Identifying aspects of mathematical epistemology that might influence productively student reasoning beyond mathematics
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ORIGINAL ARTICLE
Identifying aspects of mathematical epistemology that might influence productively student reasoning beyond mathematics Paul Christian Dawkins1 Accepted: 22 May 2020 © FIZ Karlsruhe 2020
Abstract The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting “critical thinking skills” or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old “Theory of Formal Discipline” that claims that mathematics learning fosters generally improved reasoning. This is ostensibly done by providing students with access to aspects of mathematical epistemology, which are taken to have some value beyond mathematics itself. The evidential basis both for learning mathematical epistemology and for its influence beyond the mathematics classroom are relatively thin, in part because they are hard to define and operationalize for research. In this paper, I will identify some challenges inherent in studying whether mathematical epistemology might contribute to productive reasoning beyond mathematics and proffer particular aspects of mathematical epistemology that could be useful for instruction and research thereupon. Given that mathematicians and many policy makers believe in the power of mathematical epistemology to improve people’s general reasoning, this appears a worthwhile avenue for investigation, even if the challenge is daunting. Keywords Mathematical epistemology · Logic · Teaching · Learning Modern higher education operates amidst a number of tensions about the nature and goals of the educational experiences we provide. Among these, I wish to highlight the tension between helping students become educated citizens with “critical thinking skills” versus training students in the bodies of knowledge celebrated by the particular disciplines that comprise the academy. The former aspect appears more and more frequently in the discourse of many university administrators while the latter maintains much dominance in the curriculum, if nothing else because it remains easier to teach and assess (especially in mathematics). While mathematics overall does not appear in danger of losing its prominence in most curricula, both because of its centrality in STEM fields and because it is used in so many other aspects of society as a placement measure, many university mathematics departments experience continued pressure to articulate how our instruction addresses these overarching goals of helping students become more competent thinkers. * Paul Christian Dawkins [email protected] 1
Department of Mathematics‑MCS 470, Texas State University, San Marcos, TX 78666, USA
These kinds of educational pressures have long existed in dialogue with arguments for the value of mathematics as a specific domain with quite general value for improving reasoning. Attridge and Ingles (2013; Inglis & Attridge 2017) provide an interesting overview of the millennia-old argument that learning mathematics fosters “thinking skills.” Th
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