There are many topics in math that can be summed up in a cute phrase that helps one remember a mathematical concept. For example, the line “Please Excuse My Dear Aunt Sally” is used to help remember the order of operations in algebra (representing parentheses, exponents, multiplication and division followed by addition and subtraction.) Our college, Ursuline College, also has a tag line that is found on almost everything that advertises us to the public. It reads “Values, Voice, Vision.” It is the “voice” part of this line that I recalled recently when I found myself answering a question in my calculus class last week, as part of what might best be described as “the talk.”
One of the students asked the question that every teacher dreads hearing- “so, when are we ever going to need this, anyhow?” I was somewhat expecting it, and, as an applied math person who is also an economist, I was confident that I could come up with some good answers. However, as I started answering, one of the students suggested that we try to come up with twenty reasons why calculus is useful. No problem, I thought; I am sure that we can come up with twenty reasons why they should learn calculus. The only caveat was that I was giving this project a very limited amount of class time, after which I would stop and they would work on a worksheet that I had made for them.
And so we started listing them. It began with things like “calculus teaches critical thinking,” and progressed to thoughts from the students of “it makes you a better person.” Recalling some miserable people I have met over the years who are excellent mathematicians, I put a question mark after that one. One student even suggested that studying calculus will help you in future relationships - another question mark. And so we went on. We hope that someone involved in construction knew calculus if you ever plan to cross a suspension bridge, as calculus is necessary for the architect to build such a structure. Looking out the window at what was left of the building containing what, until a few weeks ago, used to be our swimming pool, I talked about how calculus helps us figure out the rate at which a container can be filled or drained (in our case, drained.) And then I addressed the pre-meds and pre-vet student in the classroom, saying that anytime there is a change involved, as when a medicine enters and spreads through the body, calculus is involved. We listed engineers and architects and even artists as people who benefit from calculus, if not directly, at least indirectly. In the end, I admit that I was really struggling, but we managed to find twenty situations in which knowledge of calculus helps us.
OK, so the last one I listed, NASCAR drivers (I thought of that after listing NASA as a group that uses calculus,) might not use calculus directly, but I amended it to say that designing the cars that run so fast requires calculus. In the end, they agreed that almost everyone benefits from the insights given to us by calculus. However, I think that they were still skeptical as to why they, in particular, need to take Calculus as part of their college program.
I have to conclude that my students will come to appreciate the beauty of calculus only as they progress through the course. I recall the first time I learned calculus as an undergraduate, and realize that I would never have had the courage to ask my teachers why I should take their class. However, I am glad that my students had the courage to give voice to the question, leading to our little talk.