{"id":543,"date":"2014-12-19T08:30:17","date_gmt":"2014-12-19T13:30:17","guid":{"rendered":"http:\/\/blogs.ams.org\/matheducation\/?p=543"},"modified":"2014-12-19T08:27:28","modified_gmt":"2014-12-19T13:27:28","slug":"the-liberal-art-of-mathematics","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/matheducation\/2014\/12\/19\/the-liberal-art-of-mathematics\/","title":{"rendered":"The Liberal Art of Mathematics"},"content":{"rendered":"

By Priscilla Bremser, Contributing Editor<\/a>, Middlebury College<\/em><\/p>\n

Somehow, over the last 600 years or so, mathematics has moved from the core of the liberal arts disciplines to entirely outside. We\u2019re all used to this; a \u201cliberal arts math\u201d course is understood to serve non-STEM majors, for example. The reasons for this shift are interesting to ponder (see [1] and [2]), but in this post I suggest that we consider some of its unfortunate present-day implications. It\u2019s also worth considering the broader aim of a liberal arts approach, which transcends disciplinary boundaries.<\/p>\n

A well-known exposition of the liberal arts ideal appears in a fifteenth-century treatise of Vergerius<\/a>, in which he advocates studies \u201cworthy of a free man.\u201d While Vergerius lays out specific areas of study, including the \u201cmathematical arts\u201d –the quadrivium of arithmetic, geometry, astronomy, and music — he opens with the importance of a liberal education to character development. From early on, then, the liberal arts ideal goes beyond eschewing the vocational; it values sustained engagement with abstract concepts as central to the capacity to live a good life.<\/p>\n

Although I have bristled at a smorgasbord interpretation of liberal arts, which misses the point in its focus on breadth with little attention to depth, equally concerning is the suggestion that some areas of study are more worthy of inclusion. In a recent report<\/a> of the Association of American Colleges and Universities, which calls itself \u201cA Voice and Force for Liberal Education in the 21st<\/sup> Century,\u201d \u201c[t]he term \u2018liberal arts\u2019 is used \u2026 as a description for majors in the humanities, arts, and social sciences.\u201d The common misperception of mathematics as solely practical may have contributed to its exile; it certainly adds to the challenge of teaching. It may be obvious to me that the study of Calculus benefits one\u2019s overall capacity to engage with the world, but it\u2019s not always evident to my students.<\/p>\n

When Vermont first adopted the Common Core State Standards for Mathematics, a veteran teacher-trainer told me, \u201cI worry that because the Content Standards take up so many more pages, people will focus on them, and then this won\u2019t work. The Practice Standards are key.\u201d Since then, I\u2019ve heard two of the lead writers of the CCSSM say that they worry about too much focus on the Practice Standards, and that they\u2019re meaningless without the Content Standards. Conclusion: both are important, and they work in concert.<\/p>\n

Analogously, our understandings of the liberal arts are about content and practice. Both are important, and they work in concert. We can\u2019t develop our students\u2019 intellectual capacities without carefully considering content, and we can\u2019t rely on content alone to prepare them for the challenges they\u2019ll face confronting questions we can\u2019t even imagine right now. (I don\u2019t remember Fortran, but the value of learning to write computer programs endures.)<\/p>\n

What does this say about the \u201cLiberal Arts Mathematics\u201d course? Steve Strogatz has been tweeting about the one he\u2019s been teaching, using materials from the Discovering the Art of Mathematics<\/a> project. Jessica Lahey wrote about his course <\/a>for The Atlantic. <\/em> What I\u2019ve seen suggests that it is indeed possible to engage students, even those who start the course with apprehension or even fear, in \u201cauthentic mathematical experiences,\u201d as the project intends. For this audience, figuring out how to produce a scalene triangle with one cut of the scissors is an exercise in plane geometry, a foundational topic. It\u2019s also an exercise in making mistakes and persevering, something that may not have been encouraged in their earlier mathematics courses. The authenticity is evident in both the geometric content and the exploratory approach.<\/p>\n

What does it mean for our mathematics majors if we insist that mathematics is still one of the liberal arts? For one thing, it is one way I remind myself, and my students, that too much emphasis on coverage risks losing the longer-lasting lessons of careful, detailed analysis. Those lessons go beyond the specifics of any particular course. The other day I heard a student in our common room scoff at the notion that math is just about numbers; \u201cit\u2019s about logical thinking,\u201d he said. From now on I\u2019m going to ask explicitly for that sort of metacognition in my upper-level classes. What have your mathematics classes had in common? When have you noticed advances in your capacity to think abstractly? How have your upper-level math courses changed your thinking about the earlier ones? Asking students to look for coherence and connection will, I believe, make it more likely that their mathematical studies will have a lasting impact on them as members of society, not just as workers.<\/p>\n

We mathematicians understand that our discipline involves creativity, beauty, and abstraction as well as precision and utility. An education worthy of a free person should include active, meaningful experience with all of those elements. I will continue to speak up about the historical importance of the quadrivium, the \u201cmathematical arts,\u201d in the liberal arts. At the same time, I will affirm the value of mathematical practice to intellectual development for all present-day students, not just those majoring in mathematics and the sciences. Finally, and most important, I want every course I teach to reflect the centrality and the value of mathematics, content and practice, to a modern liberal education.<\/p>\n

[1] Grant, Hardy. Mathematics and the Liberal Arts.\u00a0The College Mathematics Journal<\/em>, 30<\/strong>, No. 2\u00a0\u00a0(Mar., 1999), 96-105.<\/p>\n

[2] Grant, Hardy. Mathematics and the Liberal Arts.\u00a0The College Mathematics Journal<\/em>, 30<\/strong>, No. 3\u00a0\u00a0(May, 1999), 197-203.<\/p>\n

Many thanks to Luisa Burnham, Ben Braun, and Julian Fleron for their assistance.<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

By Priscilla Bremser, Contributing Editor, Middlebury College Somehow, over the last 600 years or so, mathematics has moved from the core of the liberal arts disciplines to entirely outside. We\u2019re all used to this; a \u201cliberal arts math\u201d course is … Continue reading →<\/span><\/a><\/p>\n

<\/div>\n","protected":false},"author":75,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[27,114],"tags":[120,119,121,60],"class_list":["post-543","post","type-post","status-publish","format-standard","hentry","category-classroom-practices","category-multidisciplinary-education","tag-common-core-standards","tag-liberal-arts","tag-mathematics-majors","tag-stem"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6C2AC-8L","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/users\/75"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/comments?post=543"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/543\/revisions"}],"predecessor-version":[{"id":545,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/543\/revisions\/545"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/media?parent=543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/categories?post=543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/tags?post=543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}