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Metaphors for learning and doing mathematics in advanced mathematics lectures

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Abstract

The metaphors that students form and encounter have been shown to exert a powerful influence on how they think about mathematics. In this paper, we explore the linguistic metaphors about learning and doing mathematics that were prevalent in 11 advanced mathematics lectures. We present four metaphor clusters that were common in the corpus that we analyzed: Learning Mathematics is a Journey, Doing Mathematics is Work, Mathematics is Discovery, and Presenting Mathematics is a Story. We conclude the paper by discussing the implications of the metaphors that mathematicians use and students hear in their mathematics courses.

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Notes

  1. Steen (2011) illustrated this point by considering the linguistic metaphor “Lakoff attacked Glucksberg”, which linguists commonly identify as an instance of the “Argument is War” metaphor (e.g., Lakoff & Johnson, 1980). Steen argued one could both utter and comprehend this text without considering war; for instance, ‘attack’ could idiomatically mean “finding holes in an academic argument”. Nonetheless, Steen interpreted this as a “non-deliberate metaphor” because a metaphorical interpretation was possible. We further note that neither the target domain (argument) nor the source domain (war) are explicit in the text. Rather, both were inferred by the researcher as a sensible way of interpreting the passage.

  2. Cambridge English Dictionary: https://dictionary.cambridge.org/us/dictionary/english/verge

  3. Cambridge English Dictionary: https://dictionary.cambridge.org/us/dictionary/english/with-your-bare-hands

  4. Cambridge English Dictionary: https://dictionary.cambridge.org/us/dictionary/english/discover

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Acknowledgments

We would like to thank Michael Oehrtman for his detailed comments on an earlier draft of this manuscript.

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  1. Graduate School of Education, Rutgers University, 10 Seminary Place, New Brunswick, NJ, 08901, USA

    Joe Olsen & Keith Weber

  2. Department of Mathematics, Texas State University, San Marcos, TX, 78666, USA

    Kristen Lew

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  1. Joe Olsen
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Correspondence to Joe Olsen.

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Olsen, J., Lew, K. & Weber, K. Metaphors for learning and doing mathematics in advanced mathematics lectures. Educ Stud Math 105, 1–17 (2020). https://doi.org/10.1007/s10649-020-09968-x

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