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ZDM

, Volume 46, Issue 4, pp 589–601 | Cite as

Teaching methods comparison in a large calculus class

  • Warren Code
  • Costanza Piccolo
  • David Kohler
  • Mark MacLean
Original Article

Abstract

We report findings from a classroom experiment in which each of two sections of the same Calculus 1 course at a North American research-focused university were subject to an “intervention” week, each for a different topic, during which a less-experienced instructor encouraged a much higher level of student engagement, promoted active learning (answering “clicker” questions, small-group discussions, worksheets) during a significant portion of class time and built on assigned pre-class tasks. The lesson content and analysis of the assessments were informed by existing research on student learning of mathematics and student interviews, though the interventions and assessments were also intended to be compatible with typical course practices in an attempt to appeal to practitioners less familiar with the literature. Our study provides an example of active learning pedagogy (including materials and assessment used) for students at this level of mathematics in a classroom of over one hundred students, and we report improved student performance—on conceptual items in particular—with a switching replication in that each section outperformed the other on the topic for which it received the intervention.

Keywords

Calculus Teaching experiment 

Notes

Acknowledgments

This work was supported by the Carl Wieman Science Education Initiative at the University of British Columbia, Canada. The authors would like to thank Carl Wieman and members of the Special Interest Group for Research in Undergraduate Mathematics Education of the Mathematical Association of America for discussions in earlier stages of our work, as well as the reviewers whose comments were extremely helpful in completing this article.

Supplementary material

11858_2014_582_MOESM1_ESM.pdf (3.2 mb)
Supplementary material 1 (PDF 3282 kb)

References

  1. Adair, J. G., Sharpe, D., & Huynh, C.-L. (1989). Hawthorne control procedures in educational experiments: A reconsideration of their use and effectiveness. Review of Educational Research, 59(2), 215–228.CrossRefGoogle Scholar
  2. Ambrose, S. A., Bridges, M. W., DiPietro, M., Lovett, M. C., & Norman, M. K. (2010). How learning works: Seven research-based principles for smart teaching. San Francisco, CA: Jossey-Bass.Google Scholar
  3. Andrews, T. M., Leonard, M. J., Colgrove, C. A., & Kalinowski, S. T. (2011). Active learning not associated with student learning in a random sample of college biology courses. CBE Life Sciences Education, 10(4), 394–405.CrossRefGoogle Scholar
  4. Asiala, M., Cottrill, J. F., Dubinsky, E., & Schwingendorf, K. E. (1997). The development of students’ graphical understanding of the derivative. The Journal of Mathematical Behavior, 16(4), 399–431.CrossRefGoogle Scholar
  5. Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.) (2003). How People Learn: Brain, Mind, Experience, and School. Psychology (Expanded.). Washington D.C.: National Academy Press.Google Scholar
  6. Bressoud, D. M., Carlson, M. P., Mesa, V., & Rasmussen, C. (2013). The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology, 44(5), 685–698.CrossRefGoogle Scholar
  7. Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378.CrossRefGoogle Scholar
  8. Crouch, C. H., & Mazur, E. (2001). Peer Instruction: Ten years of experience and results. American Journal of Physics, 69, 970.CrossRefGoogle Scholar
  9. Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved learning in a large-enrollment physics class. Science (New York, N.Y.), 332(6031), 862–864.CrossRefGoogle Scholar
  10. Dubinsky, E. D., & McDonald, M. A. (2002). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The teaching and learning of mathematics at university level (pp. 275–282). The Netherlands: Springer.CrossRefGoogle Scholar
  11. Engelke, N. (2007). Students’ understanding of related rates problems in calculus. Arizona State University.Google Scholar
  12. Epstein, J. (2013). The calculus concept inventory—measurement of the effect of teaching methodology in mathematics. Notices of the AMS, 60(8), 1018–1026.CrossRefGoogle Scholar
  13. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74.CrossRefGoogle Scholar
  14. Hora, M., & Ferrare, J. (2009). Structured observation protocol for instruction in Institutions of Higher Education (IHEs). WI: Madison.Google Scholar
  15. Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22(2), 1033–2170.CrossRefGoogle Scholar
  16. Kogan, M., & Laursen, S. L. (2013). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39(3), 1–17.Google Scholar
  17. Kwon, O. N., Rasmussen, C., & Allen, K. (2005). Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105(5), 227–239.CrossRefGoogle Scholar
  18. Martin, T. (2000). Calculus students’ ability to solve geometric related-rates problems. Mathematics Education Research Journal, 12(2), 74–91.CrossRefGoogle Scholar
  19. McGivney-Burelle, J. & Xue, F. (2013). Flipping Calculus. PRIMUS, 23(5).Google Scholar
  20. Michael, J. (2006). Where’s the evidence that active learning works? Advances in Physiology Education, 30, 159–167.CrossRefGoogle Scholar
  21. Ruiz-Primo, M. A., Briggs, D., Iverson, H., Talbot, R., & Shepard, L. A. (2011). Impact of undergraduate science course innovations on learning. Science (New York, N.Y.), 331(6022), 1269–1270.CrossRefGoogle Scholar
  22. Schoenfeld, A. H. (2004). The Math Wars. Educational Policy, 18(1), 253–286.CrossRefGoogle Scholar
  23. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2001). Experimental and quasi-experimental designs for generalized causal inference. Boston: Houghton Mifflin.Google Scholar
  24. Speer, N. M., Smith, J. P, I. I. I., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior, 29, 99–114.CrossRefGoogle Scholar
  25. Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.Google Scholar
  26. Stylianides, A. J., & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: Classroom-based interventions in mathematics education. ZDM—The International Journal on Mathematics Education, 45(3), 333–341.CrossRefGoogle Scholar
  27. Tallman, M., & Carlson, M. P. (2012). A characterization of calculus I final exams in U.S. colleges and universities. Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education (p. 217–226). Portland, OR: Portland State University.Google Scholar
  28. Tsai, F. S., Natarajan, K., Ahipasaoglu, S. D., Yuen, C., Lee, H., Cheung, N.-M., Magnanti, T. L. (2013). From boxes to bees: Active learning in freshmen calculus. In 2013 IEEE Global Engineering Education Conference (EDUCON) (pp. 59–68).Google Scholar
  29. Tziritas, M. (2011). APOS Theory as a Framework to Study the Conceptual Stages of Related Rates Problems. Analysis. Concordia University.Google Scholar
  30. Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Student performance and attitudes in courses based on APOS Theory and the ACE Teaching Cycle. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), Research in Collegiate Mathematics Education V (pp. 97–131). Providence: American Mathematical Society.Google Scholar

Copyright information

© FIZ Karlsruhe 2014

Authors and Affiliations

  • Warren Code
    • 1
  • Costanza Piccolo
    • 1
  • David Kohler
    • 1
  • Mark MacLean
    • 1
  1. 1.University of British ColumbiaVancouverCanada

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