Giving a Math Course for Non-STEM Majors
By Keith Devlin @profkeithdevlin
At the Joint Mathematics Meetings in Denver, CO last month, I participated as a panelist and group discussion leader in an MAA Project NExT session on mathematics courses for non-math majors. I focused primarily on non-STEM majors. The session was well attended, and it was clear that there is considerable interest in giving such courses. That was definitely not the case in the 1970s and 80s, when I was one of the relatively few university instructors who actively sought to give non-majors courses and enjoyed doing so, both in the UK in the early part of my career, and then later in the US.
Taking part in the JMM session, and being asked by the organizers to provide attendants with any materials I had, I realized that in all those years, I had put virtually nothing into the public record about the nature of the courses I’d given, the philosophies behind them, and my experiences in giving them. Time to rectify that.
Starting this month, I am going to start posting articles about those non-majors courses on my personal blog prokeithdevlin.org. (As an MAA outlet, Devlin’s Angle is not the right venue for what will inevitably be a “show-and-tell” series, put out on a “take it or leave it” basis. Although my hope is it will be viewed on a “take it or modify it or reject it basis,” which is how I am approaching it. We all learn from the experiences of others, even if what we learn is how we do not want to do something!)
In the meantime – and this is going to be one of the shorter Devlin’s Angle posts — let me just list here the main philosophical assumptions that have driven all my different attempts to teach non-STEM-majors courses. Judging by what I have learned from others who give such courses, including my four co-panelists in Denver, these are pretty common starting points for designing and giving such courses.
1. A non-STEM-majors course is usually offered to provide students with an option to fulfill a one-course mathematics requirement for graduating, which avoids a traditional STEM-oriented math course such as calculus or linear algebra. Such graduation requirements are extremely common and with good reason.
2. Many of the students who select such a course do not like math, and some of them are math-phobic. They just want to get that dreaded math requirement out of the way. They come, some of them, with an attitude or at least a negative mindset.
3. For almost all the students in the class, this will be the last math course they ever take. For those whose experience with mathematics so far has been predominantly negative, this is the last chance a representative of the mathematics community (you, the course instructor) has to turn things around a bit and leave them with a more positive view of the subject. Doing so successfully will likely make you feel good for a few minutes after the course is over and the grades are posted, which is nice, but it could have a dramatic, beneficial effect on the entire arc of their future life and career. (No need for me to explain why that is the case to an MAA audience.)
4. In addition, students who leave university with a positive attitude to mathematics are inevitably going to pass that attitude on to their children, which will increase the likelihood those offspring succeed in math. So it’s not just the course graduates who can benefit from the course.
5. All in all, giving a non-STEM course is likely to have a far greater impact on the students and on society than any one regular course you give for STEM majors! That’s worth reflecting on. It’s also possible that one or more of your students will end up in leadership positions in society, where they control or have an influence on mathematics-related policies. Think about that as well!
6. Talking about grades, as I did three paragraphs back, my own view, based on my experience as a math instructor is that, in a non-STEM course, grades are fine but they should be based on effort and overall intellectual quality, not mathematical performance. The course is not intended to make them better mathematicians. If they are in your non-STEM course, they probably long ago convinced themselves they cannot “do math.” And so they won’t be able to.
[ASIDE: I would strongly reject any suggestion that the courses I gave were easy or lacking in mathematical depth. Indeed, I frequently got requests from math majors to take my non-STEM course, even at elite universities like Stanford. Math majors heard about the course contents from their non-STEM friends and wanted to be part of the action. I usually said no, but that was because I had a strong rule of no more than 25 students in the class, and wanted all the places to go to those who needed it most — in order to graduate! But a math major could certainly get a lot out of such a course. Read on for more details on possible course content.]
7. My personal philosophy was always, and remains, that the course should involve doing some mathematics; not just reading, talking, and writing about mathematics, and watching (then discussing and writing about) math videos. My courses always had plenty of that, but they were never all that. Courses that are all that are sometimes referred to as “mathematics appreciation” courses. In my case, I felt (and feel) that since mathematics is an activity (not just a body of knowledge), an important part of the course is to experience doing math. So I always made such an experience a major part of the course.
These days, having them experience doing math is easy to arrange in a way the students can handle. Absent the requirements of
speed (which should never be part of mathematics learning),
accuracy (computers do that for us these days, and beat us hands down in speed for that matter), and
the ability to manipulate symbolic expressions, solve equations, draw graphs, and execute mathematical procedures (computers again for all of them),
anyone who has gained entry to a university is able to experience doing mathematics.
In fact, given the degree to which computers have revolutionized mathematical praxis, doing mathematics in a non-STEM course with digital tools handling all the heavy lifting, is not unlike the way today’s math pros work. (This approach was not possible prior to the 1990s. See the linked references at the end of this post for more on modern mathematical praxis.)
[ANOTHER ASIDE: Regarding the name “mathematics appreciation course” I referred to above, I avoided using it for my courses, because to me it implies an absence of that all-important experience-of-doing. But I think the name is okay. On the other hand, I never liked the popular “Math for Poets” name. I appreciate the non-threatening, humanities-and-arts friendly impression it tries to convey, but I can imagine designing and giving a math course that is really for poets, and that course would be mathematically deep and challenging. (It would involve a lot of mathematical linguistics, meter, patterns of cognitive arousal and surprise, and other topics.)
8. As to assigning course grades, my experience has been pretty consistently at highly-selective universities and colleges, where the students were used to being graded, expected it, and in most cases thrived on it. My few attempts to ease back on grading were rapidly abandoned when it became clear many in the class were then simply blowing the course off with minimal or no effort. (They’re human, after all, and they weren’t there out of love for the subject.) So I used simple fact recollection tests to give them a video-game-like reward structure for completing reading assignments (of which there were a fair number) — with a minimal threshold to be achieved, to make sure they did the reading and hence could participate in class discussions and activities — and based the final grade primarily on individual or group term-long projects.
9. What kind of projects? I tried a fair number of formats over the years. They all worked out pretty well. Purely as an example, I’ll end with the one I have used most recently. It was simply this. Look at the tracking data below for a package sent door-to-door from California to New Jersey by UPS “Three Day Guaranteed”. Based on that data (and anything you can find out about UPS on the Web or elsewhere in the public domain), reverse engineer the UPS routing algorithm.
I have used that project successfully with non-STEM students at Princeton, adult education students at Stanford, and high school students in the Bay Area (twice at each of those three venues). Working in teams, with my guidance (as a project consultant), it’s remarkable just how much detail the students can reconstruct from that one little dataset. Not just about the routing algorithm, but how the UPS empire is organized and the costs to UPS of its various operational units.
One thing I like about this project is it involves handling and interpreting data – a hugely important topic today for everyone. (Note that the record does not have the final tracking data. It ends at Louisville. That turns out to not be a problem. On the other hand, the peculiar sequence of entries in Oakland turns out to have huge informational value.)
The project also brings in the whole issue of how algorithms work, where they are used today (everywhere), and the social, ethical, and legal issues that arise from their use, all hugely important issues for today’s citizens.
And on top of all that, the project pretty well requires a number of detours through various mathematical topics, including some “pure math topics” that are staples of many, less-applied-oriented, non-STEM-majors, math appreciation courses! (Euclidean geometry, hypercubes, linear equations, and the selection of baseball teams arise naturally.)
For that project, I supplied the students with my own dataset, since it was a good one (that curious Oakland sequence in particular is highly revealing, but it has other fascinating features) and extracting important information from the data was sufficiently challenging that it required group work by the students (in groups of no more than four students) where the different groups exchanged ideas and progress reports on a regular basis, which was possible only when all the groups were working on the same dataset. But other projects could begin with each student group collecting its own data.
In case you are intrigued by the UPS project, I discussed (some aspects of) it as an illustration in three Devlin’s Angle posts in 2018, so you can find some details there:
How Today’s Pros Solve Math Problems Part 1
How Today’s Pros Solve Math Problems: Part 2
How Today’s Pros Solve Math Problems: Part 3 (The Nueva School Course)
But I will give a fuller account of that project, and suggest others that should work well, in my forthcoming series of posts at profkeithdevlin.org. Starting soon.
Read archived posts.