Abstract
In this study, we sought to identify how feedback about classroom observations affected novice university mathematics instructors’ (UMIs) teaching practices. Specifically, we examined how a Red–Yellow–Green feedback system (RYG feedback) affected graduate student instructor (GSI) scores on an observation protocol (GSIOP). The protocol was developed specifically for this population, and both the GSIOP and RYG feedback were used within a peer mentoring program for GSIs, wherein novice GSIs were mentored by more experienced GSIs. Mentors observed novices’ classrooms using the GSIOP and provided RYG feedback as part of observation–feedback cycles. We analyzed 100 sets of scores, each collected over the course of a semester containing on average three observation–feedback cycles. Analyzing the semester-long datasets longitudinally provided insight into what types of feedback informed and influenced observed teaching. After qualitatively coding the feedback provided to the GSIs by their mentors along multiple dimensions, we found certain forms of feedback were more influential for observable changes in GSIs’ teaching. For example, pedagogical feedback that included contextualization (context and focal events) demonstrated a more positive change in GSIOP score than feedback that lacked contextualization. Our results suggest that contextual formative feedback has a positive change to student-focused and teacher-focused observations.
Similar content being viewed by others
Notes
GSI was used instead of TA (Teaching Assistant) because GSI references graduate students who are UMIs with the responsibilities of instructors of record.
GSIOP is copyrighted by Bowling Green State University (2018). All rights reserved. Rogers and Yee (2018b).
Supported by Collaborative National Science Foundation Grants (NSF DUE 1544342, 1544346, 1725295, 1725230 and 1725264).
References
Alsina, C. (2001). Why the professor must be a stimulating teacher. In D. Holton & M. Artigue (Eds.), The teaching and learning of mathematics at university level: An ICMI study (Vol. 7). Berlin: Springer.
Belnap, J. K., & Allred, K. (2009). Mathematics teaching assistants: Their instructional involvement and preparation opportunities. In L. L. B. Border (Ed.), Studies in graduate and professional student development (pp. 11–38). Stillwater, OK: New Forums Press, Inc.
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74.
Brawdy, P., & Byra, M. (1995). Supervision of preservice teachers during an early field teaching experience. The Physical Educator, 52(3).
Bressoud, D., Mesa, V., & Rasmussen, C. (Eds.). (2015). Insights and recommendations from the MAA national study of college calculus. Washington, DC: Mathematical Association of America Press.
Cannon, M. D., & Witherspoon, R. (2005). Actionable feedback: Unlocking the power of learning and performance improvement. Academy of Management Perspectives, 19(2), 120–134.
Creswell, J. W., & Clark, V. L. P. (2017). Designing and conducting mixed methods research. London: Sage Publications.
Ellis, J. (2014). Preparing future professors: Highlighting the importance of graduate student professional development programs in calculus instruction. In Proceedings of the 37th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 9–16). Vancouver, BC: PME.
Ellis, J. (2015). Professional development of graduate students involved in the teaching of calculus I. In D. Bressoud, V. Mesa, & C. Rasmussen (Eds.), Insights and recommendations from the MAA national study of college calculus. MAA notes (pp 121–128).Washington, DC: Mathematical Association of America.
Ellis, J., Deshler, J. & Speer, N. (2016a). Supporting institutional change: A two-pronged approach related to graduate teaching assistant professional development. In T. Fukawa-Connelly, N. Infante, M. Wawro, and S. Brown (Eds.), Proceedings of the 19th annual conference on research in undergraduate mathematics education. Pittsburgh, PA.
Ellis, J., Deshler, J. & Speer, N. (2016b). How do mathematics departments evaluate their graduate teaching assistant professional development programs? International Group for the Psychology of Mathematics Education Annual Conference, Szeged, Hungary.
Gamlem, S. M., & Smith, K. (2013). Student perceptions of classroom feedback. Assessment in Education: Principles, Policy & Practice, 20(2), 150–169.
Gibbons, L. K., & Cobb, P. (2017). Focusing on teacher learning opportunities to identify potentially productive coaching activities. Journal of Teacher Education, 68(4), 411–425.
Gibbons, L. K., Kazemi, E., & Lewis, R. M. (2017). Developing collective capacity to improve mathematics instruction: Coaching as a lever for school-wide improvement. The Journal of Mathematical Behavior, 46, 231–250.
Gleason, J., Livers, S., & Zelkowski, J. (2017). Mathematics classroom observation protocol for practices (MCOP2): A validation study. Investigations in Mathematics Learning, 9(3), 111–129.
Goodwin, C., & Duranti, A. (1992). Rethinking context: Language as an interactive phenomenon. Cambridge: Cambridge University Press.
Harbour, K., & Livers, S. (2018). Using coaching cycles to transfer and sustain effective instructional practices. In Proceedings from 40th conference of the North American chapter of the psychology of mathematics education (PME-NA). Greenville, SC.
Harlen, W., & James, M. (1997). Assessment and learning: Differences and relationships between formative and summative assessment. Assessment in Education: Principles, Policy & Practice, 4(3), 365–379.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.
Hollingsworth, H., & Clarke, D. (2017). Video as a tool for focusing teacher self-reflection: Supporting and provoking teacher learning. Journal of Mathematics Teacher Education, 20(5), 457–475.
Holton, D., & Artigue, M. (Eds.). (2001). The teaching and learning of mathematics at university level: An ICMI study (Vol. 7). Berlin: Springer.
Johnson, S. M., & Kardos, S. M. (2002). Keeping new teachers in mind. Educational Leadership, 59(6), 12–16.
Kastberg, S. E., Lischka, A. E., & Hillman, S. L. (2018). Characterizing mathematics teacher educators’ written feedback to prospective teachers. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-018-9414-6.
Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), 254.
Kluger, A. N., & DeNisi, A. (1998). Feedback interventions: Toward the understanding of a double-edged sword. Current Directions in Psychological Science, 7(3), 67–72.
Laursen, S. L., & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 5, 129–146.
Lutzer, D. J., Rodi, S. B., Kirkman, E. E., & Maxwell, J. W. (2007). Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2005 CBMS survey. Providence, MA: American Mathematical Society.
Moir, E. (2005). Launching the next generation of teachers. In H. Portner (Ed.), Teacher mentoring and induction: The state of the art and beyond (pp. 59–73). Thousand Oaks: Corwin Press.
Nilsson, P., & Ryve, A. (2010). Focal event, contextualization, and effective communication in the classroom. Educational Studies in Mathematics, 74(3), 241–258.
Portner, H. (2005). Teacher mentoring and induction: The state of the art and beyond. Thousand Oaks: Corwin Press.
Reinholz, D. (2016). The assessment cycle: A model for learning through peer assessment. Assessment & Evaluation in Higher Education, 41(2), 301–315.
Reinholz, D. L. (2017). Not-so-critical friends: Graduate student instructors and peer feedback. International Journal for the Scholarship of Teaching and Learning, 11(2), n2.
Rogers, K. C., & Steele, M. D. (2016). Graduate teaching assistants’ enactment of reasoning-and-proving tasks in a content course for elementary teachers. Journal for Research in Mathematics Education, 47, 372–419.
Rogers, K. C., & Yee, S. P. (2018a). Peer mentoring mathematics graduate student instructors: Discussion topics and concerns. In Proceedings from 21st conference of the research in undergraduate mathematics education (RUME). San Diego, CA.
Rogers, K. C., & Yee, S. (2018b). GSIOP: Graduate student instructor observation Protocol: Retrieved from http://personal.bgsu.edu/~kcroger/research.html.
Rogers, K. C., Petrulis R. A., Yee, S. P., & Deshler, J. (2019). Mathematics Graduate Student Instructor Observation Protocol (GSIOP): Development and Validation Study. International Journal of Research in Undergraduate Mathematics Education (IJRUME). https://doi.org/10.1007/s40753-019-00106-4.
Roller, S. A. (2016). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education, 19(5), 477–498.
Sawada, D., Piburn, M. D., Judson, E., Turley, J., Falconer, K., Benford, R., & Bloom, I. (2002). Measuring reform practices in science and mathematics classrooms: The reformed teaching observation protocol. School Science and Mathematics, 102(6), 245–253.
Seymour, E. (2005). Partners in innovation: Teaching assistants in college science courses. Lanham, MD: Rowman & Littlefield.
Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153–189.
Siedentop, D. (1981). The Ohio State University supervision research program summary report. Journal of Teaching in Physical Education, 1(s1), 30–38.
Speer, N. M., & Murphy, T. J. (2009). Research on graduate students as teachers of undergraduate mathematics. In L. L. B. Border (Ed.), Studies in graduate and professional student development (pp. xiii–xvi). Stillwater, OK: New Forums Press Inc.
Speer, N. M., Gutmann, T., & Murphy, T. J. (2005). Mathematics teaching assistant preparation and development. College Teaching, 53(2), 75–80.
White, S. (2007). Investigating effective feedback practices for pre-service teacher education students on practicum. Teaching Education, 18(4), 299–311.
Wiliam, D., & Black, P. (1996). Meanings and consequences: A basis for distinguishing formative and summative functions of assessment? British Educational Research Journal, 22(5), 537–548.
Yee, S.P., & Rogers, K. C. (2017). Mentor professional development for mathematics graduate student instructors. In Proceedings from 20th conference on research in undergraduate mathematics education (RUME, pp. 1026–1034). San Diego, CA.
Acknowledgments
This work was supported by Collaborative IUSE NSF grants (#1544342 & 1544346; #1725264, 1725295, & 1725230). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We also want to thank the University of South Carolina Reading and Research Group in Mathematics Education for providing insightful feedback.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Yee, S., Deshler, J., Rogers, K.C. et al. Bridging the gap between observation protocols and formative feedback. J Math Teacher Educ 25, 217–245 (2022). https://doi.org/10.1007/s10857-020-09485-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-020-09485-x