Discplines in Education

Note that the title says "disciplines", not "discipline".  I'm not talking about punishment for bad behavior at school.  Instead I want to say a bit about the role of disciplinary boundaries in education.  This has been a big issue for me lately as my college struggles with the process of General Education reform.  Our current Gen Ed model is built around students taking courses in a variety of disciplines, but with no obvious or explicit goals for those courses other than that they are in various disciplines.  We are considering a model (which I helped to craft) that builds requirements around a list of goals, and courses that satisfy a requirement must make the case that they address the goal of that requirement.

It's a tough issue.  We are all trained in specific disciplines, at least to the extent that we are awarded degrees in specific fields.  We have expertise within our discipline that we likely do not possess outside of it.  What makes any of us think that we can teach something that doesn't lie comfortably within the traditional boundaries of our discipline?

These are legitimate questions, and I understand why some of my colleagues think they are vitally important, but I confess they just don't worry me that much.  They come from a point of view that sees education as primarily the transfer of knowledge from the master to the pupil.  But if you view knowledge as something that students must build for themselves, then there is not as much emphasis on the specialized expertise of the instructor.  In fact, the instructor and students could be learning together.  And, I think, some of the most interesting and important learning takes place in just those places where disciplinary boundaries get fuzzy and we are forced to transgress the boundaries and venture forth from our comfy boxes.

At least historically, rigid disciplinary boundaries can stifle knowledge.  The strict divide between natural philosophy and mathematics (aka astronomy and astrology) likely held back the progress of what we would now call science for centuries.  I'm just about finished with Bob Westman's The Copernican Question, and today I read his description about what Johannes Kepler had to say about disciplinary boundaries.  Kepler, as you may know, was largely responsible for breaking the rigid barriers between natural philosophy and mathematics (or physics and astronomy, if you want to use more modern terms).  Westman's description has to do with the aftermath of Kepler's publication of a Copernican textbook, the Epitome of Copernican Astronomy.

Here's what Westman and Kepler have to say:

Kepler was explicit about challenging traditional disciplinary authority in his dedication: at stake, he wrote, are the "rules of the Academies" (leges Academiarum), the "honor of the Academics" (honor Academicorum), and the "boundaries of Academic Philosophy" (Academicae Philosophicae limites).  Patrons were obliged to protect these boundaries, Kepler acknowledged, but a wise prince "knows that the boundary posts of true speculation are the same as those of the fabric of the world" and not those "set up in the narrow minds of a few men."  Kepler understood the resistance that he could expect from the universities: "They are established in order to regulate the studies of pupils and are concerned not to have the rules of teaching change very often: in such places, because it is a question of the progress of the students, it frequently happens that the things which have to be chosen are not those which are most true, but those which are most easy."

I have always felt special sympathy for Kepler.  Even more so now.

But then you can't trust my opinion on this.  I am a PhD physicist who teaches astronomy courses that make extensive use of history.  I clearly have no respect for disciplinary boundaries.  I'm sure some must think that my students are being irreparably harmed by having such an instructor, but I'm more concerned with what my students think (and what they learn).  For the time being I will continue to delude myself that I'm teaching what is most true rather than what is most easy, and I will hope that some wise prince (or princess) out there will agree with me.

The Celestial Sphere

In today's class we took the metaphor from the Game of Science and started applying it to the night sky.  The first step is to watch the game being played, so we used an open source planetarium program called Stellarium to observe the motion of the stars across the night sky as seen from Rome, GA.

The students quickly spot some patterns.  The stars all move together as a bunch, not each on their own independent path.  That, of course, is why we can speak of "constellations".  But they find other things.  One star doesn't move much at all, and its angle above the horizon just so happens to be the same as the latitude of Rome, GA.

Eventually we they are led to their first theory: the stars are all stuck on the inside of a giant sphere, with the vastly smaller Earth at the center.  The Celestial Sphere theory is really quite amazing.  It explains the motion of all of the stars across the night sky.  Not one of them, not most of them, but all of them.  Not just tonight, but tomorrow night and every night for the foreseeable future.  (As long as you don't measure to high enough precision, or wait around long enough for precession effects to be large, then it pretty much works all the time.)

Such a simple, beautiful theory.  It explains so much with so little.  If you had not been taught something different since Kindergarten it would be difficult not to believe that this wonderful theory is true.  You would be totally convinced that you had found one of the "rules of the game".

We also learned about coordinate systems: for our sky (altitude and azimuth - using the EJS Local Coordinates Model) and for our newly proposed Celestial Sphere (right ascension and declination - using the EJS Equatorial Coordinates Model).  These coordinate systems are useful and important, but they are so obviously human inventions.  They just don't have the beauty of the whole Celestial Sphere idea.  There is no sense in which one is tempted to think of these coordinate systems as "true" - they are just useful in practice.  The Sphere is useful too, but it seems to transcend mere practical utility.  One can easily believe that it was "discovered" rather than "invented".  If your brain wasn't clouded with a modern education, you might really believe that the Celestial Sphere is up there in the great big sky, spinning inexorably about us.

No wonder people held on to this idea for 15 centuries, and even then gave it up only with extreme reluctance.

On Thursday we are going to take a look at what's up with the Sun.  Is it, too, stuck to the Celestial Sphere?

The Game of Science

Today was the first class meeting for my Copernican Revolution course.  We had a two hour lab period, of which the first 45 minutes was the typical course introduction (snore...).  But then I started talking to them about Gestalt Psychology and shifts of perception.  Maybe not what they were expecting.  We looked at the standard faces or vase image, which they all probably recognized. Then we looked at another image that they had never seen before. I let them come up with some wild guesses before I told them it was a cow. They didn't see the cow. Then I made them see the cow.

What, you may ask, does gestalt have to do with astronomy?  Well, it has a lot to do with scientific revolutions.  The Ancient Greeks saw the Sun and Moon as planets, and the Earth as very much a non-planet.  We see the Earth as a planet, the Sun and Moon not so much.  We are SEEING the same things, but we see them AS something different.  When I first showed the second picture my students and I were seeing the same image, but I saw it AS a cow and they did not.  Then I showed them how to see the cow, and now they, like me, cannot NOT see the cow.  That's how it goes.  Today it seems obvious that Earth rotates and orbits the Sun, but to get here we had to be taught how to see the cow.  Copernicus and others taught us how to do that, even though we (and by we I mean humans generally) resisted. 

So now my task is to try to help my students NOT see the cow.  We need to observe the night sky (simulated) without building all of our "knowledge" into what we see.  Then we can start constructing models.  That's what real scientists do.  They don't know already that it is a picture of a cow.  They can't see the cow when they start.  They have to discover the cow, and then teach others to see the cow.

To simulate how this works, we played a game.  Seriously.  It's a thing called the Game of Science and it was developed by Masters and Maloney at IUPUFW.  Each group of 4-5 students gets a game board, playing pieces, and descriptions (lists of moves) for several complete games.  They have to try to play through the games (with nothing more than the list of moves, in cryptic code, like "4 -> 6 [C]") and try to figure out what the rules of the game are. 

My class today did great.  They got right into it, and pretty quickly branched into two competing camps with different theories about how the game worked.  I brought them all together for a "conference" (just like scientists!) where they could give their theory of the game and defend it.  In the ensuing discussion I could have vanished and most of my students wouldn't have noticed.  Awesome!  They were doing exactly what I wanted them to do, and I didn't even need to be there.  Those days are the best.

Anyway, there was some controversy over the rules.  We didn't come to agreement.  And I didn't tell them the answer.  There is a good reason for that: I have never seen the rules to the game.  I don't know any more than they do (although I've done it several times, and I'm pretty sure I know how it works - but I didn't even give them that).  That's how science is.  It is not at all like what they are trained to do in typical science courses, where they can work the problem and then check their answer with the back of the book.  There is no "back of the book" when you are doing real science, there is only the world.  Sometimes the world is good about telling you that you are wrong, but it never quite tells you that you are right and it NEVER shows you the answer in plain text.  It's all about building confidence.  At some point your theory works so well that you become supremely confident in it.  That's about the time when you run into what is called an "anomaly" (there was one of those in the game, too) and things get fun again.

I also tried to point out that they did not approach their task as either automatons or blank slates led purely by the empirical data.  They made use of prior experience (they have all played board games, and most of them quickly concluded that this game was a lot like checkers - which may or may not be true).  They also had to get creative, especially when faced with the "anomaly".  This, too, is part of science.  Scientists attack any new problem with a set of assumptions about what constitutes an acceptable solution and what strategies are viable.  Those assumptions are based on their education and previous research experience (and maybe their religious convictions, political beliefs, personality, ethnicity, musical taste, etc, etc).  But science is also a fundamentally creative activity, a fact that few non-scientists seem to recognize.

I felt like it was a smashing success.  I just wish we had more time to argue about the game.  We could have gone on for another 30 minutes, at least, before reaching consensus.  But that's not so bad.  More than a century passed between the publication of Copernicus' De Revolutionibus and widespread consensus that the Earth really does orbit the Sun.

Where do we go from here?  We watch another game being played.  This one involves stars and planets moving around in the night sky.  Maybe we can figure out the rules for that game.  But we just might run into a situation where we have two competing theories about how it all works....

Scaling the Universe

This blog is primarily a place for me to record my reflections on teaching the history of astronomy. I teach two college-level astronomy courses for non-science majors. Both of my courses look at the historical development of astronomy. The Copernican Revolution focuses on the development of planetary astronomy from Aristotle to Newton. The Scale of the Universe examines the development of ideas about galaxies and cosmology from Aristotle to the discovery of the Cosmic Microwave Background Radiation. Both courses emphasize active inquiry (often mediation by computer simulations) and an understanding of the nature of science.

This semester I am teaching The Copernican Revolution, and I will try to post a reflection here after each class meeting. We'll see if I can stick to it!

For anyone interested in my courses, or the curricular materials I have developed, you can visit my web pages:

The Copernican Revolution

and

The Scale of the Universe.

You can also find many of the computer simulations I have developed for these courses in the Open Source Physics Collection.