So far so good

As promised, the time I spend in front of the class ‘lecturing’ for my introductory mechanics class remains minimal — well below 1/3 the class time. Today was a case in point: As the students walked in, I handed them a card from a well-shuffled deck of playing cards, asked them to find people with the same number and to sit with them. I asked them to talk with each other for a few minutes and generate questions from the reading that they had that they would like me to discuss. I talked about these questions at the board when I had collected the few that were voiced. Once that was done, I turned them loose on the problems I had chosen for this section — and which I had mailed to them before class — and away they went. I should probably note that I have a student assistant in the class with me, circulating with me.

After the last two classes, there are a few crucial house-keeping things that I have concluded are necessary to this kind of teaching and made sure to do today: (1) The groups needed to be assigned groups, and in the absence of any strong reason to socially engineer, I went with the random method. (2) I told them why I was insisting they work in groups (because it is pedagogically valuable; I will tell them about the ‘real world’ and how they can’t avoid working in groups very shortly). (3) I also told them that they were all to turn in an evaluation at the end of the class that would comment on their contribution to their group, as well as the group’s value to them, including how they felt they were treated by the group. And (4) I asked for the standard ‘one thing you still don’t get’ feedback.

The responses were excellent — they overwhelmingly liked the groups, were surprised by how well the randomly-generated groups worked, and expressed a great deal of comfort with the structure. The point I have made repeatedly to them is that the way we test grasp of this material is through problem-solving and as such, they like that they get to practice it. And they love being most of the way through the homework so early.

A few weren’t very sure they preferred this to the standard lecture, but didn’t really see any major reason to complain yet. Except for one student, who doesn’t understand what’s going on, doesn’t feel like he’s contributing to the group, and is lost and worried. I think I know what to do with and for him, but given only 1 student complaint — so far so good. I like how I am spending my time, and I like how the students are spending their time.

Of course, this is only kinematics. On Wed we hit Newton’s laws, and that will be a crucial test of this technique.

Administrating

As I’ve mentioned in passing before, this year I have acquired a new role as an administrator — as co-director of CISMI (the Carleton Interdisciplinary Science and Mathematics Initiative). The first few months I was still getting used to doing it, mostly consumed by the excitement of participating in the writing of a giant proposal, and getting some new ideas off the ground. But this last week, as I’ve attempted to get back into the groove for the new term, CISMI-related activities are very visible, more routine, and hence feel very much administrative. The administrative assistant for CISMI is also the Physics Department’s admin, and there was a morning last week when I was trapped in a loop for what felt like half-a-morning but was probably a lot less: I was stopped with a CISMI-related question when I stepped out of the office for coffee, had to go back to my office to shoot off an email/make a phone-call to sort things out, and when I headed back towards to the coffee machine, stopped again, and so on. All that administrivia made focusing on physics a little difficult, to say the least.

Why did I say yes to the Dean (Scott Bierman) when he asked whether I would take on this position? He made the request/offer to me a week after calling me to let me know I had tenure — he claimed that this gave me a fair shot at saying no. (Full disclosure, as a smart game-theorist economist, he asked for service on multiple fora when he did this, and I said ‘no’ to all the others. We’ve joked about his strategy — that Scott was banking on it being easier to say yes to one of many requests if they were presented all together.)

As is typical in academia, it’s not because there’s enormous rewards associated with it. Actually, on the surface, none. There are course-releases associated with it (for me and Fernan, the Director of CISMI) but they barely compensate for the added work, something I hadn’t really appreciated from outside.

And it’s not because I am done with being a professor and itching to move on: I love teaching and doing physics, and have plenty of other college-wide involvements, thank you very much. So what, then? The following are my musings on motivation, apologies for some of the ambiguities inherent.

One reason stems from something Scott has said repeatedly: There is an enormous amount of Carleton College’s activities that relies on this kind of ‘volunteer’ work from faculty. Which means that either one of us has to do it, or it doesn’t get done. The pool of people who could fill this spot isn’t that large, so really it’s a question of ‘doing your tour’, in some ways. I have often characterized myself as being pretty good in the role of ‘heckler’ — someone who is happy to hang back and comment (constructively, one hopes) on ideas put forth by the people nominally running things. It felt like time to try the role on the other side.

It’s the same reason why I’ve felt like teaching the Cross-cultural studies course was beneficial for me, or why I write a column for the ‘The Indian American’, and why I am maintaining this blog, in some ways. Apart from my research field, and of course my courses, I haven’t been asked to take a stand or create the target for criticism about much. It’s about time to see if a coherent story can be made from the scattered thoughts I’ve generated about all sorts of things.

Another is that I get to push/facilitate the growth of/ two ideas that are close to my heart: (1) Complex systems thinking as embedded in interdisciplinary science (through the curricular development funds that we get to disburse) and (2) broadening access to education and to science for under-represented minorities, again through curricular issues, as well as through helping guide conversations on classroom climate and pedagogical techniques.

All of what I get to do is facilitation and suggestion rather than direction, really, given that everything goes through an advisory board composed of some very smart people with strong opinions — yes, hecklers — and that it’s directed at moving faculty along (which, as we all know, is somewhat on the lines of herding cats, particularly when you have no power over them at all).

So it’s about making meaning, creating a story, on a larger scale than your discipline and your teaching, and for a place I definitely feel like I belong to, and which perhaps has begun to ‘belong’ to me. Which compensates somewhat for taking care of the paperwork and the logistics. I also get to have long chats with Fernan, which I have begun to enjoy greatly — they are officially about CISMI but land up ranging all over the place, as you probably experience in conversations with any collaborator.

And a short while ago we heard back from that big grant we had requested: We were approved! It’s still not officially announced (so more details later) but it means that we — the Carleton science community specifically — will get to do some of the things we had hoped to do, and it’s nice to feel like one has helped facilitate that.

Spring Break and new experiences

It was Spring Break at Carleton, and I took advantage of that to journey through India with a 5-year-old kid in tow. I could write about the trip through a cross-cultural studies perspective, I suppose. The external and cultural differences between the United States and India, even as they shrink every month, every minute practically, remain huge. And yet I find that I am just at home when I step off the plane in either direction. Perhaps it’s because I am never fully at home in either place.

But this trip was far too personal an experience for me to analyze in this forum at the moment. Suffice to say that I am back in circulation, tired but happy for having made the trip. And ready — whether I like it or not — for the new term which starts tomorrow.

I have two unusual experiences ahead of me this term, with regards to teaching. The first: I am trying out something new in my introductory mechanics class, and I’ll blog the results over the next few weeks. This class suffers from the same issues as introductory mechanics did at Rice (where I taught before I came to Carleton) and at almost every other school, I’ll bet, although being at Carleton it is relatively small (the cap is ‘only’ 48 students).

This course has a large and varied population. This variation exists (a) in terms of previous exposure to the material, (c) likewise in terms of interest in continuing in Physics (it is part of the requirement for Chemistry majors and pre-meds but we also recruit our majors in this course), and (c) comfort with mathematics. It is also a fast-paced course with a lot of techniques to be mastered, in principle. At the same time, however, there are relatively few major concepts to be grasped (if not just the one: F= ma)

I taught this course my first 3 years at Carleton, and it was a fundamentally frustrating course in terms of trying to find the right rhythm and pace while trying to accommodate everyone’s preparation, inclination and speed in mastery. One result of my frustration was that I created a course that used Chabay and Sherwood’s ‘Matter and Interactions’ format (with a focus on computation and modeling) to draw away some of the more prepared students — but this was a small group, extra-prepared.

I am teaching the ‘big’ course for the first time in 4 years this Spring, and here is what I intend to do: Some of it will be consistent with what I have tried with success in other, smaller classes: I ask students to read the textbook, email questions to me before class, and then I construct lectures or activities in response to these questions. Students also spend a fair amount of in-class time working on problems together while I circulate between the various groups. This spring, I will do an extreme version of this: Students will be asked to read the textbook and come into class prepared to work on problems. With a class of 48, I will not be able to read and respond to questions from all the students. Also, in my estimation, there are not enough complicated ideas – as opposed to applied techniques – for me to use a lot of class time lecturing. So the focus will be entirely on problem solving, and self-paced mastery. I will be able to provide directed help as needed by the students, and monitor individual learning. This comes at the expense of exposition time, of course, but I am reasonably sure this is a fair trade-off in this class.

I expect this to be somewhat successful, but it is unlikely things will work as well as I would like the first time with this approach. But here goes anyway.

The other new experience will be co-teaching an Interdisciplinary Computational Modeling course with my colleague Cindy, which I will write about more later.

Relativistic economics

While posting the relativistic poems and songs, I was delighted to find Tyler Cowen’s blog post on the effects of including relativistic effects in economic analysis. Specifically, for example, you could deposit a little bit of money in a high-yield savings account, and then blast off for a round trip at high speeds and come back to find lots of money in there while you are still young enough to enjoy it (due to time-dilation effects). This means that the interest rates applicable cannot be such that it is profitable to do so.

A completely tongue-in-cheek hypothetical scenario, of course, but hey. If quantum mechanics could turn computer science on its head — in terms of setting limits (’information is physical’), there’s no reason why relativity couldn’t set some  limits for economics (’utility is physical ?’). Enjoy!

Relativity poem

Here’s a poem from one of my students, Meaghan Foster.
I stand upon this face of earth, this cliff.
You speed by sudden, slender, contracted
like the quintessential caterpillar, afraid
that my outstretched arms will catch you tight.
We fear different things; we both think they are true.
I see you as you see me: shrinking, dissolving into this relative world.

If you accelerate away from me now, if you find another orbit
someday years later when you return
you may find me old and gray, closer to death than you—
having measured my life by different increments,
obeyed the ticking of another clock.

And when you have stretched the taffy surface of space-time to extremes,
when you have twined it supple and compliant round your firmly fleshed finger,
will you then (although, what is ‘then’ to us?)
will you then stay on earth as I blast away,
to wait until we are brought back into alignment
so that we may again meet at a coordinated intersection of time and space?

The other shoe will drop, be it by gravity or acceleration.
It makes no difference; the outcome will be the same.
Light will move at speed c—more constant than love
and sharing a reference frame will be but a dream.

Relativity songs

Part of my ‘Revolutions in Physics’ class grade is given for a ‘creative’ project, where I’ve gotten all sorts of cool things over the years, some useful, some silly, some very thought provoking.

Last year Gaetan Damberg-Ott (an IR major) wrote a side-splitter of a relativistic noir (I wonder how many times those two words have appeared together before :-)) detective story he called The Case of the Missing Time which was picked up by APS News for their ‘Zero Gravity’ column. Gaetan had a blast annoying the graduating physics seniors with his claim that he was a published physicist.

Once in a while I get an original song. Here’s two for your listening pleasure: Dear Electron (Adam Fetcher) (from a few years ago) and Relativity (Tom Weishan) (from last week).

Quantum jokes

What’s your favorite quantum mechanics joke?

I got the following in early morning email:

How do you know you’re dealing with the physics mafia?
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They make you an offer you can’t understand.

——

And my response:

How do you know you’re dealing with the quantum physics mafia?

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.

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Because you wake up with a horse on your bed that’s both dead and alive.

Oh come on, that’s half-decent. You smiled.

It’s clearly silly season at the end of the term here at Carleton College. Your contribution appreciated.

Life at the Olin Outpost, or a whole new way of doing quantum mechanics …

Carleton Physics majors are always studying in Olin. Don’t they ever do anything fun? Of course they do!

Concept maps

Towards the end of one of the comps presentations I’ve attended this year, the student said: ‘And now for a concept map, Arjendu-style’. And she laid out the ideas she’d talked about, with links showing which features of the system were crucial for which properties, and which were understood, and so on.

Once or twice a term, on one of those many occasions when I see students’ eyes beginning to glaze over in class, I call for a time-out. We take 10 - 15 mins during which the students stand at the various boards and put their heads together to sketch out the recent ideas they have encountered, while I circulate and chat with them. I do it because I think students get lost in the details and forget the big picture of what they are doing. But also to wake them up. I’ve been doing this in all sorts of classes, including quantum and stat mech. And I was pleased to see that it had at least become part of one student’s thinking style.

At the NSBP conference, Chandralekha’s presentation on cognitive issues and student learning in physics reminded me why I had started doing this. As she said, if you give the same problem to a novice and an expert and ask them to think out loud, you will see a completely different intellectual structure to the approach. For an introductory mechanics problem, for instance, a student will say things like “oh, it’s an inclined plane. I should think about which forces are involved. Wait, is there friction? What about the normal force? What axes should I choose? Oh no, this is a complicated one — there’s gravity and a spring as well.” And so on. An expert will say something like: ‘Hmm, that’s probably best done by a conservation of energy analysis. Ok, which potential energies do I have to track …” And so on. Neither approach misses the point, but the latter constrains you, and focuses you much faster. And you can see this in maps that you can get people to draw. So I figure anything I can do to help people to get from novice maps to expert maps is a good thing. And by making their conceptions explicit, I am able to do this to some extent: At the end of the exercise, I will quickly sketch my own version of the concept map which I hope helps with this transition.

I talked with a colleague about this, and a couple of days later, his wife, who actually leads workshops around the world on teaching techniques sent me an email that I thought worth sharing with the world:

‘[I heard about your conversation about] concept maps - quite a coincidence because just today I was putting together my handouts on concept maps for my upcoming faculty workshops in Taiwan. It is one of the most versatile, useful but seldom used teaching techniques.

I’ve trained faculty in active teaching techniques in Ukraine, Uganda, Oman, Cambodia and now Taiwan - it works in all cultures. I’ve trained only in schools of education and business but in Taiwan I will also be dealing with engineers. Interestingly enough, it was “invented” by a science faculty member at Cornell.

One of the business faculty I worked with in the Ukraine did a great job in combining it with collaborative learning. She had 3 groups of students create a concept map for something in business (I can’t remember what), had them put it on sheets on the walls and then present it to the rest of the class who questioned them about their concepts and they had to explain or revise. There was SO MUCH learning going on …’

And she also sent me a link:
http://cmap.ihmc.us/Publications/ResearchPapers/TheoryCmaps/TheoryUnderlyingConceptMaps.htm

So this post is mostly a reminder to myself to keep using this technique — it’s not just a fun way to wake up students, it seems to have some sound pedagogical theory to back it up!

How quantum is a given state?

One of the puzzles I have been thinking about for a little bit (triggered by trying to explain to Referees that we were definitely seeing a quantum phenomenon) is trying to answer the question: Given a certain quantum state, can you quantify how quantum it is?

I have a sharp senior working on it (whenever he can not manufacture sufficient number of excuses relating to his two comps exercises in Math and Physics, his robotics projects, and general life excitement, sigh) right now. The starting point of our analysis is the idea that you can take the Wigner function corresponding to your quantum state, find out how much ‘negativity’ there is in that Wigner function and call the amount of negativity a measure of the quantum-ness of the state.

This seems fundamentally fair: Classical probability distributions in phase-space are positive-definite, and it is clear that Wigner function negativity comes from interference effects, so quantifying this should be a pretty good measure of quantum-ness. It is, except in a handful of cases, a numerical exercise, which is a bit of a pain, but that’s fine.

However, there is something counter-intuitive about what emerges from this calculation, and my instinct is that this should be a resolvable issue. Our project figuring this out is moving slowly however, and I’m not completely comfortable revealing all of our thinking so far on this particular project. So I’ll leave it as an exercise to the reader — take a look at that paper by Kenfack and Zycskowski (which has since been published in J. Phys. A) and see if you can find what’s weird about the one (semi-)analytic result they have on the harmonic oscillator.

And if you want to talk about it with us — and in particular about resolutions of the weirdness –  that would be great; as I’ve said before, I’m always open to fresh collaborations/conversations.

What I like about this project is that it has all the hallmarks of a classic liberal-arts-college theorist project: Deep enough to be very provocative, but simple enough for an undergrad to make progress. Of course, I could just be completely out of the loop on some critical literature. We shall see.