Where Calculus and Engineering Converge: an Analysis of Curricular Change in Calculus for Engineers


Calls to increase the number of STEM graduates on a global scale have created pressure on universities to graduate higher numbers of quality engineers. In response, many engineering and mathematics departments have begun to develop variations of calculus courses specifically for engineering majors. Using a mixed methods research design, we investigated similar curricular changes in calculus that were designed to support engineering students at two large research-intensive universities in the United States. The curricular change at one university was sustained over time while the other was not, which focused our study on understanding what accounted for the curricular sustainment or termination. A finding from our study illustrates that stakeholders’ perceptions of the engineering calculus course impacted the success (or failure) of the variation over time.

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  1. 1.

    Note that all names presented in the narratives are pseudonyms.

  2. 2.

    We use singular “they/them” throughout the results section to anonymize the results and conform to APA guidelines around pronoun usage: https://apastyle.apa.org/style-grammar-guidelines/grammar/singular-they

  3. 3.

    It should be noted that the pass rates in engineering calculus are also significantly lower compared to the regular course, so this could be at least partially explained as a function of eliminating those students from the engineering sequence that would more likely underperform in the PDE course.

  4. 4.

    The mathematics chair explained that the engineering department made substantial efforts to grow their program about five years prior to our visit, and enrollment increased from about 300 to 1000 students in a relatively short amount of time. Likely as a result of this growth, the size of the engineering calculus lecture sections increased to about 90 students, while the regular calculus sections maintained smaller class sizes of about 34 students in lecture.


  1. Al-Holou, N., Bilgutay, N. M., Corleto, C., Demel, J. T., Felder, R., Frair, K., & Wells, D. L. (1999). First-year integrated curricula: design alternatives and examples. Journal of Engineering Education, 88(4), 435–448.

    Article  Google Scholar 

  2. Anthony, J. M., Hagedoorn, A. H., & Motlagh, B. S. (2001). Innovative approaches for teaching calculus to engineering students. In Proceedings of the 2001 American Society for Engineering Education Annual Conference and Exposition (pp. 6.589.1–4). American Society for Engineering Education.

  3. Aroshas, S., Verner, I. M., & Berman, A. (2003). Calculus for engineers: An applications approach. In Proceedings of the 2003 International Conference on Engineering Education, ICEE-2003, Paper No. 4607.

  4. Bressoud, D., 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.

    Article  Google Scholar 

  5. Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. G. (2015). Learning to improve: How America’s schools can get better at getting better. Harvard Education Press.

  6. Christensen, O. R. (2008). Closing the gap between formalism and application — PBL and mathematical skills in engineering. Teaching Mathematics and Its Applications, 27(3), 131–139.

    Article  Google Scholar 

  7. Chung, C. (2011). Changing engineering curriculum in the globalizing world. New Horizons in Education, 59(3), 59–70.

    Google Scholar 

  8. Colson, P., & Roegner, K. (2008). Redesigning the Calculus sequence for Engineering students. In Proceedings of Mathematical Education of Engineers Joint Conference with IM. https://www3.math.tu-berlin.de/matheon/projects/Z1.4/publications/proceedings-MEE2008-colson.pdf

  9. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Inc: Sage Publications.

    Google Scholar 

  10. Eleri, B., Prior, J., Lloyd, S., Thomas, S., & Newman-Ford, L. (2007). Engineering more engineers—bridging the mathematics and careers advice gap. Engineering Education, 2(1), 23–32.

    Article  Google Scholar 

  11. Froyd, J., Layne, J., & Watson, K. (2006). Issues regarding change in engineering education. In Proceedings of Frontiers in Education 36th Annual Conference (pp. 3–8). https://doi.org/10.1109/FIE.2006.322595.

  12. Graham, R. H. (2012). Achieving excellence in engineering education: The ingredients of successful change. London: Royal Academy of Engineering.

    Google Scholar 

  13. Hagman, J. E. (2019). The 8th characteristic for successful calculus programs: Diversity, equity, & inclusion practices. PRIMUS, 1–21.

  14. Hensel, R., Sigler, J., & Lowery, A. (2008). Breaking the cycle of calculus failure: Models of early math intervention to enhance engineering retention. In Proceedings of the 2008 American Society for Engineering Education Annual Conference and Exposition, Pittsburgh, PA (pp. 22–25).

  15. Horwitz, A. L. A. N., & Ebrahimpour, A. R. Y. A. (2002). Engineering applications in differential and integral calculus. International Journal of Engineering Education, 18(1), 78–88.

    Google Scholar 

  16. Klingbeil, N. W., Mercer, R. E., Rattan, K. S., Raymer, M. L., & Reynolds, D. B. (2004). Rethinking engineering mathematics education: A model for increased retention, motivation and success in engineering. In Proceedings of the 2004 American Society for Engineering Education Annual Conference and Exposition (pp. 1–9). American Society for Engineering Education.

  17. Laoulache, R.N., Pendergrass, N.A., Crawford, R.J., & Kowalczyk, R.E. (2001). Integrating engineering courses with calculus and physics to motivate learning of fundamental concepts. In 31st Annual Frontiers in Education Conference. Impact on Engineering and Science Education. Conference Proceedings (Cat. No.01CH37193) (Vol. 2, pp. F1B-13).

  18. Lattuca, L. R., & Pollard, J. R. (2016). Toward a conceptualization of faculty decision-making about curricular and instructional change. In Organizing academic work in higher education: Teaching, learning and identities (pp. 89-108). Taylor and Francis Inc.

  19. Lattuca, L. R., & Stark, J. S. (2009). Curriculum: An academic plan. In Shaping the college curriculum: Academic plans in action (pp. 1-22). John Wiley & Sons.

  20. Loch, B., & Lamborn, J. (2016). How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources. International Journal of Mathematical Education in Science and Technology, 47(1), 29–44.

    Article  Google Scholar 

  21. Lowery, A., Kane, S., Kane, V., Hensel, R., & Ganser, G. (2010). Joint math-engineering projects to facilitate calculus success in first year students. In American Society for Engineering Education (pp. 15.820.10-15.820.12).

  22. Marra, R. M., Rodgers, K. A., Shen, D., & Bogue, B. (2012). Leaving engineering: a multi-year single institution study. Journal of Engineering Education, 101(1), 6–27.

    Article  Google Scholar 

  23. Martinez, A., Gehrtz, J., Rasmussen, C., LaTona-Tequida, T., & Vroom, K. (2020). Promoting instructor growth and providing resources: Course coordinator orientations toward their work. In S. S. Karunakaran, Z. Reed, & A. Higgins (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. Boston, MA. (pp. 390–397). http://sigmaa.maa.org/rume/RUME23.pdf

  24. Merton, P., Froyd, J. E., Clark, M. C., & Richardson, J. (2009). A case study of relationships between organizational culture and curricular change in engineering education. Innovative Higher Education, 34(4), 219–233.

    Article  Google Scholar 

  25. Neubert, J., Khavanin, M., Worley, D., & Kaabouch, N. (2014). Minimizing the institutional change required to augment calculus with real-world engineering problems. PRIMUS, 24(4), 319–334.

    Article  Google Scholar 

  26. Nguyen, D. Q. (1998). The essential skills and attributes of an engineer: a comparative study of academics, industry personnel and engineering students. Global Journal of Engineering Education, 2(1), 65–75.

    Google Scholar 

  27. Nortvedt, G. A., & Siqveland, A. (2019). Are beginning calculus and engineering students adequately prepared for higher education? An assessment of students’ basic mathematical knowledge. International Journal of Mathematical Education in Science and Technology, 50(3), 325–343.

    Article  Google Scholar 

  28. Ohland, M. W., Yuhasz, A. G., & Sill, B. L. (2004). Identifying and removing a calculus prerequisite as a bottleneck in Clemson’s general engineering curriculum. Journal of Engineering Education, 93(3), 253–257.

    Article  Google Scholar 

  29. Quintanilla, J., D’Souza, N., Lui, J., & Mirshams, R. (2007). Integration of engineering concepts in freshman calculus. In Proceedings of the 2007 American Society for Engineering Education Annual Conference and Exposition (pp. 2007–1878). American Society for Engineering Education.

  30. Rasmussen, C., Apkarian, N., Hagman, J. E., Johnson, E., Larsen, S., & Bressoud, D. (2019). Brief report: characteristics of precalculus through calculus 2 programs: insights from a national census survey. Journal for Research in Mathematics Education, 50(1), 98–111.

  31. Rasmussen, C., & Ellis, J. (2013). Students who switch out of calculus and the reasons they leave. In Martinez, M. & Castro Superfine, A. (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 457–464). University of Illinois at Chicago.

  32. Rasmussen, C., & Ellis, J. (2015). Calculus coordination at PhD-granting universities: More than just using the same syllabus, textbook, and final exam. In Bressoud, B., Mesa, V., & Rasmussen, C. (Eds.), Insights and recommendations from the MAA national study of college calculus, 107-116.

  33. Rasmussen, C., Ellis, J., Zazkis, D., & Bressoud, D. (2014). Features of successful calculus programs at five doctoral degree granting institutions. In Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA36 (Vol. 5, pp. 33–40). PME.

  34. Seymour, E., & Hewitt, N. M. (1997). Talking about leaving: Why undergraduates leave the sciences. Westview.

  35. Steen, L. A. (Ed.) (1987). Calculus for a new century: A pump, not a filter. MAA notes, number 8. The Mathematical Association of America.

  36. Van Biesen, L. P., Rahier, H., Vanherzeele, H., Willem, R., Hubin, A., Veretennicoff, I., et al. (2009). Engineering skills education: the bachelor of engineering programme of the ‘Vrije Universiteit Brussel’ as a case study. European Journal of Engineering Education, 34(3), 217–228.

    Article  Google Scholar 

  37. Varsavsky, C. (1995). The design of the mathematics curriculum for engineers: a joint venture of the mathematics department and the engineering faculty. European Journal of Engineering Education, 20(3), 341–345.

    Article  Google Scholar 

  38. Voigt, M., Apkarian, N., Rasmussen, C., & the Progress through Calculus Team. (2020). Undergraduate course variations in precalculus through calculus 2. International Journal of Mathematical Education in Science and Technology, 51(6), 858–875. https://doi.org/10.1080/0020739X.2019.1636148.

    Article  Google Scholar 

  39. Willcox, K., & Bounova, G. (2004). Mathematics in engineering: Identifying, enhancing and linking the implicit mathematics curriculum. Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition, Session (No. 2465). American Society for Engineering Education.

  40. Wilson, E. A., Rudy, D., Elam, C., Pfeifle, A., & Straus, R. (2012). Preventing curriculum drift: sustaining change and building upon innovation. Annals of Behavioral Science and Medical Education, 18(2), 23–26.

    Article  Google Scholar 

  41. Yin, R. K. (2003). Qualitative case study methodology: study design and implementation of novice research. The Qualitative Report, 13(4), 544–559.

    Google Scholar 

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Correspondence to Brittney Ellis.

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Ellis, B., Larsen, S., Voigt, M. et al. Where Calculus and Engineering Converge: an Analysis of Curricular Change in Calculus for Engineers. Int. J. Res. Undergrad. Math. Ed. (2021). https://doi.org/10.1007/s40753-020-00130-9

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  • Calculus
  • Engineering
  • Course variations
  • Curricular change