Sarah J. Greenwald, Appalachian State University
Many students never learn about the mathematical achievements of women and minorities even tough incorporating these achievements into clases has been shown to be beneficial to all students. In addition, women in math courses are often taught as women's studies classes that do not include mathematical content.
This talk will examine a course on women in math that combines significant mathematical content with history and equjity issues. We will discuss the benefits and effects that this course had on the students in addition to classroom suggestions.
Daily class work and other information has been placed on the web at www.mathsci.appstate.edu/~sjg/womeninmath in the hope that this will help teachers incorporate women's mathematical achievements, history and equity issues into their classrooms.
Women in math courses are often taught without significant mathematical content, focusing instead on history and equity issues.
I approached IDS (Department of Interdisciplinary Studies) at my school about teaching a women in math course combining math with history and equity issues. My school, Appalachian State University, is a comprehensive public university with 12,000 students. We have a small master's program in mathematics.
IDS funded the course, which ran last fall as a senior level math class cross listed as a junior level IDS class. The course met for three 50 minute sessions each week, on Monday, Wednesday and Friday. The course lasted one fifteen week semester. Prerequisites for the course were a sophomore level math class - either Introduction to Linear Algebra or Calculus with Analytic Geometry III
I had 7 students, 2 of whom were men. 6 of the 7 were planning to become math teachers, mostly secondary education.
I've put lots of resources on the web including a page for those interested in teaching a similar course, and another page which includes classroom activities and assignments.
In this talk, I'll be giving you and overview of these web resources as I discuss both the students and my experiences with the class.
Since there are numerous web pages that include syllabi for equity and history based women in science courses, I'll focus on the mathematics and on how to weave math, history and equity into one course.
I wanted the students to learn about the lives and mathematics of women mathematicians.
I wanted them to be able to research history, mathematics and equity issues in a variety of sources including books, the web, MathSciNet and the library. MathSciNet is an AMS web site where one can search for papers on or by mathematicians. AMS donated it for use during the course and since then our library consortium has purchased it.
Also, given any one source, I wanted them to be able to summarize and critically evaluate it.
Given many sources on a woman mathematician, I wanted them to develop the ability to summarize her life and work.
But, I wanted them to also do some mathematics, not just summarize it, so I wanted them to develop the ability to focus on a reasonable math aspect to research, write up in their own words and speak on.
I wanted them to develop written, oral and web communication skills.
I realized during the first week that there was one additional goal that I'd left off of the syllabus.
At the end of the semester, we examined some of this research. This list of references, compiled with help from Dr. Andrew Nestler, is accessible from my web page, as is everything else you will see today.
Given that 6 out of my 7 students wanted to be high school or elementary school teachers, I realized very early on that I had left off the goal of exploring how to incorporate the mathematics into their future classes.
We did do this throughout the semester and I will explicitly list this as a course goal next time I teach the class.
We began the course with a discussion of a reading on the history of women's education to give us some historical perspective on the women that we would soon learn about.
We then delved into the life and possible mathematics of Hypatia.
I modeled the process that the students themselves would soon be going through to write papers:
I am grateful to Dr. Edith Prentice Mendez for her help and advice on Hypatia's life and work.
I handed out folders containing relevant articles and they were directed to find additional resources through web searches that we started in the class computer lab.
The paper was to contain two parts:
Part 1 - An overview (in their own words) of the mathematician's life and work.
Part 2 - A detailed description (again in their own words) of the mathematics that I
described in the assignment.
For the math, they were also told to give simple examples.
The goal of paper 1 was for students to learn how to summarize material from many sources, learn how to write on a focused math topic and learn how to communicate their work to the rest of the class.
I was pleasantly surprised to find that the students were fairly independent, as I had assumed that they would spend lots of time in my office hours. One pitfall of this independence was that the group doing Emmy Noether had checked out all the books from the library with the words Noetherian Ring in the title. They eventually came to me and told me that they just didn't understand even though they had tried reading it over and over again.
I was happy to see that they were trying to dive into the mathematics. We discussed that they needed to step back an level and look at books with Abstract Algebra as the title. Next time I teach the class, I plan to have a meeting early on with each group.
While they were working on their first draft, we had readings on equity issues and had class discussions based on these readings. I was pleased with their first drafts and handed them back to them with comments.
They prepared 30-40 minute long presentations to the class. After each presentation, we discussed highlights of the life and math within the context of the equity issues that we had been learning about. We also looked for similarities and differences in these women's lives to see if we could come to any conclusions about the period that they lived in. We talked about the focused math and about how we could incorporate this math into high school and elementary school classrooms. I was pleased with the results!
I was excited about the energy level and work ethic. They found articles on MathSciNet and dived into them. It was really exciting to see this happening!
Early on, each group turned in a list of preliminary references along with the topic of focused mathematics that they had chosen.
As they were working on their papers, we had class discussion on equity issues from readings again.
Student presentations were very nice and afterwards we discussed them in the context of equity issues and the period the women mathematicians lived in. We also looked for ways to incorporate the math into the student's future classrooms.
Since the students had been working so hard all semester, I had been concerned that they might be burned out at this point. I was happy that this was not the case, as I was asking them to do a lot more for this paper. They needed to do lots of independent research to find which woman they would like and what math aspect they would like to focus on. Many of the students chose a woman mathematician by first choosing a general mathematical area that they wanted to learn more about, and then finding a woman who worked in this area.
I was pleased to see them jumping into research papers and trying to figure out what they could understand.
I also asked them to include a full list of published papers and any students.
After each presentation, we did some of the same analyses as before.
For the final web project, they were directed to choose one of their previous papers and expand it to a series of web pages that would be accessible to anyone. We used Microsoft Word to convert their work to html, and I edited their html files if the converted had problems with formatting.
They were also asked to come up with a list of web references and a critique of their opinion on the usefulness, validity, etc. .. of each reference.
You may also be wondering about my time and effort. Setting up the framework took a lot of time. Deciding on the equity papers I would use for the class took some time, but I based my choices on syllabi that I found on the web, such as Dr. Helen Moore's women in science course. Deciding on references that I would put in folders for the first two papers was harder since I couldn't find any syllabi of women in math courses that included mathematical content. I looked at the references in Grinstein's book and supplemented these with web research and talking to people. My choices are on the web, although I am still finishing up the references for paper two.
Researching Hypatia's mathematics also took a lot of time, but I have put detailed info on the web for future reference.
The class itself ran very smoothly and took little time and effort once it started. Of course grading the three papers took some time, but because of the format of classroom discussions based on readings, and student presentations, I really was not putting in much time outside of class after the initial setup. As part of an NSF ROA, I worked on the course during the summer beforehand, and my department also gave me some release time during the previous spring.
On the exit survey, I asked them to name ten women mathematicians along with the mathematics that each worked on. While not all of the students could name ten with math, everyone in the class could name at least seven along with the math, which I was pleased about.
I believe that the course goals were met. When asked to comment on the goal of having students develop the ability to focus on a reasonable aspect of mathematics to research carefully, write up and speak on, one student remarked that this was kind of hard sometimes, but very good. Another student said that she felt that this class helped her in advancing her ability to do research and speak about math, and that it was very encouraging.
Even though I forced the students to work very hard and to be independent, my evaluation number was very high, a 4.93 out of 5.0.
Both the students and I learned a ton of new math. We all learned about women mathematicians in the context of equity issues, the period that they lived in and their mathematics. I loved teaching the course and was very pleased with the results.
I would suggest making the course Women and Minorities in Mathematics instead of just Women in Mathematics. I plan to teach the course this way in the future.
I was happy when a student who plans to be a high school teacher commented on his evaluation that this was one of the few classes in the department that he could walk away from and actually say "I will use this in my classroom."