Thursday, September 27, 2007

The Seven Liberal Arts, Part I

The classic seven liberal arts were the trivium (grammar, rhetoric, and dialectic [or logic]), and the quadrivium (arithmetic, geometry, music, and astronomy). These were preparatory studies for the more advanced fields of philosophy and theology.

Are our students well-grounded in these fields? Should they be?

Many of my students claim not to have studied grammar at all. Some students do study grammar at the college level: by studying a foreign language. In classical times, much of grammar was also taught through studying other languages: Greek and Latin. Why is grammar so devalued now? Is there value to understanding that language has structure, and that different languages can be structured very differently?

It seems to me that grammar has been devalued because one can develop a good grasp of grammar without actually acquiring a workable fluency in speaking another language, or without acquiring good writing skills in one's own language. And people raised speaking several languages can speak those languages fluently and can write quite eloquently without consciously knowing grammar. But to use these observations as a critique of the study of grammar is to make a mistake about the purpose of studying grammar. The value of understanding the structure of language has little to do with whether it makes you a fluent speaker or a poetic writer. The latter skills are valuable in their own right, but are not the reasons for studying grammar.

The reason for studying grammar is to learn the different ways that language is structured. It is only when one closely studies the structures of different languages that one begins to understand the difference between language and thought (so closely related that most modestly-educated people think that there is no difference at all).

Tuesday, September 25, 2007

The Ideal of Liberal Education

Today is the day of the Crimmel Colloquium at St. Lawrence University. In honor of this event, I would like to quote from Professor Crimmel's book, sharing his view of the ideal of liberal education:

The ideal of liberal education is: "the development of wise people--that is, people who possess the capacity and inclination to act on the basis of knowledge of reality and ideality" (Crimmel, Henry H., The Liberal Arts College and the Ideal of Liberal Education: The Case for Radical Reform, University Press of America, 1993, p. 125).

Here is a later expansion: "The wise person [is] one who possesses the capacity and inclination for rational action. To act rationally is to act on the basis of knowledge of what is and what ought to be, and with prudence, and with the aid of moral virtues" (Crimmel, p. 217).

One more statement I would like to quote: "The wise person acts to transform reality into ideality" (Crimmel, p. 222).

And here are other statements of ideals that he does not think are as worthy:

Ideals Giving Priority to Theory:

To provide a religious faith
To provide specialized knowledge
To provide general knowledge
To provide both specialized and general knowledge
To understand the Great Books
To develop cultural literacy
To provide an understanding of Western culture
To provide an understanding of world cultures
To provide an initiation into the forms of knowledge
To develop the critical thinker

Ideals Giving Priority to Practice:

To provide vocational training
To prepare students for graduate school
To prepare for a mature, effective, adult life
To provide political liberation
To develop solidarity
To actualize human potential
To cope effectively with change
To develop the citizens of a free society
To develop "the democratic personality"
To develop a person

Ideals Giving Priority to Interests

To satisfy student interests
To satisfy a plurality of interests

It is not that all of these other statements of ideals are unworthy. He argues that his statement of the ideal is superior to all of these other statements. (His arguments can be found on pp. 127-163.)

As I look over his list of other statements of ideals, I see that the ones that give priority to theory all neglect the question "to what purpose?" The ones that give priority to practice point to goals but do not fully articulate them or justify them. Of each of those implicit goals, the further question "why?" still can be asked. This is not necessarily a problem. It just means that a person must choose such a goal outside of the educational system that supports that goal. But those who have set such goals for themselves might find such educational systems quite meaningful. I am inclined to agree with Professor Crimmel, however, that these would not count as institutions providing liberal education. I also agree that orienting education around interests is problematic.

I am struck most of all by the emphasis Professor Crimmel places on the study of ideality. I agree with him here (and have written previously about a similar theme here in the SLU Philosophy Blog). We seem to put more emphasis on the study of various dimensions of reality. And we often delude ourselves into thinking that "ideality" is not really real. Setting ideals and choosing values is just a matter of personal preference, and it is a bit rude (even an infringement of "academic freedom") to question each other about our values and our moral choices. And yet these relativistic attitudes about ideality, about what ought to be, miss the point completely. "Ought" gains much (most, all?) of its meaning from the reality of our essential interconnectedness with each other. It is crucial for us to be able to examine this, study it, question each other about it.

Our lives are permeated by the force fields of many "oughts" that compete for our attention. Our lives are so much more than aimless wanderings through a dispassionate world of what is. We always regard that world through lenses of "ought." All of our actions are oriented towards transforming the "is" we find ourselves in to the "ought" we want it to be.

It does seem to me that the wise person gives some serious consideration to the study of ideality, as well as the study of reality. To ignore paying explicit attention to understanding ideality is to unthinkingly follow the force-fields of "ought" that others have set up and that you happen to wander into unawares. I agree with Professor Crimmel that such a person is not very wise. Our "oughts" are not always good ones. Nor do we always succeed in effecting the transformations we hope for. This is why it is good to study ideality, and also good to study "practical wisdom," or, how to be effective in transforming reality to ideality.

Saturday, September 15, 2007

More on Grading: Living with What We Have

In yesterday's posting, I explained why I am unhappy with our system of numerical grading. But I do have to live with this system. So I thought I would pose a few questions about how to use it as responsibly as possible.

1. I have noticed that different faculty convert between a 100-point (or percentage) grading scale to our 4.0 scale in different ways. Is this a problem? Students get upset: to receive a 93% in one class may earn them a 3.25; in another class a 3.5; in another class a 3.75; in another class perhaps even a 4.0. The defense I heard from a math professor is that it does not matter that different professors align their scales differently, because some professors make their exams so hard that a 93% does indicate a remarkable achievement warranting the top grade of our grading scale (4.0), while others align their expectations a bit differently.

2. My own solution is to avoid all conversions altogether. I grade everything on the 4.0 scale, and then just average these grades (using weighted averages as appropriate). Here's how to round to .25 intervals: you take the raw averaged grade, multiply by 4, round this number to the nearest whole number, and divide by 4. It's easy to make a spreadsheet that does all of this for you.

3. My system of grading yields this question: Which is more appropriate for grading within the course, before the final averaging and rounding: (a) use only the .25-interval grades, (b) use even finer gradations (e.g., .125-interval grades), or (c) use coarser intervals (.5-interval grades, or even just the whole number grades, since these are the only ones whose meanings are defined: excellent, good, satisfactory, low-pass, and fail)? Or does it not matter? (Mathematically, do the averages mean something different on these three different scenarios?)

I hope someone can answer question 3 with a convincing and mathematically well-grounded rationale.

Friday, September 14, 2007

The Meaninglessness of Numerical Grading

The following is adapted from my web page on grading.

In 2005, St. Lawrence changed its grading system, from the grades of 4.0, 3.5, 3.0, 2.5, etc. (0.5-interval grading) to grades of 4.0, 3.75, 3.5, 3.25, 3.0, 2.75, etc. (0.25-interval grading).

It was the students who wanted the finer gradations. They said that they wanted the grades to more accurately reflect their performance in their courses. The faculty passed this proposal (but not without debate, and not without some faculty arguing in a very different direction). The new grading system went into effect in the 2005-2006 academic year.

It is interesting to note that this change is not really just a refinement of an existing system. The two systems are in fact different enough that it is inappropriate to think that the Grade Point Averages (GPAs) computed in each system can be directly compared.

The following chart shows how GPAs do in fact change if you round grades in different ways. This table shows the kinds of rounding historically used at St. Lawrence University. Other schools often use +/- systems, which numerically convert to grades such as 3.3, 3.7, 4.0. What my little table shows is that it is dubious to compare GPAs on 4.0 grading scales if the systems of rounding are different.


.25 Rnd

.5 Rnd

.0 Rnd





















Note that not all sets of grades would necessarily always round down on .25 intervals and up on .5 intervals. What is interesting is just that the GPAs are different. Two students with the same grades would have different GPAs depending on whether they started before or after the change in grading intervals – and yet those students who came in the midst of the change have both kinds of grades averaged together, as if averaging these incommensurable scales is legitimate!

Here is a table showing what happens when you average together the grades of students graded under both systems. Imagine these five hypothetical students who happen to get exactly the same raw grades in their courses every year (the grades from the above table) -- but the grading system changes for all except Student 1 sometime during their time here. This table shows the differences in their final GPAs at the end of their four years (the yearly GPAs are taken from the table above):

Yr 1 GPA

Yr 2 GPA

Yr 3 GPA

Yr 4 GPA

Final GPA

Student 1






Student 2






Student 3






Student 4






Student 5






In this case, the student lucky enough to have arrived before the change has the highest GPA. The student unlucky enough to have spent all four years under the new grading system has the lowest. Again, it is not the case that this change results in lower GPAs for all students -- the point is that the very same raw grades average out to different GPAs depending on the grading system. Worse, these GPAs are then compared to those of students from schools that may use the .3/.7 intervals (plus/minus grading) -- an altogether different system, but because it is also a 4.0 scale we think it is essentially the same!

We place a lot of faith in these numbers that we are not in fact even computed in a mathematically responsible way. Can we really say that the GPA has a stable and unambiguous meaning?

I wish we could switch to a system of grading that does not convert grades to numbers. My favorite option is to use a high-pass, pass, fail system. The "high pass" would be a grade specifically to indicate that the student did so well that you regard that student as having graduate school potential. After all, the main distinctions we wish to make are whether the student should pass, and whether the student has worked with the material so well that you would recommend them for more advanced study in that field.

But I would also be content with a return to A, B, C, D, F grading: no pluses or minuses, and no attempt to convert these grades to numbers. The meanings here are excellent, good, satisfactory, low-pass, and fail.

When I criticize the grading system, people often leap to the assumption that I want to replace it with narrative evaluations of all students. But that is not true. I see the value of our having a shorthand way of representing the quality of students' work. What I object to is converting grades to numbers, averaging these numbers, and tying so much to this average (sometimes taken out to the thousandth decimal place) when this use of numbers is not warranted and thus highly misleading.

Saturday, July 14, 2007

Philosophy, Language, and Conceptualization

The study of philosophy helps us to become multi-lingual within our own native language.

According to the philosopher Ludwig Wittgenstein, natural languages are composed of multiple "language games": different patterns of language use that take shape within a given natural language. Wittgenstein noticed that different communities of speakers use language in different ways. We are most aware of this when we spot regional differences in language use, or complain about the "jargon" associated with highly specialized interest groups, professions, or academic disciplines. But it is worth noticing that there are other (and often more subtle) ways that language use may vary.

Regional differences and jargon are easy to spot because unusual words leap out at us. The new or unfamiliar words signal immediately to us that our native language is being used in a way we may not readily understand. What is harder to perceive is when common words are used in different ways from language game to language game. Many important words that are in common usage among nearly all speakers of the language are so rich in meaning that different communities of speakers focus the meanings of such words in different ways. Sometimes these differences are only slightly different. Other times they are much more radically different than people may realize. For example, the word "God" has different meanings depending on whether the word is being spoken by those who adhere to different religious traditions or those who call themselves atheists. Other important words whose meanings change significantly from speaker to speaker or community to community include "justice," "freedom," "love," "truth," "good," "bad," or "loyalty," to give just a very few examples.

Being multi-lingual in your own language means recognizing that other people may very well be using words like these differently from how you use these words. It means refraining from getting into arguments about what the word is "really" supposed to mean, and developing the mental agility to tune into how others are using the word, as a method for facilitating better communication. Those who are multi-lingual in their own language also can become skilled translators when witnessing others mis-communicating because of not recognizing that they each are using important key words differently.

Skilled translators are very rare. Most people do not realize this complexity about language. People are easily fooled by the superficial resemblances of different language games into thinking that we all speak the same language and have no need for "translating" within our natural language. People often woefully misunderstand each other, without even realizing it. The mass media exaggerates this tendency. It codifies certain usages of language, making those usages seem authoritative.

A good example is how Christianity gets portrayed in the popular media. Only an oversimplified, distorted version of one contemporary language game of Christianity is visible. Even people who are well-educated often take that image to represent all that Christianity is (or ever was). But there are other communities of speakers that use Christian language very differently, yet those communities remain invisible. If those communities were to give up their usage of this language as lost, they would lose a primary way of being able to conceptualize and communicate their experience.

In fact, such communities already have largely lost their ability to communicate through their language because they already know not to speak this language except to people they know will understand. They already know how to "translate" or else be silenced from speaking meaningfully of their experiences. Even so, they still do feel somewhat silenced, because translation always has its limits. While there may be other language games in existence that are as rich and deep that would do equally well, it takes time and effort to find them and learn them or develop them, and even so there is still no guarantee that those languages would do any better at communicating except to their own fluent speakers. And it is also important to remember the community component of language games in order to realize that exchanging one rich language for another is also to leave one community and join a new one. People tend to cling to a language game that works for them not only because of their already acquired fluency but also because that language connects them to a community of family and/or friends in which they feel at home.

Those who are philosophically inclined learn multiple language games, so to speak. It is an important component of philosophy education to learn different conceptual systems, which is also a way of learning different language games. And so those who have studied philosophy become multi-lingual in their own language. They can continue as "native speakers" of their own original language games, but they acquire the ability to speak other language games as well.

Those who are multi-lingual in their own language tend to develop their own hybrid languages, enriching their own ability to conceptualize more complexly, but not necessarily improving their ability to communicate if they insist on speaking their own preferred hybrid language to everyone, no matter what. Improved communication ability requires developing "translator" skills. Or, put another way, improved communication requires the development of rhetorical sensitivity: understanding who your audience is, and adjusting your own language use to match theirs, as much as you can. Or, if you must introduce words (or definitions of words) not already present in their vocabulary in order to be able to speak what you need to say, you take the time to do so in a way that best helps others to understand.

I write about this not only because it is relevant to philosophy education and in fact liberal arts education more generally, but also because I find myself frustrated at how often I feel stifled from speaking my own native language game freely without fear of being seriously misunderstood because of how the mass media has severely distorted and diminished so many of the words I normally would wish to use. My own coping strategy has been to study philosophy, and, in so doing, to develop translation abilities. And so I am nearly always translating, which actually works quite well. But there are times when I wish others were more skilled at listening and at translating too.

Friday, July 13, 2007

An Idea: Having "Public" Components of Intro Courses

I have been thinking more about what I wrote about last time.

First, I tried this thought experiment:

The Anti-Transcript

Go through your university's course catalog. Look at the listing of majors and minors. Make a list of all of the majors or minors that you never took even one course in, in college or graduate school. This is your "Anti-Transcript": the shadow-side of all of your intellectual accomplishments!

(Humbling, isn't it?)

A Practical Idea

What if everyone who taught Intro courses created a lecture series that formed the backbone of this course but could also stand on its own, and opened the lecture series to anyone who was interested in attending? Maybe there would be one lecture per week, lasting a an hour. Not only would interested students audit these lectures, to fill out their education more fully, but professors would attend as well. What if it were the part of our university's culture that every student and faculty member "audited" at least one of these lecture series per semester?

The credit-bearing version of the Intro course would consist of more than just these weekly lectures, of course. These lectures would be integrated into the full Intro course that some of the students would be taking for credit. Those students then would have extra time with the professor above and beyond these weekly lectures. They would have time for additional in-depth discussion, for covering more material, and for reading, writing, engaging in laboratory sessions, performing, creating portfolios, etc. For those students, it would be pretty much like Intro courses already are. The only difference is that for one hour per week, some extra people would attend to hear the lecture of the week.

So, some questions for professors to think about:

  • Could your Intro course be adapted in this way?
  • Would you like this opportunity to give a "what I wish everyone knew about my field" lecture series (without this actually adding to your current responsibilities!)?
  • Would you attend such series offered by your colleagues in other fields? If so, which would you attend first, and why?

Tuesday, June 19, 2007

Well-Roundedness vs. Specialization

In our conversations about the kind of education we are trying to offer at St. Lawrence, we often look to the University's "Aims and Objectives," found in our Catalog. We note the relationship between the numbered list of items and our general education requirements, and puzzle over the anomalies: the ones that do not map clearly onto our distribution requirements.

And there is talk about rethinking entirely how we structure our program of studies. Do we want to revise the Aims and Objectives? Do minors serve a meaningful purpose? Do we have too many minors? Should we eliminate majors and minors altogether, and have advisors (or "faculty mentors") work closely with each student to help them design meaningful programs of study? These are some of the questions I keep hearing.

What is difficult about talking about the general education requirements is that we faculty tend to be trained in specialized disciplines. We feel more comfortable talking about how to design our majors and minors than we do designing a more broad-based liberal arts framework of study. Within the latter, we each tend to advocate our own discipline or program as "essential" for all students, and feel hesitant about advocating too far beyond our own area of expertise.

I suspect that some of this discomfort comes from our awareness of the holes in our own educational backgrounds.

Not only can our students complete their entire four years of study here, playing fully by the rules, and yet neglecting ____________ (fill in your own favorite "essential" field of study), most of us as faculty -- even those who received their undergraduate degrees from small liberal arts colleges -- have also missed out on several important fields of study.

For example, by fulfilling my science requirement with courses in physics, I did not take biology in college. I studied German, but not Chinese. I took anthropology, but not economics. I played music, but did not take courses in music theory, or art history.

My liberal arts education did allow me to explore areas of study beyond my specialization. It also helped me to appreciate the value of a broad-based, well-rounded education -- to the extent that it inculcated in me a deeply-rooted regret for all that I haven't myself studied!

One day recently, while proctoring a final exam, I took the SLU Catalog and decided to see whether it would be possible for a student to study at least one course in every one of our departments (while still fulfilling major and distribution requirements) and the answer is "probably not." Students take 33.5 units. If you subtract the 3 FYP/FYS units, and the 8 minimum number of courses required for a major (but many majors require 9, 10, or more courses), there are 22.5 courses left. Taking the intro course for every department would probably result in fulfilling the distribution and diversity requirements. So some motivated student might achieve this, but such a curriculum would be a bit frowned-upon because most or all of the coursework outside of the student's major would be at the introductory level.

So we give students choices, but their choices necessarily leave holes in their education. We faculty have holes in our own education, and we can all too easily be biased in favor of what we ourselves have studied.

I am wondering whether there is a way to educate students and faculty in disciplines beyond what they have the time to take courses in. I suspect that all faculty have their own list of what they wish that every educated person knew about their discipline. Is there a way to structure an educational program that would allow students and faculty together to fill in those holes, at least a little?

Wednesday, May 30, 2007

Welcome and Introduction

At St. Lawrence University, it is part of the faculty culture to talk with each other about the ideals of liberal education. At the end of the academic year, faculty and staff gather for a three-day event called "May Faculty College," to share with each other their newest ideas, their most compelling questions, and their best teaching practices.

I always find May Faculty College inspiring. At the end, I have piles of notes about what I have newly learned about St. Lawrence, about our students, and about teaching. I try out my new ideas in my teaching the following year, and sometimes then report on what I have learned at the next May Faculty College.

This year during a May Faculty College session on academic blogging, I had the idea of starting a blog to share some of my own questions, insights, concerns, and ideas about liberal education. What's nice about the blogging format is that others can comment if they are so inspired. Blogging is a way of sharing ideas that invites further dialogue. And so I would like to invite you to feel free to join the conversations that hopefully will emerge.

A lot of blogs remain relatively unnoticed, hiding in plain view, so to speak, and that may well be the fate of this one as well. But still, I find a journalling format a helpful way to log my own ideas and questions, and I like the idea of sharing in case others may find these thoughts helpful.

The question of the role of liberal education in today's world is an important one. Establishing yet another little corner of the web as a space to talk further about this may have some value.