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Relationships Between Teachers’ Interactions with Learner Errors and Learners’ Mathematical Identities

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Abstract

Engaging with learner errors in mathematics classrooms is an important aspect of teacher pedagogy which can support learner identification with mathematics. This study examined the opportunities that teachers provided for the construction of learner identities based on how the teachers spoke about and interacted with learner errors in two secondary school mathematics classrooms. Data were collected over two years in the form of videotaped lessons, field notes, photographed learner notebooks and audiotaped interviews with participants, and were analyzed qualitatively. Two ways in which teachers spoke about errors are discussed: errors are contagious and errors are lessons. How the teachers spoke about and interacted with errors were informed by their views of learners and their reasoning in mathematics, which shaped the identities they offered learners. We show that while learners’ experiences of their teachers’ approaches to errors informed their identification with mathematics to some extent, the learners also played a role in the construction of their mathematical identities.

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Notes

  1. Traditional pedagogies dominate classroom instruction, both in South Africa and internationally, and are characterized by textbook-based, teacher-dominated practices (Boaler & Greeno, 2000; Umugiraneza, Bansilal, & North, 2017). Traditional pedagogies are often compared with inquiry-based reform pedagogies, which are characterized by learners engaging collaboratively on open-ended problem-solving activities (Boaler, 2002). Inquiry-based pedagogies are argued to promote deep mathematical reasoning, with competence being evaluated on learner reasoning rather than obtaining the correct answers.

  2. While we did not find any learner in our larger study resisting any of the social identities offered to them, we have included the category in our framework for completeness, as other studies have shown that learners can resist the social identities offered to them (see for example, Nasir & Shah, 2011).

  3. In some situations, teachers may continue offering these learners identities of marginalization, as resistance to the offered social identity of marginalization can be seen as a form of resistance to the authority of the teacher. In other situations, teachers may offer learners a new social identity of affiliation when they see learners resisting the offered social identity of marginalization. Only when learners are offered a new social identity of affiliation, instead of marginalization, can they identify with the offered social identity to develop their mathematical identities as affiliating members of the community.

  4. Within the wider sample, there were learners who developed their identities in marginalization from the community. No learners in the wider study resisted any of the social identities offered. See Gardee (2019).

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Acknowledgements

We acknowledge all who supported this study, including learner participants, parents/guardians, teachers and the school principal.

Funding

Funding for this study was provided by the National Research Foundation (UID 105210).

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Authors and Affiliations

  1. University of the Witwatersrand, 27 St Andrews Rd, Parktown, Johannesburg, 2193, South Africa

    Aarifah Gardee & Karin Brodie

  2. Johannesburg, South Africa

    Aarifah Gardee

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  1. Aarifah Gardee
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  2. Karin Brodie
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Correspondence to Aarifah Gardee.

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Gardee, A., Brodie, K. Relationships Between Teachers’ Interactions with Learner Errors and Learners’ Mathematical Identities. Int J of Sci and Math Educ 20, 193–214 (2022). https://doi.org/10.1007/s10763-020-10142-1

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