I have offered papers for a variety of classes. For most students, the idea of writing a math paper is completely foreign to them. As a mathematics educators, we should encourage the learning of all of the mathematics out there, and I have taken this past opportunity to offer historical papers. I think it would otherwise be difficult for mathematics students to write a mathematically rigorous paper on the mathematics that they are just learning now.
Depending on the level of students, I have required different lengths of papers. Below is a full copy of the assignment I have offered to have them write on, though I leave open the option for them to find other topics.
Please write a (minimum) five-page (double spaced, 1 in margins all around,
Times New Roman 12-point font, APA formatting) paper emailed to me by 11:59PM,
May 16. List all your sources. Each of these topics below has more than
enough material to fill five pages, but there are lots of other topics that
can also be written about. You must confirm your topic with me before you
One possible outline:
• Introduction: Give a general overview of the subject
• Body: Explain the topic. Explain why it is important. How does it related
to anything in the world today? What other fields is it connected to?
Expand on one (or more) particular idea, and go over it in detail.
• Conclusion: Explain what you learned doing the research. Was there
anything that was familiar you came across during your research? List all
sources used. What was the most interesting thing in the research to you?
Examples of Extra Credit Topics:
The number e, its history, and uses
The number π, its history, and uses
The Fibonacci numbers
The Mandelbrot Set
Pigeon Hole Principle
Carl Friedrich Gauss
Joseph Louis Lagrange
Augustin Louis Cauchy
Jean Baptiste Joseph Fourier
Peter Gustav Lejeune Dirichlet
Outcomes: It has been a few years since I incorporated this in a class, but as I recall, most students chose not to write a paper. Many expressed that they thought it was impossible to write 3-4 pages on a mathematics topic. There were some who chose to write the papers though. Those who did, saw how much was out there, they were amazed at how much they had to cut out.
Did Students Learn Things? This is difficult to quantify from my assignment. The main goal I was trying to accomplish was to have my students learn that there is a lot of other math out there; that it's not just pushing numbers around. I would say that those students who took the assignment seriously did see that there was at least some other aspect of mathematics.
What would I do differently? After first giving this assignment, I found that many students were drawn to write about the well-known mathematicians. After reading 3 papers on Newton that provided nothing new for me to learn about him, I eliminated him, along with a few others perhaps (I think Einstein may have been on my original list).
Would I do this again? I just gave this to a remedial class the other day. When I receive the papers, I will post on more results. I will continue to offer this as an extra credit assignment for appropriate classes until I find something more valuable.