{"id":1524,"date":"2018-05-29T10:52:52","date_gmt":"2018-05-29T14:52:52","guid":{"rendered":"http:\/\/blogs.ams.org\/inclusionexclusion\/?p=1524"},"modified":"2018-06-14T13:12:15","modified_gmt":"2018-06-14T17:12:15","slug":"toward-humanizing-undergraduate-mathematics-education-a-re-imagining-through-historical-perspectives-in-mathematics","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/inclusionexclusion\/2018\/05\/29\/toward-humanizing-undergraduate-mathematics-education-a-re-imagining-through-historical-perspectives-in-mathematics\/","title":{"rendered":"Toward humanizing undergraduate mathematics education: A re-imagining through historical perspectives in mathematics"},"content":{"rendered":"

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Photo from Dr. Sara Hottinger’s Coastal Carolina faculty profile webpage<\/p><\/div>\n

This blog post was inspired from my reading of Sara Hottinger<\/a>\u2019s book, Inventing the Mathematician: Gender, Race, and Our Cultural Understanding of Mathematics <\/em><\/a>(2016). Hottinger\u2019s book advanced my thinking about how cultural contexts of mathematics perpetuate gendered, racialized, and other systemic forms of exclusion. She adopts a cultural studies approach to examine how four sources of mathematical representations \u2013 textbooks, histories of mathematics, portraits of mathematicians, and ethnomathematics<\/a> \u2013 limit opportunities for building \u201cindividual and cultural relationship[s] to the field\u201d (p. 7). Hottinger (2016) uses the term mathematical subjectivity <\/em>to refer to how individuals make sense of themselves in relation to mathematics across these four sources. Her analysis highlights how exclusionary representations of mathematics result in the \u201cconstruction of normative Western subjectivity and in the construction of the West itself\u201d (p. 6) that limit possibilities of positive mathematical subjectivities among members of historically marginalized populations.<\/p>\n

Considering the inclusion\/exclusion<\/em> blog\u2019s focus on issues of social marginalization in mathematics<\/a> and my research interest in increasing inclusive educational opportunities in undergraduate mathematics, I focus on Hottinger\u2019s analysis about the history of mathematics \u2013 an area of inquiry associated with a special interest group of the Mathematical Association of America<\/a> and incorporated in courses of study for mathematics majors in the United States. I begin with summarizing Hottinger\u2019s distinction between internalist <\/em>and externalist <\/em>historical accounts and their respective influences on the construction of mathematical subjectivities. This is followed by a discussion of how Hottinger\u2019s insights can be applied to re-thinking pedagogical practices in undergraduate education that challenge traditional representations of mathematics as void of sociohistorical contexts and personhood.<\/p>\n

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\"\"Internalist and externalist accounts of mathematical history. <\/em><\/strong>Hottinger distinguishes internalist and externalist traditions of writing histories of mathematics. The internalist approach is most widely used with representations of mathematics as universal and discovered, resulting in the de-centering of individuals and social contexts associated with mathematical knowledge production.\u00a0Texts presenting internalist historical accounts, for example, often reserve insights about biographies and cultures on side margins or at the end of chapters.\u00a0 Thus, Hottinger argues that the prioritization of ideas over individuals in internalist histories of mathematics result in the disappearance of mathematical subjectivities.<\/p>\n

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Front cover image of David Burton’s (2010) “The History of Mathematics: An Introduction” from the McGraw Hill Education website<\/p><\/div>\n

Externalist histories are written with representations of mathematics as a human activity situated in cultural and historical contexts. With such foregrounding of individuals and their progress in mathematical knowledge production, texts presenting externalist accounts of history are often organized chronologically and incorporate relevant biographical insights in discussions about the development of mathematical ideas.\u00a0Hottinger draws on David Burton\u2019s\u00a0The History of Mathematics: An Introduction<\/em><\/a>\u00a0(2010) as an illustrative example of an externalist text. While Burton\u2019s text \u201chumanize[s] the history of mathematics\u201d (p. 63) through the centering of individuals and social contexts, Hottinger argues that this externalist account also limits constructions of mathematical subjectivity through portrayals of mathematicians as heroic figures. Burton\u2019s (2010) representation of Isaac Newton, for example, illustrates how a mathematician\u2019s subjectivity is constructed in alignment with discourses of mathematics in Western culture \u2013 namely, \u201cdifficult, cold, abstract, ultra-rational, important and largely masculine\u201d (Ernest, 1992, n.p.). Thus, Newton is represented as an \u201cideal mathematician\u201d (Hottinger, 2016, p. 76) and thus perpetuates gendered, racialized, and other socially restrictive opportunities for identifications with mathematics.<\/p>\n

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Front cover image of Imani Goffney and Rochelle Guti\u00e9rrez’s (Eds.) “Annual Perspectives in Mathematics Education 2018” (National Council of Teachers of Mathematics)<\/p><\/div>\n

Historically humanizing undergraduate mathematics education. <\/em><\/strong>With recent calls for (re)humanizing mathematics education (e.g., Goffney & Guti\u00e9rrez, 2018<\/a>; Mukhopadhyay & Greer, 2015<\/a>), Hottinger\u2019s analysis of mathematical subjectivity across internalist and externalist accounts brought me to consider how undergraduate mathematics educators can leverage her insights to (re)humanize mathematics, including students\u2019 mathematical learning experiences. Narrow conceptions of mathematics and mathematicians through written histories can frame institutional practices in undergraduate mathematics education that produce inequitable opportunities to learn and identify with the discipline. Thus, I encourage undergraduate mathematics faculty to critically reflect on pedagogical possibilities for more humanistic presentations of mathematics and its history that motivate what Hottinger (2016) calls \u201cfeminist \u2018aha\u2019 moments\u201d (p. 5) among students. Such moments provide undergraduate students a new lens for making sense of themselves, including their mathematical subjectivities and positions in the world.<\/p>\n

Below I pose several questions for undergraduate mathematics course instructors to consider on how they pedagogically engage the history of mathematics for more inclusive opportunities of developing positive mathematical subjectivities across their classrooms. What cuts across these questions of practice is a re-imagining of undergraduate mathematics education\u00a0toward \u201cliv[ing] mathematx<\/em>\u201d (Guti\u00e9rrez, 2017<\/a>, p. 18) by centering the voices, experiences, and practices often deemed non-mathematical in historical accounts. (Mathematx<\/em>, inclusive of Western and Aboriginal forms of mathematizing, refers to \u201ca way of seeking, acknowledging, and creating patterns for the purpose of solving problems (e.g., survival) and experiencing joy\u201d (Guti\u00e9rrez, 2017, p. 15).)<\/p>\n