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Linguistic conventions of mathematical proof writing across pedagogical contexts

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Abstract

This paper presents the findings from a survey used to investigate how mathematicians perceive the genre of mathematical proof writing at the undergraduate level. Mathematicians were asked whether various proof excerpts highlighted in four partial proofs were unconventional in each one of three pedagogical contexts: undergraduate mathematics textbooks, what instructors write on the blackboard in undergraduate mathematics courses, and how students write mathematics in these courses. There are four main findings. First, there are some potential breaches of mathematical language that participants found unconventional regardless of the context in which they occur. Second, there are some differences in how mathematicians perceived the linguistic conventions in blackboard proofs and student-produced proofs. Third, textbook authors are expected to adhere to stricter writing norms than mathematics instructors and undergraduate students when writing proofs. Fourth, there were some potential breaches of mathematical language that the literature suggests were unconventional, which were not evaluated as unconventional by the mathematicians. We argue that this diversity of expectations regarding the language of mathematical proof writing in undergraduate classrooms, together with the potential disconnect between those expectations and the types of proofs that students see presented in those classrooms, could make it difficult for students to become proficient in this important mathematical discourse.

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Notes

  1. As ranked by the USNews.com “Best Graduate Schools” list of “top mathematics programs”.

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Acknowledgements

We thank Drs. Matthew Inglis and Keith Weber for their useful comments on and suggestions throughout this project.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Kristen Lew

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

    Juan Pablo Mejía Ramos

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  1. Kristen Lew
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  2. Juan Pablo Mejía Ramos
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Correspondence to Kristen Lew.

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Appendices

Appendix 1

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Survey instructions

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Appendix 2

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Lew, K., Mejía Ramos, J.P. Linguistic conventions of mathematical proof writing across pedagogical contexts. Educ Stud Math 103, 43–62 (2020). https://doi.org/10.1007/s10649-019-09915-5

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