Using Analytics to Support Instructor Reflection on Student Participation in a Discourse-Focused Undergraduate Mathematics Classroom

  • Daniel L. ReinholzEmail author
  • Kenneth Bradfield
  • Naneh Apkarian


This paper describes a method for using instructional analytics to support changes in teaching practice. The study took place in a discourse-focused undergraduate mathematics classroom taught by an experienced instructor. Using the classroom observation tool EQUIP and social network surveys, we generated quantitative data on patterns of student participation in this classroom that were presented to the instructor at the end of the semester. Our analysis focuses on how the instructor made sense of these analytics and ultimately changed his teaching practices in a future semester. This paper provides insight into how three data sources can be triangulated—classroom participation, student experiences, and teacher perspective—to better understand discourse-based participation in undergraduate mathematics. We also discuss the implications of using this methodology for faculty professional development.


Instructor/lecturer professional development Classroom interaction and discourse Postsecondary Mixed methods (quantitative and qualitative) 


Compliance with Ethical Standards

Conflict of Interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18(3), 439–477. Scholar
  2. Cohen, E. G., & Lotan, R. A. (1997). Working for equity in heterogeneous classrooms: Sociological theory into practice. New York: Teachers College Press.Google Scholar
  3. Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483.Google Scholar
  4. Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 23, 8410–8415. Scholar
  5. Grunspan, D. Z., Wiggins, B. L., & Goodreau, S. M. (2014). Understanding classrooms through social network analysis: A primer for social network analysis in education research. CBE-Life Sciences Education, 13(2), 167–178. Scholar
  6. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.Google Scholar
  7. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81–116.Google Scholar
  8. Ingram, J., & Elliott, V. (2014). Turn taking and ‘wait time’ in classroom interactions. Journal of Pragmatics, 62, 1–12. Scholar
  9. Kogan, M., & Laursen, S. L. (2014). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39(3), 183–199. Scholar
  10. Larsen, S., Johnson, E., & Bartlo, J. (2013). Designing and scaling up an innovation in abstract algebra. The Journal of Mathematical Behavior, 32(4), 693–711. Scholar
  11. Lombrozo, T. (2006). The structure and function of explanations. Trends in Cognitive Sciences, 10(10), 464–470. Scholar
  12. Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454–482.Google Scholar
  13. McAfee, M. (2014). The kinesiology of race. Harvard Educational Review, 84(4), 468–491. Scholar
  14. McGee, E. O., & Martin, D. B. (2011). “You would not believe what I have to go through to prove my intellectual value!” stereotype management among academically successful black mathematics and engineering students. American Educational Research Journal, 48(6), 1347–1389. Scholar
  15. Mehan, H. (1979). “What time is it, Denise?”: Asking known information questions in classroom discourse. Theory Into Practice, 18(4), 285–294.Google Scholar
  16. Michaels, S., O’Connor, M. C., Hall, M. W., & Resnick, L. B. (2010). Accountable talk® sourcebook. Pittsburgh: Institute for Learning.Google Scholar
  17. Rasmussen, C., & Kwon, O. (2007). An inquiry-oriented approach to undergraduate mathematics. The Journal of Mathematical Behavior, 26(3), 189–194.Google Scholar
  18. Reinholz, D. L. (2015). Peer-assisted reflection: A design-based intervention for improving success in calculus. International Journal of Research in Undergraduate Mathematics Education, 1(2), 234–267. Scholar
  19. Reinholz, D. L., & Shah, N. (2018). Equity analytics: A methodological approach for quantifying participation patterns in mathematics classroom discourse. Journal for Research in Mathematics Education, 49(2), 140–177.Google Scholar
  20. Rowe, M. B. (1986). Wait time: Slowing down may be a way of speeding up! Journal of Teacher Education, 37(1), 43–50.Google Scholar
  21. Sadker, D., Sadker, M., & Zittleman, K. R. (2009). Still failing at fairness: How gender bias cheats girls and boys in school and what we can do about it. New York: Simon and Schuster.Google Scholar
  22. Speer, N. M., & Wagner, J. F. (2009). Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. Journal for Research in Mathematics Education, 40(5), 530–562.Google Scholar
  23. Stinson, D. W. (2008). Negotiating sociocultural discourses: The counter-storytelling of academically (and mathematically) successful African American male students. American Educational Research Journal, 45(4), 975–1010.Google Scholar
  24. Wawro, M., Rasmussen, C., Zandieh, M., Sweeney, G. F., & Larson, C. (2012). An inquiry-oriented approach to span and linear Independence: The case of the magic carpet ride sequence. PRIMUS, 22(8), 577–599. Scholar
  25. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsSan Diego State UniversitySan DiegoUSA
  2. 2.Department of Teacher Education, College of EducationMichigan State UniversityEast LansingUSA

Personalised recommendations