Chris Buddle had his undergraduate students read E. O. Wilson’s recent editorial and then discuss the role of mathematics in ecology. Inspired by Chris’ idea, I also asked my undergraduate students to read and react to Wilson’s editorial. Here’s what they had to say.
First, some background. The responses come from my population ecology class, a heavily-mathematical upper-level class required of ecology majors at the University of Calgary. Everyone in the class was an ecology major, or the equivalent in the case of two exchange students from France. Unlike Chris, I didn’t have an in-class discussion of the editorial, although that’s something I’ll consider for future years. There were very few class sessions left in the term by the time the editorial came out, and I needed them all to cover the course material. So instead, I gave the students the option of reading and responding to the editorial as a “participation activity”. During the term, students have the opportunity complete up to five participation activities, which usually involve reading a paper from the primary literature and answering some questions about it. For each one they do, they get a very small bump to their final mark in the course.
For this participation activity, I asked students to read the editorial and write a page or so responding to it. I deliberately gave them only broad guidance on what to talk about. I asked them whether they agreed or disagreed with Wilson, or perhaps agreed with some points but disagreed with others. I asked them whether they had any other reactions–did they find the piece surprising or inspiring, for instance. And I asked them how their experience as ecology majors at Calgary had shaped their response to the piece. Would they have reacted differently had they read this piece as first year students? I told them that the piece had been much discussed in the science blogosphere, but I carefully avoided letting them know what I or anyone else thought of it. As far as I know, none of the students had read the editorial before or read anything about it, so I’m pretty sure that their reactions were purely their own. And I emphasized to them that I wanted their own reactions, not their guesses as to what I thought they should say. I emphasized that there were no “right” answers here.
The class had 23 students, seven of whom chose to complete this assignment. So not a big sample size, and not necessarily a random sample. But still, I found the reactions interesting, and in some cases surprising. All of the students who completed it gave me permission to quote them anonymously.
One thing that surprised me was that “math phobia” was rare. Several of the students talked about how they were comfortable doing math. Or at least, they used to be. Several students felt like they weren’t asked to use math (except perhaps for statistics) in their science courses until the most advanced courses. Which they then found harder than necessary, because they’d forgotten all the math they used to know. A related running theme was that the relevance of first-year calculus and physics was never clear and so seemed pointless. Students emphasized that they didn’t mind math, and even liked it, when they could see the biological or scientific point of it. One student wrote:
Math never really scared me away from science. I knew (and I did) that if I worked hard at it, I could master it, just as Wilson describes. The only thing that frustrated me was the lack of its use in other courses…. It seems like a waste! Now that I have forgotten most of my calculus, I wish that classes had incorporated that somewhat dull math class in such a way that demonstrated to me how that knowledge could be applied to what I was interested in – zoology and ecology…Unfortunately, by the time I was able to take courses that use some math, it had been long enough for my math skills to become a melancholic memory of what I once could do.
When reading this piece, I had to admit to myself that some people may worry about their mathematical skills when pursuing science, although I never have worried greatly over this. Math is a mixed thing for me: I am very gifted at it… when it is taught well (A in Calculus I, one of my top marks), or I perform extremely poorly (C+ in Calculus II, entirely from teaching myself patterns, I’ve always been great at patterns). And regardless of how well I learned, the math was quickly forgotten through disuse. I suppose I do not worry about math, because I feel I can learn it when it becomes necessary…If I had read this as a first year, I would have wondered why I need to take calculus and statistics anyway (just like o-chem and o-chem II – least useful courses ever…). As I approached 315, 425, and 439 [our most quantitative biostats and ecology courses], I was excited (and nervous) to learn what the methods and results sections in articles actually meant, rather than just skimming through them. After taking those courses, I feel like the groundwork has been laid and I am more capable of taking on higher statistics and branching out into more challenging studies. But it was also disappointing for me. While I feel more competent, I feel the math we learnt could be done by students in grade 9.
A third wrote:
Considering that I am taking a double major in ecology and zoology, quite “sciencey” subjects, the fact that those math skills have degraded demonstrates that, rather than me not being “good at math”, it is due to the lack of using it (especially considering my math grades). If science university courses do not use, or build on the math classes first years are forced to take, one would hope that to be a “great scientist”, those math skills are not the most important skill to have. Otherwise, what would be the point of teaching students things which will not help them to reach their aspirations of becoming great scientists?
A fourth wrote:
[First year] I took physics and math courses in calculus and linear algebra. Taking those in the first year as pre-requistes for higher-level science courses made me assume I was being prepared for what was to come. However, as I got farther into the biological sciences, I realized that those classes were, for the most part, only tangentially related to what I would be studying.
Not only weren’t the students scared of math, they all saw value in having some understanding of relevant mathematics, especially statistics. Not that they thought that great scientists had to be great at math–in fact, most said that they agreed with Wilson that you can be a great scientist without being a great mathematician. But they all thought that knowing math would make you a better scientist, and that it would be pretty hard to be a scientist at all (never mind a great one) without knowing at least some mathematics and statistics:
I do agree with Wilson with the statement that progress comes in the field writing notes…but he fails to mention the part of field work which involves study design using quantitative methods.
However speaking for biological sciences especially ecology and evolutionary biologically I do believe statistics are essential…For other ‘types’ of math like calculus and algebra I don’t think it’s essential to be excellent at it.
A third wrote:
I’m a bit surprised at E.O. Wilson article, because from my experience in science thus far, math has played an important part.
A fourth wrote:
I didn’t know much about statistics before entering ecology, but I’m now very fond of it. My views on other types of math is also a little bit better as well. Ecology has been able to improve my views on it because instead of just crunching numbers to answer some meaningless question as was required in high school, there’s real relevance and applicability to the math I’m doing. This is especially true with statistics; the ability to use math to make biological statements about the world is very appealing.
A fifth wrote:
I can’t agree with the fact that a biologist shouldn’t care about mathematics and doesn’t need to know statistics to do his work, because firstly even if he doesn’t develop new models, a biologist is always using mathematical models (especially in ecology), and he can’t use them well if he doesn’t understand these models.
Besides those general themes–students appreciating the value of relevant math, but being turned off by seemingly-irrelevant math and by not being asked to use mathematics throughout their coursework–there were some other comments I wanted to share. For instance, there was this pointed reminder that there’s much more that goes into determining whether any given student chooses to go on in science than whether or not they like math:
Next, I felt doubt that he [Wilson] worried about any real undergraduates turning away from science – probably only figurative ones. At the University of Calgary, I felt no real notice or encouragement from professors until my last year, and I feel most people would drop out of science long before that point. Even now, if I was considered “bright”, I feel professors would honestly hope I fit in somewhere, but they wouldn’t want to be the one to extend the hand.
I smiled at one student’s recognition that things may have changed since Wilson’s day:
I felt real surprise that he learnt math and calculus so late in his career. I do not think that sort of thing would be allowed anymore. Maybe degree requirements are more demanding these days?
And I smiled again when one student unknowingly echoed both me and Mike the Mad Biologist by writing:
Wilson seems to be saying that if you don’t know math, and while analyzing results, you have no idea what to do, then just pass along your work to people who will know what they’re doing, which seems like a cop out. He also seems to be saying that just because he didn’t need much math skills, most people will not either, which doesn’t ring true.
Overall, I found the responses encouraging, and very helpful, while of course recognizing that they may well not be representative of any population (students who choose to major in ecology, students who choose other majors, whatever). I plan to share them with my colleagues at Calgary, with a view to revisiting our course requirements and course content in light of the issues raised.