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.
Another wrote:
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.
Another wrote:
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.
Dynamic Ecology 
Thanks for sharing. I’m curious, but I don’t know if you can answer this: did the two exchange students answer, and were their answers different from those of the Canadian students?
One of the exchange students answered. This answer was broadly in line with the others, save that of course it didn’t talk about the student’s experience at Calgary.
Jeremy – interesting responses – and I think what is also fascinating is the the ‘tone’ differed quite a bit between Calgary & McGill students – for example, the ‘math phobia’ was certainly expressed by a lot of my students. Institutional approaches/cultures and the style of an academic program likely play a big role in how students might react and respond to the question of mathematics in ecology. A common thread, however, is that ‘using’ math is key and using it in a relevant and applicable manner is critical – this was such a strong message from my students – they really saw value in math when they could see its role in ecology, for example.
I also love the quote about the “….part of field work which involves study design using quantitative methods”. Brilliant!
Institutional approaches/cultures and the style of an academic program likely play a big role in how students might react and respond to the question of mathematics in ecology.
You wrote exactly what I was thinking.
During undergraduate experience in South Africa, most illustrative examples were about megaherbivores. To me, ecology was explained by big mammals. Now that I am entrenched in a, mostly, experimental culture in Belgium for my PhD, I am starting to realise that the local students see ecology very differently. To them, all ecology can be explained by Daphnia. (of course, I am generalising to make a point)
I can imagine that students from a more theoretical institution will experience ecology, not from the illustrative perspective of an Impala or a Daphnia, but as a set of equations.
I am not going to claim that one set of experiences is necessarily better than the other. On the contrary, they all have a common thread… the actual ecological processes. Maybe the only way to truly understand these processes is by using complex maths? It is very possible. Nevertheless, I still believe that maths should never take precedence over understanding the ecological processes.
…they really saw value in math when they could see its role in ecology…
Exactly! The ecology is the first priority; not the maths itself. (but if you can’t do the first part without the second then, sure, its time to learn more maths)
Many of these comments mirror my own experience as an undergrad 20 years ago. I was a strong math student, 97 in first year calc. Learned stats as a collection of formulas to memorize. Math didn’t show up again until 4th year, in a theoretical ecology class. By that time I’d forgotten most of what I’d learned.
In retrospect, I don’t think many of the faculty were very strong in math and stats. It’s very common for profs to complain that students are afraid of math, bit I suspect the real problem is the professors. Some students are afrid of the Krebs cycle, but we still cover it.
If math really is important, that ought to be reflected in the curriculum. Which means, after first year compulsory courses are done, that mathematical content should be part of some courses each year.
As it was for me, and still is, math is used more as a hazing than pedagogical tool in many biology programs.
Your students’ responses mirror my own experience with math in ecology. At my university I took the required math courses in the first year or two (Calc and Stats), then had two years of biology/ecology courses that largely ignored the existence of math. Then the last year of college you have one or two classes that use some of the concepts you learned in an abstract way 3 years ago. Is this typical? No wonder so many ecologist feel they are weak or bad at math. Why not interweave mathematics into the coursework throughout undergraduate education?
Seems like in the current situation, people with strong quantitative skills in ecology either came from a different disciple (mathematics, physics, or stats) or are self taught. Fortunately there are quite a few books out there (e.g. Otto and Day) that are great for self-teaching.
What strikes me in these comments is the feeling that the students did not have a continuous exposure to math through their undergraduate careers, such that they felt their skills had stagnated. For myself, I too feel that I did not get enough out of my undergraduate mathematics courses, and the only stats courses I took were for “biologists”, which is to say anyone going into any number of mostly health-related fields. There were no courses to delve deeper into statistics and modelling without being a math major. One prof I had during my Masters told me that I could take the more advanced stats classes, but that I would be at a severe disadvantage being in a class for math majors. With thesis research to do I could not take the time to do this..
I wonder if the solution would be for Biology departments to take the mathematical education of their own students on as a responsibility, and teach courses that are relevant and useful for biology. This way, we could move beyond the bland intro courses and dumbed-down stats courses and study techniques and models relevant to modern biological research.
Anyway, I think the main ingredients for making a talented biologist are interest, creativity and passion. These are the qualities that drive innovative research and help people persevere through difficult problems. A robust mathematical education can help, but I tend to think the true mathematical geniuses among us see the forest for the trees and move to Wall St. to learn how to make money for nothing, retire at 30 and do whatever the hell they want afterwards .
Excellent idea Chris & Jeremy. And thanks for sharing the students’ comments!
I’m becoming increasingly convinced that biology departments need to step up the level of mathematical and related quantitative content in their courses, across the board, and not expect math and stats departments to pick up their slack. The main obstacles I see are (1) a lack of good curricular materials that successfully integrate the biology content with the relevant math and stats; (2) the challenge of training educators to have a broad level of comfort with the very diverse set of quantitative tricks and tools used in their area of (biological) expertise, (3) the problem that many/most students coming out of high school have really poor math/stats/computing skills.
You mentioned revisiting course requirements and course content — care to elaborate on the directions you think undergrad biology education needs to go in this regard?
I was thinking about this, too. I took, as a grad student, my institution’s introduction to evolution class for undergrads. It was a large lecture class, and the professors (team-taught) tried to integrate some basic mathematical understanding of evolution. The thing was, evolution is a big field and there are many topics to cover in a class like this. Every time math was taught, the class bogged down significantly. Those who were good at math got bored, while other struggled to understand. I wonder how much math is excluded or minimized from ecology courses so as to cover more topics in a limited time.
I agree with Paul and others that if biologists think math is important, we need to teach that math out of the biology departments and integrate it into the curriculum.
I do think the main challenge as both Paul & Margaret said is the lack of preparation of students. I recall the first time I was teaching the 300 level intro ecology class for natural resource students. The degree to which their eyes glazed over when I put up even the simplest differential equation (think exponential growth or logistic) was a real teaching moment. I could either drop the ecology I was planning to cover and spend two weeks teaching the concepts (rates of change, equilibria, etc), or just simplify it (here is what goes in, here is what comes out, here is what the graph looks like).
I chose the latter. Most of these students wanted to be ranchers or game wardens and it was a stretch for them even to take a general ecology class (a real focuser of the mind – this is the only ecology class most students would ever take). Would a deep understanding of the logistic equation help them in their careers? Kind of. Its not unuseful. But then having two extra weeks to learn about things like mycorrhizae is also not unimportant. So it is still not obvious to me which is the right path.
The solutions I think have to be systemic – whole departments, whole curricula. This is not something one professor alone can change. This is unfortunate because it involves a lot of time and energy to change, including – yech – a lot of meetings.
And to reiterate, I think biology departments can’t farm this out to math departments if we want students to see the usefulness and applications to ecology that they’re interested in. The math and biology need to be integrated. Also, I’ve mentioned before how inefficiently upper level math courses (linear algebra, differential equations) are arranged for ecologists (not surprisingly they’re arranged for mathematicians. Engineering departments I think get this – they teach most of their own upper level math classes beyond calculus under rubrics like “engineering math”. For that matter, many physics departments do this too.
I have found the run-around on this blog, and others, about Wilson’s commentary to be highly entertaining. I have a simple question about this particular exercise, Jeremy. How many of your biology majors will become academics/scholars? I would wager that it is less than 10%. When revising your curriculum you should consider the application of quantitative skills to a much broader set of scenarios than those found in academia. Furthermore, it is worth asking, what is the nature of the quantitative challenges that these students will face and how can changing our curriculum to be more quantitative help them over the course of their lifetimes?
Oh, I’m sure hardly any of our undergrads will become academics! But we don’t consider what they might need for specific careers when designing curricula. The curriculum needs to prepare them for a wide range of careers, and I think our curriculum does that, as evidenced by the fact that our graduates do indeed go on to a range of careers. Plus, the skills and knowledge needed for any particular career are rarely so specific as to dictate curriculum content in any great detail. Plus, while training for a career is one function of a university education, it’s not the only one.
What about the ethnicity, socioeconomic class and high school preparation of your students?
Maybe students who could be amazing scientists from disadvantaged backgrounds (arguably, Wilson’s origin) would respond differently. At least in the US, there is a demographic need to diversify the sciences, and that will require bringing in those with crappy math experiences in high school. (Of course math is important, we all agree.)
The University of Calgary is a large public* research university. The vast majority of students are from Calgary or elsewhere in the province of Alberta, where they attended public schools. The majority are from middle class backgrounds. The majority are white.
Would I teach differently if I had students from different backgrounds? Of course. That’s why I noted at multiple points in the post that the students who responded to this assignment are a small and non-random sample of any population you care to name.
The key thing is background preparation, I think. What can we as instructors count on them having mastered, or being able to recall with a bit of review or reminding?
The demographic diversity of the sciences isn’t something that can be addressed with curriculum design, I don’t think. The ethnic and socioeconomic makeup of the student population in my courses broadly reflects that at my university. I think making universities more diverse will require policy and other changes that affect students’ lives well before it comes time to apply to university.
*Note to British readers: Throughout, I’m using “public” in the American sense. For “public”, read “state”.
NSF clearly thinks, for what it’s worth, that curricular changes are critical for attracting and retaining scientists from underrepresented groups. Grants to fund this are the ones with (relatively) high funding rates. I’m co-PI on two such proposals at the moment. Do they work? Well, fixing K-12 would be more effective, but that rock is harder to budge for economic and political reasons.
Sure. We’re on the same page on this–changing K-12 would be more effective, but changing what happens in universities isn’t mutually exclusive with changing K-12.
Several comments are hitting on similar themes, so rather than replying to everyone individually I’ll try to cover those common themes.
I agree that addressing the issues my students raised is a matter for entire departments, looking at their whole program of course offerings. It’s not a matter of tweaking one or two courses. As Brian notes, this is a lot of work. It can happen, though, and it can even happen without everyone being ordered to do it by the head of department. At Calgary a couple of years ago, our department all sat down at a retreat and agreed to completely replace several of our “core” courses (the courses in the first two years required of all students in our entire biology department). The revisions covered both content and pedagogy. It was a massive amount of work for the people charged with doing it. But it was necessary, and it’s a big improvement. I’m actually kind of looking forward to the time when it’s my turn to teach in our first year courses, because I’m so excited about the changes.
Of course, I don’t know whether there’d be agreement among all of my colleagues at Calgary (even just the ecologists & evolutionary biologists) as to whether we should beef up the quantitative content throughout our program. The content of upper-level courses is very much up to the individual instructors. Presumably, those instructors are already teaching the stuff they think is most important. So if, say, our behavioral courses don’t include much game theory, and our evolution courses don’t include much mathematical population genetics, and our conservation courses don’t include a lot of PVAs, etc., well, that just reflects the pedagogical choices of the people who teach those courses. Just as the fact that I teach population ecology with a heavy emphasis on theory (though not on formal math) reflects my choices (and those of Ed McCauley, who taught the course before me and whose approach I like and largely adopted).
As to bringing the teaching of mathematical content “in house” so as to ensure it’s taught in a way that’s relevant to biologists, we (and I think many other biology depts.) already do this to some extent. Specifically, students in our department take biostats courses from us, not stats courses from the dept. of mathematics & statistics. It’s been that way at Calgary for over 20 years, precisely because the stats courses taught in the math & stats dept. don’t teach the material in a way that’s relevant to biologists (Importantly, they also don’t teach students how to actually *do* stats using software like R, which is an essential skill for scientists but not for math & stats majors. Nor do they teach experimental design). But our biology dept. (again, like many others) does not teach first-year calculus. Instead, we require students to take a year of calculus from the math dept. And frankly, we simply don’t have the teaching staff to bring first-year calculus in house, we just don’t have enough people. So the alternative would be to go to the math & stats dept. and say “our majors comprise the largest chunk of students taking your first-year calculus courses, you should completely revamp those courses to our specifications.” I suppose it’s possible that math & stats might be open to this–but it’s possible they wouldn’t be. I suspect similar issues would arise in many places; I doubt Calgary is unique on this.
Speaking of making classes relevant to biology/ecology, I think the student who mentioned organic chemistry speaks for many, many, many biology undergraduates.
Yes, I know. I didn’t see its relevance either as an undergrad. But the problem with dropping requirements that most students don’t see as relevant at the time is that some will go on to find it relevant. Much the same could be said for math, and indeed for *any* chunk of material. It is not possible to design a curriculum that includes all and only material that all students taking it will see as relevant at the time, and will continue to see as relevant in the future.
I agree. Physics might be another course that people would want to cut, if we went on an apparently-not-relevant-to-biology-cutting-spree.
I think the most important thing might be just what you said – you can’t get rid of things that students (or famous scientists) don’t see as relevant. However, I feel like educators could make a better effort at selling the relevance of the material that they’re teaching. Like your students pointed out, if they don’t see the relevance and importance of what they’re doing, they’re going to forget everything after the exam. And if educators can’t actually come up with any reasons for why the material is relevant/important, then maybe it really shouldn’t be required in the curriculum?
I’ve been lately wondering how much my mathematical background is limting my development as a theoretician. Most of my research involves empirical tests of reasonably well established theories. I don’t need to use differential equations very often to build relationships between environmental variables and biota. Instead I have been able to get by just fine with good experimental designs and the ability to use basic statistics or track down and implement more sophisticated methods. Frankly, the abundance of materials online and the simple coding of complicated methods make it a snap if you are willing to apply yourself. However, I do not foresee the day that I will publish in American Naturalist. Taking abstract theoretical ideas and transcribing them into a formula is beyond my abilities right now. I wonder if this is a common math education-related cutoff in abillity? Please don’t use this argument as an ego boost, theoreticians!
Good question Tom. I think what you’re getting at (at least in part) is precisely how much math and programming one needs to know in order to be able to correctly translate theoretical models into testable predictions in some specific system. I say “correctly” translate because it’s quite possible to mistranslate theory. The confused history of empirical research on diversity-stability theory is one example. As you say, one doesn’t really need to know theory (as opposed to stats) to, say, build up an empirical understanding of environment-biota relationships. But to be able to interpret those empirical results in light of theory, how much math do you need to know? Good question, one to which I’m unsure of the precise answer.
Here’s a thought: my (medium-sized) undergrad institute had dual tracks for computer science classes. Majors took one set of intro classes in which certain things (like really good coding practice) were stressed. Non-majors took a different set of intro classes (although they were allowed to take the major track if they were so inclined), which stressed concepts over technique and ability. I know that physics and chemistry, likewise had an “honors” track for majors and a “regular” track for non-majors.
If ecology was taught starting at the freshman level, then presumably one could do the same thing — majors get a good dose of math mixed in from the start; non-majors get primarily concepts.
At my (large) graduate institution, however, courses like intro ecology and intro evolution are junior-level classes. So the problem may be in having a silly prerequisite list. (In fact, this is a sore point for me; I wanted to take ecology classes as an undergrad as a non-major, but there was such a long list of biology prereqs in which I had absolutely no interest — cell biology, organic chemistry, etc. — that I gave up and never took one.) I’m sure the issue varies from institution to institution, though.
Yes, it’s not uncommon for science departments to offer introductory courses in two versions, one for majors and one for non-majors. Courses for non-majors can differ from those for majors in various ways. By being less technical, by not having labs, by being more “applied”, etc.
It’s a bit unusual for something like introductory ecology to be a third-year class with a long list of prereqs. I think the way we do things at Calgary (and the way they were done at my own undergrad college) is more common: intro ecology is a second-year course, the only prerequisites for which are first-year biology plus maybe other first-year science courses like calculus I/II, intro chemistry, and intro physics.
Things vary more for evolution classes, I think. At Calgary, the course called “evolution” is taken by students in 3rd year and above because intro ecology is one of the prereqs (as is intro genetics, another second-year course, if I recall correctly). But there’s actually an unusually large amount of evolution in our first year biology courses, which are organized along conceptual lines rather than as “first year cell/molecular biology” and “first year organismal biology” as at many universities.
Hi-
Just following up here on your response to my comment about spandrels, Gould, etc. Marks is great – yes! Those analyses he did of cathedrals, BEFORE all the current software was developed, were fantastic. As a student of art history who went on to civil engineering, I have to say that I have since learned that much discussion of architecture in histories and criticism would be vastly improved if the writers had some basic statics under their belt. Instead, writers feel free to wax impressionistically about “lines of force” and what not, much as I, ignorant of music theory, would discuss symphonies if I had an urge to do so.
I guess some of this applies to evolution too.
As for E.O. Wilson and math, don’t you think his point has some validity? That is, if you are truly fascinated by biology, go for it, and just assume you will be able to master the math you need? He isn’t really saying you DON’T need it at all, is he? Intellectual creativity, a fascination with ideas, isn’t that the crux of moving science forward? Math, like experiment and observation, is just one way of keeping the whole deal honest, right?
On the other hand, Wilson has written some philosophical stuff that I consider pretty awful, because he apparently lacks an interest in the fundamentals of the questions and their history.
Back on math – as an engineering student, I did the standard drill, and I hardly use any of it every day, but if I hadn’t done it, I sure would feel lost. It doesn’t ONLY teach you useful techniques, it teaches an important approach to problems. Now…pure mathematicians…they are in a totally different universe..!
I don’t understand why introductory topics like calculus and linear algebra are even taught by math departments. The sort of calc/lin-alg that students encounter at the end of highschool or start of university does not require a mathematician to teach; in fact, a mathematician does more harm than good for the typical (i.e. one that isn’t a math major) science student. I think each department (or nearby groups of departments, say physical sciences, life sciences, social science, etc) should offer their own versions of the basic math courses that focus on the parts relevant to their discipline, motivated by examples from their discipline, and taught by theoreticians from their discipline.
I have seen the damage a math prof can accidently do first hand when TAing slightly higher level (although still basic for the physical sciences) math courses for engineers. The students had their own version of a first course on ODEs (separate from the math majors) but that term the departments were low on teachers and a pure mathematician was put in charge of the course. Needless to say, my tutorials were quickly overflowing with very confused engineers.
Engineering, computer science, and physics programs already do math course specialization to some extent (at least where I did undergrad: McGill). Sometimes math courses are still listed under the math department, but have different flavours for each of the 3 disciplines and yet another one for math majors and a 5th for honours. This also exists for statistics, with each department typically offering their own stats course. Unfortunately here there is a tendency to oversimplify sometimes (as I learned from tutoring some Psych Stats students), but that is still better than not learning the skills or writing them off as irrelevant.
Of course, delegating intro math courses to individual departments instead of a requirement for all science students, does run a risk of some departments cutting courses out. For instance, the physics department at McGill doesn’t require a statistics course even from its Honours Math & Physics students. However, it could be argued that those students are relatively prepared for basic statistics after their experimental methods and statistical mechanics courses. However, I feel I would have been (even more) completely helpless at statistics if it wasn’t for the required probability courses through computer science.
A related annecdote: I had to take an advanced mechanics course as an engineering student. The professor I had was known as a genius in theoretical physics – he had zero interest in the intellectual travails of aspiring civil engineers. Students would come in and say, “Professor, we don’t understand this problem here [e.g. something about a rotating mechanism]” and he would respond, “Hmm…that’s not a very interesting problem. HERE’s an interesting problem!” And he go off on the mechanics of colliding rotating galaxies. Guy had a good sense of humor, but no general teaching skills. I think he gave everyone a pass to avoid having to explain why everyone flunked.
One point that hasn’t been touched on in this discussion is the role inadequately prepared students have on course content. I began college level teaching with rather unrealistic notions about student mathematical (or arithmetical) abilities. It didn’t take long to discover that I would have to fail the entire class and thus terminate my own employment. I did come to my senses and re-evaluated what the purpose of the courses I was teaching should be. Courses like ecology can be approached non-quantitatively if they are low-level courses. And general students need to understand ecological concepts even if they don’t seem to know or understand the mathematics of logistic or exponential equations. This puts most biology courses into an auto-catalytic downward spiral — eliminating math makes for more palatable courses and results in the absence of any math in most of the lower-level curriculum. It’s no wonder that many of the students in upper-level courses have atrophied math skills. I wish I knew the solution to this problem, but I don’t.
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