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Conceptions of span in linear algebra: from textbook examples to student responses

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Abstract

Using Balacheff’s (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set of a given set of vectors. An analysis of the correctness of the application of these strategies provides a more nuanced understanding of student responses that might be more useful for instructors than simply classifying the responses as right or wrong. These findings add to our knowledge of the textbook’s presentation of span and student understanding of span. We discuss implications for research and practice.

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Notes

  1. Most research on student understanding of spans includes linear (in)dependence. See for example, Rasmussen and Wawro (2017) and Stewart et al. (2019) who provide a comprehensive review of these topics.

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Acknowledgements

Thanks to the Undergraduate Research Opportunity Program and to the Research on Teaching in Undergraduate Settings lab at the University of Michigan.

Funding

This work was supported by the National Science Foundation under Awards IUSE 1624634, 1821509, 1625223, 1626455, and 1821329.

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Authors and Affiliations

  1. University of Michigan, 610 East University Ave. #3118, Ann Arbor, MI, 48109, USA

    Saba Gerami, Eric Khiu & Vilma Mesa

  2. Stephen F. Austin State University, Nacogdoches, TX, USA

    Thomas Judson

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  1. Saba Gerami
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Correspondence to Saba Gerami.

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Gerami, S., Khiu, E., Mesa, V. et al. Conceptions of span in linear algebra: from textbook examples to student responses. Educ Stud Math 116, 67–89 (2024). https://doi.org/10.1007/s10649-024-10306-8

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