Mathematics Instruction, an Enthusiastic Activity

By William Yslas Vélez, Professor in the Department of Mathematics at the University of Arizona.

The best recruiting tool I have to convince students that they should continue in the study of mathematics is the mathematics that I am teaching, no matter the level. It is all fascinating. In almost every lower division course that I have taught I have convinced at least one student to add the mathematics major. The last time I taught second semester calculus, three students added the math major and one the math minor (and the student selecting the math minor simply could not fit in the last three mathematics courses for the major). One of those students is now a graduate student in biostatistics at Harvard.

I have been fortunate that our department has insisted on teaching mathematics in classes no larger than 35 students. Given the small class size, I require each student to come to my office to talk about his or her career plans. I ask about their goals and I suggest how taking more mathematics can help the student meet those goals. During class time I often mention more advanced courses that will touch on the material being presented. When my students begin registering for courses I offer my assistance in selecting courses for the following semester and beyond. I tell them that I would be pleased to talk to them if they want to stop by in the future to discuss their career plans.

If we viewed our function as communicators of mathematics differently, we would greatly increase the mathematical preparedness of our students. We teach the most fascinating subject in the world. We need to communicate this to our students.  Mathematics holds a unique place in university studies. Most programs of study include mathematics as a requirement and mathematics is often part of the recommended first-year course of study. Why?

There are quantitative aspects of programs of study for which mathematics is essential. The growth in the amount of data that is now available is enormous and is a relatively recent event. The mapping of the human genome and the data that the internet generates every day are mined to obtain information about individuals and societies. This amount of data is a new phenomenon and it has impacted many different fields of study, increasing their quantitative needs, and thus increasing their mathematical requirements. This increase in the quantitative needs of other disciplines represents an opportunity for mathematics departments. We can revamp/create mathematics courses to entice more students to include more mathematics in their undergraduate curriculum. All of this is good for mathematics departments, as we are given the opportunity to interact with students at many stages of their careers.

There is another answer to the “Why?” question. Some popular programs, which have limited resources, place mathematics courses as barriers, hoping to keep the size of their program to manageable levels. Mathematics courses, and mathematics departments, now take on a very different function. We are the ones who weed out students from these popular careers. The result is that those students who could not succeed in university mathematics courses come away with a negative view of mathematics. Many of us have encountered individuals who state that they cannot do mathematics, and they seem to say this with pride. However, I have never heard a person tell me that he/she cannot read! It seems to be acceptable in this country to be mathematically illiterate but unacceptable to be illiterate.

The inability of students to pass our mathematics courses has a dramatic impact on their lives. We often hear that a student chose this or that career. This is far from what really happens. The lack of mathematical training precludes entrance into so many careers. It is a fact that the more mathematics a student takes, the more careers are available to that student. This fact places a responsibility on us, as communicators of mathematical ideas. We should not lay the blame on pre-college instruction. It is up to us to address effective instruction in university mathematics courses.

The role of gatekeeper is not a role that we should relish and I want to suggest that mathematics departments embark on a new strategy. Surprise!

All of our courses, no matter how elementary, should be taught with enthusiasm and with the view that we are preparing students for the next mathematics course. We should surprise these popular programs of study by increasing the passing rate of our courses, and at the same time, increasing the number of students pursuing further mathematical studies [1,2]. Our role is not to keep students out, but rather to help students to reach their goals.

The unique role that mathematics holds in our educational system places on our mathematics departments a responsibility. It is up to our teaching staff to provide a broad mathematical education for our students, one that motivates students to the further study of mathematics. In fact, the goal of a mathematics course is not to teach this or that. It is to show the students that the material is so interesting, so germane to their lives, that they have to take the next mathematics course.


[1] Increasing the Number of Mathematics Majors, Focus, March 2006, pp 24-26.

[2] Not business as usual, Opinion Piece, Notices of the American Mathematical Society, May 2003, pg. 533.

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2 Responses to Mathematics Instruction, an Enthusiastic Activity

  1. Amila Appuhamy says:

    A short article that tells the role of a math teacher. Communication between the student and teacher is very important.

  2. Igor Fulman says:

    “Many of us have encountered individuals who state that they cannot do mathematics, and they seem to say this with pride. However, I have never heard a person tell me that he/she cannot read! It seems to be acceptable in this country to be mathematically illiterate but unacceptable to be illiterate.”

    Moreover, it seems to be acceptable in this country TO BE PROUD OF BEING MATEMATHICALLY ILLITERATE. So many times, when I said in a company: “I am a mathematician” or “I teach mathematics”, somebody would say with pride, or almost with pride: “And I don’t know **** about math”. Sadly, it is a part of American culture – to be proud of not knowing something…

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