Using crowdsourced mathematics to understand mathematical practice
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ORIGINAL ARTICLE
Using crowdsourced mathematics to understand mathematical practice Alison Pease1 · Ursula Martin2 · Fenner Stanley Tanswell3 · Andrew Aberdein4 Accepted: 5 July 2020 © The Author(s) 2020
Abstract Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of collective intelligence); human–computer interaction (on the factors that led to the success of one such project); network analysis (on the differences between collaborations on open research problems and known-but-hard problems); and argumentation theory (on modelling the argument structures of online collaborations). We also give an overview of qualitative approaches, reviewing work from empirical philosophy (on explanation in crowdsourced mathematics); sociology of scientific knowledge (on conventions and conversations in online mathematics); and ethnography (on contrasting conceptions of collaboration). We suggest how these diverse methods can be applied to crowdsourced mathematics and when each might be appropriate.
1 Introduction While mathematicians have collaborated since antiquity, online collaborations among large numbers of mathematicians are a novelty in terms of scale, speed, anonymity, and transparency. They provide new opportunities for the practice of mathematics, and thereby for scholars of that practice in general, and mathematics education researchers in particular. Many mathematics educators agree that students should be exposed to the practices of working mathematicians, even if they do not always agree what those practices are (Stillman et al. 2020). Records of online collaborative activity form temptingly accessible, novel, rich, searchable and sizeable sources of data. Unsurprisingly, scholars of mathematical practice have started to look to such sources for insights we should expect to impact mathematics education. Specifically, much mathematical practice research * Andrew Aberdein [email protected] 1
University of Dundee , Dundee, UK
2
University of Edinburgh , Edinburgh, UK
3
Loughborough University , Loughborough, UK
4
Florida Institute of Technology, Melbourne, USA
either lacks access to the knowledge generation process, as with historical studies, or is at some level artificial, as with laboratory studies of mathematicians. Crowdsourcing addresses both limitations.1 In this paper we ask three questions: What can we learn from these new socio-technical projects? How does crowdsourced mathematics differ from traditional mathematics? How can studies of crowdsourcing be u
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