Renewal in Collegiate Mathematics Education

Learning from Research
  • David A. Smith


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It is to be hoped that the near future will bring reforms in the mathematical teaching in this country. We are in sad need of them. From nearly all of our colleges and universities comes the loud complaint of inefficient preparation on the part of students applying for admission; from the high schools comes the same doleful cry. Educators who have studied the work of [foreign] schools declare that our results in elementary iristruction are far inferior.


Active Experimentation Learning Cycle Mathematical Association Slope Field Calculus Instruction 
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  1. 1.
    F. Cajori, The Teaching and History of Mathematics in the United States,1890. Cited by W Mueller in “The History of Calculus Reform,” to appear.Google Scholar
  2. 2.
    A. W Chickering and Z. F. Gamson (eds.), Applying the Seven Principles of Good Practice in Undergraduate Education, in New Directions for Teaching and Learning No. 47 ( Jossey—Bass, San Francisco, 1991 ).Google Scholar
  3. 3.
    A. H. Schoenfeld, “When Good Teaching Leads to Bad Results: The Disasters of ‘Well-Taught’ Mathematics Courses,” Educational Psychologist 23 (1988): 145–166.CrossRefGoogle Scholar
  4. 4.
    A. Solow (ed.), Preparing for a New Calculus, MAA Notes No. 36 ( Mathematical Association of America, Washington, DC, 1994 ).Google Scholar
  5. 5.
    A. C. Tucker and J. R. C. Leitzel (eds.), Assessing Calculus Reform Efforts ( Mathematical Association of America, Washington, DC, 1995 ).Google Scholar
  6. 6.
    A. W. Roberts (ed.), Calculus: The Dynamics of Change, MAA Notes No. 39 ( Mathematical Association of America, Washington, DC, 1996 ).Google Scholar
  7. 7.
    A. P. Camevale, L. J. Gainer, and A. S. Meltzer, Workplace Basics: The Skills Employers Want (The American Society for Training and Development and the U.S. Department of Labor, Washington, DC, 1988 ).Google Scholar
  8. 8.
    Alverno Magazine, May 1992. Also see “Alvemo’s Eight Abilities” ( Milwaukee, WI, March 17, 1999 ), Scholar
  9. 9.
    Evergreen State College, “We believe” (Olympia, WA, October 5, 1998), http:// Scholar
  10. 10.
    R. E. Boyatzis, S. S. Cowen, and D. A. Kolb, Innovation in Professional Education: Steps on a Journey from Teaching to Learning ( Jossey-Bass, San Francisco, 1995 ).Google Scholar
  11. 11.
    Accreditation Board for Engineering and Technology, ABET Engineering Criteria 2000 (Baltimore, February 22, 1999),–00_Criteria.htm#EC2000.Google Scholar
  12. 12.
    Pew Higher Education Roundtable, “A Teachable Moment,” Policy Perspectives 8(1)(June 1998):1–10 (Institute for Research on Higher Education, Philadelphia).Google Scholar
  13. 13.
    R. M. Diamond, “Broad Curriculum Reform is Needed if Students are to Master Core Skills,” The Chronicle of Higher Education (August 1, 1997 ): B7.Google Scholar
  14. 14.
    R. M. Diamond, Designing and Assessing Courses and Curricula ( Jossey-Bass, San Francisco, 1997 ).Google Scholar
  15. 15.
    D. A. Kolb, I. M. Rubin, and J. M. McIntyre (eds.), Organizational Psychology: Readings on Human Behavior in Organizations, 4th ed. ( Prentice-Hall, Englewood Cliffs, NJ, 1984 ).Google Scholar
  16. 16.
    J. E. Zull, “The Brain, The Body, Learning, and Teaching,” National Teaching & Learning Forum 7 (3) (1998): 1–5.CrossRefGoogle Scholar
  17. 17.
    M. S. Gazzaniga, Nature’s Mind: The Biological Roots of Thinking, Emotions, Sexuality, Language, and Intelligence ( Basic Books, New York, 1992 ).Google Scholar
  18. 18.
    J. LeDoux, The Emotional Brain: The Mysterious Underpinnings of Emotional Life ( Simon & Schuster, New York, 1996 ).Google Scholar
  19. 19.
    C. Hannaford, Smart Moves: Why Learning is Not All in Your Head ( Great Ocean Publishers, Arlington, VA, 1995 ).Google Scholar
  20. 20.
    A. R. Damasio, Descartes’ Error: Emotion, Reason, and the Human Brain, ( Putnam’s Sons, New York, 1994 ).Google Scholar
  21. 21.
    G. M. Edelman, Bright Air, Brilliant Fire: On the Matter of the Mind ( Basic Books, New York, 1992 ).Google Scholar
  22. 22.
    R. Sylwester, A Celebration of Neurons: An Educator’s Guide to the Human Brain ( Association for Supervision and Curriculum Development, Alexandria, VA, 1995 ).Google Scholar
  23. 23.
    G. Harel, “Two Dual Assertions: The First on Learning and the Second on Teaching (or Vice Versa),” American Mathematical Monthly 105(1998):497–507.Google Scholar
  24. 24.
    D. A. Smith and L. C. Moore, Calculus: Modeling and Application ( Houghton Mifflin, Boston, 1996 ).Google Scholar
  25. 25.
    N. L. Hagelgans, B. E. Reynolds, K. E. Schwingendorf, D. Vidakovic, E. Dubinsky, M. Shahin, and G. J. Wimbish, Jr., A Practical Guide to Cooperative Learning in Collegiate Mathematics, MAA Notes No. 37 ( Mathematical Association of America, Washington, DC, 1995 ).Google Scholar
  26. 26.
    J. Bookman and C. P. Friedman, “Student Attitudes and Calculus Reform,” School Science and Google Scholar

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© Springer Science+Business Media New York 2000

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  • David A. Smith

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