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Critical moments: pre-service mathematics teachers’ narrative arcs and mathematical orientations over 20 years

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Abstract

This study explores narratives about critical moments in mathematics learning written by K-8 pre-service teachers’ (PSTs) in the United States over a 20-year period. These critical moments, such as a single memorable task, course, test, or comment from a teacher, had a powerful and sustained impact on PSTs’ mathematics identities, which they carried with them as they entered the teaching profession. We classified narratives using McCulloch et al. (Sch Sci Math 113(8):380–389, 2013) and Drake’s (J Math Teach Educ 9(6):579–608, 2006) categories and found a potentially new category, Taking the Reins. We also classified PSTs’ mathematics orientations as either relational (oriented toward creative problem solving and conceptual understanding) or instrumental (enacting rote procedures without meaning) (Skemp in Math Teach 77(1):20–26, 1976). Many PSTs identified a causal relationship between their mathematics orientations and narrative arcs: relational learning opportunities encouraged positive narratives, while instrumental learning opportunities either resulted in negative narrative arcs or positive but fragile mathematics identities that crumbled under minor stress. We found little variation over time in the nature and prevalence of the narrative arcs and mathematics orientations, suggesting that any changes in mathematics teaching practices over time were not reflected in students’ learning experiences.

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Notes

  1. These sketches were a required part of a participation grade and were assessed by the course instructor based upon completion (but not content). They were used to stimulate discussion during the class to share both positive and negative mathematics experiences as part of building a safe space and understanding the potential mathematics experiences of PST’s future students.

  2. The AP (advanced placement) exams are used in the U.S. to demonstrate that a student has covered a first-year college course during high school and should receive college credit. The GRE exams are used for graduate school admittance. Both are typically only taken by students who are very strong academically.

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Authors and Affiliations

  1. Graduate School of Education, Teaching, Learning, and Teacher Education, University of Pennsylvania, Philadelphia, PA, USA

    Rowan Machalow, Lindsay T. Goldsmith-Markey & Janine T. Remillard

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  1. Rowan Machalow
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  2. Lindsay T. Goldsmith-Markey
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  3. Janine T. Remillard
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Correspondence to Rowan Machalow.

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Machalow, R., Goldsmith-Markey, L.T. & Remillard, J.T. Critical moments: pre-service mathematics teachers’ narrative arcs and mathematical orientations over 20 years. J Math Teacher Educ 25, 35–61 (2022). https://doi.org/10.1007/s10857-020-09479-9

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