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Pitfalls and Potential Solutions to Your Primary Source Problems: Introduction

Adam E. Parker (Wittenberg University)


In 2005, I was a newly-minted algebraic geometry PhD who had earned a job at a small liberal arts school with two senior algebraists already on staff. Not surprisingly, I wasn’t assigned any algebra classes. Instead, I inherited the upper calculus and analysis classes. Unfortunately, I had (and have) no talent or background in these areas. While I was able to teach the content, I lacked (and still lack) the depth of understanding and experience with the material to create an engaging classroom. I needed to improve my very traditional, very by-the-textbook, very boring lectures. And I needed to do it quickly, as my teaching evaluations weren’t magically improving on their own.

Advertisement for 2008 Ohio Section Short Course on using primary sources to teach mathematics.
Figure 2. Advertisement for “Study the Masters.” Ohio Focus 8(6)(Spring 2008): 4.

So, in the summer of 2008 I attended an Ohio MAA Short Course entitled, “Study the Masters: Using Primary, Historical Sources in Teaching and Research.” The course was run by Danny Otero from Xavier University and David Pengelley from New Mexico State University.[1] The many benefits to using primary sources were central to the short course and were later summarized in an AMS blog post by members of the TRIUMPHS grant team:[2] 

Teaching from primary sources has long been common practice in the humanities and social sciences. Reading texts in which individuals first communicated their thinking offers an effective means of becoming mathematically educated in the broad sense of understanding both traditional and modern methods of the discipline. The use of original sources in the classroom promotes an enriched understanding of the subject and its genesis for instructors as well as students.

In contrast to many textbook expositions, which often present mathematical ideas in a distilled form far removed from the questions that motivated their development, original sources place these ideas in the context of the problem the author wished to solve and the setting in which the work occurred. Problems and the motivations for solving them are more apparent and natural in primary sources, and the works of these thinkers are more compelling than traditional textbook expositions. Exposing the original motivations behind the development of “esoteric” mathematical concepts may be especially critical for placing the subject “within the larger mathematical world,” thereby making it more accessible to students. Further, primary texts seldom contain specialized vocabulary (which comes with later formalism), thereby promoting access to the ideas by students with varied backgrounds [Barnett et al. 2015].

This was exactly what I needed: a technique to enrich my classroom and improve learning that didn’t depend on years of experience with the material. As added bonuses, this method was one that I personally found interesting and it was general enough to be applied across several classes.

Since that short course, my evaluations have improved and my professional activity has expanded. I've been lucky enough to write six Primary Source Projects (PSPs)[3] under the TRIUMPHS grant; multiple publications in Convergence,[4] The College Mathematics Journal,[5] and Mathematics Magazine;[6] and uncountably many[7] anecdotes, stories, and other primary source teaching materials. While I started by constructing projects for real analysis, I’ve now pivoted into differential equations, with multivariable calculus in my crosshairs.

I always hope that creating a lesson using primary sources will be smooth, but it never is. Challenges inevitably arise, and new projects seem to bring new dilemmas. The process often feels like Cantor’s diagonalization argument—as soon as you think you've listed all the issues out . . . you find another that wasn’t on the list. So, please don’t think of the following pages as exhaustive, but rather just as a personal collection of pitfalls and potential solutions that I share to hopefully save you time and headaches. The issues are presented roughly in the order that you may encounter them in the creation of a project, and so there may be a higher probability of experiencing those that appear earlier in this article. Luckily, those are also accompanied by more and better words of advice.

[1] Fittingly, it was David Pengelley at the 1992 meeting of the International Study Group on the History and Pedagogy of Mathematics in Toronto who encouraged Danny Otero to start using primary sources as he revised Xavier's “Calculus from an Historical Perspective” class.

[2] TRIUMPHS is the acronym for an NSF-funded grant, TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources, under which classroom materials were created from 2015 to 2022. Additional information, along with details on the editorial and peer review standards for PSPs, can be found on the project’s website. The grant’s mission is being continued by the newly-formed TRIUMPHS Society.

[3] You can find these projects at [Parker 2020a], [Parker 2020b], [Parker 2020c], [Parker 2020d], [Parker 2021a], and [Parker 2021b].

[4] You can find these papers at [Engdahl and Parker 2011], [Andre et al. 2012], [Cummings and Parker 2015], [Parker 2021c] and [Parker 2022].

[5] You can find these papers at [Parker 2013] and [Parker 2016].

[6] You can find this paper at [Leanhardt and Parker 2017].

[7] Not actually true.


Adam E. Parker (Wittenberg University), "Pitfalls and Potential Solutions to Your Primary Source Problems: Introduction," Convergence (December 2023)