By William Yslas Vélez

(Photo credit for cover photo:  Dr. Donald Cole. Photo also appears on the Math Alliance website.)

Beginning in the late 1980s I began my efforts to help minority students succeed in calculus. As I worked with minority students it slowly dawned on me that majoring in mathematics would be beneficial to a student’s career path. It is embarrassing how long it took me to realize this. With time I changed my strategy. Instead of working with students in a particular class, I decided to contact as many minority students as possible to inform them of the benefits of including more mathematics in their undergraduate program of study. This strategy served to increase the number of minority mathematics majors in our department so that approximately 15%-20% of the mathematics majors were minorities. In 2003, when I became director of the Math Center at The University of Arizona, I brought to that position an aggressive attitude of reaching out to students and years of experimenting with what to tell students to convince them to take more mathematics. “Just take one more mathematics course” was my mantra [1].

In [2], I described a twenty-minute advising session with a student. In my many visits to mathematics departments I had always wanted to arrange an advising session with a student, and have faculty look on. I looked forward to the critique. This would have led to very useful discussions, but I was never able to arrange this. COVID presented an opportunity to share an advising session with the community. The Institute for Mathematics and its Applications at the University of Minnesota had partnered with the Math Alliance to hold a summer workshop on mentoring, and I was asked to give a presentation. In preparation for this workshop, I held a zoom advising session with a student and that advising session was recorded. The zoom recording is not of high quality, but it is sufficient to listen in and more importantly, to hear the reactions from the student.

The student (M) in the video was enrolled in his third semester of study. In his first year M had taken calculus I and II, a physics course and a computer science course. Even though I had retired I was still looking at student enrollments and sending students messages asking them to stop by my office. M had enrolled in calculus III and so appeared on my list of students to contact. M replied and I set up the zoom advising session. This is the only zoom advising session that I ever recorded, and I asked M for permission to record the session. I never talked to M again. Ordinarily I would have followed up as M enrolled in more mathematics classes, but I was retired and not following up on students as I did when I was working.

In this article I will break down that advising session into several parts, explaining what my goal was and commenting on M’s reactions. This article gives an example of an implementation of [2].

Part 1 (2:36):

I want to know the student’s major, what they are involved in and what their career plans are. M was already working on a research project and had set some goals. In listening to a student, I try to determine why enrolling in more mathematics courses would benefit the student. Even though the student is only in their second year of study, I bring up the possibility of going to graduate school. Most students at this point in their studies have never thought of graduate studies nor do they know that they are paid to attend graduate school. Notice M’s reaction when I mention that a student is paid to attend graduate school. Priceless!

Part 2 (3:22):

I go on to describe the benefits of attending graduate school. Besides being supported financially, students have travel opportunities and are also able to obtain paid internships during the summers while they are in graduate school. I also point out that a student can work on very applied problems in a graduate mathematics program. I want to make a very important point here. Majoring or minoring in mathematics as an undergraduate makes you more competitive for graduate school in any other area. That is one reason why taking more mathematics is beneficial for a student. For students who want to enter the workforce after graduation, a strong background in mathematics, combined with computing skills, makes the student’s application stand out.

Part 3 (0.57):

I never suggest that a student change their major to mathematics. I suggest adding the mathematics major to their program of study, which I did in this case. I thought that M’s interests would be better served by taking more courses in computer science. M was enrolled in the second semester of a  programming course which suggested to me that M continue to explore computer science as a minor or major and of course continue on with physics.

Part 4 (2:17):

I went over the schedule of courses that M was enrolled in. M had enrolled in two physics courses, a computer science course and calculus III. I suggested that M replace one of the physics courses with the sophomore level course in linear algebra. (Though this does not appear in the video, the physics advisor had suggested that M enroll in two physics courses, even though the two courses overlapped in time. That is the reason that I suggested to M to only take one physics course.) I mentioned what mathematics courses M would take the following semester as a mathematics major and briefly described some of the options available for the mathematics major. I viewed the third semester as one of guided exploration. Once that semester was over M could go on in several different directions. Notice the reaction of M to the advice provided.

Part 5: (2:22)

I told M that I would send a link to look for research and internship opportunities. There is an “Annotated List of Summer Opportunities” available on the Math Alliance website.  Students with good grades should apply for summer positions as soon as possible. For M, look at the courses that will be completed by the end of the sophomore year: calculus, linear algebra, differential equations, introduction to proofs, 3-4 courses in computer science and physics. M looks like he could be majoring in any of these three areas and therefore competitive for applying to a variety of summer research or internship opportunities. And let us not forget about the life sciences. Even though M has not taken courses in the life sciences, M would be an attractive asset to a life sciences program. I have seen many mathematics majors work in life sciences laboratories very early in their careers. It is especially important for mathematics majors to take programming courses. In our department, weekly messages are sent to mathematics majors. These messages inform the students of opportunities for employment and many other things. It is critical to describe special opportunities that exist on your campus for students.

Part 6: (0:38)

Part 7a: (1:15)

One of the biggest obstacles that students have in applying for summer positions is the lack of individuals who will write a letter of recommendation. This is even the case for students who perform well in their courses. These students feel that they do not need to attend office hours. Students don’t understand the role of office hours. Office hours present an opportunity to establish a relationship with faculty. By establishing such a relationship, faculty can then support students later in their studies.

Part 7b: (0:06)

Students benefit from advice. Developing an advising program that reaches out to students would result in more mathematics majors and more students who have developed programs of study that are richer in mathematical content.

Part 8: (0:55)

The importance of having a resume. Here is a link to a sample resume that I have used for many years.

Mathematics majors should have resumes and departments should require them of their students. A resume is quite useful. It develops a sense of professionalism in the student.

Part 9: (0:29)

Nice to see the appreciation that M expresses. M has developed an exploratory program of study that can lead in many different directions.

Epilogue: M followed my advice for the third semester. M enrolled in calculus III, linear algebra, a computer science course and a physics course. For the fourth semester, M took differential equations, an introduction to data science and two computer science courses. M took no more physics. M changed the physics major to a computer science major and completed the requirements for a minor in mathematics.

The role that mathematics plays in society is dramatically different from the last century. Mathematics is ubiquitous. The more mathematics a student takes, the more opportunities that are available. But how would a first-year student know this? It is our responsibility as mathematicians to inform students of the importance of including more mathematics in their curriculum. If we could convince every first-year student to take more mathematics, we would change the world. 

References

1. Arizona’s Math Center Wins AMS Award. Notices of the AMS, Volume 58, #3, May 2011, pages 718-721.

2. Inreach is the New Outreach, MAA Focus, Volume 45, No.4, August/September, 2015, pages 4-5.

William Yslas Vélez is Professor Emeritus at The University of Arizona, having retired in 2018. In 2003, when he became the director of the Math Center he had one simple goal. Every student at the UA should be a math major or math minor. Though he did not meet this goal, he more than doubled the number of math majors, at the same time increasing the percentage of minority mathematics majors. He has tried not to fail at retirement, but his work to increase the number of mathematics majors, especially minority students, has earned him a D in retirement.