What is a College Degree? or Why an Engineering Student Takes French and Why a Paleontology Student Takes Calculus

Recently, I read a conversation online where an individual asked why a typical ‘paleontology’ degree (i.e. geology or, sometimes, biology) requires calculus. People gave the typical answers, but they rarely give the answer that I think makes sense. This answer does not even appear to readily exist in people’s minds. I see similar questions get asked all the time: forget calculus, why does a paleontologist have to take hard-rock petrology? Why does an engineer have to take French? Why does an English major have to take biology? These aren’t likely to be directly ‘useful’, at least not professionally, to these students. So why take them?

I’d like to talk about that today. I don’t usually talk about my philosophical view of teaching, even privately. One of my mentors in academia has actually complimented me on how practical my teaching statements are written, detailing precisely what activities and tasks would be involved in particular courses. But I don’t believe we can do anything well without a strong theoretical foundation for structuring how we should move forward, so here it is. Here’s my theory.

First, I’m going to preface all of this by saying this is entirely just my viewpoint on the subject. I’m an academic, but I am poorly read on philosophy of education, or the larger end-goals of education, or the historical purpose of secondary education. That is probably pretty typical for most scientists. Also, my perception of college and its apparent goals is strongly colored by my observation of American universities. So, I might be a little off my rocker here, and I apologize if anyone with actual background in those areas reads this and shakes their head sadly. That’s fine, and if so, let me know what you know that shows maybe there is some other intention designed into our college system. I’ll also more or less use ‘university’ and ‘college’ interchangeably, which might annoy some who see a very clear distinction.

What I’ll say here largely comes from my own thinking, discussion with others and two sources, both of which I was first exposed to as a graduate student in an education seminar at the University of Chicago:

Booker, H. G. 1963. University Education and Applied Science. Science 141(3580):486-576.

Richter, F. 1991. Geology and the university. Geotimes 36(9):5.

They aren’t very long reads; if you can’t get these and want a copy, please contact me. Another thought-provoking read that I encountered later, which expresses somewhat opposing arguments, is:

Crow, M. M. 2012. Citizen science U: The best way to teach today's hyperconnected students is to get rid of the departments of geology and biology. Scientific American 307(4):48-49.

So, let’s cover the ‘typical’ answers to the question of why a paleontologist needs calculus. Well, the most immediately proximal causation, and least helpful answer, is that that’s how modern universities work: you have ‘common’ or ‘general’ education requirements you need to fulfill for any major or specialty. Some are for any student enrolled at all, while some are for certain degrees, like how geology Bachelor degrees often require calculus in addition to ‘general’ requirements. Ultimately, students are effectively required to take classes from nearly every broad area of education in the college. You don’t have to be extremely shrewd or know much about how financial matters are solved ‘behind the scenes’ at a university to know that this is very financially convenient for certain departments, especially those with small numbers of students actually majoring in that field. It is also very convenient for graduate students in those departments, as it means there are teaching assistantships available for graduate students associated with those classes, and thus they can have financial support while they get their degree.

But there’s better answers than this. If nothing else, we can reject this simple answer because if a student was only fulfilling general course requirements for the university’s financial gain, then (a) the courses required would be completely random, when generally a very similar set of course requirements exists across all universities, and (b) whether you actually took these courses, or your performance in them, wouldn’t be of concern to most graduate degrees admissions committees, when generally, they are actually quite important (if sometimes of less consideration than other qualities as an indicator of future success).

The most common rationale I see given to this line of questioning is to attempt to find some specific reason why that specific course is somehow related to the actual field. And, sure, there are plenty of application of calculus in paleontology, mainly related to biomechanics issues. There’s also plenty of engineering literature in French. But these are corner cases: the vast majority of paleontologists never do any calculus. There’s lots of math in paleontology today, and I would recommend anyone in the natural sciences (paleontology, geology, biology) to be familiar with univariate and multivariate statistics at a bare minimum.  Now, I work with math and quantitative analysis much more often than most paleontologists, and even I handed off the one derivation I’ve encountered in my work to a statistician colleague, rather than do it myself. In general, you will be hard pressed to show how anyone found specific uses for every single general requirement class they took in college. And, to be honest, I doubt that many non-engineering students retain the knowledge and capability to derive and integrate for more than a year or two after passing Calculus, anyway. At this point, I only vaguely remember how to integrate. So, if the goal is that students should gain and retain specific skills for future use, the system doesn't seem optimal for that.

One answer I see given infrequently given is that a student takes such classes to 'broaden' themselves; that may be infrequently given because it sounds like a line from a university propaganda pamphlet. But no one seems to know what that means. I’d argue that the best reason is precisely this ‘broadening’, but we need to be able to explain what that is. How does ‘broadening’ aid in our professional development?

The answer is that secondary education has *nothing* to do with your professional development: getting a job and getting a college degree are at cross purposes. Booker (1963) and Richter (1990) argue, collectively, that secondary education is ultimately about developing yourself as an individual. You take courses in a subject area to expose yourself to the particular mode of thinking applied by that subject area. Every subject area in a liberal arts college is ultimately a different approach to addressing some set of questions. Why does a student take a basic English class? To learn how comparative analysis of literature and writing can be used to address issues. Why does a student take French? To be exposed to how the vocabulary of another language works, and the basic concept that the language you use can make it easier (or harder) to communicate and express certain thoughts.

Why does a student take a basic geology class? To learn how geologists approach scientific questions about the earth’s history and environment, and that of other planets. Think about it: one of the most common topics in an introductory geology class is training students to understand and appreciate the magnitude of the geological timescale. Dealing with time and spatial scales that are much larger than those we interact with daily is part of the mental toolbox of a geologist. Taking an introductory geology course exposes you to this toolbox, and allows you to add those tools to how *you* go forward and approach problems. While I imagine that many of those who have taken an introductory geology class do not recall the names of the geologic periods or their exact order, hopefully what they do retain is a lasting impression of the immensity of time in earth history.

And that’s really what I think college is: building a mental toolbox that helps you see how to approach problems. They could be problems you encounter in your work, your personal life, your hobbies, whatever! And the key to getting that toolbox is being exposed to a diverse array of fields of study and gaining those important conceptual insights and perspectives unique to those disciplines. So, why does a paleontologist need calculus? So that they comprehend concepts like the relationship among successive derivatives of a given function, the relationship of derivatives to the concept of the area under a curve defined by a function, etc.

And, I think, that many students who get through a calculus sequence gain that conceptual understanding for the long-term. In my opinion, college classes generally succeed at the unstated goal of broadening the perspective of students. However, I don’t think this is entirely intentional on the part of the educators. First, I should state the caveat that many college educators give considerably more time and effort to the art of education than public perception gives them due for, and I think many give a great deal of consideration to understanding what the ultimate goal of education is. I think the stereotype of the professor who treats teaching as a burden to be avoided at all costs mainly results from the fact the majority of time spent ‘teaching’ isn’t contact hours (i.e. time spent lecturing or managing a lab session) but rather the many hours spent outside of the classroom preparing lectures, assignments, exams and grading. However, teaching is hard work, and I think it is not uncommon to lose sight of what the greater goal is of course work. Being actively cognizant of such a goal, and the need for the course to transmit a new way of thinking to the students, and actively working toward that is a difficult mental task to juggle, and so I think many do not actively think about this when making course materials, because often, just making course materials at all is a high enough bar. Thus, my perception (flavored mainly by my state school undergraduate education) is that the end result of this is that many college educators do not think of their role in terms of exposing students to different lines of investigation, or any similar goal. Thankfully, the nature of the college system seems to counteract the need for active recognition of the end result, because that end-result is hard-wired in the system, a result of how majors are designed and how a diversity of courses are required from outside of the discipline. Thus, I think the system generally achieves the goal of expanding student perspectives even without directed intent.

That said, even having a discussion about the ultimate objectives of higher education could have a great benefit. Regardless of whether the system works currently (and I think it does), it could work even better. We should design our courses to embrace the presentation of new perspectives and the process of investigation in that field. I think there are many ways of doing this, but I think there are also many ways that do not work toward this goal. In particular, courses that depend on rote memorization and a small number of examinations (particularly multiple choice) incentivize a superficial understanding of the material, focused on memorization of details rather than an understanding of the larger-scale patterns and processes. This results in students cramming before exams as their study strategy, followed by regurgitating that information at every written answer question in hopes that some phrase in that mess is close enough to score some more valuable grade points. Little, if anything, is retained long-term in such classes in my experience, which is ironic as many courses with this design are intended to play a critical role in various degree programs, providing background information for later classes. Furthermore, this course structure may also incentivize cheating, with grades often determined more by exams than any other form of assessment, and made easier when exams are based on repeating a litany of facts rather than critical assessment of ideas.

Now, you might say ‘but students have to know an exhaustive amount of knowledge from introductory course for later courses they are prerequisites of’, and on those grounds, you perhaps will argue that it is necessary to test all of those areas, to make sure they know all of it. Well, personally, I don’t see how testing for it one class at all guarantees, or even necessarily correlates with knowing it for a later class. My guess is that most students forget most of the factual details, but do retain the cognitive, investigative tools that I’m arguing is the actual purposes of college. For example, I’d wager that the majority of students who take introductory geology probably doesn’t retain information like what time interval the breakup of Rodinia occurred during, although they might recall that Rodinia is the name of some paleo-continent; rather, they’ll retain the ability to read a time-scale, the ability to use stratigraphic relationships to interpret the order of deposition of rock units, general knowledge of how continental drift works, the general position of the antecedents of modern continents over the Phanerozoic, etc. If, for example, a class two years later gives them a reading assignment that assumes they know the what, when and where of Rodinia, a student well-prepared by previous courses may not know off the top of their head, but can go look it up very easily and understand what they find. As college educators, perhaps we shouldn’t rely on students coming into a class knowing any particular background details, but rather that they have the thinking skills and conceptual basis to comprehend new material, and the ability to go back and fill in holes in their knowledge about old material.

If we accept this theory that university curriculum is intended to diversify a student's ability to handle novel problems, than that idea disagrees strongly with the belief that college should encompass any significant element of professional training.  College isn’t about preparing you for job skills: in general, you will learn day-to-day job skills on the job. College is about teaching you how to think, and my sense is that this is also the opinion of many employers: they want employees who can think and thus learn new skills quickly, rather than students who have the wrong skillset and have to be retrained. Do not interpret this as my admonishing courses that teach any sort of practical ability. Learning how to do certain procedures, such as applying statistical techniques or writing computer code, brings a student face-to-face with the investigative approach used by that field. Courses with such practical material are important components of many programs and absolutely essential elements for graduate. What I am opposed to are courses that attempt to teach based on the demands of the mercurial job market, particularly if done at the expense of demonstrating to the students the broader aspects of the course's subject matter. Choosing to teach specific skills for the sole purpose of making a student into an ideal job candidate is making a risky gamble that the job market will remain the same for any length of time, or that that targeted industry will still exist in a decade (and has that ever been a good bet?). It seems like a better bet and more efficient to leave job training for when graduates become employed, and instead teach them how to think, which gives them the flexibility to deal with the unpredictable things that will happen over their lifetime.

If there is any particular demographic that is the source for the belief that college should be job training, it is current college students, many of whom appear to think that they have been conned into taking classes that are a waste of time; distracting from obtaining that desired employment. A university degree provides no special ingredient essential to professional development, but rather makes the statement that the bearer has had a series of courses in which they encountered a diverse set of approaches to handling questions of knowledge, and thus might show more creativity and comprehension than a job candidate who does not hold such a degree. But you can certainly have many of the positive attributes of a college graduate without attending college, and there are many experiences that trump college in providing raw perspective. Of course, the flip-side of this is that college degrees shouldn’t be a prerequisite for getting a job. In some sense, our modern society expects applicants for many positions to hold a college degree, thus reflecting the cultural saturation of degrees, and further reinforcing the notion that a college education is job training, and thus committing a great disservice to our colleges and universities by perpetuating that erroneous belief.

In Pirsig’s Zen and the Art of Motorcycle Maintenance (a book with both considerable strengths and weaknesses), an extended discussion of the meaning of higher education ends with the suggestion that college shouldn’t be seen as a requirement thrust upon every citizen, but an experience selected as the result of a careful, thoughtful decision to devote additional years to learning and personal betterment. I think this describes an ideal world, one I would personally prefer to live in, rather than our current society which treats college as an inevitability, considers the choice to actively not go to college (if able) as a mild insanity, and deems the lack of a college degree as a serious disadvantage on one’s opportunities. If you are honest about what a college educations is, you should recognize many individuals already have the perspective and thinking skills that college would grant them without ever attending, and unless they want to go even further with their understanding of a subject matter, it isn’t actually useful for them to attend college. Furthermore, some individuals may never want what college offers, regardless of whether they already have it or not. I think in an ideal world, these sets of individuals would get to opt out of our societal expectations, because we shouldn’t be able to simply force higher education on them.

However…we don’t get to live in that ideal world. The reality is that many jobs arbitrarily require a college education, and increasingly require more advanced graduate degrees as the marketplace saturates with bachelor’s degrees. This puts an enormous amount of pressure for the core mission of colleges and universities to change, to fit the perceived notion of what ‘college is for’: mainly, to match the perception of students and their families who mistake college for glorified job training. Some have suggested that the very concept of college is on the verge of changing dramatically. It is hard in this modern digital age to argue that any traditional institution is invulnerable or unchangeable, as we have already seen many areas of society where technological ‘disruption’ has, well, disrupted an entire industry. However, university and higher education are centuries old institutions: and it is equally hubris-incurring to point out any particular long-lived institution and forecast that it must change to survive, or to predict that institution as being ripe for extinction. Regardless, it is unclear how our college system will adapt to changing pressures. My hope is that we can communicate the value of the current system, where students are required to sample a diverse array of academic fields, and where courses place theory and discussion, rather than move toward conveying technical skills for professional development (after all, we already have tech schools).

So let’s go back to where I started this discussion.

We’ve now built this argument that the structure of college education is to increase one’s exposure to the diversity of thought, not professional development. But let’s step back a bit. Does that actually argue for requiring that an undergraduate student interested in paleontology take calculus? No, not quite. The ultimate goal cannot support the claim that each and every typical course requirement is a necessary element of the degree. What I think is important is that every liberal arts degree reflect a diverse set of experiences, rather than a hyper-focused, specialized formula that provides no broader perspective. What needs to be attained is the diversity. Some programs of study recognize this, and are lenient and allow exceptions or course substitutions, although not for every student. Going beyond that, many students have ‘creative study’ majors, where student build their own ‘major’, their own program of study from available courses. Instead of being hyper-focused and allowing students to escape prerequisites they find aren’t useful, though, generally students in such programs tend to take diverse courses, as it was their desire for an interdisciplinary focus that drove them to creative studies to begin with. I think there’s a lot to be celebrated in that. Now, that said, many undergraduates interested in paleontology do end up taking calculus, and I think in the long-term, that course has benefits that are difficult to measure or enumerate, even if they later lose the ability to derive and integrate.

So what do you think?