On twitter I posted this, which I think captures the essence of the conversation:

4 me: title, abstract, figures, variables, conclusion, finally the details. For them: title, abstract, 1st para, 2nd para, etc. very diff—
Andy Rundquist (@arundquist) June 19, 2013

(really I just put that to try to get a few more of you to see the power of twitter, sorry).

So, what did I do? First, I made sure that I hadn’t looked at the papers before we sat down together. They found them, based on a forward search (using the awesome Google Scholar), and a few of them had read a few of them (wow, that’s a really unclear sentence fragment). But I wanted to show them how I would approach them, so, even though they found them the day before, I didn’t really look at them other than the titles.

We sat around a table, each of us with paper copies, along with our awesome Livescribe Sky pen taking notes and recording the conversation, which sync-ed immediately to Evernote (I’m really loving that). We decided what order we’d do them in and we jumped in. I decided to just talk out loud about how I would go about reading the first one. That took an hour! After that I asked them to use a similar process on the other three papers.

Here’s how that hour went (in general terms):

1. I analyzed the title to see what the authors were proud of. There was a funny pun-like title, but not much other than that to show that it was connected to our work.
2. I looked at the abstract with a similar eye. It was interesting that they talked about how the system was interesting because the final setting was calculable by minimizing the virtual work done by the tension. I told my students that that just meant that it obeyed Newton’s laws. What I went on to explain was that they used a great tool, one they were good at, but, ultimately, just one of many tools that could do the same thing.
3. I flipped to the first figure, happy to see that it was a diagram of the main experimental setup. We analyzed the variable names, and I asked them to sketch various s vs z curves (s was the length of the hanging rope, z was the height variable) because I noticed a nearby equation that asked for ds/dz. There was one angle shown, so I asked them to figure out how that angle changed over the length of the whole curve. I told them that having a good handle on the functions would let them image where the math might be going.
4. I flipped to the next few figures, which were comparisons of simulations to experimental data. We noted how similar they were to our our data, but we were mystified as to why they didn’t do an overlay. I told them it was probably because the overlay wouldn’t have been as good as they claimed in the text, but later we realized that it would have been nearly perfect if you compared the data to the full-blown theory. The problem was that they wanted to brag about how good an approximate (read: easy) theory’s prediction was. Yes, they looked similar, but an overlay to that theory would have been pretty crappy.
5. I scanned the text to find the first mentions of the various data/theory figures to see what they said beyond the figure captions. I told my students that we’d be able to see what they were proud of there, rather than the figure captions.
6. I jumped to the concluding paragraph to see what the authors thought was the big deal.

All along we had conversations about why I was doing what I was doing. One thing that came up was that we weren’t really poring over their math. I told them that the big mistake I used to make was to check author’s algebra all the time. I told them that it’s mostly a fruitless endeavor, talking up the power of peer review. I said that if we were to go through the derivation, then we’d be forced to go down the path the authors wanted us to regarding their data. But what if we wanted to go down a different path? The derivation will be very useful to us moving forward, but my approach above helped us figure out what we really cared about in the paper. Now we know which math portions are going to be helpful to us.

I was shocked to see that an hour had gone by, but I think it was really a great activity. We ended with a short, half-page section of notes about what the paper did for us, and I asked them to do something similar for the other three. I plan to check in with them about that tomorrow. We’ll see!

So what do you do in situations like this? How do you read journal articles?

Some sample comment threads for you:

• You have to check the math! You can’t just swallow it whole!
• You should have read it first and spoon fed it to them. They’d get it better rather than throwing them in the deep end.
• Can you post the pencast of the session?
• I was one of the students, and I thought it really sucked. It was one of those rare gorgeous Minnesota summer days and we had to waste it in the basement of the science building.
• I was one of the students, and I thought it was great! Andy just spoon fed us the useful stuff and I zoned out the whole “let’s learn how to read” stuff.

So, what might eight standards look like? I’d like to use this post to begin brainstorming that. First, let me say that covering the labs for this course really helps me be flexible. In our department we’ve established 10 or so common labs that everyone uses whenever they teach this course. I’m thinking of changing most of them to be, not only SBG-worthy (instead of cookbook-y), but also supportive of the 8 major ideas of the course.

Ok, here’s a stab at a few. Note that I like them to start with “I can . . .” so that it’s clear what they should be able to do. Of course, the action verbs after that are really where the work lies. Please hold me accountable in the comments.

1. I can describe the wave nature of sound.
   1. We’d have to study waves for this, of course.
   2. This could include all of the following
      1. wave propagation
      2. diffraction
      3. interference
      4. doppler
      5. standing waves (though, as noted below, this will likely get its own standard)
      6. beats
   3. I guess simple harmonic motion would have to be here too
2. I can analyze the standing waves of a one dimensional system.
   1. strings for sure
   2. tubes
      1. flutes and  clarinets
   3. excitation mechanisms?
3. I can analyze frequency/time issues of a complex sound
   1. Using something like Audacity
   2. Analyze harmonic structures
   3. Analyze the early time structures
   4. Determine what sort of instrument it might be
   5. Determine the room acoustics?
   6. This one seems too broad
4. I can explain how sound is recorded, stored, and played back
   1. microphones
   2. digital compression
   3. speakers
   4. bare minimum of electronics, I guess
5. I can describe the range and limits of the human ear and voice
   1. The book we’ve used (Berg and Stork) has a lot on this, though I’m not planning on using that book, so we’ve done a lot of this.
   2. However, it’s a lot more physiology than physics, so I go back and forth on it.
   3. It’s fun to teach the dB scale with the ear, though
   4. The vocal tract is a rich resonant chamber to study.
   5. Helium voice can be a fun lab, I suppose.
6. I can do a scientific investigation
   1. This could quite possibly by the last science course they ever take.
   2. The labs will be like “measure the speed of sound using whatever is in your pocket and our campus”
   3. This standard will be given context from the labs we do
      1. of course, using my typical SBG approach, that means only the last lab counts, so that’s a problem
7. I can design, build, characterize, and communicate about a new musical instrument.
   1. We’ve done this a lot, so we know how to support this
   2. Often people build guitars, but there’s often a lot of creativity involved.
   3. I focus more on the engineering to achieve a particular pitch, while my colleague tends to focus on musical qualities.

Ok, so that’s only 7, but it’s an interesting start. I’d love to get some feedback. Here are some starters for you:

• I think 8 is far too few. You need some on _____ and _____.
• I think 8 is far too many, you should just have _____ and _____.
• I think the human stuff is way too much physiology and not enough physics.
• Everything is physics!
• I think you need to have one on the (fast) fourier transform.
• You should definitely teach about analog synthesizers!
• Keep the labs out of your SBG approach. Let them teach the students about scientific process
• Your last two are the same.

Last year I wanted my students to explore lots of different types of engineering. Really the whole class was centered around the idea that most students don’t really know what engineering is coming into college, even though they signal their interest in it 3x more often than they do physics, and that’s for a school that doesn’t have an engineering program! So I wanted them to pair up and prepare one day’s worth of class-time to explore a particular type of engineering. The types were available first-come-first-served and they had anywhere from 1 week to 1 month to prepare. They had to have a ~20 minute mini-presentation on the topic, and a plan for the following ~50 minutes of discussion/activity. They also had to update our google site explaining their type of engineering.

What went well

The pairs of students chose some great engineering types. They basically covered all the major ones I was hoping for along with some cool tangential ones. In class, after a couple times at least, they settled into a short talk and a long engineering challenge based roughly on their field. These ranged from dropping eggs to building towers with paper to building electromagnets to pick up paperclips. The challenges often lead to some great conversations about things like learning from failure, creativity, corporate espionage (spying on other groups), corporate sabotage (wrecking other groups’ designs), time management, and an iterative design process.

What didn’t go well

The presentations were often little more than reading the MIT web page for that particular type of engineering. The same was true of the google site submissions. Also, the challenges were sometimes pretty far removed from the type of engineering they were presenting on.

What I’d like to try

I’d like to have them continue to pick a type of engineering, but to investigate a particular case study, identifying all sorts of issues like learning from failure etc. Take civil engineering, for example. Could they give a report on Boston’s “Big Dig?” Could they look into the challenges that were faced and dealt with, in an effort to better understand the field of engineering? Could they then design the in-class challenge to be a microcosm of the type of challenges found in the case study. For the “Big Dig” maybe they could do something like traffic management on a small scale, or something, possibly involving software.

What I don’t want to lose

The students seemed to genuinely enjoy class when we did the challenges. They jumped up and started working right away, and enjoyed the competition and the discussion afterwards, when we analyzed what we’d learned.

I also think that the MIT copying they did kept this pretty low key form a stress perspective. We do a lot in this class, so I don’t want to kill them with this, though, perhaps, this should get more weight if I can get them to get more out of it.

Your thoughts?

Some ideas you could pursue in the comments below:

• Here’s a great idea for a/an  ______ engineering case study
• What kind of rubric do you use to assess the class period?
• If you don’t offer engineering, why are you running this class?
• Engineering is too big of a field to ask things like “what is engineering?”
• I’m teaching a similar class, let’s hook up
• Why don’t you have them do a major project rather than short ones in one class period?

First, I thought it was interesting that they both pointed out that peer copying is the biggest problem. I’ve always felt that finding online solutions is a bigger problem, so I was interested to hear what they had to say. They showed timing data showing how many students were able to get problems right within seconds of seeing them, drawing a conclusion that they were using the results of a peer. The argument goes that if they’re using other sources, they’d have to spend time reading the problem and going to hunt for solutions, which would take longer than the few seconds they took to complete the problem. What wasn’t clear to me was whether you could analyze the people who took much longer to get an inordinate number of correct answers on the first try.

Second, I was struck by the futility of the “whack-a-mole” approach to deal with cheating. They do this, we do that, repeat. I started thinking about some of the more authentic assessment methods I’ve heard of, and I realized that one of the biggest problems with their mass adoption is their scale-ability. Take my standards-based grading with voice approach: I watch screencasts of students solving problems, assessing their confidence and approach as much as what’s on the page. It comes a close second in authenticity to oral exams, but, while it scales a little better than orals, it can’t scale easily past the 40-person class I’ll have this fall.

Then I started thinking about the impressive project/problem-based learning that so many of my high school teacher friends do. I think that teachers like that would have been a little bewildered by the session, as they don’t worry about things like peer copying, online solutions, and, to a certain extent at least, student motivation. Those students are given an opportunity to do things like launch a weather balloon with a cell phone attached and they jump to it, being involved in the brainstorming, design, execution, analysis, and communication about the project.

That reminds me of the conversations that we have so often in the Global Physics Department, about what the best high school preparation for a student would be. We almost always land on “deep, not broad” because we college teachers have recognized that taking a student who’s seen how science works can be helped with their content deficit better than students who’ve seen everything at a surface/homework level can be helped learn what science really is.

So what can be done with these huge introductory college courses, especially those that use online homework? Well, whack-a-mole is one way. Another is something like standards-based assessment, where homework is not graded, but is rather for learning. A third approach is to try to envision a project-based approach where students are encouraged (possibly in teams) to work toward something that’s easy to motivate and assess, but doesn’t have the cheating enforcement so prevalent. Now, admittedly I don’t teach such huge courses, but I guess I’m just expressing how depressed I was in those sessions. We kept hearing about students who would find ways to defeat the system, and then we’d see statistics showing how it would hurt their learning. THEN we’d learn how, if the researchers shared their findings with the students, MORE cheating took place, as, basically, the sharing simply introduced more students to the tools to cheat with. Ugh. Blah. Give me an oral exam. Or a weather balloon!

So, what do you think? Here are some choices to seed the conversation:

• Students aren’t motivated to learn, so we have to get them to jump through these homework hoops. Whack-a-mole is where it’s at.
• What do you mean with whack-a-mole? I love that game at the carnival. Another ugly mole pops up, and I whack it. I love being innovative in how I can predict where that next mole will be, and I know if I whack the one on the left, the next one will be on the right. Fun!
• Standards based grading, especially with voice, just can’t scale. So lucky you that you have small classes, it just won’t work for me.
• I think giving points for out-of-class work is unethical. Students can pay for cramster.com‘s premium package that’ll guarantee an eight hour turn around for even teacher-written homework, so the rich kids can get those points for free and the poor ones are left behind.
• I don’t care if students cheat on homework, they’ll always fail my test if they do so. I give points for homework just to get them to do it.
• I find the students who help their peers get their homework right are the ones who become the strong majors, and they get practice teaching this way, which is the best way to learn.
• Other thoughts?

• Electricity and Magnetism
• Theoretical (or classical) Mechanics
• Quantum Mechanics
• Thermo/statistical Mechanics

This conversation was seeded by Steve Whisnant, who is the chair of the James Madison University physics department. He shared how they’ve developed several tracks, mostly to aid in recruiting. As he says, most physics students (and their parents) don’t know what to do with a physics degree, so they make tracks that have a more immediate connection with careers.

As he was laying these tracks out for us, one of the chairs in the audience asked if it was true that they were granting BS physics degrees with students who don’t take quantum. It lead to a short but spirited discussion, and I’m glad that I was in the breakout session later with the person who brought up the question. In that breakout session, we talked at length about what all physics majors should know (or, perhaps more accurately, be exposed to). Lots of related issues came up, including:

• What the core should be
• Is there a difference between a “physicist” and a “physics major graduate?”
• Is computation now in the core?

I found myself thinking about an analogy with typical high school physics curriculum, which is often dominated by mechanics/kinematics. As I’ve written about before, while that dominates most of society’s understanding of physics, there are few physicists who study that particular field. However, it makes sense to teach it, I think, because it’s such a fantastically successful model, and physics is really just model building/applying/refining/testing.

So I raised my hand and said “the core courses we’re discussing are the most powerful models we have. It makes sense to teach them, but, really, we’re teaching our students how to do physics, ie, modeling.” Now, some thought I was talking specifically about computer modeling, but I meant modeling like the very popular high school curriculum where students are encouraged to develop their own understanding of a model like the “constant velocity model.” They look for what its characteristics are (graphical, equations, patterns, applications, etc) and use it until they’re forced to find situations where it breaks. Then they refine and are directed on the road to the “constant acceleration model” and many others.

What I was trying to say was that we need to prepare our majors to be able to do such model building, and it makes sense to expose them to very successful models. However, I was also saying that the modeling idea is more important than hitting all the big models, so I was defending the choice of the JMU physics department.

So what do you think? What is physics at the undergraduate major level? Does the traditional format of intro physics, some labs, advanced lab, and the core above still make the most sense? Should graduation education change from how it (specifically the coursework) has looked for 50 years? I’m really hoping to catch just a little of the passion of that breakout session in the comments below. Chime in!

As is my wont, here’s some easy choices for comments if you can’t organize your thoughts:

• I was in that breakout session, and you’ve got it all wrong . . .
• We need all those core courses and second semesters of at least the first 3
• The physics major should just be a whole bunch of projects where students learn what they need to do their investigations.
• You were at that conference?! Why didn’t you say hi?
• What do you mean there’s a difference between a physicist and a physics major?
• If we just do modeling, we’re just teaching math

What I really want

Here are the features that I’m looking for. Please add any others that are important to you in the comments:

1. Nice pdfs
2. Nice html
3. Ease of editing
4. Easy hyperlinking/navigation
   1. For external links
   2. For internal links
      1. sections
      2. equations
      3. figures
5. Equation numbers (that are automatically numbered)
6. Ease of building in interactivity
   1. this can be in the form of links to things like the PhET simulations
   2. But they can also be easily created by me

Home built LMS

Several years ago, I finally decided that I’d had it with Blackboard. So I wrote down what I wanted/needed for a learning management system, and I built my own, using php/mysql. It includes

• A place for notes for each class day. I call those daily outlines, and I often pull them up in class. Here’s an example. It shows how I can (easily) build in links, and . It also interfaces with my grade book to show what’s been assigned and what’s due.
• A page to edit for the syllabus, where I can also edit the titles of all the daily outlines
• A grade book that allows for a very flexible set of algorithms (even some invented for a particular class).
• The ability to collect daily summaries and outlines from my students

It does the job, but it really falls down with internal hyperlinking, equation numbering, figures, and interactivity. I used to put a lot of webMathematica into them, but we’ve lost support for that, and it was relatively difficult to make those as well.

LaTeX

I would guess that many people would see my list above and jump to the conclusion that LaTeX is the way to go. I would simply point out that interactivity is out (except for the linking kind), and ease of use is a little down as well. Here’s an example: I can make an equation in Mathematica much faster than I can in LaTeX, even though I’m pretty fast at the latter from all the blogging that I do.

Also, LaTeX->html isn’t a fun experience. There’s latex2html, but it takes a while to run. It produces decent html, but it could use some better styling. Here’s a mini-text I wrote in LaTeX and then exported to html using that tool.

MultiMarkDown

MultiMarkDown provides the ability to write readable text documents that can then be separately converted to tex or html. I like it a lot, especially the styling you can do compared with latex2html, and I’ve been able to get the equation numbering and local hyperlinking to work quite well.

I was really sold on it a few weeks ago, but lately I’ve been realizing how many figures I make in other software (namely Mathematica, see below) that makes a clumsy workflow.

Computational Document Format

Wolfram Research (of Mathematica and Wolfram Alpha fame) created the Computational Document Format a few years ago. Basically, you can use the CDF reader to read documents created in Mathematica. Any interactivity you’ve built into the Mathematica document will still work in CDF, though simple Mathematica calculations that don’t have specific interactive elements will just show up as static calculations.

As I’m sure comes as no surprise, I use Mathematica all the time. I love all the keyboard shortcuts it has, allowing me to very rapidly typeset equations. What CDF does is allows me to author documents in this very powerful (and, yes, expensive) software, but deliver the results freely to anyone who downloads the CDF player.

I had long ago decided to stop using Mathematica to edit documents because it didn’t (as far as I knew) allow you to number equations and put in the type of internal links you could so easily do in LaTeX. I also assumed it couldn’t do bibtex integration (how I do bibliographies in LaTeX), figure captions, footnotes, and more. It turns out, I’ve been wrong (at least since Mathematica 8 came out), and CDF’s can do all of those things, most quite easily.

And, of course, you can put in all the figures and interactivity without worrying about exporting things. It’s all just right there. And, as long as you surround things with “Manipulate” commands, the interactivity will be available for your students.

It also opens up the possibility of changing up my “flipped class” approach. In fact, it would seem to put me in a position to do things similar to the UIUC physics department, that uses online tools for students to explore before coming to class ready to work on problem solving and ask questions. Now I have my students watch me play with most of these tools on videos that I create. I think it would be cool to give them all kinds of things to interact with, right in the text they’re reading, before coming to class.

Where am I now?

Well, you’ve probably been able to tell where I am now (CDF). But I’d love to hear about issues you think I’m either not giving enough attention to, or giving too much attention. As is my custom lately, here are some potential conversation starters:

• PhET is great. Just posts links to that and let them play (as the PhET makers always suggest first).
• Just have them buy a good text. Many are very well done, and have thought through many issues that you’ve only guessed at
• You won’t provide a thorough enough “text” for them this way, so just put in additional links for them to augment their book
• What!? You figured out how to get the equations numbered and hyperlinked in both the tex and html formats in multimarkdown? Share!
• I assume your “wikipedia is my textbook” experiment has failed miserably, since you sidestepped that conversation in the first paragraph. Tell us the truth!

1. Study physical pendula This is a mix of reminding them what they’ve done with rigid bodies before, but also showing the Lagrangian approach for finding the period of oscillation. Some big ideas:
   1. The axis is fixed
   2. Size affects period for realistic pendula
   3. While the speed of every particle might be different, they’re all related to the angular frequency
   4. For the heck of it, I might ask them to analyze how frisbees can bounce, or why discs fade left for right-handed backhand throws.
2. Consider L and omega There are lots of situations where the angular momentum and angular rotation vector are not parallel. Sometimes L is fixed and omega moves around it, and sometimes it’s the other way around. Omega is fixed if the axis is fixed (like step 1 above). L is fixed if there’s no torque (like free fall with tumbling). Big ideas:
   1. L isn’t always parallel to omega
   2. Wheel balancing saves the bearings that have to provide the torque if it’s unbalanced.
   3. Tumbling objects don’t always rotate around the same body axis
3. Orientation Next we work out how to describe the orientation of an object (either about a fixed point or the center of mass if there is no fixed point). There’s the typical Euler rotations, but last time my students just worked out how to do it with the chairs in the room. It was funny because they picked a different “line of nodes” than our book did. It wasn’t their fault, it’s truly arbitrary. It meant I had to whip up some notes for them to show how the equations in the book changed, but it wasn’t that big of a deal for me to do that. Big ideas
   1. It takes 3 angles (actually, I’m not sure if that’s strictly true, but I feel like it must be, since 2 put the ultimate axis in place, and the third rotates about that).
   2. If something tumbles, the dynamical variables are those three angles
4. Tackle a simple system We consider a system composed of a small number of masses that are rigidly connected. We figure out their position at any time by doing the appropriate rotations using the dynamical variables. This leads to a Lagrangian approach for those angles.
   1. The kinetic energy is a heck of an ugly expression involving the angles and the orientations of all the points.
   2. It doesn’t scale very well (8 points -> 10 seconds in Mathematica. 20 particles, more like a minute)
5. Show a better way finally we get around to the inertia tensor, pointing out that the body frame is a much better way (computationally) to consider the problem.
   1. You have to do 6 sums with your particles. That’s it. It’s pretty fast, even for 100′s of particles. Their orientations are set and these 6 sums make up the (fixed) inertia tensor
   2. You have to re-describe the omega vector in the body frame. This is, by far, the hardest part.
   3. You solve it in the weird rotating body frame, but make pictures/animations in the lab frame. Luckily we’ve already done that (using the same variables) in step 4
6. Revisit L vs omega The animations/simulations from the previous 2 steps show the complicated tumbling that can happen for non-symmetric systems. Why does that happen? Because the tensor isn’t diagonalized. So are there any axes you can rotate around that aren’t crazy? I have the students rotate the system, constantly recalculating the inertia tensor until they get zeros where they want them (they typically focus on the third column, since that’s how we’re set to spin the system). If you can get zeros (you can!), then you discover axes that won’t tumble strangely.
   1. You can find those zero’s systematically (it’s not just random hunting)
   2. Sometimes you get zeros and the system still tumbles crazily. That’s because you have small instabilities when rotating about the axis with the middle principle moment (middle as in the not the smallest nor largest value). This is the famous tennis racket problem (hold it so the face is pointing up and flip it (like a juggler). The racket will always twist in midair.
   3. For motion about those axes, L and omega are parallel
7. Add torque Now look at systems with a fixed point and some initial rotation. You’ll see precession and nutation. Have fun!
   1. It’s a one line change in the code to add in gravitational torque. You just set the potential equal to m g times the height of the center of mass.
   2. You can look at Feynman’s idea of falling to precess.

Well, that’s the plan, anyways. Any thoughts? As is often my custom, some sample comments you can choose from:

1. What the heck are you doing teaching this without Linear Algebra as a pre-requisite?
2. Cool, how do you have them manipulate the structures to minimize the tensor terms?
3. Whoa, wait, are you not deriving all the precession and nutation equations in class?
4. How do your students figure out the orientation part?

1. Count the number of ways light can exist in a cavity. This is done by counting standing waves.
2. Determine the energy in each way (or mode) of light. Rayleigh and Jeans say “Oh, every mode just gets kT on average, duh, just like 19th century physics tells us about systems that can share/swap energy.” Planck says “Well, let’s pretend that the oscillators in the walls can only have certain energies and see what happens. Huh, you don’t get kT anymore, you get a nasty formula that needs a constant. I think I’ll name it after me!”

The student did a great job talking about how the kT decision by R/J leads to the ultraviolet catastrophe (infinite amount of energy coming out of the blackbody, concentrated at the low end of wavelengths). Really, she did a great job with just about the whole conversation.

One thing I asked her about was whether R/J should have not bothered telling anyone their results, given that, while it fits long wavelengths well, it really messes up at small wavelengths. She thought it was still useful in certain circumstances, so, yeah, R/J should be proud. We then explored how similar that was to the notion that kinetic energy isn’t 1/2 m v^2 but that it’s useful in certain circumstances.

Then I asked if she would be brave enough to suggest Planck’s approach, given that he seemed to suggest that pendula can’t have any starting amplitude. She laughed and said she wasn’t sure, since she still has a hard time buying that.

So that leads to my challenge:

What if Planck had decided to make a crazy suggestion about how to count standing waves? In other words, leave the kT part alone, and come up with a crazy scheme for deciding which waves are allowed so that the data still fit.

I asked my student about this, and at first she said “but we know how many standing waves there are. If you said that some weren’t allowed for some crazy reason, it seems we could easily disprove that.” But I reminded her about the crazy notion that pendulum can’t have just any amplitude, and that launched a great discussion.

So, what do you think? Can you come up with a way to correct the standing wave count so that you can match the observed blackbody spectrum, assuming that each standing wave has an average of kT energy? How implausible would it be? Would it be “worse” than Planck’s approach?

This semester I’ve experimented with setting the standard for the day at the end of class, as I’ve written about before. That’s been working pretty well, both in Theoretical Mechanics and Modern Physics. Often, with ~5 minutes left in class, we take stock of what we’ve been up to (it’s a “flipped” or “inverted” class, so we’re using doing group problem solving) and decide on the standard. Often it becomes a vote between a philosophical/descriptive standard like “I can explain why we use complex numbers in quantum mechanics” and a problem solving/calculation-type standard like “I can calculate for a gaussian wave function.”

What I wanted to write about is what happened today. We were working together (in groups) on how to calculate expectation values of things given a wave function. We were tackling a gaussian wave function and asking things like what’s the average value of x or x squared. But then I realized that it was a cool problem, possibly even . . . “interesting.” So I stopped them and said “Wait! this is still interesting until we finish what we’re up to.” They voted to stop because they felt they understood the concept and wanted to show me they knew it rather than seeing it all the way through in class. Which, of course, would mean they’d have to apply it to a different problem on their own. We had just finished x and x squared and just getting started thinking about how we’d do p and p squared (that’s “p” as in “pomentum,” by the way). That’s the much harder part of this problem, mostly because it’s conceptually difficult to figure out the p-operator.

Some context: today was the last day before spring break, and, as this is an afternoon class, it was the last class for all of them today. I’ll admit that colored their vote a little, but not much.

They unanimously decided to stop and leave it as the standard. I asked if they felt confident they could finish, and they, to a person, said yes. So we left it.

So what are the pros and cons of this approach? Let’s do the cons first:

• Of course they said yes, then they don’t have to re-apply the approach to a new situation.
• They’ve been given a large fraction of the work for free (in their notes) to copy from.
• They’re not shown the super cool result that a gaussian is the best you can do from the Heisenberg Uncertainty Principle perspective. Hopefully they’ll get it on their own, but will they take stock and notice?
• Other (please add in the comments below)

Ok, now the pros:

• They requested to not be spoon fed
• They’ve been given some scaffolding for a difficult problem.
• We got to get out of class early SPRING BREAK!!!!!
• I can give individualized feedback to guide them to the aha moment about the Heisenberg point made above.
• They get to debate with each other whether it’s better to see the end result or work on it on their own.
• They see value in working on it on their own.
• Other (please add in the comments below)

I’m pretty excited about this right now, but I know, for example, that the last “pro” above, especially, is likely wishful thinking. Rather, the first “con” above might be a better way to spin that.

So what do you think? Possible comment starters for you here:

• You are spoon feeding them, giving them half the problem! Force them to apply tools to new systems!
• This is cool, when is the best time to say “Wait! This is still interesting!”?
• Seriously, what’s your hang up with complex numbers (ok, that’s for a few select readers, you know who you are).
• Is the class debate dominated by people seeking to improve their learning or people trying to ease their workload?
• Wait, you do flipped class? Don’t you know that’s the evilest evil that’s ever existed?
• Wait, you do flipped class? Cool, how do you like it?

I think interpreting those two equations is of interest as well. Essentially the spatial curvature of one produces temporal changes in the other and vice versa. That’s actually pretty cool as you could stare at a snapshot of both the two and predict what’s going to happen in the next moment of time.

Last week it was fun to ask my students about how weird they thought wave functions were when they considered that they were complex. We really haven’t gotten to the Schroedinger equation yet, but we have talked about de Broglie waves, and I mentioned that assuming they were cosine or sine waves was problematic from the probability perspective ( as a probability density has a bunch of spots where you couldn’t find the so-called free particle). I showed them how  works out better in that regard, and then we had the conversation about the use of complex numbers.

Some of them had seen complex numbers used when talking about waves before. Of course, in those cases, it’s always used as an accounting trick, where we throw away the crazy imaginary parts at the end of the calculation. Here we seem to need to keep them.

I mentioned my old blog post, and we spent some time exploring why complex numbers bother them so much. (Note, at least one student made it clear that it didn’t bother him at all.) Mostly we landed on the fact that there’s so much cultural baggage around the word “imaginary.” So we spent some time exploring other ways to think about it.

I asked whether it would ever make sense that a farmer had 3+2i cows (I asked another first year seminar class a similar question, once, where we were talking about how human consciousness is going to change in the future). We decided that didn’t make any sense. Then I asked if it might make sense if I said I had 3+2i “pencils-and-pens” (spoken fast together). They said that they could interpret that as 3 pencils and 2 pens. Then we got talking about things that often get partnered up. One student suggested hot dogs and buns. What do you think? Does it make sense to say 3+2i “hot dogs and buns?” We were buying it, anyways.

What was interesting about that conversation is that I kept bringing it back to the wavefunction, asking if using the notion of keeping track of two things seemed less weird that a “complex” wavefunction. It seemed that it was.

I did point out the less-than-supportive comments on my last post on this. I was quick to tell them that some of those could be dispensed with if I admitted that the complex number approach is certainly a very handy way of doing things. But right now I care more about them buying into the fact that something is waving than knowing how to calculate things. That’ll come later.

Some of the other comments were also interesting. One talked about other non-spatial eigenfunctions, and, I agree, those are harder to deal with. Another talked about how you can get separate equations for the amplitude and phase of the wavefunction. I think that’s cool, but I’m really excited for the spatial stuff we can do this week using real and imaginary parts (see the quote above).

So, what do you think? Do you agree with our text that “you can’t ask what’s waving?” Do you ever say “wow, our universe has real and imaginary parts!”? What did you think about when you first learned about this?