{"id":19191,"date":"2025-02-18T12:04:00","date_gmt":"2025-02-18T17:04:00","guid":{"rendered":"https:\/\/notes.math.ca\/article\/the-triumphs-society-transforming-instruction-understanding-mathematics-via-primary-historical-sources\/"},"modified":"2025-04-10T09:06:58","modified_gmt":"2025-04-10T13:06:58","slug":"the-triumphs-society-transforming-instruction-understanding-mathematics-via-primary-historical-sources","status":"publish","type":"article","link":"https:\/\/notes.math.ca\/en\/article\/the-triumphs-society-transforming-instruction-understanding-mathematics-via-primary-historical-sources\/","title":{"rendered":"The TRIUMPHS Society: TRansforming Instruction: Understanding Mathematics via Primary Historical Sources"},"content":{"rendered":"

Learning a discipline by reading the original writings of the field\u2019s most important and innovative thinkers is a long and honored tradition in the humanities and social sciences. What better way to grapple with postmodern historiography than by reading Michel Foucault<\/a>? What would one read other than the Dialogues<\/em><\/a> to become familiar with the ideas of Plato? Why would someone even try to learn about Shakespeare\u2019s plays<\/a> and sonnets<\/a> without reading them oneself?<\/p>\n

But what about learning mathematics? Can you imagine asking your students to read Cantor<\/a> in an introductory topology course? What about reading Cauchy<\/a> in a course on linear algebra? And how about reading Gauss<\/a> in a second semester calculus course? Oh my! And yet this is precisely what the members of a small but growing community of mathematics instructors in North America have not only been proposing should <\/em>be done for several decades now, but are actually doing themselves, using classroom modules known as Primary Source Projects (PSPs) [1].<\/p>\n

Based on a guided reading approach to primary sources, PSPs are intended to replace the standard textbook treatment of core topics in the undergraduate mathematics curriculum, and to do so in about the same amount of time as a typical textbook-lecture approach to teaching a given topic [2]. Each project melds excerpts from primary sources with carefully-crafted tasks that interrupt students at specific points in their reading of the source material. This design lends itself especially well to student-centered instructional strategies (e.g., small-group discussions) as an alternative to lectures. PSPs also include commentary on the historical context and mathematical significance of the questions that the historical author set out to explore.<\/p>\n

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Figure 1. <\/strong>Primary source excerpt from Euler\u2019s 1738 article \u201cObservationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus\u201d (\u201cObservations on a theorem of Fermat and others concerned with prime numbers\u201d), featured in the 2017 TRIUMPHS Primary Source Project \u201cPrimes, Divisibility, and Factoring,\u201d by Dominic Klyve. Digital Commons at Ursinus<\/a>.<\/h6>\n

Since 2005, the development and classroom testing of PSPs has been supported by three grants from the US National Science Foundation, the latest of which was TRa<\/em>nsforming Instruction in Undergraduate Mathematics via Primary Historical Sources<\/em> (TRIUMPHS<\/em>). As a result of TRIUMPHS\u2019 efforts, approximately 100 PSPs were developed for use in university mathematics courses ranging from beginning algebra to topology, all of which are freely available for download and classroom use at https:\/\/blogs.ursinus.edu\/triumphs\/<\/a>. Through these projects, students are given the opportunity, for example, to study the derivatives of the sine and cosine functions directly from Euler<\/a>, uniform convergence of function series from the writings of Abel<\/a>, and ideals directly from the words of Dedekind<\/a>.<\/a> Classroom testing of these and other PSPs by over 120 university mathematics instructors in 200+ classrooms at a wide variety of institutions across the US and Canada also took place under the auspices of the TRIUMPHS grant [3].<\/p>\n

Of course, teaching with primary sources is not without its challenges . . . but neither is it without its benefits, for students and instructors alike. For instance, here are just a few of the benefits of using PSPs that instructors who served as site-testers under the TRIUMPHS grant reported:<\/p>\n