{"id":1931,"date":"2010-07-05T11:30:58","date_gmt":"2010-07-05T11:30:58","guid":{"rendered":"http:\/\/meeseeks:5080\/blog\/?p=1931"},"modified":"2025-01-12T21:30:22","modified_gmt":"2025-01-12T21:30:22","slug":"the-cultures-of-mathematics-education","status":"publish","type":"post","link":"https:\/\/vukutu.com\/blog\/2010\/07\/the-cultures-of-mathematics-education\/","title":{"rendered":"The cultures of mathematics education"},"content":{"rendered":"<blockquote><\/blockquote>\n<p>I posted recently about the <a href=\"http:\/\/meeseeks:5080\/blog\/2010\/03\/macho-mathematicians\/\" target=\"_blank\" rel=\"noopener\">macho culture<\/a> of pure mathematics, and the undue focus that school mathematics education has on problem-solving and competitive games.<\/p>\n<blockquote><\/blockquote>\n<p>I have just encountered an undated <a href=\"http:\/\/www.dpmms.cam.ac.uk\/~wtg10\/2cultures.pdf\" target=\"_blank\" rel=\"noopener\">essay<\/a>, <em>&#8220;The Two Cultures of Mathematics&#8221;, <\/em>by Fields Medallist Timothy Gowers, currently <a href=\"http:\/\/www.dpmms.cam.ac.uk\/~wtg10\/\" target=\"_blank\" rel=\"noopener\">Rouse Ball Professor of Mathematics at Cambridge<\/a>. <\/p>\n<blockquote><\/blockquote>\n<p>Gowers identifies two broad types of research pure mathematicians:&nbsp; <em>problem-solvers<\/em> and <em>theory-builders<\/em>.&nbsp; He cites Paul Erdos as an example of the former (as I did in my earlier post), and Michael Atiyah as an example of the latter.&nbsp;&nbsp; What I find interesting is that Gowers believes that the profession as a whole currently favours theory-builders over problem-solvers.&nbsp; And domains of mathematics where theory-building is currently more important (such as Geometry and Algebraic Topology) are favoured over domains of mathematics where problem-solving is currently more important (such as Combinatorics and Graph Theory).<\/p>\n<blockquote><\/blockquote>\n<p>I agree with Gowers here, and wonder, then, why the teaching of mathematics at school still predominantly favours problem-solving over theory-building activities, despite a century of Hilbertian and Bourbakian axiomatics. &nbsp;Is it because problem-solving was the predominant mode of British mathematics in the 19th century (under the pernicious influence of the <a href=\"http:\/\/meeseeks:5080\/blog\/2009\/10\/the-mathematical-tripos-at-cambridge\/\" target=\"_blank\" rel=\"noopener\">Cambridge Mathematics Tripos<\/a>, which retarded pure mathematics in the Anglophone world for a century) and school educators are slow to catch-on with later trends? &nbsp;Or, is it because the people designing and implementing school mathematics curricula are people out of sympathy with, and\/or not competent at, theory-building?<\/p>\n<blockquote><\/blockquote>\n<p>Certainly, if your over-riding mantra for school education is <em>instrumental relevance<\/em> than the teaching of abstract mathematical theories may be hard to justify (as indeed is the teaching of music or art or ancient Greek).<\/p>\n<blockquote><\/blockquote>\n<p>This perhaps explains how I could learn lots of tricks for elementary arithmetic in day-time classes at primary school, but only discover the rigorous beauty of Euclid&#8217;s geometry in special after-school lessons from a sympathetic fifth-grade teacher (<a href=\"http:\/\/meeseeks:5080\/blog\/2009\/09\/thinkers-of-renown\/\" target=\"_blank\" rel=\"noopener\">Frank Torpie<\/a>).<\/p>\n<blockquote><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>I posted recently about the macho culture of pure mathematics, and the undue focus that school mathematics education has on problem-solving and competitive games. I have just encountered an undated essay, &#8220;The Two Cultures of Mathematics&#8221;, by Fields Medallist Timothy Gowers, currently Rouse Ball Professor of Mathematics at Cambridge. Gowers identifies two broad types of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,50,51],"tags":[],"class_list":["post-1931","post","type-post","status-publish","format-standard","hentry","category-culture","category-mathematics","category-matherati","p1","y2010","m07","d05","h11"],"_links":{"self":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/1931","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/comments?post=1931"}],"version-history":[{"count":4,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/1931\/revisions"}],"predecessor-version":[{"id":13603,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/1931\/revisions\/13603"}],"wp:attachment":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/media?parent=1931"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/categories?post=1931"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/tags?post=1931"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}