board.

    Google Scholar 

  11. Committee of the Graduate Club of Harvard, in Co-operation with Committees of Similar Clubs at Cornell, Johns Hopkins, Yale. (1893). Graduate courses: A handbook for graduate students, with a list of advanced courses announced by eleven universities of the United States for the year 1893–1894. Boston, MA: Ginn & Company.

    Google Scholar 

  12. Committee of the State Teachers’ Association of Missouri. (1896). Report of the committee of the state teachers’ association of Missouri. The School Review: A Journal of Secondary Education, 4, 546–548.

    Google Scholar 

  13. Coolidge, J. L. (1936). William Elwood Byerly—In memoriam. Bulletin of the American Mathematical Society, 42, 295–298.

    Article  Google Scholar 

  14. Cummings, H. S. (1884). Dartmouth college: Sketches of the class of 1862. Washington, DC: H.I. Rothrock.

    Google Scholar 

  15. Daston, L., & Galison, P. (2007). Objectivity. New York, NY: Zone Books.

    Google Scholar 

  16. Etsy, T. C. (1931). George Daniel Olds. October 14, 1853–May 10, 1931. Bulletin of the American Mathematical Society, 37, 644.

    Article  Google Scholar 

  17. Fisher, E. B. (1918). William A. Greeson. In Grand Rapids and Kent County, Michigan: Historical account of their progress from first settlement to the present time (Vol. 2, pp. 138–139). Chicago, IL: Robert O. Law Company.

  18. Fuess, C. M. (1940). Calvin Coolidge, the man from Vermont. Boston, MA: Little, Brown, & Company.

    Google Scholar 

  19. Greenwood, J. M. (1895a). Supt. J. M. Greenwood. In Discussion of Francis W. Parker’s, the report of the committee of ten—Its use for the improvement of teachers now at work in the schools. In National Educational Association. Journal of Proceedings and Addresses, Session of the Year 1894, Held at Asbury Park (pp. 453–454). St. Paul, MN: Pioneer Press Company.

  20. Greenwood, J. M. (1895b). Supt. J. M. Greenwood. In Discussion of W.T. Harris’s, the curriculum for secondary schools. In National Educational Association. Journal of Proceedings and Addresses, Session of the Year 1894, Held at Asbury Park, New Jersey (pp. 514–515). St. Paul, MN: Pioneer Press Company.

  21. Harris, W. T. (1893). Report of the commissioner of education for the Year 1889–90. Washington, DC: Government Printing Office.

    Google Scholar 

  22. Harvard College (1891). Annual reports of the President and Treasurer of Harvard College 188990. Cambridge, MA: Harvard University Press.

  23. Hubin, D. R. (1988). The scholastic aptitude test: Its development and introduction, 1900– 1948. Ph.D., University of Oregon.

  24. Inglehart, F. C. (1919). Theodore Roosevelt: The man as I knew him. New York, NY: The Christian Herald.

    Google Scholar 

  25. Ingraham, A. (1903). Swain school lectures. Chicago, IL: The Open Court Publishing Company.

    Google Scholar 

  26. Jones, R. W. (1901). Our proposed new requirements for admission to college. The School Review: A Journal of Secondary Education, 9, 105–113.

    Google Scholar 

  27. Kevles, D. J. (1995). The Physicists: The history of a scientific community in modern America. Cambridge, MA: Harvard University Press.

    Google Scholar 

  28. Krug, E. (1964). The shaping of the American high school. New York, NY: Harper & Row.

    Google Scholar 

  29. Mallory, V. S. (1943). Mathematics for victory: An emergency course. Chicago, IL: Benj. H. Sanborn & Co.

    Google Scholar 

  30. Marché, II, J. D. (2005). Theaters of time and space: The American planetarium community, 19301970. Ph.D., Indiana University.

  31. Moore, C. (1915). William A. Greeson. In History of Michigan (Vol. 3, pp. 1586–1588). Chicago, IL: The Lewis Publishing Company.

  32. Moyer, A. E. (1992). A scientist’s voice in American culture: Simon Newcomb and the Rhetoric of scientific method. Berkeley, CA: University of California Press.

    Google Scholar 

  33. National Educational Association. (1893). Journal of Proceedings and Addresses, session of the year 1892, held at Saratoga Springs. Published by the Association, New York, NY.

  34. National Educational Association. (1894). Report of the committee of ten on secondary school studies, with the reports of the conferences arranged by the committee. New York, NY: American Book Company.

  35. Newcomb, S. (1903). The Reminiscences of an astronomer. London: Harper & Brothers.

    Google Scholar 

  36. Parker, F. W. (1895). The report of the committee of ten—Its use for the improvement of teachers now at work in the schools. In National Educational Association. Journal of Proceedings and Addresses, session of the Year 1894, held at Asbury Park (pp. 442–451). St. Paul, MN: Pioneer Press Company.

  37. Parshall, K. H. (1990). A century-old snapshot of American mathematics. The Mathematical Intelligencer, 12, 7–11.

    Article  Google Scholar 

  38. Robertson, A. (1890). The principles of double-entry bookkeeping: A plain exposition of the fundamental principles of the science. South Orange, NJ: Press of the South Orange Bulletin.

    Google Scholar 

  39. Safford, T. H. (1887). Mathematical teaching and its modern methods. Boston, MA: D.C. Heath & Co.

    Google Scholar 

  40. Salmon, L. M. (1888). Unity of standard for college entrance examinations. Academy, 3, 222–231.

    Google Scholar 

  41. Searle, A. (1902). Truman Henry Safford. The Proceedings of the American Academy of Arts and Sciences, 37, 654–656.

    Google Scholar 

  42. Seaver, E. P. (1894). Fourteenth annual report of the Superintendent of Public Schools of the City of Boston. In The annual report of the school committee of the City of Boston 1894 (pp. 3–56). Boston, MA: Rockwell and Churchill.

  43. Servos, J. (1986). Mathematics and the physical sciences in America, 1880–1930. Isis, 77, 611–629.

    Article  Google Scholar 

  44. Shepard, I. (1901). First annual report of the permanent secretary to the Board of Trustees. In National Educational Association. Journal of Proceedings and Addresses of the Fortieth Annual Meeting Held at Detroit, Michigan, July 8–12, 1901. University of Chicago Press, Chicago IL, pp. 43–50.

  45. Veblen, O. (1929). Henry Burchard Fine–In memorium. Bulletin of the American Mathematical Society, 35, 726–730.

    Article  Google Scholar 

  46. Webster, A. G. (1904). Presidential address, some practical aspects of the relations between physics and mathematics. The Physical Review, 18, 297–318.

    Google Scholar 

  47. Wentworth, G. A. (1892). Plane and spherical trigonometry. Boston, MA: Ginn & Co.

    Google Scholar 

  48. Wentworth, G. A., & Hill, T. (1888). A high school arithmetic. Boston, MA: Ginn & Company.

    Google Scholar 

  49. Yale University. (1893). Catalogue of Yale University, CXCIV year, 1893–94. New Haven, CT: Tuttle, Morehouse, & Taylor.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Andrew Fiss.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fiss, A. Problems of Abstraction: Defining an American Standard for Mathematics Education at the Turn of the Twentieth Century. Sci & Educ 21, 1185–1197 (2012). https://doi.org/10.1007/s11191-011-9413-9

Download citation

Keywords

  • Mathematics Teacher
  • Private School
  • Physical Science
  • College Entrance
  • College Entrance Examination