Last week I tried to expand a bit on the concept of the Liberal Arts as "the skills of a free man". I described the purpose of the ancient and medieval liberal arts education as being to develop a general and adaptable set of skills that allowed the liberally educated person to understand and reason about the world, and I attempted to contrast this type of education from being trained to perform some one task or set of tasks well.
The classic set of liberal arts is: Grammar, Logic, Rhetoric, Arithmetic, Geometry, Music, Astronomy
Some of these disciplines are defined rather differently now than they were in the pre-modern world, and the modern world presents its own particular challenges to understanding, so I think it's worth thinking a little on how one might update this list. The following is rather unrigorous, but hopefully the exercise of thinking it through is illustrative even if the conclusions are far from the last word.
History and Literature
In the classic liberal arts, one would have read and memorized a lot of this during one's early education, and since grammar and rhetoric were taught in the context of examples, one would also have studied much of the best historical, literary, legal and political writing of the age as part of learning grammar and rhetoric. Further, I'd argue that context in the doing and writings of people in other times and places is essential to help free one from some of the modern world's assumptions about how the world works.
Writing and Rhetoric
Not only is the ability to write and speak clearly and persuasively essential to communicating to others one's own ideas, but the process of writing or speaking in an organized and persuasive fashion can help one refine and improve one's thinking. Further, understanding persuasive and reasoned discourse can serve to help one see through the ruses of those who misuse those arts.
Philosophy
The ability to use logic remains as essential as in the ancient world, and the ability of think about ethical and metaphysical issues in some manner other than "feelings" is equally so.
Language/Grammar/Linguistics
I found my background in studying Greek and Latin surprisingly useful in mastering skills such as programming. While I certainly don't think that one must study the ancient languages, it seems like the process of learning how to express or understand thoughts conveyed in a language other than one's own allows to learn things about how thought relates to language that it's hard to learn any other way. In that regard, I feel like one of the major gaps in my education is that I never learned to speak a foreign language fluently (Greek and Latin being read rather than spoken languages, at least the way I learned them.)
Mathematics
This is an area where I wish I'd learned more when I was in school, though I've been able to make up some ground since. I went through calculus in high school, but I was self-teaching using the Saxon textbooks, and I never took any college level math classes, which I regret. I think one key element is that one should get far enough in math and geometry to deal with proofs and see the way in which logic and mathematics meet up: that there are abstract concepts which are absolutely provable which we can then turn around and see reflected in how the world works. Also, given the extent to which we live in a mass society in which statistics and probabilities are constantly discussed, I think freedom in the modern world almost requires a certain basic understanding of statistics and probability. Otherwise, one finds oneself at the mercy of those who use (or misuse) these arts.
Science (Physics, Chemistry, Biology, etc.)
Again, this is an area discussed so commonly (and receiving so much reverence) in modern society that some understanding is, I think, essential to the free life. Especially essential, I think, for those who are acquiring only a passing familiarity with science would be a conceptional and process understanding: how he scientific method works, what it's capable of determining, etc. Also, enough of the basics of physics, chemistry and biology to see how it ties in with the mathematics and geometry one has learned.
The more abstract elements of Computer Science and Engineering
Again, for the non-specialist, I think the key elements here would be on concepts that have more general conceptual application and that intersect with other fields. Thus, for instance, understanding how physics and geometry drive machine and architectural design elements. Some understanding of the problem solving methodology and process development aspects of engineering. The basic grammatical concepts of computer programming would also seem key (algorithms, loops, etc.) I'm tempted to say that some understanding of database concepts (normalized data, relating tables through keys, etc.) is also of general application, but I kind of suspect that this is over-reaching.
Political Science, Economics, Anthropology
Here I hesitate a bit, because it can get kind of sketchy pretty quickly how much can actually be known from the social sciences. However, there are definitely concepts and approaches to analysis that should be learned here.
What to make of these?
I think it could be useful to take a whole post to look at how the concept of a liberal arts education relates to real higher education as we find it these days, rather than taking this post to absurd length to try to address that as well. But let me at least touch on a couple things.
The scope here is necessarily very wide. The concept, after all, is of a general and adaptable education. I think the breadth is important. Fr instance, looking back at my own education I do regret that I took no college level math, science, computer science or economics. I've picked up amounts of these since, but I feel like I had a lopsided emphasis in my own education.
At the same time, different people have different interests and abilities, and so it seems clear that different people would put far more emphasis on certain areas of the liberal arts than others. This seems fine and indeed very good. I don't want to try to make a case against specialization in study (I think there's a particular value to having a field of specialization and knowing one subject area quite well) but in keeping with the idea of a liberal education it seems to me there has to be some breadth as well as depth.
FROM THE ILLUSTRATED EDITION.
5 hours ago
15 comments:
I'm honestly shocked that it's even possible to get a liberal arts degree, or a college degree of any kind, with no math in it.
That seems like a real disservice to people in those majors. It sounds like you recognize this.
A lot of BA programs don't require any math, though it depends on the major and the school.
An area in which I could have used some guidance in that is that I wasn't even really sure what I would necessarily take if I took some math. My ideas on the topic were pretty formed by the standard "four years of high school math" approach I'd dealt with in Saxon, and although I did okay at it, Saxon is very heavy on rote and very low on concept, so I don't think it occurred to me how mathematics fit into the liberal arts (or that it could be interesting) until several years after I was out of college when I found myself using math enough for work that I started trying to self study.
In particular, I would think that proof-based geometry would tie in neatly to the liberal arts curriculum. You could easily put a historical emphasis or logic emphasis on it, or even use it to substitute for a different type of logic course. I plan to use proof-based geometry as the main way of including logic in my homeschool curriculum.
But geometry is so useful with such wide application that it goes beyond logic. Geometry, the calculus specific to understanding related rates, and maybe a study of functions -- any of these could be applied to a wide range of intellectual activities.
Proof based geometry is what I took for my college math. Euclidian/non-Euclidian geometry to be exact. It wasn't a great course because the teacher was annoying and it certainly could have been made to "fit" better into the overall curriculum. But it was there.
I went to college with four years of high school math under my belt. Even managed to pass high school calculus. I wasn't too concerned with doing a lot more in college. I kind of felt like I'd explored the subject and reached the point where I couldn't go much further and really was ready to focus on other things. But I know I'm not the norm.
See, I would think that the key to making math work as a liberal art is to think of it as a means of expanding cognitive abilities. It isn't all calculation - it is a means of understanding the world and what is in it, how stuff moves around, interferes with other things, increases and decreases. Think of it like playing a musical instrument - there is a lot of drill and practice,but it opens up whole worlds of creTive possibilities once you develop the skill past a certain minimum. Still, you should have before you access to lots of great music to listen to so you can see the possibilities as you slave away at scales and arpeggios. Many people don't get to see the beauty of mathematics, even if someone has been wise enough to show them its utility.
Also, if you have to only have one science, I nominate physics. But it would be better to have a little physics, a little chemistry, a little bio, and then maybe an elective.
How to design such a course in order to create scientifically literate citizens would be instructive. And difficult: it certainly barely scratches the surface of chemistry to take two semesters. You would want to design it from scratch, not just rely on the introductory material that science majors have to take. And in many universities that would be hard: the chemistry department will want to save its best teachers for its own students (the chemistry majors). So unless you have buy-in from the department chair, and professors who have a passion for sharing their subject with students in other majors, it'll be so hard to put together a quality science series.
We had that happen in reverse at my alma mater. Engineering students used to be required to take Technical Writing as one of our English requirements. English majors didn't flock to it. The English dept, undermined it and the requirement was eventually totally dropped without a substitute.
That's where I think I hit a cognitive wall; but maybe it was just poor instruction. I could understand in the abstract that calculus can help to understand the world and what's in it, I could do the calculations-- mostly. But whatever that leap was, and I saw many of my classmates were able to take it, I couldn't do. I was in hs calculus and physics with a bunch of guys who went on to do science and engineering at MIT and RICE and UT's honors program. Those guys were able to get things that I just couldn't. And I think seeing that I'd hit a wall as far as my ability was concerned made me less interested in pursuing math and science much further. I began to focus on lit and history and languages because there I don't hit a wall that I can't see over.
At UD we were lucky in that the science departments did take science for non-majors fairly seriously. I took biology for non-majors with a tenured professor who was a former department chair. I took astronomy for non-majors with the physics department chair. These guys liked teaching those classes.
I've found this discussion particularly interesting, since for reasons I've been reading up on reforms of liberal arts education in the nineteenth century. William Whewell wrote a book called Of a Liberal Education in General (which is online) in which he argues for updating the liberal arts curriculum at Cambridge in much this way.
(His comments on geometry are almost identical in parts to bearing's -- geometry was already part of the curriculum, because of Euclid, and he's arguing that this should be expanded to include things like physics insofar as it can be put in geometry-like form -- which all basic Newtonian mechanics can be, and Whewell's most widely used textbook was his Mechanical Euclid which is precisely that. "The key to making math work as a liberal art is to think of it as a means of expanding cognitive abilities" would make a good summary of much of his argument for keeping geometry and using it to expand into things like physics. He argues for natural history and against chemistry, except insofar as it is directly called up by natural history.)
I intended to draw a conclusion, but I guess I never did; my point was just that this seems to be the kind of discussion that needs constantly to recur to prevent liberal education from collapsing entirely, so it's nice to see people looking at it.
I don't want to get political in this discussion nor sound like I am liberal-art-bashing, but I also think that a good healthy dose of the physical sciences and of mathematics, in which one learns that material objects obey the laws of nature whether one likes it or not, might serve as an inoculation against a tendency toward wishful thinking that one sometimes sees promoted among the elites who would like to solve problems through social and economic engineering.
(E.g., that battery- or capacitor-powered cars can be made to be just as satisfactory as internal-combustion-engine-powered cars, because we want them.)
Very interested in this Whewell guy! I found a book by him about the history of science in my library and reserved it.
I should add that I think it quite possible to teach science organized historically, while still making it a "science" course and not a "history" course. A chemistry course would be particularly fun to design. I thought about doing this in the homeschool before I decided I didn't have time to put it together. In my imaginary course, the students would re-enact significant historical experiments in their labs, and understand how they fit into the contexts of what was already known at the time. So you'd do Priestly and Lavoisier's experiments that proved phlogiston wasn't real and oxygen was, and the "database" that Mendeleev made that turned into the periodic table, and... Well... More of these...
My favorite was the isolation of fluorine, but I guess I don't recommend that for, er, amateurs.
Bonus: my word verification number is 42!
Bearing, I knew a great many liberal arts people who chose their course of study specifically to avoid having to take any math in college. One of the ways I've tried to make our homeschooling different from my own experience is that I'm trying to present math as a mode of thinking, not just as an exercise in memorization. (Brandon, you'll be pleased to hear that we've had some success here in working through adding and subtracting fractions by remembering we have to be in the same universe of discourse, denominator-wise.)
I, like Darwin, worked my own way through Saxon Math, but although I learned much about following formulas exactly as they were presented to me, I learned little to nothing about mathematics as "understanding the world and what is in it, how stuff moves around, interferes with other things, increases and decreases". (What is it they say about those who are self-taught having idiots for teachers?) But that could also be because math and science had never, not even in my early years at school, been presented as anything other than formulas or drudge. I do think that if I had been inculcated with an interest in, if not a love for, math from an early age, my later studies would have borne more fruit. But I also think that having a good instructor would have been key.
I did take a survey of physical science course in college as part of my core requirements. Unfortunately, it was taught by a professor who treated us non-science majors (and maybe everyone, I don't know) as kindergartners, coming in at 8 AM and chirping, "Who's excited about science?" Although the class did light some sparks -- I was deeply impressed by the elegance of the table of elements and would have enjoyed delving deeper into chemistry -- the professor was not the person to kindle those sparks into flame. Most of us there for our core requirements felt justified (at the time) at having gotten out of science while the getting was good.
It would behoove colleges, I think, to assign good dynamic professors to survey courses for non-majors (math, science, english, what have you) so that there really is cross-disciplinary interaction -- so that those who might have had no interest in a field can come out of the class realizing that this discipline has worth, not just as a footnote to thier own studies, but in itself.
"It would behoove colleges, I think, to assign good dynamic professors to survey courses for non-majors (math, science, english, what have you) so that there really is cross-disciplinary interaction -- so that those who might have had no interest in a field can come out of the class realizing that this discipline has worth, not just as a footnote to thier own studies, but in itself."
Agreed- but for that to happen you would have to get buy-in into the mission from every department. It is, I bet, tempting to write off the non-majors as not worth the time of the best professors. I am not optimistic.
The self-teaching thing worries me. My oldest is a self-starter and I basically let him work at his own pace through, you guessed it, Saxon. I am planning to directly teach geometry myself, though, and maybe precalculus and calculus too -- if only because I miss math.
bearing,
Whewell's definitely interesting. His historical works were the best history-of-science works in the nineteenth century, and while they are dated in parts, there are parts that are still good, and I've often thought that his approach is one that should be considered more often.
MrsD,
Definitely always pleased at people taking care to make sure they are in the right universe of discourse!
More thoughts from me here on mathematics, sciences (especially physics), languages, and computer science in the liberal arts curriculum. Also on chemical engineering as a liberal engineering discipline, and why skill mastery is important for the generalist.
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