Wednesday, July 09, 2008

Vocational Training vs. Classical Christian Education?

When it comes to classical Christian education (cCE), I am all for it. However, there's a trend in cCE of which I'm not sure I approve. I haven't given it deep thought, but I have given it enough to blog about it and hope that one or two of my rare readers will debate it. The question concerns vocational training.

The classical component of cCE is all about training the mind how to think, and how to learn. This is so important to many in the field (such as the faculty of New St. Andrews College, e.g.), that I wonder if they haven't over-reacted against vocational training. Here's a quote from the Wiki on cCE:
After the Industrial Revolution and the World War I, progressive theories of education along with cultural conditions that suggested a new era of democracy and human capability were dawning combined to lead many to turn from the traditional classical curriculum and experiment with new more pragmatic approaches to education that emphasized vocational and professional training over the "making of the man" that was the aim of the traditional classical curriculum.

I have heard, though I can't produce the source off-hand, something to the effect that New St. Andrews college rejoices in giving their students a degree that can't land them a job. There does seem to be a strong feeling against vocational training in cCE.

Now I wonder, is this the way cCE needs to go?

Consider the following issues pro and con this anti-vocational training bent:


Granted that the modern K-Ph.D. vocational training route usually fails to teach students how to think or learn. The exceptions seem to be the students bright enough to figure that out on their own.


1. Surely, in today's economy, we must have division of labor. We need people in the engineering and science fields, for example.

2. Someone with God-given talents and abilities in science/engineering (I pick on these fields not because they're the only such fields out there, but because they make a good test case for what I'm talking about) who receives a cCE, without extensive further training on the order of a degree, will assuredly NOT be able to get a job doing science or engineering.

3. Today's market has changed a fair amount. In the private sector, employers seem to be getting rid of their more experienced employees who can train in the new guys. As a consequence, more and more jobs are requiring already experienced applicants. Employers want recruits who can hit the ground running, not someone who needs a year of extensive training before he's worth anything.

4. If a man does not work, he shall not eat. We have it on pretty decent authority that if a man does not eat, he will not live. The commandment not to murder says that we are to promote life. Therefore, it is a logical consequence that a man must work. Given that work is THAT important, why would an education purposely try to avoid giving a man specialized tools?

It seems to me that specialization does seem to be one of the main issues here. Classical Christian education rightly points out that a man gets to be mentally one-sided if all he does is vocation. I would almost claim that a man would get to be physically one-sided if all he did was cCE! Where's a balance?

Here's my proposal. For K-12, hit the cCE as hard as you want. If you do that bit well, he should be prepared, as Dorothy Sayers says, for life. In today's world, that's probably going to mean that he has to get a degree in order to earn a buck, though there are, of course, exceptions. So let's say he has to get a degree. Well, he has the tools of learning. Put them to work in vocational training (which you can sort of view as an extension of the Quadrivium, if you like). Make the post-secondary education vocational, with the assumption that the students are classically trained.

As one German chemist put it, "Give me a student who has learned his Latin grammar, and I will answer for his chemistry."

Visit Math Help Boards for friendly, free and expert math help.

Friday, July 04, 2008

Book Review: The History of the Calculus and its Conceptual Development, by Carl B. Boyer.

Dover published this book in 1959, although Boyer no doubt wrote it earlier.

I picked this book up mainly because I wanted to know as much as possible about any subject I want to teach, calculus being very high on that list. This book was definitely an eye-opener. There were several main points Boyer wanted to get across, namely the following:

1. There are many instances in which historians ascribe some complicated, nuanced concept such as the limit to an early thinker like Archimedes, when in fact said early thinker did not have the concept fully in his head (or so we judge by his writings).

2. The founders of the calculus, and even some who came after, did not invent calculus in a vacuum. Although Newton and Leibniz may have bundled the existing algorithms into a nice package and thus deserve to be called the inventors of the calculus, the story was not over then, and even so bold a thinker as Lagrange didn't get some things right (at least, as we think of "right" these days.)

3. The development of calculus did not happen overnight (more like over the span of 2500 years!).

There are some interesting criticisms of Boyer's book on Amazon. I'd encourage you to read them. I found a few of them to be right on. For though there are few books which collect all of the information in one place like Boyer's, he does have some hidden assumptions, especially modernism.

Another criticism I would have of the book is the disassociation of calculus from physics. Physics provided a good deal of the motivation for developing the calculus in the first place, but Boyer barely mentions it.

Is it worth reading? Yes, if you want to teach calculus or write about the philosophy of math or the history of math. It would even be useful for students to read so that they don't get the impression that calculus fell out of the sky in the "perfect" delta-epsilon form we have today.

For that matter, my Dad wrote a calculus book in which in put forth the Third Derivative Test, which is not in any textbook of which I am aware. Calculus, while a full, rich body of knowledge, cannot possibly be complete. (See Goedel's proof of the incompleteness of first-order logic.)

Visit Math Help Boards for friendly, free and expert math help.