Why mathematicians read proofs

Juan Pablo Mejia-Ramos and Keith Weber have written a very interesting article that was published in the last issue of Educational Studies in Mathematics (Volume 85, Issue 2, February 2014). The article is entitled: “Why and how mathematicians read proofs: further evidence from a survey study”. I have just had the time to read this article today, and I found it very interesting! Their study builds upon a previous study, where the same authors conducted two small-scale interview studies on why and how mathematicians read proofs (Weber & Mejia-Ramos, 2011). In the previous study, nine research mathematicians were interviewed about their strategies when reading mathematical proofs (in published articles etc.). In their study back then, the authors identified three general strategies. When reading proofs, the research mathematicians:

  • appealed to the authority of other mathematicians who had read the proof
  • read the proof carefully line-by-line
  • applied modular reading of the proof

Based on their results from that study, they designed an internet-based survey that was distributed to 118 practicing mathematicians in the USA. When analyzing the results of this study, Mejia-Ramos and Weber (2014) found that the mathematicians had very much the same strategies as the mathematicians they had previously interviewed. When reading proofs, the mathematicians were not so much focused on checking whether or not the proof was correct – they appealed to the reputation of the author and journal on that – but they were more focused on the insights that could be gained. Oftentimes, the mathematicians would investigate how particular steps in a proof could apply to other examples, and they were also focusing on understanding the more overarching ideas and methods in the proof. For me as a mathematics educator, I find studies like these very interesting. The worlds of research mathematicians and mathematics education researchers often seem to be far away from each other, but they shouldn’t be! I think we as mathematics educators need to have a close relationship with research mathematicians, and I also think we can learn a lot by learning about how research mathematicians think when they approach mathematical problems, proofs, etc.

References
Mejia-Ramos, J.P. & Weber, K. (2014). Why and how mathematicians read proofs: further evidence from a survey study. Educational Studies in Mathematics, 85(2), 161–173.

Weber, K. & Mejia-Ramos, J.P. (2011). Why and how mathematicians read proofs: an exploratory study. Educational Studies in Mathematics, 76(3), 329–344.

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