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Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking

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Abstract

This study contributes to the growing body of research that highlights the usefulness of professional noticing of children’s mathematical thinking for understanding the complexity and variability in teaching expertise. We explored the noticing expertise of 72 upper elementary school teachers engaged in multi-year professional development focused on children’s fraction thinking. Our assessment addressed the three component skills of professional noticing of children’s mathematical thinking: (a) attending to children’s strategy details, (b) interpreting children’s understandings, and (c) deciding how to respond on the basis of children’s understandings. We used a latent class analysis to empirically identify three distinct “profiles” of noticing expertise—subgroups of teachers who responded similarly to each other and differently from teachers in other profiles. The profiles differed in their overall noticing expertise as well as their patterns of strengths and areas for growth across the component skills. Thus, the profiles provide a concise, multi-dimensional characterization of noticing expertise that integrates expertise in each of the component skills. The profiles also provide tools for differentiating learning opportunities for teachers in professional development. In addition, our design allowed us to compare teachers’ expertise in two common forms of deciding how to respond: deciding on follow-up questions and deciding on next problems. In all three profiles, teachers demonstrated more expertise when deciding on follow-up questions than when deciding on next problems, suggesting not only a starting point for teacher learning but also the need for a line of research focused on different forms of this component skill.

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Notes

  1. In this paper, we focus on teacher noticing during instruction, which is consistent with most of the research on mathematics teacher noticing. However, Sherin (2017) noted that researchers have recently begun to question this boundary. Under question is whether the teacher noticing construct should include not only when teachers interact with children, but also when they prepare for and reflect on their teaching (see, e.g., work on curricular noticing [Amador et al., 2017; Dietiker et al., 2018]).

  2. Teachers’ attending scores for each instructional scenario were generated in two steps given that our prompts requested that teachers describe each strategy (see Table 2 for the prompts). First, we scored individual strategy descriptions for a scenario. Second, we averaged the scores for individual strategy descriptions for that scenario, and all further analyses used this average as the attending score for that scenario. Averaging multiple strategy descriptions within a scenario provided a more stable measure of teachers’ expertise in attending to children’s strategy details given that individual strategies can have both typical and idiosyncratic mathematical details of interest.

  3. For example, in our larger study, we also conducted classroom observations for 49 teachers, and we used a 4-point scale to evaluate the teachers’ capacity for questioning to build on children’s thinking during instruction. We found a significant, moderate correlation between teachers’ noticing profiles and their questioning scores (r (47) = .56, p < .05). For more information, see Empson & Jacobs (2021).

  4. We also wondered if differences in years of teaching experience could help explain our profiles, but the mean number of years of teaching was 12 years for all three profiles, suggesting that teaching experience was not a source of our profile differences.

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Acknowledgements

This research was supported in part by the National Science Foundation (DRL–1316653 and 1712560). The opinions expressed do not necessarily reflect the position, policy, or endorsement of the supporting agency. An earlier version of this paper was presented in 2021 at the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. We thank the teachers who graciously agreed to participate in our multi-year collaboration and allowed us to explore their learning and development. We also thank our long-term collaborators, Jessica Bishop and Lisa Lamb, for their support and helpful feedback on earlier drafts.

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Authors and Affiliations

  1. University of North Carolina at Greensboro, Greensboro, NC, USA

    Victoria R. Jacobs

  2. University of Missouri, Columbia, MO, USA

    Susan B. Empson

  3. Georgia State University, Atlanta, GA, USA

    Naomi A. Jessup

  4. University of Illinois Springfield, Springfield, IL, USA

    Amy Dunning

  5. University of Notre Dame, Notre Dame, IN, USA

    D’Anna Pynes

  6. William and Mary, Williamsburg, VA, USA

    Gladys Krause

  7. University of California, Los Angeles, Los Angeles, CA, USA

    Todd M. Franke

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Jacobs, V.R., Empson, S.B., Jessup, N.A. et al. Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking. J Math Teacher Educ (2022). https://doi.org/10.1007/s10857-022-09558-z

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