Any questions about this video?

As part of preparing for our impending move from Indy to Grand Rapids, my family and I have made a couple of visits to the area. These by necessity combine business with pleasure, since our three kids (ages 2, 5, and 7) don’t handle extended amounts of business well. On the last visit, we spent some time at the Grand Rapids Childrens Museum, the second floor of which is full of stuff that could occupy children — and mathematicians — for hours. This “exhibit” was, for me, one of the most evocative. Have a look:

I asked this on Twitter a few days ago, but I’ll repost it here: In the spirit of Dan Meyer’s Any Questions? meme, what questions come to mind as you watch this? Particularly math, physics, etc. questions.

One other thing — just after I wrapped up the video on this, someone put one of the little discs rolling on the turntable and it did about a dozen graceful, perfect three-point hypocycloids before falling off the table.

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What I learned at the ICTCM, day 1

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Busy day here at the ICTCM. I need both an extended time for brain-dumping and a full night’s sleep, and I think the latter is going to win. So here’s a brief listing, in no particular order, of some of the standout items I’ve learned today.

• I learned first thing this morning that rigorous, scientific scholarship of teaching and learning does actually exist, and it’s being done by Dave Pritchard of MIT. Prof. Pritchard was our keynote speaker this morning. In his words, he has basically forsaken a successful career in atomic physics (in which role he mentored or taught three Nobel laureates) to devote his energies to physics education. His keynote this morning gave me enough reading material for a semester and a whole new outlook on what educational research could look like.
• I learned (through Pritchard’s keynote) that there is a school of thought that says partial credit in math and science courses should not be given, because — and I quote — “Partial credit rewards partial understanding”. More to think about here.
• I learned that, thanks to the research of Pritchard and his cohorts, there is a growing field of educational data mining, or one might say educational informatics, out there, designed to take data from online assessment tools and making observations about student learning. There’s even a journal.
• I learned that the difference between novice and expert behaviors in learning pretty much describes all the issues I’ve encountered with the MATLAB course and other courses I’ve taught.
• I learned, through Scott Franklin’s prezi on this subject this morning, that online lectures can be done that aren’t just lectures.
• I learned that Geogebra is pretty cool, and I’ll learn more tomorrow as I take a minicourse on that software.
• I learned there’s a whole website out there — and probably more than this one — for project-based learning ideas.
• I learned that MATLAB has an interactive GUI…. for creating interactive GUI’s. Definitely something to play with later.
• I learned that Gino’s East Pizza is among the best stuff I’ve ever ate, and the copious amounts of it in my stomach right now are a strong argument for sleeping over brain-dumping.

Tomorrow will be a Geogebra minicourse, as I mentioned, and more sessions which I haven’t mapped out yet. We’re getting sporadic wireless access, so I’m able to tweet a lot. More to come!

“This is a science course. Lasers are not voodoo.”

The teacher who graded this dismal paper from a physics class is either a lot  braver than I am or cares a lot less about his/her relationships with students; and s/he certainly has better artistic skills and a lot more time on his/her hands than I do:

Read the whole essay and especially the teacher’s marginalia. I think it captures the temptation of every teacher to grade papers by unloading our own cleverness onto  hapless, writing-impaired students.

But the article has a fair question — how does something this bad get a 3/3 grade?

Algebra meets astrophysics

Abstract algebra and astrophysics don’t have much to do with each other, right? Well, perhaps not, after all. Here’s a story about the results from a researcher in gravitational lensing being used to prove an extension of the Fundamental Theorem of Algebra to rational harmonic functions. Snippet:

In 2004, [mathematicians Dmitry Khavinson and Genevra Neumann] proved that for one simple class of rational harmonic functions, there could never be more than 5n – 5 solutions. But they couldn’t prove that this was the tightest possible limit; the true limit could have been lower.

It turned out that Khavinson and Neumann were working on the same problem as [astrophysicist Sun Hong Rhie]. To calculate the position of images in a gravitational lens, you must solve an equation containing a rational harmonic function.

When mathematician Jeff Rabin of the University of California, San Diego, US, pointed out a preprint describing Rhie’s work, the two pieces fell into place. Rhie’s lens completes the mathematicians’ proof, and their work confirms her conjecture. So 5n – 5 is the true upper limit for lensed images.

“This kind of exchange of ideas between math and physics is important to both fields,” Rabin told New Scientist.

Indeed, and very cool. The paper that Khavinson and Neumann wrote, with an update that addresses the relevance of Rhie’s result on gravitational lensing, is here.

In memoriam: John Wheeler

John Archibald Wheeler — a giant in the world of physics, colleague of Einstein, teacher/mentor to Richard Feynman, and inventor of such terms as “black hole” — has died at the age of 96. Daniel, who blogs at Cosmic Variance and who was one of Wheeler’s more recent students, has this touching tribute, which serves as a profound example of the power of professors to induct students into the world of ideas for life. 

John Wheeler co-wrote a book on spacetime physics which was the textbook of one of the three most influential academic courses I ever took. The course was a one-hour colloquium/seminar course on spacetime physics for Honors Program students at Tennessee Technological University, and I took it when I was a junior. We learned about special relativity, temporal paradoxes, causality, and all manner of related mind-bending material in that course. The book was just a set of typed-up notes at the time, but extremely well-written and including a learning component which at that time was highly innovative: computer software that gave visual simulations of the physics phenomena we were studying, like the apparent contraction in length of an object moving close to the speed of light. Every Thursday, we’d stagger out of the spacetime physics course, our minds overwhelmed with crazy ideas about photons having mass and time running at different rates for different people. It was fantastic. We all loved — we learned to love – having our minds blown like that each week. It was through that course, I think, that I graduated from being just a student who knows how to score enough points to have a high GPA, to a person who can find passion and enjoyment in the world of ideas bigger than myself. 

At the end of that semester, we made a t-shirt for ourselves with a screenshot of the computer software on the front and a list of “Top Ten Ways to Recognize TTU Spacetime Physics Students” on the back. (“They are constantly resetting their watches”; “They complain about having only meters to get to class”; and so on.) We sent t-shirts to Profs. Wheeler and Taylor too. Prof. Wheeler sent a handwritten letter back to us, and I remember him writing something like, “Having fun and learning new things at the same time — who could ask for anything more?” 

Indeed! Thanks, Dr. Wheeler.