Well, it was another ridiculously busy day. I’ve a headache and I got up too early to begin the day…. dozed off a touch in Christian Roemelsberger’s (of the Perimeter Institute) excellent seminar just after lunch (triple problem for inducing sleep in seminar: (1) early start after late night, (2) lunch immediately before… (3) sitting in darkened stuffy room with a solo voice talking). Interestingly, I followed everything and only did “power-dozes”, so was able to ask intelligent questions during and after….
Taking a short break. It is after six o’clock on a week day, so I’m allowed some alcohol….this time in the form of a glass of wine. (Picked up this ad-hoc rule from my wife -back before she left- and she from her father, I gather…. it’s a nice tradition to keep up….) The rule gets broken when one is called on to go to receptions of various sorts on campus, of course…… Neccessities of work, you see. Duty calls, and all that. And on the weekends the rules are totally different.
Well, after going to sleep at 1:00am after reading postdoc applications, I got up early -6:00am- to prepare the final exam for that course I was telling you about a while back, and then I gave it at 9:00am. It was not a take-home. Those have their place, but I also like trying to set interesting exams in the classroom, where both the examiner (me) and the examined (them) have a good time. I remember this from my days as a student. I loved interesting exams. You come in the room, the scene of possible triumph or disaster. You’ve prepared, and you’re as ready as you will ever be, and the teacher hands out the papers, and then it is you vs the examiner. Fixed time, and all you have is you, your pen, and your brain. (And your sweat.) You turn over the paper and the battle begins…. Excellent drama!
One of my favourite interesting exams was when during my final exams as an undergraduate, at Imperial College, London University, 1989. The quality of my BSc. degree depended on a single week of peak performance (this was back in the day when there was little stock placed in spreading the load over the course of the year…..sudden death ruled! I could get anything from a First to a Desmond (or maybe worse), depending upon that week.). Rather late in the day, I discovered how interesting a number of my courses were as a result of studying hard in the weeks leading up to the finals, surveying the course, the careful notes I took (even when I did not understand them – a technique I stress in my students today but they ignore me), etc… I really appreciated the deeper aspects of condensed matter physics and nuclear physics in those weeks. The nuclear physics course had seemed really tedious…..just lots of rather ad-hoc looking models of things, and lots of classifying and bean-counting and no overall theme…it seemed. Things began to make more sense once I had al the course notes in front of me. Then the exam came (the lecturer was T.S. Virdee, I wonder if he is still there?) and I loved it. (I was sure that I was not going to do so well in that course as I did not like it very much, but then I got enthusiasm for it and it just overnight changed my ability to do things in it …. see my comment here on another thread about the importance of enthusiasm…) My favourite question (getting back to the point) started off as a seemingly tedious question about the “liquid drop” model of the nucleus, and you had to estimate the sizes of nuclei using a technique which estimates the force on on nucleon due to the presence of all the others…… You get out the usual numbers. But then the question took an interesting turn, which was not in the lecture course! (You can’t do that these days, you get sued….) He asked what would happen if you took into account Newton’s gravitational force as well. Well, you do the estimate and it is just not important at all…it would seem. It is vanishingly smaller than all the other forces governign the structure of a nuclues. How silly, you think, but you carry on anyway, since you’re getting points for doing what was asked. The question then takes you to the point where you increase the number of nucleons until the gravitational component does become significant. You get a huge number. You carry on anyway. You then estimate the size of this new bound object, you get …after checking the computation again for errors!… about 11 kilometers. The last question on that section is then something like “can you identify this object?”. Then it comes to you in a flash…it’s a neutron star!
That’s one of the reasons I love writing exams that take the student to new places where they learn new stuff in the act of doing it. You’re just not supposed to do that anymore….. bad practice. You’re just supposed to test students with thinly-veiled versions of what you already told them in the lectures. Very thinly. Anything challenging had better be in an open-book exam or a take-home. No arena. No drama. No sweat. Sad.
But I try to do it at graduate level still, since most graduate students in physics are not from the USA and so don’t realize that they can sue me. (Kidding…..slightly….)
It does not always work, but I think that it worked this time.
So today they started with (technical stuff coming up) examining the properties of a particular conformal minimal model – the Lee-Yang model- and I tested their conformal field theory knowledge by getting them to extract the scaling operator dimensions from the Kac table, and deducing various properties of the model from that…. critical exponents, non-unitarity, etc. Then they turned to the subject of KPZ scaling, looking at the properties of the partition function of a conformal field theory coupled now to fluctuating surfaces as opposed to fixed ones. After reflecting upon the critical exponents encountered there, they moved to the meat of the exam: solving a specific model using matrix models techniques. The matrix model allows you to actually do the sum over random surfaces explicitly (by discretising them first) and extract the KPZ behaviour (by taking a careful continuum limit) for a class of conformal models obtained by tuning to a critical point in the model and carrying out the famous “double scaling limit”, which I talked about briefly here. In the end, they get a result for the partition function of the model, and if they’ve done everything properly (I walk them through it), they see KPZ scaling and they discover that they’ve derived the model of the Lee-Yang model (from the first part of the exam) coupled to random surfaces. We’ve come full circle, and they learned how to explicitly solve one of these models on their own, and tune it too find the critical behaviour that defines the continuum limit, etc. (It was only a 90 minute exam, so my plan to have something on solitons (something else we did in the course) was dropped. There was enough computation to be done in the stuff I gave.)
I was reading their solutions on the way home on the bus just now and I think that they all enjoyed it…. A success!
It’s 7:30pm now. Better stop blogging and go back to working. Got to (1) work on documents for a proposal; due tomorrow (2) work on two dossiers for postdoctoral candidates for a fellowship; due tomorrow (3) write several sections of a collaborative project, and edit two; due tomorrow (4) finish work on an encylopeadia entry; due a month ago….
Gosh! I’d better go.
-cvj
November 30th, 2005 at 11:17 pm
So, I take it that you ended up teaching a course that was both an intro to field theory and an intro to interesting topics that wouldn’t be taught in an ordinary field theory course? Sneaking up on string theory from around the back?
My students are taking their take-home final right at this moment. I think for once I gave an exam that can actually be completed in the allowed time; we’ll see.
November 30th, 2005 at 11:27 pm
A very timely post. As I write this I’ve just finished a blog post, am currently working on the final exam for my graduate Mathematical Methods class, and have had a couple of glasses of an excellent New Zealand Sauvignon Blanc while doing both.
November 30th, 2005 at 11:32 pm
Sean: Yes… I think so…. in addtion to the stuff I mentioned in that previous “The Challenges…” post, they even saw prototypes of integrable systems, understood key things about solitons, topological conserved charges carried by such, and prototype of BPS conditions…fluctuating random surfaces….. matrix models (including the original nuclear applications) and their modern uses……….. and all through lots of very hands-on physics of ciritcal phenomena, etc…. did not get to D-branes, but you know…they’re smart kids…. there are plenty of sources for the standard treatments they can read on their own. Harder for them to thread a path through the stuff we did….
Cheers,
-cvj
November 30th, 2005 at 11:35 pm
Sounds great. Except: count me in the camp that thinks exams are uniformly horrifying. Problems may be interesting and exciting, but exams are just necessary evils.
December 1st, 2005 at 12:07 am
Yes. But the trick is to find a way to extract enjoyment from the necessary evil.
-cvj
December 1st, 2005 at 12:13 am
Undergrad final exams….. I still get the willies everytime I hear “The Ride of the Valkyries”. At 6:00 AM on Monday of finals week tradition has it that every stereo on the Caltech Campus blasts “the ride” to get people in the mood for finals. I can still hear the not quite synchronized 1st few notes of that piece blasting across the campus as a freshman.
and it was over 35 years ago….
Elliot
December 1st, 2005 at 12:44 am
I can’t take anymore exams…had enough of that, thank you.
Meanwhile tonight, while drinking the last of a nice Santa Lucia Mountains Pinot, I finished my contribution to the Summer Snowmass proceedings. It is due tomorrow, so am I just in time.
December 1st, 2005 at 1:14 am
Jeez, cvj, that really sucks. I’m so sorry.
But I hear a *lot* of stories about physicist’s wives leaving them. Scary. Please don’t tell me I should not get married if I want to be a physicist!
December 1st, 2005 at 1:37 am
Jack, thanks. It happened a while ago and I’m fine now. But that was not the subject of the post, really, just something mentioned in passing. It’s not appropriate to go into it any further here, save to say that scientists are regular people and so regular stuff happens to them…good and bad. I appreciate the comment.
Let’s get back to the subject now and leave the other alone!
Cheers,
-cvj
December 1st, 2005 at 1:39 am
are you sure it was just one glass of wine? your subject is a little meandering.
December 1st, 2005 at 1:42 am
Dissident… My subject is always a little meandering. What’s new? I’m surprised my co-bloggers put up with me, frankly.
-cvj
December 1st, 2005 at 4:43 am
Oh no! I’ve been hijacked! The Dissident of #10 is not the Dissident you’ve all come to love so dearly in months past. Grumble…
December 1st, 2005 at 1:43 pm
Back to the “necessary evil” of exams then. I agree with Clifford that it’s important to make the exam as fun as possible. One of the best I’ve taken was a take-home Cosmology exam that George Ellis gives in his 4th year cosmology course and I remember that I’d learnt more from that one exam than whole other courses even. It was great! Very structured and walked you through the entire thing; from writing down a metric to extracting measureable quantities from it and eventually why this partcular cosmological model can’t work. If one gives some (ok, probably a lot) of thought to it, exams can be quite as enjoyable (in hindsight obviously) as the rest of the course, I think.
December 1st, 2005 at 6:43 pm
I wonder if it’s a personal experience. Based on my time working for someone doing physics education on the side, and some pondering, and some total BS, I have firmly come to believe that exams are supposed to be pure assessment (and that the students should be told this). I don’t believe “exams are learning experiences” and that occasionally someone can put something extra together that makes things more wondrous during an exam, but that’s clearly the exception, not the rule. And if you design an exam to exact that from a student, many people will not do well.
December 1st, 2005 at 6:44 pm
Or, I should say, the average student will be less able to demonstrate achieved competency.
December 2nd, 2005 at 10:27 am
[...] As I type, the students in my Spacetime and Black Holes class are putting the finishing touches on their final exams. Unlike Clifford, I prefer to give take-home finals rather than in-class ones. Not a strong conviction, really; it’s just easier to think of interesting problems that can be worked out over a couple of hours than ones that can be done in half an hour or so. Here’s the final (pdf), if you’d like to take a whack at it. The colorful problem 4 was suggested by Ishai Ben-Dov, the TA; the terse calculational ones were mine. [...]
December 3rd, 2005 at 9:30 pm
[...] Sorry…. I’m hungry and so all I can think of (almost) is food. Before I see to that, and go see the movie “Kiss Kiss Bang Bang”, I thought I’d suggest the following. Since I mentioned a neutron star in a recent post (somewhere in the babble), why not pop over to Centauri Dreams and look at a larger version of the photo below, with commentary. It is a Hubble space telescope image of the Crab Nebula, (mostly a light fluffy souffle of hydrogen gas) which contains within it a neutron star, left over from a supernova explosion that probably happened in the year 1054. Yes, a neutron star is a bit (a bit) like a giant nucleus…. it is a large collection of neutrons bound together by gravity (any protons that were present find it preferable to each aabsorb an electron and become a neutron in this situation)…. Normally, neutrons live happily with protons in a bound state which is very small…. the nuclei that make up the atoms that make us up, and other ordinary matter. A single nucleus is about 10^(-15) meters across. Tiny. A nuetron star is about 15-20 km…so 10^4 meters across. Way bigger. [...]
February 13th, 2006 at 9:35 pm
[...] The process of preparing exams for the freshman level is very different from the sort of exam preparation I spoke about earlier. Here, the students are still learning a lot of the language of expressing themselves coherently in properly formed mathematical statements, and still developing intuition for how the physical world works…. crucially they are learning (I hope) to abandon a lot of the dreadfully confusing phrases that pervade our language, which they hold onto, which then pollutes their physics….. And most importantly they are still learning to be confident about making the physics -and the processes I have taught them- work for them consistently, so it is a delicate time, and they’re easily confused at this stage. So one must prepare very straightforward questions, with extra clear instructions, and no clever sting in the tail. Sadly, I think we’ve been erring more on the side of caution in this area every year (no matter what institution I’ve taught at), and things get simpler and simpler to the point that it is difficult to go back. (But I understand that this is what is called “progress”, and so onwards and upwards we go…..) [...]