Week 4 Lecture, Law of Large Numbers, Intro to Central Limit Theorem and Related Terminology

Yesterday was the 4th week of Junior Lab, and the third lecture (no class Labor Day week).  We started discussing some of the fundamentals that underlie a lot of data analysis.  To do so, we started with a group exercise that involved flipping coins and recording the number of heads and tails.  One of the main goals of the group exercise was to get students involved and contributing to the discussion.  In my opinion, that goal was successful. Out of 16 students, I can recall at least six students who were actively contributing to the discussion for the whole hour. 

The other goal was to use the coin flip as a launching point to discuss probability distributions, probability functions, parent distributions, the law of large numbers, central limit theorem(s), independent measurements, random error, systematic error, etc.  I think this goal was achieved as well.  Below are two photos of the chalkboard, following our 30 or 40 minute discussion. 

Almost all of the words / equations on the left chalkboard were contributed by students.  To spur discussion, I collected the results of their coin flip trials, and then asked an open-ended question "what can we say about these data?  What should we do with them?"  Mean and standard deviation were suggested by Alex.  I used this to define Xi, Xbar as we will talk about them during this semester.  One group of students recorded ten heads in a row.  I pointed out that set of Xi and asked, "how come you were reluctant to report this?  Who cares that it was 10 heads in a row?"  This got students to mention things like "unlikely" and "probability" and even mentioning binomial distributions.  One student, I think Kirstin, described in words how the probability function for 10 coin flips would look, which led to the drawing in the right photo above.

My memory is hazy at this point, but we started talking about how to test whether the coins were actually fair.  I asked what the measurements would look like if I asked them to measure the widths of the coins.  Students' intuition, not surprisingly was that most sets of observations we thought of would have a bell-shaped distribution.  I asked if anyone knew why this was, and there were many good intuitive explanations.  Alex, brought up the Central Limit Theorem, which delighted me.  At that point, I wrote down in words / symbols a version of the central limit theorem, and we ended class pretty much on that note.  I then showed them a Google spreadsheets example of the Central Limit Theorem in action for uniformly distributed random numbers from 0-1, see below.

Central Limit Theorem Spreadsheet


All in all, I think the class was successful, but I don't have any real measurement of that.  Many students were very engaged, and almost all of the terminology and principles were contributed by students as opposed to me.  I told them my goal for them is not to memorize any formulas or theorems, but rather to gain an understanding of them and an intuition so that when they encounter data analysis tasks in the future, they will know that there is an underlying theoretical framework that they can go read about and relearn.  I feel like the kind of discussions we had yesterday will likely achieve that goal for most of them.

Next week, we'll continue along these lines.  We'll look at their coin-flip data and approach the question, "how do we test whether the coins are fair coins?"  Or, we may do another group exercise that generates new measurements that we can look at.  Or, a third option is to use data that students generate during the lab sessions.  My gut is telling me to continue trying to do small group exercises at the beginning of class, since it does seem to be boosting student engagement quite a bit relative to prior years.  Thanks to TA Katie Richardson for suggesting I do the group exercises!

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5th Lecture, Wave intereference, standing waves, resonance, sound

I felt like today was a really good lecture. Almost every time I looked at students' faces for feedback, I saw most of the class interested and focused. I felt like it was a class session that "clicked" and I believe that's true. I wish I knew the magic ingredient! Actually, I don't think there was a magic ingredient. I don't have any scientific evidence, but my feeling is that were a few key ingredients to making today's class effective:

• Fascinating physics. Waves are fascinating. Wave interference is even more fascinating. On top of it being fascinating, I think the topics were new to most students.
• Solid demos and applets. The core demos today were the wave table (fantastic) and the flame tube (not as fundamentally solid as the wave table, but gets a tremendous boost from using fire). The core applet was again the Falstad ripple tank, which we used for study of wave interference. I've already mentioned how awesome that applet is. But I should mention it again. That applet is awesome.
• Solid youtube videos. We looked at some resonance things, culminating in the famous Tacoma narrows bridge collapse.
• I was having fun and I think I provided good context and connection of all these things. Besides their facial expressions, I also got direct feedback after class from a few students saying they enjoyed the class. I could be wrong, of course, but I really feel like people learned.
  

So, below, I've embedded the slideshare slides from today. I don't want to go over ever slide, but I'll point out a couple things that seemed to work well (besides the general things above).

• I think the students enjoyed looking at the "student answers" to the homework question. I've been doing this for a couple years, and I think it's related to "just in time teaching (JiTT)" that I learned about at the new faculty workshop. It's actually quite time consuming to do this, though, and even after about 3 hours that I put into reading through their answers, I didn't feel like I was completely fair in picking the "best" answers. But I explained this to the students, and I think they are fine with that. Also, by the way, I thnk that while 3 hours is a bunch of time to spend on something like that, I do feel it's worth the investment.
• I think that demonstrating wave interference with the wavetable was very effective. I asked for a student volunteer, and Ashley was quick to jump up and help. We were easily able to synchronize two counter-propagating traveling waves on the wave table. When the waves met in the middle, the amplitude clearly visually increased. Furthermore, the constructive interference was large enough amplitude for the rods to hit the table and make a "ding" sound. I love the "ding" sound, because I feel like it announces to the whole room that the waves interfered to produce a bigger wave. Thanks, Ashley, for your help with this demo!
  
• The video of someone creating standing waves with the wavetable was effective. I'm not talented enough to do this live in front of the class, so the video is very helpful. I think you can find the videos here.
  

OK, that's my update for today. I'm very happy that I think it was an effective class, and I'm also very happy for another reason that I can hopefully blog about in about 30 days!

05 Waves, Sound, Interference, Resonance

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2nd lecture in conceptual physics course, atoms and Brownian motion

Last Thursday was my second lecture in the conceptual physics course, and the first "real" lecture in terms of physics concepts I'd want the students to remember. I liked how Feynman started out with atoms in his lecture series, so when I started this course, I figured I couldn't do any better than he did. (Although I was recently told by a leader of physics education at U. Minnesota that Feynman's lectures were not effective at all in terms of the learning of the Cal tech students...whoops!) I had assigned the students some reading from Feynman's lecture and also from our textbook about the structure of matter.

I've posted the lecture slides on Slideshare. Before getting into Brownian motion, we did a brainstorming exercise where students suggested things that are in the room, and I tried to classify them in real-time using powerpoint on the overhead projector. By the time we'd finished, the students had come up with many of the things which we'll study this semester and I had tried to classify them in terms of concrete versus abstract and complex versus fundamental. I didn't tell the students the classification system, and they were able to guess what it was after watching me file things away. I don't know if this exercise accomplishes much, but the students seemed engaged. At the end, I pointed out concepts on the page and how they were interconnected and there is no obvious order in which to approach the concepts. I then used this an explanation for the order in which we're approaching things: matter, waves, light, sound, etc.

In terms of Brownian motion, I like the "molecular motion" overhead demonstration. This is a device that sits on top of a regular overhead projector and has a corral that can shake ball bearings. Unfortunately, I didn't get to practice with the demo, and the ball bearings I chose were not well shaken at all. I'd wanted to demonstrate Brownian motion by putting a big ball bearing in with a bunch of small ones, but I pretty much crashed and burned. Hopefully the Brownian motion applets we'll see tomorrow will make up for this. I definitely got lots of laughter, and being laughed at is better than being slept at, in my opinion.

The laser speckle demonstration worked very well in my opinion. I described this a bit in my previous post. As far as I could tell from a show of hands, everyone in the entire room could easily see the shimmering laser speckle pattern on the wet paint. We'll revisit this again later in the semester when talking about interference. Thank you to Dan Ralph @ Cornell Physics for showing us this demo back when I was in grad school!

I'm not sure whether students enjoy the discussion of scanning tunneling microscopy or not. The reason I include it is because I think it's yet another great demonstration of the existence of atoms -- you can practically see them.

Tomorrow's lecture will be about Brownian motion (discussion of homework question, applets) and introduction to energy and conservation of energy. The in-class demos will be the "rattleback" and the nose basher.

02 Matter Is Atoms That Move After Class

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First lecture in conceptual physics course, Wason selection task was effective

Yesterday I presented my first lecture of the semester in Physics 102, "Introduction to Physics." The alternate course title I like best would be "Conceptual Physics," and others are "Physics without Math," "Physics for Poets," "Why the Sky is Blue," etc. You can find my syllabus on Scribd. Here are the goals stated in the syllabus:

The primary goal of the course is to help students develop a better understanding of a variety of physics concepts that they experience or hear about in their every day lives. We will strive for true understanding of the concept versus tiresome memorization of facts and trivia. This may lead to a heightened enjoyment of everyday physics wonders (such as rainbows, sunsets, waves, phases of the moon), improved ability to understand technological issues (such as energy shortages and sources, nuclear power and radiation, cell phone communication), and a deeper understanding of future scientific material including biology, chemistry, geology, medicine, and possibly a subsequent more advanced physics course!

I like these goals, but they are not measurable, really. I did not take the time this semester to implement pre-testing and post-testing assessment as I had hoped. Perhaps partially the reason I didn't is I'm still quite annoyed that this is the last time I'm going to teach this class for a number of years. Our department has a custom of switching courses every 3 years, and also I was told that I need to show diversity in teaching in order to get tenure. I strongly disagree with both of these notions, but well, you know...

In any case, the goals are to have fun learning some physics concepts and to come away from the course with a positive impression of physics and science and an ability to enjoy learning about them. I don't have rigorous data, just informal student feedback (thank you emails, which I absolutely love to receive) and the scantron feedback forms. But this anectdotal evidence indicates that our goals were achieved the first two years. Plus, I have really enjoyed it and felt good that many students learned a lot and enjoyed the course. The only negative is that it takes a lot of time, especially the first semester I taught the course, where I developed about 28 powrepoint lectures from scratch, 75 minutes each--that utterly kicked my ass. I would like to put all of my powerpoint lectures on Scribd, in case they could ever be useful to someone else. The only thing keeping me from doing this is that I know I've missed attribution of some of the pictures I've "borrowed" for my lectures. Plus, I definitely don't have copyright on many of the non-CC licensed images I've used. Any comments on how to deal with this? I have in mind that I could try to correct this as I present the lectures this term, but realistically, that's not going to happen.

I did post my yesterday's introduction slides on Slideshare. I think the only stuff I use is from wikipedia and I attribute it. Overall, the lecture went well and I had a great time. Once again, the students are fantastic and I am sure I will enjoy getting to know them and seeing them succeed. I have some comments on a couple specific things from yesterday.

Wason Selection Task

One thing I do during my first lecture is take pictures of all of the students while they are doing group discussion. This accomplishes a number of things. First, it gets them acquainted to talking with their neighbors, which we do several times / lecture. Second, it allows me to practice learning names over the next couple weeks. I have each group write down their names along with physical description and then I go around the room taking photos of the group and telling them their group number. It will take me a couple hours to put the names with the faces in powerpoint, and then a couple more hours of studying. Combined with interacting with the students, I've been able to learn quite a few of their names. I did pretty well with 120 students last year, but this semester I have 154 students registered, so I'm nervous whether I'll be able to do this or not. I think it's important, though, and the ability to talk to people by name adds a lot of value for students. Incidentally, I'm helped by the fact that students tend to sit in the same areas every day, so I'm basically making a seating chart without imposing one. This is a technique I learned from TA training, and it works really well. Thank you to whoever did TA training at Cornell Physics in 1996!

OK, so in order to carry out this exercise on the first day, I need an entertaining puzzle for the students to debate with each other. The first two years, I tried using the Monty Hall paradox. That worked pretty well, but this year I switched to the Wason selection task. I was REALLY happy with the way this turned out. First, I had them use their iClickers with the number / color version of the selection task. Since most of them did not yet have iClickers, I also had them shout out their answers (surprisingly, it's pretty easy to poll 150 students this way, and the shouts matched the iClicker graphs). Most people got the puzzle wrong (which is what always happens), and after debating, a consensus developed on the "wrong" answer (to flip over all the cards). The reason I liked this puzzle so much is because when I showed the same logic puzzle with the beer / under 21 version, then entire class immediately picked the correct answer. I could then show the two questions next to each other and blab some stuff about how learning is contextual. I think it does demonstrate that, but the important thing is that they probably had fun while I took photos and probably remembered the exercise in a positive light and some probably even tried it out on their friends after class. I'll definitely use this for my next large class.

Wireless in the classroom

Someone on friendfeed recently posted an article talking about either the perils or opportunities of wireless in the classroom. It turns out my classroom has wireless for the first time, so I brought this issue up with the students. I basically told them I was worried about the possible distraction, but that the worry was far outweighed by the possible benefits it could have. I was telling them I didn't really know how we'd leverage it, but that I encouraged people to use it. While saying this, I saw a Mac laptop in front of someone, so I said, "Like you, Mac Guy (I don't know their names yet)...you're probably already checking out our facebook page, aren't you?" He said, "Yeah! actually I am...I'm looking at photos of you." (At this point I realized that there must be a bunch of embarrassing photos of me on facebook.) I said, "like what?" and he said, "Some marching band photos..." I made a perfect dramatic pause and then addressed the class, "Well...you already knew I was a dork." This drew much laughter, which made me happy. OK, that little anecdote was unnecessary, but it was funny if you were there. This wireless experiment will be interesting throughout the semester. The one thing I have in mind is that we look at a lot of applets during lecture, and I'm hoping the students will be trying them out themselves while I'm showing it on the projector. I can see that this could turn into mayhem, but I also feel that the level of learning will be much higher if they can play with the applet themselves. We'll see!

Tomorrow we'll do the first real physics lecture, where we'll talk about the structure of matter, focused around Brownian motion. The two demos will be a demo that shakes ball bearings on an overhead projector (to give an idea of molecules in a gas) and a demo where we look at laser speckle off wet and dry paint. This latter demo is really cool and easy to do, and I find it a fascinating demonstration of Brownian motion without need for a microscope. I learned it from Dan Ralph during his graduate solid state physics course at Cornell back in 1997-ish. You'll need to see it with your own eyes (maybe I can take a video of it?), but the laser speckle pattern on dry paint does not change if you keep your head still. On wet paint, the pattern shimmers, due to the microscopic latex particles undergoing Brownian motion. So, basically you can see evidence of Brownian motion with a cheap laser and paint. Laser speckle is a great demo, because you can see it from any distance away, and it's fun to look at whether or not it's shimmering.

01 Course Intro, Administrative, Etc After Class

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