# Intro to Proof in Four Weeks Part I: You want me to do what?

The teaching load for tenure-track faculty here at Washington and Lee University (W&L) is 5.5 courses per year. No, we don't have anything that really counts as a half course. Instead, what the administration means is that the long-term average number of courses each faculty member teaches in a year is 5.5. (We do have credit hour valuations on courses, but they're basically all three, four, or one. In math, all standard courses are three credits.) For most of us, that means we alternate between five courses and six courses. We also have a rather unusual academic calendar. We have two 12-week terms that we treat as semesters and then a four-week Spring Term. (Math faculty tend to teach 3-2-0, 3-2-1 in alternation, although some colleagues prefer 3-3-0 in their six-course years.) Until about a half dozen years ago, Spring Term was six weeks, and students took two courses. As part of W&L's last SACS reaccreditation, the project selected for the QEP was to revitalize the Spring Term. The way this was done was to shorten the term to four weeks, have students take a single four-credit course (possibly plus a PE skills course), and aim to offer a fully immersive experience. (If you're interested in knowing more about the design and intent of Spring Term, our administration has you covered.) Originally, all students were required to enroll for Spring Term, but we now allow them to "exercise the spring option", which basically amounts to taking time to look for a job, prepare for an internship or graduate/professional admissions exam, or even just relax. This year, about one in six students exercised the spring option.

Unlike some of our peers that offer a similar-length term as a "fun" experience for students and faculty, Spring Term is Serious Business™ at W&L. We already get some guff from SACS for only requiring 113 credit hours for graduation, and our design for that assumes 16 credits from Spring Term (four 4-credit classes). Sure, there are lots of spring term abroad courses (The Chemistry of Cooking in Italy, Exploring the West of Ireland, Medieval Spanish Cultures, and Photography & and the City), but there are interesting sounding courses on campus such as CSI: W&L, Psychology Mythbusters, Introduction to Engineering Design (usually involves building a bridge or concrete canoe), Cross-Cultural Documentary Filmmaking, and Politics & Film: The Politics of Mad Men. There are a number of lab science courses offered, which tend to be popular with upper-division humanities majors who've been putting off their lab requirement. The recurring theme, however, is that most of these courses are not something that someone would offer as a 12-week course here (or a 14-week course on a more typical calendar). The lab science courses are specifically designed for Spring Term. I think even the literature courses have been designed from the ground up with the special calendar in mind. Our dean has repeatedly told us that it took her several tries to get her Spring Term course "right".

What does the math department do for Spring Term? We teach a lot of sections of the bridge/foundations/introduction to proof course. We also alternate numerical analysis and the math of puzzles and games for more advanced math majors. Last year a colleague ran a popular set theory course. Some years, we have a 100-level cryptography course. Those all are, to some degree, courses designed for Spring Term. However, the idea of trying to help students make the transition to abstract mathematics in only four weeks was a jarring one to me. Most every upper division mathematics text refers to some amount of "mathematical maturity" expected of students. How could I develop that in only four weeks? Well, it wasn't like I had much of an option. By the last of our students had registered for Spring Term, we had two 15-student sections of MATH 301: Fundamental Concepts of Math full, and another 15 on waiting lists. Some grovelling before the dean resulted in opening another section. In the end, we had 44 students enrolled in our three sections. (I only had 14 in the end, while my two colleagues had 15 each.)

For those unfamiliar with a bridge course of this nature, here's our generally worthless course description: "Basic analytical tools and principles useful in mathematical investigations, from their beginning stages, in which experimentation and pattern analysis are likely to play a role, to their final stages, in which mathematical discoveries are formally proved to be correct. Strongly recommended for all prospective mathematics majors." Basically, the idea is to do things to help the students transition from their experience of mathematics in calculus (and for some a computation-heavy linear algebra course) to what will be expected of them in real analysis or abstract algebra. (Our majors must take a full year of each. Our minors must take a full year of one, and we just learned we have one of the four most popular minors on campus. I think we're first or second amongst minors that also have a corresponding major, which rules out things like poverty studies.) It should be noted that this course is not a pre-requisite for any mathematics course on the books. Nor is it a degree requirement for the math major. It is one of two courses that satisfy some pre-requisities/degree requirements in computer science. (The other is the discrete mathematics course that I seem on track to teach almost every year from now until the end of time, but it's a fun course, so I'm not complaining.) This course is part language course, part writing course, and part math course. Oh, and part programming course, since I required the students to learn $${\LaTeX}$$.

I think the last piece of stage-setting to give you is that this term, all three MATH 301 sections were scheduled for two hours per day, five days per week. I drew the unpopular (because it interferes with socializing time) afternoon time slot, but I did wind up with four former students (one each from each of the three calculus courses and one from discrete mathematics) and one of my first-year advisees in the class. Knowing over one-third of the class before it starts was a new experience for me, but it was good. Fortunately, I quickly built a rapport with most of the rest of the class, so it wasn't like there were "favorites" who I knew from past courses. In addition to the 10 contact hours per week, the University's expectation is 20–30 hours of work outside of class each week for each student. Survey data indicates faculty think students are putting in that amount of work, but students don't self-report numbers that high for Spring Term Courses. Thus, we've got one classroom with six beautiful slate blackboards, 14 students, one professor, two hours per day, and four weeks to try to learn how to write proofs. I only know of one other place (Bates College) that only offers this course as a short term course. (Some large public universities have a standard semester course of this nature that they cram into four weeks in the summer, but I consider that a different beast to our situation, where if a student wants this course, Spring Term is their only option.) If you know of others, please chime in with a comment; I want to form a support group for everyone who does this!

Coming up in this series of posts:

• Course design decisions (including rejected ideas)
• Course execution (no students were executed in the offering of this course)
• What do I want to do different next time?