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Factors mathematicians profess to consider when presenting pedagogical proofs

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Abstract

This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised.

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Notes

  1. Nardi (2008) was an exception to this, as mathematicians responded to specific student work and gave their impression of students’ conceptions.

  2. According to the U.S. News and World Report 2010 rankings of mathematics graduate schools.

  3. Transcripts were lightly edited to improve their readability. We omitted short phrases that did not convey meaning, such as mumbling or repeated phrases. At no point did we add text, and we do not believe we altered the meaning of what the participants said.

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Acknowledgments

We are indebted to the participating mathematicians for opening their reflection and work to this study. We are grateful to the editor and the anonymous reviewers for their comments about the writing and structure of this paper, and to the Mathematics Teaching and Learning to Teach group at the University of Michigan, especially Deborah Ball, Hyman Bass, Mark Thames, and Lindsey Mann, for comments about the framing of the paper. Any flaws that remain are solely our own. We are grateful to Aron Samkoff for transcribing interviews. This work was supported by grants from the National Science Foundation (#EHR-1008317, #DUE-081736, and #DRL-0643734) and by an Investigating Student Learning Grant from the Center for Research on Learning and Teaching at the University of Michigan.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE, USA

    Yvonne Lai

  2. Graduate School of Education, Rutgers University, New Brunswick, NJ, USA

    Keith Weber

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  1. Yvonne Lai
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Correspondence to Yvonne Lai.

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Lai, Y., Weber, K. Factors mathematicians profess to consider when presenting pedagogical proofs. Educ Stud Math 85, 93–108 (2014). https://doi.org/10.1007/s10649-013-9497-z

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