Mathematics Education pp 135-145 | Cite as

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

- 895 Downloads

## Abstract

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.

## Keywords

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

### Acknowledgments

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.

## References

- Andrews-Larson, C., Wawro, M., & Zandieh, M. (2016).
*A hypothetical learning trajectory for conceptualizing matrices as linear transformations.*Manuscript submitted for publication.Google Scholar - 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 - 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 - Freudenthal, H. (1991).
*Revisiting mathematics education*. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar - 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 - 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 - Mazur, E. (2009). Farewell, lecture?
*Science, 323*, 50–51.CrossRefGoogle Scholar - McDuffie, A. R. (2001). Flying through graphs: An introduction to graph theory.
*Mathematics Teacher, 94*(8), 680–683.Google Scholar - 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 - 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 - Plaxco, D., & Wawro, M. (2015). Analyzing student understanding in linear algebra through mathematical activity.
*Journal of Mathematical Behavior, 38*, 87–100.CrossRefGoogle Scholar - Rasmussen, C., & Kwon, O. N. (2007). An inquiry oriented approach to undergraduate mathematics.
*Journal of Mathematical Behavior, 26*, 189–194.CrossRefGoogle Scholar - Rasmussen, C., Wawro, M., & Zandieh, M. (2015). Examining individual and collective level mathematical progress.
*Educational Studies in Mathematics, 88*(2), 259–281.CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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