That darn inverse square law comes up in so many places — electric fields drop off as 1/r^2, so does light intensity, gravity, and a bunch of other things that I’m not thinking of at the moment.

I just came across some fun things in my archives from some master teachers on how they teach the inverse square law.

First, here is a really nice example of expert use of screencasting to explain a nice single concept like this:

Deb’s inverse-square-law presentation at Menlo School.

by Paulmann on Wikimedia

I can imagine students watching this little video several times.  She gives a nice pictorial representation of how intensity drops off over distance, using a physical analogy (butter sprayed on toast).  She gives a formula.  She shows how the formula applies in a few instances.  And it’s nice because the handwritten form of this screencast (rather than PPT slides) forces her to slow down to thought-speed.

Craig Young, from Sacramento schools, shared this activity that he uses to help students “discover” the inverse square law on their own:

Materials: 1 sheet black construction paper, 1 sheet graph paper with 1 cm lines, 1 MagLite, 1 meter stick

1.  Set up a MagLite flashlight in candle mode (removing the lens over the bulb).  It works best with MagLites because they have a very small bulb – almost a point source.

2.  Cut a square 1 cm on each side out of the middle of a sheet of black construction paper.

3.  Put the MagLite at the end of the meter stick.  Hold the construction paper vertically at 10 cm.

4.  Start with the graph paper at 10 cm, on the opposite side of the construction paper from the MagLite.  Students count how many squares on the graph paper are illuminated (quantitative) and how bright they look (qualitative).  It should be one square at this initial position.

5.  Move the graph paper to the 20 cm mark and repeat the counting and brightness observation.

6.  Repeat step 5 moving the graph paper 10 cm further each time.  If you can turn out the lights in your room, students should be able to get data out to about 80 cm (8 data points).

The light spreads out, covering more squares at each consecutive distance.  For gravity and electromagnetic forces spreading out in a complete sphere, the area of the sphere increases with the square of the radius of the sphere.  So the intensity decreases as the inverse square of the radius

I’m always struck by how many of these high school level activities would be appropriate at the college level to make sure that students have an intuitive grasp of what some of these numbers really mean.

On the other hand, it’s easy to imagine light particles spraying out and falling off as the inverse square, but how does one help students understand that electric and gravitational fields do the same when there’s nothing “spraying” out, except for those sort-of-physical field lines?  That next level of abstraction is definitely a difficult one.

I wish I could embed this visual tool here so that you’d see how awesome it is and jump up and down in your seat like I did when I first saw it (at least, if you’re an edu-geek like me).

But no, I can only provide you with a link and say go here.

Visit this link now.

What will you find there?  It’s an interactive 3-D model of learning objectives.  Learning objectives are a way to describe what you want your students to do at the end of your course or a unit, to help design instruction based on clear goals.

On this visualization tool, you can explore learning objectives from different perspectives at once:

1. On one axis is Bloom’s Taxonomy — a way of classifying lower-order to higher-order skills, such as “understanding” to “applying” to “synthesizing”.
2. On the other axis are the types of knowledge (factual, conceptual, procedural, metacognitive).

As you mouse over each item, it gives you an example of a learning goal on at that space — for instance, a factual, understanding learning goal is “list primary and secondary colors.”  On the other hand, a factual, evaluative learning goal is “check for consistency among sources.”

So, as you mouse along one type of knowledge from lower order to higher order thinking, you get a sense of what that type of knowledge is and how you can test whether students have a grasp of it on a shallow or deeper level.

Image by Rama on Wikimedia. Some rights reserved.

Or as you mouse along a single Bloom’s level, you see how the different types of knowledge come into play for that single level of depth of understanding.

Of course, if you visited the link, you got all that in a quick glance, without all these words.  That’s the power of a great visual representation.

Have you visited the link yet?

I haven’t been doing much straight science journalism lately, having gotten my grubby mitts deep into science education and education research and seemingly unable to extract them.  But recently I was contracted to write some research pieces for JILA (an institute of CU-Boulder and NIST that focuses a lot on atomic and molecular physics, among others.

Two of those pieces have since been published.  The first was “Simulating a Starquake” which was a really fun little piece to write about how rearrangements of the crust of neutron stars results in the emission of gamma ray bursts.

The second was much harder — Schrodinger Cats Light the Way.  The topic — quantum spectroscopy — was very difficult to understand.  And then, to explain in a way that is at least somewhat understandable to a layperson, without being able to use terms like “quantum statistics” or “quantum state” (or explain what those terms mean), was a real challenge.  This one took exactly twice as long to write as the first one.  I think physics writers should get paid double, this stuff is hard.  It’s much easier to get the gist of some new evolutionary pathway of fish than it is to connect spectroscopy to strange quantum states to the inner workings of semiconductors.  I think the logical chains inherent in this stuff are really hard to weave into a tight story with a clear narrative arc.  I did the best I could!

Enjoy!

You must read this book.  YOU MUST READ THIS BOOK.  I believe I’m not just enthusiastic about this because I have various deep professional connections to its subject — Frank Oppenheimer — but also because it’s a deeply inspirational look at a deeply inspirational man and his ideas.  He founded the Exploratorium Museum of Science, Art and Human Perception, where I spent a wonderful two years.  The Exploratorium has a wonderful page on Frank Oppenheimer, including biographies, videos, and articles about the man.  This book — Something Incredibly Wonderful Happens: Frank Oppenheimer and the world he made up — is not just a lovingly written autobiography, but a biography of ideas.  K.C. Cole does a fantastic job of describing the educational philosophy of her mentor, as well as how it infuses the institution that he built.

Frank was the brother of Robert Oppenheimer, of Manhattan Project fame.  Frank was also on the Manhattan Project, working on the bomb, but Robert directed the project.  He was blackballed during the McCarthy anti-communist era, and couldn’t do physics.  He spent ten years as a cattle rancher in Pagosa Springs, Colorado.  He was eventually offered a lectureship here at the University of Colorado back in 1959, and I work closely with the instructor who now occupies the position that was created for Frank (senior instructor Mike Dubson).  Here, he created many of the experiments that are seen as a prototype for the Exploratorium exhibits.  Those exhibits are mostly lost — some have been absorbed into our lecture demonstration area.  I recently spoke with lab coordinator Jerry Leigh, who was interviewed for this book, and he gave me the original copies of the lab manuals created by Frank.  I’ll blog about those later, as I’m hoping that I can share them with the broader physics community.  Frank then went on to create the Exploratorium in 1969.

As you can see, I have several connections with Frank — physics, the University of Colorado, and the Exploratorium.  What struck me was that I recognized so many names — both here at CU and at the Exploratorium — who had connections with this man who died about 25 years ago.  Jerry Leigh, here at CU-Boulder, Mike Dubson, who now occupies Frank’s position, and many many names of people at the Exploratorium who I had no idea were there when Frank directed the museum.  And they’re still there.  What a testament to the vision that Frank had, and how important his colleagues feel it is to continue to breathe life into.

Being at the Exploratorium changed my life. I began to notice things in the world in a different way.  To stop, to take pleasure, and to wonder.  I’m not an innately playful person, at least when it comes to professional life, and the Exploratorium helped infuse me with some of the sense of whimsy that I’d like to make more a part of my life now.

To give you a taste of what I found so inspiration about the book, here are a few guiding principles of Frank’s vision as outlined by K. C. Cole in “Something Wonderful”:

Sightseeing

Sightseeing, said Frank, is the basis for discovery.  We look around at the world, and discover patterns.  But so often, the kind of sightseeing that we offer to students in a classroom is the kind of sightseeing that happens from a train window:

….unstoppable, irreversible, and dominated by the smells, sounds, and motions of the train rather than the landscape outside.  The people and towns along the way never become part of your experience.  The train is always rushing towards its next destination.

Real sightseeing requires you to get out of the train, wander at will, get lost, get dirty, linger as long as you like, and try things out just for the heck of it.  You can’t be guided, and you can’t have an agenda.

So, the Exploratorium was Frank’s “antidote” to the rushed schooling that we’ve experienced.

Legitimizing Play

Frank wanted children to run in the museum. He wanted a lack of control, to create an environment that was welcoming and comfortable.

Visitors could make genuine discoveries — not the kinds of discoveries students are urged to make in the “discovery method” of teaching, where they can discover only what the teacher had in mind.  Instead, all kinds of unexpected things were discvoered in the exhibits, even by the people who built them.  Frank thought play was serious business.

Frank described a time when he mixed everything in the house and got a horrible brown mess.  A waste of time?  No, research physicists get paid to “waste time” in this exploratory way.  The exhibit developers in the Exploratorium get paid to “waste time”, similarly.

“Occasionally, though, something incredibly wonderful happens,” he said.

Hence the name of the book.  When you play, you have the opportunity to create something new.

For Frank, play was never off limits, so he was usually a hoot to have around.  He might invite you to a meal that consisted entirely of experimenting with different ways of eating ears of buttered corn (if you slice each row down the middle with a sharp knife, for example,  you can eliminate the crunch).

Cole describes one time that Frank smashed a red lifesaver with a hammer, so the tiny ground particles looked white, because of scattering.  This is the same principle as why clouds look white, or sea foam.

Noticing

A similar theme in the book is the importance of noticing.  Like the sightseeing analogy, it is important to not just breeze through life, taking what you perceive for granted.  Half the time, we aren’t really looking.  According to Frank:

Artists and scientists are the official noticers of society.

I was always amazed at the exhibit builders at the Exploratorium:  they were so thoughtful, tuned into aesthetic, and — yes — they noticed.  They would spend hours tinkering with apparatus, seeing what happened if they sprayed lotus flowers with finer and finer droplets, or what happened when they tweaked the frequency in a vibrating platform.  One of my favorite exhibits is called Icy Bodies.  An image from this exhibit is below (and you can download this and many other for free to make wonderful desktop wallpaper):

Chunks of dry ice fall onto a surface covered with a thin film of water.  They swirl and jet across the surface, propelled by streams of sublimating dry ice.  The exhibit developer, Shawn Lani, described part of his development of this exhibit to me.  Originally, he had a button on the exhibit where visitors could drop more dry ice onto the watery surface.  But he found that then that became the point of the exhibit, and kids were hurriedly pressing the button.  They weren’t stopping to notice the beautiful formations.  So, in a seeming anti-Exploratorian move, he removed the interactive component.  Dry ice now falls into the exhibit on a little conveyer belt every few minutes.  But now visitors gather around, stop, and notice.  It’s mesmerizing.  K.C. Cole describes this exhibit in “Something Wonderful” — apparently Shawn Lani was a disciple of Ned Kahn (an artist who specializes in exhibits that make the invisible visible — see my other blog post about his work).

If others have read the book too, I’ll be curious what struck you about it, and what you took away.

Phylm /’film/ n. [physics + film]

The fifth annual Phylm Prize is now open! Until May 13, anyone can enter a film — though students are especially encouraged — about physics. Year three’s winners were a set of students with the Special Relativity Rap. The second year was Science Made Fun about black holes (which I’ve inserted below), and year one was a kind of crazy video with a guy breaking flaming boards with his hand, using the Leidenfrost effect. When you drop water into a skillet and the beads dance across the surface — that’s the Leidenfrost effect. The beads of water are insulated from the hot pan because the liquid evaporates before it boils, creating a vapor layer that insulates the rest of the water from the pan. Anyway…

Last year they had a tie for first place, from Henry Reich’s Minute Physics and Derek Muller’s Veritasium.com.  Both are part of a larger set of videos — check them out.  These could be useful for people wanting to do some version, even a small-scale version, of the Flipped Classroom.  Below is one of the winning videos, from Derek Muller, on misconceptions about why astronauts float.  I think this is brilliant.

Interestingly, Derek Muller even has a short video on the Khan Academy (see it here).  He’s clearly well-versed in the physics education literature, and very thoughtful about what works and what doesn’t.  Here’s what he says about Khan (which has been drawing a lot of mixed reviews in the physics education community):

It is a common view that “if only someone could break this down and explain it clearly enough, more students would understand.” Khan Academy is a great example of this approach with its clear, concise videos on science. However it is debatable whether they really work. Research has shown that these types of videos may be positively received by students. They feel like they are learning and become more confident in their answers, but tests reveal they haven’t learned anything. The apparent reason for the discrepancy is misconceptions. Students have existing ideas about scientific phenomena before viewing a video. If the video presents scientific concepts in a clear, well illustrated way, students believe they are learning but they do not engage with the media on a deep enough level to realize that what was is presented differs from their prior knowledge. There is hope, however. Presenting students’ common misconceptions in a video alongside the scientific concepts has been shown to increase learning by increasing the amount of mental effort students expend while watching it.

I’m curious about the research studies that he’s referring to.  Does anybody know more?

Regarding the Phylm prize, what I really like about this is the blending of science with art and communication. There’s just no better way to learn something than to create something that attempts to teach about it, and I think that “edutainment” about science is really fun and worthwhile. There are lots of things that can be done in media to bring out the beauty, intrigue, and weirdness of science.

Here are the rules to enter the contest.

Here is a curricular unit for physics teachers that focuses on how to make a short phylm.