Procedural, analytical, relational, innovative

Spring pause today, and I’m enjoying reading and writing while skilfully procrastinating dealing with grading today. An article that caught my eye, and that I almost put in the comments section to my previous post on lessons learned/things to remember for my write-up on my attempt to re-vamp intro mechanics, triggered this particular post.

This is from the New York Times, and it’s about learning new habits. It’s a short article, so I won’t bother summarizing here, but a couple of interesting points:

“Researchers in the late 1960s discovered that humans are born with the capacity to approach challenges in four primary ways: analytically, procedurally, relationally (or collaboratively) and innovatively. At puberty, however, the brain shuts down half of that capacity, preserving only those modes of thought that have seemed most valuable during the first decade or so of life.

The current emphasis on standardized testing highlights analysis and procedure, meaning that few of us inherently use our innovative and collaborative modes of thought.”

Hah. No kidding. I think the students in intro physics/intro mechanics have a hard time getting from procedural to analytical in the first place. That is, they expect physics to be about a certain set of equations, and also expect that I will tell them which equations to use. When confronted by the fact that a typical physics assignment requires analytical AND procedural abilities, they get slightly shaken. But these are Carleton students, so they get over that. However, when confronted by the need for relational work (’group’ problem-solving) and innovation (’ask a question, and answer it’ — part of my instructions for the last lab they did) they are palpably out of their comfort zone.

The articles goes on to say that in new experiences, there are “three zones of existence: comfort, stretch and stress. Comfort is the realm of existing habit. Stress occurs when a challenge is so far beyond current experience as to be overwhelming. It’s that stretch zone in the middle — activities that feel a bit awkward and unfamiliar — where true change occurs.”

The trick, therefore, is to stretch these minds without stressing them. Sigh.

Where did the weirdness go?

Nature just featured an excellent article on “one of the great conundrums of modern physics: the quantum–classical transition” by Philip Ball, at the semi-popular level, talking about the mystery of where and how weird quantum mechanical effects go — that is, why we know they exist, but don’t see them in daily life.

Most of my work is concerned with some aspects of this, and when I try to explain this to my research students, I talk about it as follows: If atoms are quantal, and we are made of atoms, why don’t we behave quantum mechanically? And if it’s a matter of size or complexity (nonlinearity of the system concerned) or temperature and influence of the environment on the system (as is believed) then how and when does the change from quantum mechanics to classical mechanics happen as a function of these properties? Is the change smooth or abrupt — that is, do we go from very quantal to somewhat quantal (and what does that look like?) to classical, or does it go from quantum-classical immediately? Is the transition monotonic — that is, do we only go from quantum to less quantum as we change parameters in one direction, or do you have regions of more quantum-ness and less quantum-ness? How does the quantum dynamics reflect behavior in the classical dynamics? Etc. (Some more discussion of these issues is on my research web-page.)

These are entirely fascinating questions as fundamental physics, but quantum effects are not only cool, they are impressively powerful, and very useful sometimes, so the practical question is: where can we find them?

As a theorist, I wonder about right measure of quantum-ness: How quantum is a given state? How do you measure the difference between a classical distribution and a quantum distribution? I’d like to be able to discuss all this in some sort of abstract way so I can understand the topology, the geography, really, of the quantum-classical boundary. And of course, if I do find an effect, how do I translate this into something an experimentalist might measure?

As the school year heads into the home stretch, I’m getting excited again about getting some uninterrupted (well, relatively uninterrupted, let’s be honest) time to make some progress on these questions again. It’s been a long and complicated year, and I’m looking forward to the comfort and joy (and pain, yes, and pain) of grappling with some of these intriguing questions with more focus soon.

Computational modeling

The ‘other’ class (that is, other than intro) that I’ve been teaching this term, is an interdisciplinary elective called ‘Computational modeling’; I am co-teaching it with my colleague Cindy Blaha, who is a galactic astronomer.

This is the second time I’ve taught this course. The first time was last year, with my fellow-theorist Bill Titus. This course grew out of funding from the last HHMI grant cycle, and is directed at students in geology or biology (preferably) to address the idea that (a) the typical biologist or geologist tends to be less comfortable/less prepared with mathematics than, say, the typical physicist and (b) there are a lot of cool problems in their fields amenable to quantitative analysis if only people in their fields would use some sort of modeling and that (c) current computational technology allows you to ‘code’ and model systems without being extremely mathematically or computationally adept necessarily.

I like teaching this course, and even more when I am not drowning in intro. I get to convey what I regard as the distillation of *my* scientific research attitude: Take a system you’d like to study, find a decent set of equations that capture the essence of the behavior, and then study the heck out of that system of equations. That is, ’solve’ the equations using whatever tools you can deploy, and make predictions about the behavior of the system, and in the process generalize your study as much as possible — preferably capturing the dynamics in some broad intuitive explanations.

That I am ‘modeling’ nature in my studies was not entirely obvious to me until I spent some time collaborating with Randy Hulet as well as with Barry Dunning when I was at Rice. Let me explain what I mean by what might sound like a very silly comment: As a ‘typical’ theorist, I had gone through my thesis and my post-doc with an implicit attitude where I believed in the meaning and validity of the equations I was using as the absolute truth, and thought of an ‘experiment’ as a place where the equations were approximately realized. This shifted slowly during my time at Rice. The shift started when I finally visited Randy’s lab a few months after I started talking with him about a strange phenomenon in his Lithium 7 Bose-Einstein condensates (more on this elsewhere, if requested or if I get around to it). I spent an hour or so with his post-doc and grad students being walked through the ‘atom-trapping’ equipment — the optics and the magnets, and what not — the entire complicated process needed to cool the Lithium gas down to nano-kelvin temperatures before it condensed, and the way a signal was extracted from the system. The place was stuffed to the gills with tons of expensive equipment, all beautifully arranged and tuned to produce the effects needed. I walked out of there with a better understanding of what was going on in the experiment, but also feeling a little stunned that I had only one equation to describe all of this! (For the curious, this is the the Gross-Pitaevskii equation, a nonlinear Schrodinger equation, which is a mean-field description of the condensed atoms). Sure, this was a pretty mean and nasty equation, but it felt … inadequate.

And I would argue back and forth with Randy about what exactly he and his students were doing in their lab, and how we were trying to take care of that in the equations, steadily improving my hold on the exact correspondence between the theory and the experiment. Despite the tenuous connections, in general theorists AND experimentalists have a lot of trust in this equation, particularly because the predictions did so well. Something similar happened in my discussions with Barry Dunning’s group, though since he was working on a Rydberg atom in an almost classical state, as opposed to Randy’s condensate, the interpretation issues were a little less confusing.

These interactions with experimentalists were a wonderful education, and that’s when I got a better feel for the elaborate dance between theory and experiment — experimenters trying hard to reproduce the ‘idealized’ conditions of the theory, theorists trying to extract their best models for the experimental situation, and both negotiating on the interpretation of the correspondence.

And it is this sense that I am trying to convey to my students (all of whom are biologists or geologists, except for one physicist who is a pre-med, so he’s pretty up on the biology). The equations in physics are so much more reliable, the correspondence between reality and the math so much cleaner, than those describing the messy messy messy real world systems of biology and geology, so we really do have a head-start when we ‘model’ in physics. But surely some of that attitude can pay off elsewhere? That’s what’s the effort is with this class.

Almost done

My intro class (the half I teach) has its last class meeting today, and I’ve stuck to my guns on the non-lecturing thing. There has been strong resistance from some students, though some have loved it, and on average I would say there’s about the same level of happiness/lack thereof as I would expect from this class as if I’d lectured.

Will I do this again? Absolutely. I still think we all spent our time more efficiently, that is, learned more, and taught more. What would I do different? At the moment, the following spring to mind, in some random order:

(i) As I did during the last couple of weeks, I would absolutely ensure that some subset of the class is required to send questions. It changed their sense of engagement palpably when I did that.

(ii) Students need narrative to make sense of ideas. It’s something I enjoy providing, but for some reason I lost track of this issue during the second week. By ‘narrative’ I mean a background story, a sense of the larger context for technical ideas, all that.

(iii) Remind them periodically why I am doing things this way. More steadily and pre-complaints :-).

(iv) More examples from biology/bio-physics early in the course, for motivation, if nothing else.

(v) Introduce the spring force immediately after gravity. It’s not ‘constant’. It allows one to talk about internal degrees of freedom, as well as about the Normal force (model surfaces as very stiff springs) which would enable one to stop hemming and hawing when hit with the questions ‘does the normal force do work? If not, how do things come to a halt when they hit the ground? Or how can you jump off the ground?’.

(vi) Other issues? Something I didn’t mention earlier is that, unrelated to my decision to try something new in this class, I had been shanghaied into asked to volunteer for a pilot project on the Carleton campus to film some of our classes, and two of my classes are on film at the moment. At some point later this term I will sit down and record an interview/rumination about my teaching technique as a voice-over for these films, which would force/allow me to watch the classes and re-consider my ideas. And I’m spending a week this summer writing all this up for my colleagues during which time I will probably flesh out some of the points above and discover new ones.

(vii) One last point, in response to Chad’s comments. I agree with the issue of temperament, and all that. But there is no way that lecturing allows you to cover more material — not lecturing is significantly faster in this regard. The only way I cover more material when lecturing is to speak faster (and believe me, as a New Delhi-bred English speaker, I can speak very very fast — Texas didn’t slow me down that much). But when not lecturing, I am able to pick and choose what I do in class versus what I expect students to read and understand on their own. Moving to the trimester/term system in Carleton has reinforced this particular perspective even more strongly for me. In these last five weeks, we have ‘covered’ some or most of 11 chapters in our textbook. Mastery? That’s a whole different question :-).

$1.5 Million to spend

The till-recently-embargoed good news from the grant I’d mentioned earlier? Here’s the official press-release. Fernan even got interviewed by Minnesota Public Radio — as I needled him when I heard, not only are we now rich, he’s even famous :-). I look forward to helping spend it.

Refusing to throw stones

The fatal pedagogical error is to throw answers, like stones, at the heads of those who have not yet asked the questions. - Paul Tillich

My intro class took their first test, and generalized fear and panic hit during the Dynamics section. This is predictable, perhaps, since I’ve seen that year after year, no matter what method I’ve taught (except the matter and interactions course, but there we selected for a particular kind of small cohort, so it’s not a fair question).

Intellectually it comes down to the fact that kinematics is sheer description, while dynamics is explanation. To understand why something behaves the way it does in the Newtonian paradigm means that you have to get (a) the notion of force clear in your head, (b) create the appropriate catalog of courses and then (c) learn to deploy them correctly, while (d) getting geometry and (e) algebra right throughout.

And some of the things we tell them are absolutely counterintuitive, particularly if they involve any aspect whatsoever of Newton’s 3rd Law.

So it’s not surprising that the frustration level in the class rose. And it was easy at first to blame the whole ‘refusing to lecture’ thing that I was doing. But I thought about it for a while, talked about it with colleagues (I found what was written in response to Chad’s post — thanks for picking this up, Chad — and in the comments to my last post very useful, incidentally), looked through my notes and realized: Aha! I bet they’re not reading the book. And of course they weren’t — I could tell the moment I probed lightly. They weren’t reading because they haven’t been trained to read books the right way.

It’s critical they read the book and ask me questions — both. Consider that the author’s someone who’s put a lot of thought and energy into getting precisely the right explanation for a certain concept — why do I think that I can present the basic script any better? What I can do is find out how students react to the ideas, and use my time to help them with the ideas (it’s the “guide on the side” VS “sage on the stage” perspective).

The reason they weren’t reading was because I had forgotten one of my cardinal rules of teaching: Do not expect anything from students that you have not explicitly asked them to show you, explicitly linked to their grade. Because your grading system is your way of telling them what you value.

So I sent out a note asking them write me questions before class (a subset, so I don’t get drowned), and reminded them that this was part of the implicit contract (the syllabus).

And I’m getting some superb questions as I sit at my email. Tomorrow is going to be *so* much better — I know what they don’t know, so I have some idea of what to tell them! Cool.

Stable and unstable lectures

As I’ve said a few times before in this blog, I prefer to let students read the text to get a preliminary take on physics content on their own, generate questions and confusions on which I focus during ‘lecture’, and then check their comprehension of these principles by working together on applying them via problem-solving — and doing this in my presence so I can help them work out what they do and don’t know.

I see this as directing the class’s and my energy at the biggest road-blocks to mastery. The traditional method of (i) presenting a lecture in class, (ii) asking students to respond to the lecture presentation with questions, and then (iii) go home to work on problems, seems to me to be quite inefficient.

This, I argue, is because (i) the lecture is usually being spent telling people what might be relatively simple, or missing the troublesome issues. This is because no matter how hard I’ve tried to do figure out what’s easy and what’s hard, every year and every class turns out to have different blind spots and troublesome issues (apart from the blindingly obvious things like, say, Newton’s Third Law for intro mechanics students). (ii) The students haven’t had time to think about a presented point when I ask for questions, so I am not really clearing up confusions for anyone but the fastest thinkers or the best prepared students. And (iii) when they are trying to solve problems, and true confusion pops up, they are on their own.

The way I choose do things means that I always walk into a classroom feeling slightly unstable. That is, I don’t quite know what I will be talking about and never know how the time will be spent. I figure this is a fair trade-off for the gains I’ve noted above, and on a good day, I feel like improvisation is my strength ( well-prepared lecture notes, while I can do those, certainly isn’t a strength, so something’s gotta be!).

But there is another downside that I periodically forget about: What’s happened at the end of a long discussion about ‘problems’ and ‘confusing issues’ is that unless these have been completely and totally nailed by the discussion, we’ve spent the whole class out of the students’ comfort zones, and they’ve also felt unstable through out. They haven’t had the opportunity to sit back and listen to someone tell them something they sort of know already, or find easy to understand, and as a result, their mood can be somewhat grumpy and discouraged.

I haven’t yet figured out how to deal with this, to be honest. I am fully aware that this sort of discomfort with the material would’ve been there in any case, just hidden from public view in the standard chalk and talk class and I should probably feel pleased that I am getting to confront it. But I can’t help wanting to change it some. Usually I resort to short lectures for a few classes after I hit one of these particularly discombobulating classes — I find that it reassures the students and me, stabilizes the dynamics, as it were — and then I can drift slowly back to my preferred style again. But that seems inconsistent to me, and I am going to try to come up with other ways of getting this stability this term. Any thoughts, advice, pointers from readers?

Goodbye, and thanks for all the mistakes

John Archibald Wheeler passed away yesterday, and there will be personal tributes in many fora from all sorts of people — he was a legend. I arrived in Texas a little late to be as heavily influenced by his ideas on quantum mechanics as a previous generation of students, some from my group (Wojciech Zurek, Bill Wootters, Ben Schumacher, for example) were, but his presence there was still strong. Since Wheeler wrote papers with Wojciech, who of course wrote papers with his Ph.D. adviser Bill Schieve, and Bill is my Ph.D. adviser and co-author as well, my ‘collaboration distance’ from Wheeler (generalized version of the Erdos number) is 3, and that’s pretty much as close as I got to doing physics with him.

I have a few disconnected memories of Wheeler, though: Mostly from running into him a few times in the corridors of RLM (which housed the physics, astronomy, and math departments at UT-Austin), when I was always struck by the intensity of gaze and his smile. The one time I spoke physics with him was while attending a seminar given by him in the Philosophy Department. In response to a question of mine, he turned on his smile, and threw me a penny — I gathered later that this is how he rewarded interactivity in his seminars. I’ve stolen that trick of his for my own courses for majors –of course my students don’t get quite the thrill out of getting a penny from me that I got out of getting that penny from him, but hey, it’s worth a shot.

There’s are a couple of quotes of Wheeler’s that I have frequently used and would like to re-evoke here: “The job of a theoretical physicist is to make mistakes as fast as possible.” As well as: ‘We live on an island surrounded by a sea of ignorance. As our island of knowledge grows, so does the shore of our ignorance.’

Biased epistemology

Or seeing what you want to see.

For the 1st lab in my intro mechanics class, I gave them an assignment I have stolen shamelessly from my talented junior colleague Melissa Eblen-Zayas: The students are given a sham theoretical paper (no jokes about redundant terms please) about a simple phenomenon and asked to construct, perform, and analyze an experiment to see if it’s true [I am eliding details because while I have Melissa's permission to use/adapt her lab, I certainly don't have that permission to distribute it].

There’s a lot of coaxing involved to help them figure out how to take data, to consider how much data you might take to account for random error, what amounts to enough variation in parameters to test a theory, why it makes sense to try to plot linear graphs rather than quadratic graphs, etc. The whole process is an excellent exercise in helping them understand how and when we accept our models of the material universe and all that went well — particularly with some of these discoveries coming after the fact, after the groups had come to some sort of conclusion about how the theory was supported by their data or not.

What was really compelling yesterday was to see how many groups (8 out of 10) found that the theory was right, even when the data in 4 of those cases was clearly telling them that it was wrong. And after I told them that the theory was wrong in general even though it worked all right in a limited range of experimental parameters, it was remarkable how none of the groups were unable to see that their data supported the theory (since they’d stayed in that limited range).

Not exactly a newsflash, but students are so used to ‘verifying the theory’ that they really have a hard time seeing anything other than what they expect to see. I am hoping their experience helps them get a little more wary of this sort of bias.

Of course this bias holds true of most of life for most of us so it’s a battle against ‘natural’ human behavior.

Update (courtesy Peter Morgan): This is similar to some ideas developed by ZapperZ. 

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.