Finding Synergy Among Research, Teaching, and Service: An Example from Mathematics Education Research

  • Megan WawroEmail author
Part of the Association for Women in Mathematics Series book series (AWMS, volume 7)


Being a faculty member in higher education involves the balance and integration of various roles and demands. In this chapter I present my own story, as a mathematics education researcher in the teaching and learning of undergraduate mathematics focusing on linear algebra. Using my experience as an example, I describe how synergy among research, teaching, and service can impact career goals and institutional needs.


Research in undergraduate mathematics education RUME Linear algebra Research Teaching and service 



The research discussed in this chapter is based upon work supported by the National Science Foundation under Collaborative Grant numbers DUE-1245673. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.


  1. Andrews-Larson, C., Wawro, M., & Zandieh, M. (2016). A hypothetical learning trajectory for conceptualizing matrices as linear transformations. Manuscript submitted for publication.Google Scholar
  2. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of development research. Educational Psychologist, 31(3/4), 175–190.CrossRefGoogle Scholar
  3. Dorier, J.-L. (1998). The role of formalism in the teaching of the theory of vector spaces. Linear Algebra and Its Applications, 275(27), 141–160.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  5. Laursen, S. L., Hassi, M. L., Kogan, M., & Weston, T. J. (2014). Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study. Journal for Research in Mathematics Education, 45(4), 406–418.CrossRefGoogle Scholar
  6. Lockwood, E. (2014). Both answers make sense! Using sets of outcomes to reconcile differing answers in counting problems. The Mathematics Teacher, 108(4), 296–301.CrossRefGoogle Scholar
  7. Mazur, E. (2009). Farewell, lecture? Science, 323, 50–51.CrossRefGoogle Scholar
  8. McDuffie, A. R. (2001). Flying through graphs: An introduction to graph theory. Mathematics Teacher, 94(8), 680–683.Google Scholar
  9. National Research Council. (2012). Discipline-based education research: Understanding and improving learning in undergraduate science and engineering. In: S. R. Singer, N. R. Nielsen, & H. A. Schweingruber, (Eds.). Committee on the Status, Contributions, and Future Direction of Discipline Based Education Research. Board on Science Education, Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press.Google Scholar
  10. Oehrtman, M., Carlson, M., & Thompson, P. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 27–42). Washington, DC: The Mathematical Association of America.CrossRefGoogle Scholar
  11. Plaxco, D., & Wawro, M. (2015). Analyzing student understanding in linear algebra through mathematical activity. Journal of Mathematical Behavior, 38, 87–100.CrossRefGoogle Scholar
  12. Rasmussen, C., & Kwon, O. N. (2007). An inquiry oriented approach to undergraduate mathematics. Journal of Mathematical Behavior, 26, 189–194.CrossRefGoogle Scholar
  13. Rasmussen, C., Wawro, M., & Zandieh, M. (2015). Examining individual and collective level mathematical progress. Educational Studies in Mathematics, 88(2), 259–281.CrossRefGoogle Scholar
  14. Shaughnessy, J. M. (2003). Research on students’ understandings of probability. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 216–226). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  15. Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle- grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247–280.Google Scholar
  16. Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear algebra. ZDM The International Journal on Mathematics Education, 46(3), 1–18.CrossRefGoogle Scholar
  17. Wawro, M. (2015). Reasoning about solutions in linear algebra: The case of Abraham and the Invertible Matrix Theorem. International Journal of Research in Undergraduate Mathematics Education, 1(3), 315–338.CrossRefGoogle Scholar
  18. Wawro, M., Rasmussen, C., Zandieh, M., Sweeney, G., & Larson, C. (2012). An inquiry-oriented approach to span and linear independence: The case of the Magic Carpet Ride sequence. PRIMUS Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(8), 577–599.Google Scholar
  19. Wawro, M., Rasmussen, C., Zandieh, M., & Larson, C. (2013). Design research within undergraduate mathematics education: An example from introductory linear algebra. In T. Plomp, & N. Nieveen (Eds.), Educational design research – Part B: Illustrative cases (pp. 905–925). Enschede, the Netherlands: SLO.Google Scholar
  20. Zandieh, M., Wawro, M., & Rasmussen, C. (2016). Inquiry as participating in the mathematical practice of symbolizing: An example from linear algebra. PRIMUS. doi:  10.1080/10511970.2016.1199618.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsVirginia TechBlacksburgUSA

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