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Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction

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Abstract

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about inquiry-oriented instruction relative to vertices of the instructional triangle (content, students, and instructor). Through this lens, we analyze conversations of twenty-five mathematicians who elected to attend a workshop on inquiry-oriented instruction at a large national mathematics conference. Identifying differences in talk between two breakout groups, we argue that deeper mathematical engagement in task sequences designed for students supported deeper engagement in students’ mathematical reasoning and engendered reasoning about instruction that was more frequently accompanied by rationale based in mathematics or students’ reasoning about mathematics. Importantly, deeper mathematical engagement was observed when the discussion facilitator prompted participants to engage through a mathematical lens rather than an instructional lens.

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Notes

  1. In presenting these literature findings, we are not arguing that lecture as a pedagogical tool has no instructional value. Even in inquiry-oriented instruction and other forms of active learning, there is a place for integrating teacher-centered discourse (Rasmussen and Marrongelle 2006). Additionally, research has found instructors who describe their instruction as “lecture” often report utilizing a wide variety of other instructional techniques (Johnson et al. 2018).

  2. In order to verify that a set under an operation is a group, one must ensure that when you perform the operation on any two elements, the resulting element is still in the set. For instance, if you add two integers, the result will always be an integer. Thus, we would say that the “integers are closed under addition”. However, if you divide two integers the result may no longer be an integer (e.g., 1 divided by 2); thus, we would say “the integers are not closed under division”.

  3. Note that each turn of talk could receive more than one code, so the percentages in Fig. 4 sum to over 100%. Turns of talk coded as “Other” included introductions, logistics (“Does everyone have a handout?”), etc.

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Acknowledgements

This research was supported by National Science Foundation award numbers #1431595, #1431641, and #1431393.

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Authors and Affiliations

  1. School of Teacher Education, Florida State University, Tallahassee, USA

    Christine Andrews-Larson

  2. Department of Mathematics, Virginia Tech, Blacksburg, USA

    Estrella Johnson

  3. Department of Mathematics, University of Portland, Portland, USA

    Valerie Peterson

  4. Department of Mathematics, Virginia Tech, Blacksburg, USA

    Rachel Keller

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  1. Christine Andrews-Larson
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Correspondence to Estrella Johnson.

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Andrews-Larson, C., Johnson, E., Peterson, V. et al. Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction. J Math Teacher Educ 24, 127–154 (2021). https://doi.org/10.1007/s10857-019-09450-3

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