SMURCHOM: Providing Opportunities for Undergraduate Research in the History of Mathematics - How SMURCHOM Has Changed My History of Mathematics Course

As SMURCHOM has evolved over the years, so has the way that I incorporate the conference experience into my history of mathematics course.  This course is a semester-long overview of the history of mathematics, beginning in ancient Egypt and concluding with the discovery of the calculus.  It is required for our mathematics majors who plan to teach in secondary schools.  It counts as an elective course for other mathematics majors, those minoring in mathematics, and elementary and middle grades education majors earning a second academic concentration in mathematics.  Students ideally take the course as juniors, and all have taken Calculus I as a prerequisite. Graduate students from our MS in Applied Mathematics and MAEd in Mathematics Education may also take the course; additional assignments allow these students to apply the course towards their degree program.

SMURCHOM gives my history of mathematics students the opportunity to host a regional conference and discuss their research interests in the history of mathematics with students from a variety of other institutions.  Therefore, the main goals of my history of mathematics course focus on fostering these interests and giving students the tools to become independent researchers.  Any undergraduate education should foster a student’s ability to research independently; this ability is especially vital in the history of mathematics, a subject that could never be completely covered in any series of courses.

I have always started my course with an introduction to primary and secondary sources in the history of mathematics.  Because many of these sources are now available electronically, this introduction has developed into an internet worksheet and quiz that emphasize reliable sources.  The assignment and quiz may be downloaded here.

Using the Internet to Conduct Research in the History of Mathematics Assignment

History of Mathematics on the Web Scavenger Hunt Quiz

After learning about these sources, my students begin the process of choosing a topic.  The timing of the course and SMURCHOM means that my students must get their research underway before they have completed an overview of the history of mathematics.  In past courses, this timing has resulted in students struggling with finding research topics and entirely too many research projects on easily recognizable mathematicians covered early on in the course, such as Pythagoras and Euclid.  This year (2010), I introduced a topic list in order to combat these problems. I compiled many of the entries on this topic list while attending sessions on the history of mathematics at the Joint Mathematics Meeting in San Francisco in January 2010, so that my students would pursue fresh research directions.  I worried that this topic list could constrain my students’ creativity, so I emphasized that the list should only be viewed as a starting point.  At this point in their projects, my students often visit me during my office hours to brainstorm about ideas and to search for sources.

To accompany their research topics, my students have to form a research question.  Early in the course, they read several articles from Historia Mathematica with an eye towards research questions and historical arguments.  They then write a project proposal presenting their own ideas about questions they might raise, arguments they might make, and sources they might use in their project.  I find that this one-to-two page document prevents procrastination, forces focus, and provides me with an early alert to anyone on the wrong research track.  In addition, careful editing of this document allows me to convey my expectations of writing mechanics and style.

Students presenting their poster at SMURCHOM V (photo credit: Sloan Evans Despeaux).

The addition of the poster presentation to SMURCHOM allowed me to form another intermediate step in the research project.  About one month before SMURCHOM, my students present posters based on their research topics to a panel of judges from my department.  The stakes are high: the winners of the poster competition are chosen to give talks at SMURCHOM and do not have to write a final paper.  I find that this incentive results in truly excellent posters and very motivated students.  The “runners-up” in this judging process are invited to present at the SMURCHOM poster session.  Besides being an important intermediate step in the research process, this in-class poster session helps build community among my students.

Presenting a poster or talk at SMURCHOM gives meaning and a great sense of accomplishment to my students’ projects.  I find that they take pride in their work; for example, some invite family members to the conference.  Even for students not presenting, SMURCHOM is another important step in the research process, because it exposes them to the ways other presenters ask questions and make historical arguments.

The final step in the research project is crafting the final paper.  My students have commented that all of the intermediate steps make this final one much easier.  I find that their biggest hurdles are effectively organizing the paper and providing citations for it.  Our university’s writing center is a great help with these hurdles.  In the past, I have made a visit to the writing center mandatory.  This year, I gave a “carrot” instead of a “stick”: students who used the writing center got a one-week extension on their papers’ deadline.  Unsurprisingly, almost every student used the writing center!