"Math is Fun" and Other Aphorisms

Of late, I've been following articles on how students' perception of their own mathematical abilities strongly influences their long-term mathematical performance. One that stands out is the recent Atlantic article The Myth of 'I'm Bad at Math', which should be a must-read for educators, students, and parents. The number of first-year college advisees (or students in my courses) that I've had who start their conversation with me with the statement that, "I'm just not a math person," or, "Math/Computers and I just don't get along," is worrying -- particularly because they're often fine with the math in their courses within a few weeks of adjusting and practicing.

One of my favorite recent humorous takes on this was a video-post For all the Artsy People Secretly Wondering about how Math Works that appeared on Upworthy, featuring (of all people) someone I knew from my time in graduate school up in Ithaca, NY.


There is a Chronicle of Higher Education article from earlier this year by Bryna Kra (of Northwestern University), Mathematics: 1,000 Years Old And Still Hot, that speaks more personally to me as a mathematical educator. As a particular relevant excerpt:

Increasingly, students arrive at colleges without sufficient background to take basic mathematics courses. Nonetheless, we are expected to teach them the higher-level concepts they need for classes in biology, statistics, physics, and chemistry. But mathematics builds on a previous foundation and cannot be taught starting at the end. It is like asking a student unable to read a newspaper to analyze Shakespeare.

From an early age, children are directed to books appropriate to their individual reading levels. Working within guidelines for a third grader, a good teacher or librarian directs a student to appropriate material, and schools are equipped with reading material at a wide range of levels. But elementary education in mathematics does not have specialists like librarians to present students with appropriate-level material. The result is that we bore the good students and lose the weaker ones, helping only some in the middle. Improving the STEM work force starts early—focusing on individual needs and teaching the language of mathematics.

As an assistant professor at a small, residential, liberal arts campus (Hood College in Frederick, MD), where we focus extensively on our students (class sizes capped at 24, with most classes averaging around 14 students, amply-available tutoring hours by peers, an open-door policy for most professors' offices, et. al.) we still have students slipping through the cracks or failing even the most introductory of mathematics courses. For students who place below the 100-level, the remedial coursework necessary to take even the non-calculus computational literacy Core class can take up to two semesters, and carries no college credit. These introductory/remedial classes at Hood are taught by a dedicated mathematics education specialist and have a cap of 10 students per course -- and even with the high level of resources we devote to these courses, the passing rate is still startlingly low.

One of the key parts in our drive to increase pass rates for our calculus courses (with classes typically including both mathematics and non-mathematics majors, including in particular students in computer science, chemistry, biology, or economics,) been to teach them "workshop style". The class meets for a little over five hours a week, and includes integrated laboratory and computer work, with the goal of helping students visualize the uses of calculus in modeling in the real-world. (As moderate self-promotion, here's a YouTube video featuring yours truly on iPads at Hood, showing how we use an electronic textbook, in conjunction with Notability, Dropbox and Blackboard, all in our calculus courses.)

While this course is an absolute blast to teach, I've been a little demoralized this semester at the student response. As per usual, they "hate the electronic textbook", "think Maple is confusing/impossible/evil", and "wish it was more like calculus in high school."

None of this student response is new precisely -- every semester, the students feel this way. The textbook we use, Calculus: Modeling and Application, focuses fairly heavily on solving differential equations that arise naturally in modeling real-world phenomena. Some of the problems and projects students explore are great -- for example, they use Euler's method on systems of differential equations to study epidemics (implemented in the Sage or Maple softwares, this allows them examine how changing disease parameters changes patterns of disease spread), and they use derivatives to prove Snell's law of reflection by finding the optimal (i.e. shortest) path light will take between two points.

Many articles in mathematics education claim that students working on "real" problems will engage more strongly with the underlying math. While that could well be true, from my own experience I suspect that college is a little late to start that style of problem solving and expect students who have made it all of the way to calculus (those accustomed to and rewarded by the drill-and-memorize-style of math) to enjoy it on the first go-round.