# Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion

## Abstract

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction. We analyzed a collection of 173 thinking-as-a-resource orientations inferred from scenario-based interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation’s relationship to three frameworks related to recognizing and leveraging high-potential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinking-as-a-resource orientations could support or hinder a teacher’s development of the practice of building on student thinking. The work contributes to the field’s understanding of why particular orientations might have more or less potential to support teachers’ development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers’ specific needs.

## Keywords

Teacher orientations Teacher beliefs Student mathematical thinking Using student thinking Building on student thinking## Notes

### Acknowledgements

This work was funded in part by the National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. 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 NSF. The authors would like to thank Elizabeth Fraser and Annick Rougee for their contributions to work that informed this paper.

## References

- Aguirre, J., & Speer, N. M. (1999). Examining the relationship between beliefs and goals in teacher practice.
*Journal of Mathematical Behavior,**18*(3), 327–356.CrossRefGoogle Scholar - Beswick, K. (2007). Teachers’ beliefs that matter in secondary mathematics classrooms.
*Educational Studies in Mathematics,**65*(1), 95–120. https://doi.org/10.1007/s10649-006-9035-3.CrossRefGoogle Scholar - Borasi, R. (1994). Capitalizing on errors as springboards for inquiry: A teaching experiment.
*Journal for Research in Mathematics Education,**25*(2), 166–208.CrossRefGoogle Scholar - 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.42.1.002.CrossRefGoogle Scholar - Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices.
*Journal of Mathematics Teacher Education,**12*(5), 325–346. https://doi.org/10.1007/s10857-009-9120-5.CrossRefGoogle Scholar - Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching.
*ZDM Mathematics Education,**44*(5), 601–612. https://doi.org/10.1007/s11858-012-0438-6.CrossRefGoogle Scholar - Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking.
*Journal for Research in Mathematics Education,**41,*169–202.Google Scholar - Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms.
*The Elementary School Journal,**102*(1), 59–80.CrossRefGoogle Scholar - Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., et al. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching.
*Journal of Teacher Education,**64*(3), 226–243. https://doi.org/10.1177/0022487112473837.CrossRefGoogle Scholar - Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems.
*Journal of Mathematics Teacher Education*,*9*(1), 91–102.CrossRefGoogle Scholar - Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking.
*Journal for Research in Mathematics Education*,*46*(1), 88–124.CrossRefGoogle Scholar - Lee, M. Y., & Cross Francis, D. (2018). Investigating the relationships among elementary teachers’ perceptions of the use of students’ thinking, their professional noticing skills, and their teaching practices.
*Journal of Mathematical Behavior,**51,*118–128. https://doi.org/10.1016/j.jmathb.2017.11.007.CrossRefGoogle Scholar - Lineback, J. E. (2015). The redirection: An indicator of how teachers respond to student thinking.
*Journal of the Learning Sciences,**24,*419–460. https://doi.org/10.1080/10508406.2014.930707.CrossRefGoogle Scholar - Lloyd, G. M. (2005). Beliefs about the teacher’s role in the mathematics classroom: One student teacher’s explorations in fiction and in practice.
*Journal of Mathematics Teacher Education,**8*(6), 441–467. https://doi.org/10.1007/s10857-005-5120-2.CrossRefGoogle Scholar - National Council of Teachers of Mathematics. (1989).
*Curriculum and evaluation standards for school mathematics*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - National Council of Teachers of Mathematics. (2014).
*Principles to actions: Ensuring mathematical success for all*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Peterson, B. E., & Leatham, K. R. (2009). Learning to use students’ mathematical thinking to orchestrate a class discussion. In L. Knott (Ed.),
*The role of mathematics discourse in producing leaders of discourse*(pp. 99–128). Charlotte, NC: Information Age.Google Scholar - Piaget, J. (1964). Cognitive development in children: Piaget development and learning.
*Journal of Research in Science Teaching,**2*(3), 176–186.CrossRefGoogle Scholar - Rokeach, M. (1968).
*Beliefs, attitudes, and values: A theory of organization and change*. San Francisco, CA: Jossey-Bass.Google Scholar - Scherrer, J., & Stein, M. K. (2013). Effects of a coding intervention on what teachers learn to notice during whole-group discussion.
*Journal of Mathematics Teacher Educators,**16*(2), 105–124. https://doi.org/10.1007/s10857-012-9207-2.CrossRefGoogle Scholar - Schleppenbach, M., Flevares, L. M., Sims, L. M., & Perry, M. (2007). Teachers’ responses to student mistakes in Chinese and U.S. mathematics classrooms.
*The Elementary School Journal,**108*(2), 131–147. https://doi.org/10.1086/525551.CrossRefGoogle Scholar - Schoenfeld, A. H. (2011).
*How we think: A theory of goal-oriented decision making and its educational applications*. New York, NY: Routledge.Google Scholar - Simon, M. A., & Tzur, R. (1999). Explicating the teacher’s perspective from the researchers’ perspectives: Generating accounts of mathematics teachers’ practice.
*Journal for Research in Mathematics Education,**30*(3), 252–264.CrossRefGoogle Scholar - SportsTec. (1997–2015). Studiocode [Computer program]. Camarillo, CA: Vitigal Pty Limited.Google Scholar
- Stockero, S. L. (2013). The effects of framing on mathematics student teacher noticing. In M. Martinez & A. Castro Superfine (Eds.),
*Proceedings of the 35th annual meeting of the North American chapter of the international group for the psychology of mathematics education*(pp. 709–716). Chicago, IL: University of Illinois at Chicago.Google Scholar - Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice.
*Journal of Mathematics Teacher Education*,*16*(2), 125–147.CrossRefGoogle Scholar - Stockero, S. L., Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Rougee, A. O. T. (2017). Teachers responses to a common set of high potential instances of student mathematical thinking. In E. Galindo & J. Newton (Eds.),
*Proceedings of the 39th annual meeting of the North American chapter of the international group for the psychology of mathematics education*(pp. 1178–1185). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.Google Scholar - Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking.
*Journal for Research in Mathematics Education,**30*(1), 89–110.CrossRefGoogle Scholar - Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Stockero, S. L. (2016). Conceptualizing the teaching practice of building on student mathematical thinking. In M. B. Wood, E. E. Turner, M. Civil & J. A. Eli (Eds.),
*Proceedings of the 38th annual meeting of the North American chapter of the international group for the psychology of mathematics education*(pp. 1281–1288). Tucson: University of Arizona.Google Scholar - 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*, 33–54. https://doi.org/10.1080/10986065.2017.1259786.CrossRefGoogle Scholar