Category: teaching

A misconception about extrasolar planets

A couple of weeks ago in the introductory “Astro 101” class I work in, the instructor and I confirmed that many students hold a certain misconception. I was, still am, pretty excited about this little discovery in astronomy education. If my conversations over the following few days had turned out differently, I probably would be writing it for publication in the Astronomy Education Review. Maybe I still will. But for now, here’s my story.

Our search for life in the Universe and the flood of results from the Kepler Mission have made the discovery of extrasolar planets an exciting and relevant topic for introductory “Astro 101” courses and presentations to the general public.  Instructors, students, presenters and audiences latch onto “the transit method” of detection because it is so intuitive: when an extrasolar planet passes between us and its star, the planet temporarily blocks some star light and we detect a dip in the brightness of the star. The period and shape of the dips in the record of the star’s brightness encode the characteristics of the planet.

When an extrasolar planet passes between us and its star (when it "transits" the star) we detect a dip in the brightness of the star. (Kepler/NASA image)

Our students do a nice 50-minute, hands-on lab about how to decode these “light curves” which I hope to share at the ASP 2011 conference (#ASP2011 on Twitter) in July. In a class following this lab, the instructor posed the following think-pair-share clicker question. We wanted to assess if the students remembered that the size of the dip is proportional to the area of the star blocked by the planet’s disk, which scales as the square of the diameters:

Clicker question to assess the students' grasp of the transit method of detecting extrasolar planets.

The bars in this histogram record the number of students who chose (from left to right) A to E:

Students' responses for (left to right) choices A to E to extrasolar planets clicker question.

About 60% of the class chose answers (C and E) with a 1% drop in brightness, the correct drop, and about 40% chose answers B and D with a 10% drop. This second group didn’t remember the “proportional to area” property. So, not stunning results, certainly a good candidate for pairing and sharing.

The misconception

What is stunning, though, and the source of my excitement, is that 97% of the class feels you see a black spot moving across the star. Which is not true! We only detect the drop in the brightness of the star. We can’t even see the disk of the star, let alone a tiny black spot!

Okay, okay before you jump to the students’ defence, let me (with the help of my great CAPER Team colleagues) jump to the students’ defence:

  1. The question says, “…by observing it pass in front of the distant star.” Of course the students are going to say we see a dark spot – that’s what we just told them! Perhaps I should be worried about the 3% who didn’t read the question properly.
  2. The question is vague about what we mean by “size.” Diameter? Area? Volume? Mass? “The star’s diameter is 10 times bigger than the planet’s diameter” is a much better question stem.
  3. My colleague Aaron Price points out
  4. Astronomers may not see a “dot” crossing the star right now, but they can see something comparable. Through speckle imaging, radial topography and optical interferometry we have been able to see starspots for decades. CHARA’s recent direct observations of a disk of dust moving across epsilon Aurigae shows what is being done right now in interferometric direct imaging. I predict within 10 years we’ll have our first direct image of a “dot” in transit across another star.

  5. Aaron, Kendra Sibbernsen and I all agree that the word “see” in “What would you see?” is too vague. The question I wanted to ask should have used “observe” or “detect”. Kendra suggested we write “A) a dark spot visibly passing in front of the star” and perhaps following up the question with this one to poke explicitly at the potential misconception:

With current technology, can astronomers resolve the dark spot of an extrasolar planet on the disk of a star when it is in transit? (T/F)

Was there a misconception?

Did the students reveal a misconception about transiting extrasolar planets. Nope, not at all. It’s not like they took the information we gave them, mixed it with their own preconceived notions and produced an incorrect explanation. Instead, they answered with the information they’d been given.

A teachable moment

It seems that we’re not being careful enough in how we present the phenomenon of transiting extrasolar planets. But as it turns out, this is a teachable moment about creating models to help us visualize something (currently) beyond our reach. We observe variations in the brightness of the star. We then create a model in our mind’s eye — a large, bright disk for the star and a small, dark disk for the planet — that helps us explain the observations.

This is a very nice model, in fact, because it can be extended to explain other, more subtle aspects of transiting extrasolar planets, like a theoretical bump, not dip, in the brightness, when the planet is passing behind the star and we  see detect extra starlight reflected off the planet. The models also explains these beautiful Rossiter-McLaughlin wiggles in the star’s radial velocity (Doppler shift) curve as the extrasolar planet blocks first the side of the star spinning towards us and then the side spinning away from us.

These wiggles in the radial velocity curve are caused by the Rossiter-McLaughlin effect (from Winn, Johnson et al. 2006, ApJL)

Want to help?

If you’re teaching astronomy, you can help us by asking them this version, written by Kendra, and letting me know what happens.

An extrasolar planet passes in front of its star as seen from the Earth. The star’s diameter is 10 times bigger than the planet’s diameter. What do astronomers observe when this happens?

A)  a dark spot visibly passing across the disk of the star
B)  a 10% dip in the brightness of the star
C)  a 1% dip in the brightness of the star
D) A and B
E) A and C

In conclusion

I don’t think this qualifies as a misconception, not like the belief that the seasons are caused by changes in the distance between the Earth and the Sun. We’re just need to be more careful when we teach our students about extrasolar planets. And in more-carefully explaining the dips in the light curve, we have an opportunity to discuss the advantages and disadvantages of using models to visualize phenomena beyond our current abilities. That’s a win-win situation.

Thanks to my CAPER Team colleagues Aaron, Kendra and Donna Governor for the thoughtful conversations and the many #astro101 tweeps womanastronomer, erinleeryan, uoftastro, jossives, shanilv and more who were excited for me, and then patient with me, as I figured this out.

Don't forbid phones in class, embrace them

It’s not uncommon to hear, as I wander the halls at UBC, faculty complaining about students preoccupied with their computers and phones in class. The most common solution is to just ignore it (“if they don’t want to pay attention to the class, it’s their loss…”) Can’t disagree with that, as long as students aren’t distracting others who are trying to pay attention. Another solution is to ban computers and phones. Well, some students legitimately need their computers (students with disabilities, for example) so I know of a few instructors who ask these students to sit over there, off to the side.

But here’s another solution: don’t forbid phones in class, embrace them.

Naive? Perhaps. Impossible to faciliate? Ye— Ah! Not so fast!

The April 2011 issue of The Physics Teacher contains an article by Angela M. Kelly that describes a collection of iPod Touch apps (which should also on iPhone and iPad) and how to use them to teach Newton’s Laws of Motion.  Cool idea: use the games the students are already playing to teach them physics.

I want to add to her list my own favourite physics app. This one’s not a game so it might not – no, who am I kidding, will not –  have the same appeal. But xSensor (which, at the time I write this, is free!) is a great physics app because it gives a real-time readout of the accelerometer, in the x-, y- and z-directions. The pix below are screenshots from my iPhone (captured with that magical “click on/off and home buttons at the same time” feature.) Here are a couple of screenshots that show some cool physics. The app will also record the data in a log you can email yourself.

xSensor screenshot showing circular motion. The sinusoidal curves encode the constant centripetal force.

I made this one by putting my iPhone flat on my desk and swirling it around and around. The curves sweeps across the screen recording about 5 seconds of readings. The numbers on the screen, 0.02, -0.14 and -1.18 are the instantaneous accelerations measured in g’s.  The z-acceleration is pretty constant at -1 g. Can’t get rid of gravity… The accelerations in the x-direction and y-direction show beautiful sinusoidal motion, 90 degrees out-of-phase, encoding the centripetal force of the phone’s circular motion. It’s shaky because I can’t swirl my phone smoothly.

Okay, the “can’t get rid of gravity…” line was a strawman. Because you can. If you drop your phone. Which I did. Very carefully.

xSensor screenshot during free fall when, for a brief moment, the phone recorded zero acceleration.

These graphs show me holding my phone still. About halfway through the plot, I dropped it. For a short period of time, the acceleration in z-direction snaps up to zero g’s: free fall! Then there’s a big blip as I clumsily catch my phone and take the screenshot. But there, just for that moment in free fall, my phone appeared to be force free. That’s Einstein’s Principle of Equivalence: floating free in deep space is just like freely falling in a gravitational field. (That NASA link include the famous Apollo 15 hammer/feather drop video.) It’s not a Gedankenexperiment, though. It’s the real thing, right there in your hand! Well, you know what I mean.

So, don’t ban phones from your physics, astronomy or science classrooms: embrace them! Better yet, chuck ’em across the room!

Do you have a favourite physics app? Have you discovered another cool experiment you can do with xSensor? Hope you’ll share it with us.

Learning Multiplication

I know a little bit about the differences between teaching with “blocking” or with “interleaving.” If you were teaching multiplication with blocking, you’d teach the “4 times table”, then the 5x, then the 6x and so on. With interleaving, you’d mix them up so students had to first identify what kind of question this is (“Oh, this is a 4x problem”) and then answer it. There is some nice work in cognitive psychology that shows interleaving leads to better retention.

I use the example of multiplication because that’s just what my 8-year-old was doing yesterday. He had a set of 5x flashcards that he asked me do with him. He didn’t have too much trouble, except for 5×9. As I was running through the cards, I thought of the multiplication table board I’d made a few years earlier when my other kid was learning multiplication. I remember being fascinated by a board like this when I was in Grade 3.

My home-made multiplication board. The green 1-10 along the top and left side are glued down. You put the 24-tile, for example, where the 4 and 6 intersect. Hmm, or the 6 and 4. Or 8 and 3 or 3 and 8!

The tiles are from a square hemlock spindle I got at the local hardware store, sliced on my mitre saw, sanded smooth, and then numbered. Green 1-10 tiles are glued across the top and down the left side. You put the blue 24-tile, for example, in the space where the 4 and 6 intersect.

My son and I got out this board, dumped the bag of tiles on the carpet, and he started to fill it in. The first row is easy: 1, 2, 3,…,10. Then he started on the second row. “2 times 1 is 2. 2 times 2 is 4. 2 time 3 is 6…” And about here, he stopped doing the multiplication and started counting by 2’s. I asked him how much 2 x 7 is, and he had to stop and think, despite the fact that he’d just placed the 10, 12, 14, and 16 tiles.

Uh-oh. My goal is to help him learn his times tables, I don’t want to reinforce repeated addition. What’ll he do with 104 x 56 next month?

So I turned the table on him. I started handing him tiles. “Here, where does this one go? How about this one?” That was pretty hard. For me, that is, because I had to quickly find the next tile I wanted in the big pile on the floor and hand it to him by the time he’d placed the current one.

I realize I was asking a different question: “What numbers multiply to give you 24?” is a lot different than, “What is 4 x 6?”. But this new version of the “game” worked nicely. He did some repeated addition in his head, searching for sequence that hit, say, 24. And he occasionally put a tile in the wrong place but I didn’t correct it. He discovered his mistakes as he lay down neighbouring tiles and the patterns were messed up.  It also forced him to estimate where in the empty board to place tiles any without neighbours.

He soon discovered repeated addition works vertically, too, so he could hop down the 4-column to find the 4x tables.

After a few minutes of this, I turned it up another notch (which was possible because there were fewer tiles left in the pile and I could find them faster.) I started handing him stacks of the same tile, for example, 4 40-tiles. “Here, put these down.” I only prompted him once or twice (“Well, if 4 x 10 is 40, what about 10 x 4?”) I was astonished how quickly he picked up the symmetry. “32 goes here at 4 times 8…Oh! And over here at 8 times 4!”

Older sister dropped by to help him with the high tiles – I don’t think my son’s had much practice with the 7x, 8x, 9x tables yet. The two of them finished off the board, fighting (in that friendly brother-sister way, of course) for who gets to put in the last tile.

There are so many patterns to explore on the completed board. We discovered where on the board to find the same tile (symmetric across the diagonal) :

Me: Here’s 7 x 3 and here’s 3 x 7. Here’s 4 x 6 and here’s 6 x 4. Hey, what’s up with 5 x 5? Where’s its match?
Him: It doesn’t have one, Dad, cause 5 x 5 is the same as 5 x 5. D’uh!

A friend dropped by with a 3-year-old and she asked the toddler to his age. My son helped, helping him find all the 3-tiles. And his 8-tiles. Then my daughter (who’s 11) dropped a little nugget that confirmed this “game” was worthwhile:

Well, I don’t have a tile because my age is a prime number.
[W00t! FTW, Dad!]

I’m sure the math ed people and elementary school teachers can tell me the history of multiplication boards and best practices for using them. But it was so much fun watching my son discover the patterns for himself. And to reinforce that math is something you can play with and — Zoinks! — even have fun with!

If you’ve got the tools and some patience (100 tiles is a LOT of tiles!) I highly recommend you make a set for your kid(s). Do you have any ingenious suggestions for what to use instead of cutting wooden tiles?

Creative Commons License Multiplication table  photo Peter Newbury is licensed under a Creative Commons Attribution 3.0 Unported License.

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