Vol. 30 No. 1 (2021)
Articles

Teacher Candidates’ Reflections on Responding to Errors: Exploring Their Vision and Goals

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  • Foster Graif,
  • Erin E. Baldinger,
  • Matthew P. Campbell
Foster Graif
University of Minnesota
Erin E. Baldinger
University of Minnesota
Bio
Matthew P. Campbell
West Virginia University
Bio

Published 2021-08-17

Keywords

  • responding to errors,
  • teacher candidates,
  • video elicitation interviews,
  • reflecting on practice

Copyright (c) 2021 Foster Graif, Erin E. Baldinger, Matthew P. Campbell

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Abstract

Responding to student errors is a complex practice that connects teachers’ vision and goals around students, mathematics, and teaching. We explore teacher candidates’ (TCs) reflections on responding to errors during rehearsals of whole-class discussion to gain insight into the vision and goals that might influence their thinking. We discuss five TCs’ assessment of their practice based on video-elicitation interviews to infer their vision around responding to errors and their associated goals for practice. In particular, we attend to how their vision and goals interact in shaping TCs’ reflections on practice. This work offers implications for considering TC development and support.

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References

  1. Baldinger, E. E., Campbell, M. P., & Graif, F. (2020). Sorting out definitions. Mathematics Teacher: Learning and Teaching PK-12, 113(3), 209–215. https://doi.org/10.5951/MTLT.2019.0121
  2. Baldinger, E. E., Selling, S. K., & Virmani, R. (2016). Supporting novice teachers in leading discussions that reach a mathematical point: Defining and clarifying mathematical ideas. Mathematics Teacher Educator, 5(1), 8–28. http://doi.org/10.5951/mathteaceduc.5.1.0008
  3. Boerst, T. A., Sleep, L., Loewenberg Ball, D., & Bass, H. (2011). Preparing teachers to lead mathematics discussions. Teachers College Record, 113(12), 2844–2877.
  4. Borasi, R. (1994). Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 25(2), 166–208. https://doi.org/10.2307/749507
  5. Bray, W. S. (2011). A collective case study of the influence of teachers’ beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics Education, 42(1), 2–38. https://doi.org/10.5951/jresematheduc.42.1.0002
  6. Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational Studies in Mathematics, 85(2), 221–239. https://doi.org/10.1007/s10649-013-9507-1
  7. Campbell, M. P., Baldinger, E. E., & Graif, F. (2020). Representing student voice in an approximation of practice: Using planted errors in coached rehearsals to support teacher candidate learning. Mathematics Teacher Educator, 9(1), 23–49. https://doi.org/https://doi.org/10.5951/MTE.2020.0005
  8. Ghousseini, H., Beasley, H., & Lord, S. (2015). Investigating the potential of guided practice with an enactment tool for supporting adaptive performance. Journal of the Learning Sciences, 24(3), 461–497. https://doi.org/10.1080/10508406.2015.1057339
  9. Goldman, R., Pea, R., Barron, B., & Derry, S. J. (Eds.). (2007). Video research in the learning sciences. Routledge. http://dx.doi.org/10.4324/9780203877258
  10. Grossman, P. L., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.
  11. Grossman, P. L., Smagorinsky, P., & Valencia, S. (1999). Appropriating tools for teaching English: A theoretical framework for research on learning to teach. American Journal of Education, 108(1), 1–29. https://doi.org/10.1086/444230
  12. Grossman, P. L., Valencia, S. W., Evans, K., Thompson, C., Martin, S., & Place, N. (2000). Transitions into teaching: Learning to teach writing in teacher education and beyond. Journal of Literacy Research, 32(4), 631–662. https://doi.org/10.1080/10862960009548098
  13. Hammerness, K. (2001). Teachers’ visions: The role of personal ideals in school reform. Journal of Educational Change, 2(2), 143–163. https://doi.org/10.1023/A:1017961615264
  14. Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM - Mathematics Education, 48(1), 185–197. https://doi.org/10.1007/s11858-015-0717-0
  15. Leont’ev, A. N. (1981). Problems of the development of the mind. Progress.
  16. Miles, M. B., Huberman, A. M., & Saldaña, J. (2013). Qualitative data analysis: A methods sourcebook (3rd ed.). Sage Publications.
  17. Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584–635. https://doi.org/10.5951/jresematheduc.45.5.0584
  18. Munter, C., & Correnti, R. (2016). Examining relations between mathematics teachers’ instructional vision and knowledge and change in practice. American Journal of Education, 123(2), 171–202. https://doi.org/10.1086/689928
  19. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
  20. Nesher, P. (1987). Towards an instructional theory: The role of student’s misconceptions. For the Learning of Mathematics, 7(3), 33–40.
  21. Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491–508. https://doi.org/10.1016/j.tate.2005.03.004
  22. Schoenfeld, A. H. (2011). Toward professional development for teachers grounded in a theory of decision making. ZDM-The International Journal of Mathematics Education, 43(4), 457–469. https://doi.org/10.1007/s11858-011-0307-8
  23. Senge, P. M. (2006). The fifth discipline: The art & practice of the learning organization (Rev. ed.). Doubleday.
  24. Sherin, M. G. (2001). Developing a professional vision of classroom events. In T. Wood, B. Scott Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 75–93). Routledge.
  25. Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Font Strawhun, B. T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. The Journal of Mathematical Behavior, 24(3–4), 287–301. https://doi.org/10.1016/j.jmathb.2005.09.009
  26. Smith, J. P., III, diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
  27. Son, J.-W. (2016). Preservice teachers’ response and feedback type to correct and incorrect student-invented strategies for subtracting whole numbers. The Journal of Mathematical Behavior, 42, 49–68. https://doi.org/10.1016/j.jmathb.2016.02.003
  28. Tulis, M. (2013). Error management behavior in classrooms: Teachers’ responses to student mistakes. Teaching and Teacher Education, 33, 56–68. https://doi.org/10.1016/j.tate.2013.02.003
  29. Van Zoest, L. R., Stockero, S. L., Leatham, K. R., Peterson, B. E., Atanga, N. A., & Ochieng, M. A. (2017). Attributes of instances of student mathematical thinking that are worth building on in whole-class discussion. Mathematical Thinking and Learning, 19(1), 33–54. https://doi.org/10.1080/10986065.2017.1259786