Tag: graphs

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.

Graph the graph on the graph

I was creating a worksheet for our #astro101 class about the expansion of the Universe. If the Universe is expanding at a uniform rate, it’s about 14 billion years old. If the expansion is accelerating (decelerating), a little logic tells us the Universe must be older (younger) than 14 billion years.

I wrote the worksheet as a ranking task (“Rank the 3 models by expansion rate 1 billion years ago” and so on) using the great collection at UNL as a template. There’s also a nice graph that helps summarize the current, past and future expansion of the 3 models. This is the graph for my analogy of 3 runners, Connie (who runs at a constant rate), Alice (who accelerates) and Deena (who decelerates) practicing for a 100-metre race. The Universe version is identical except “distance” is “size of the Universe” and “cross finish line” is “now”.)

Three runners cross the finish line at the same time and going the same speed. When did they start running?

I agonized (well, that’s a bit strong but you know what I mean) over getting the students to draw the 3 curves for the uniform, accelerating and decelerating Universes or getting them to identify and label the curves given in a diagram. Fortunately, we have nice set of learning goals for the course and one says, “You will be able to sketch different scenarios for the evolution of the size of the Universe, including when the Big Bang happened and the fate of the Universe.” That clearly told me to use “Sketch…” instead of “Label…”

Great. But is “sketch” the right verb? Soon, as a colleague and I started listing all the graphing nouns and verbs we use interchangeably, I realized once again that students most likely have many interpretations of these words. My “expert” interpretation is different than their “novice” interpretation of words like

  • sketch
  • draw
  • graph (noun and verb)
  • axes
  • diagram
  • figure
  • plot (noun and verb)
  • curve
  • function

It’s not inconceivable that a student could be asked to “graph the graph on the graph” or “plot the plot on the plot”. Ay caramba!

In the end, I asked the students first to “write labels Connie, Alice and Deena next to each runner’s curve in the graph” (the one above). I figured that showed them the critical feature of the story, that all three runners crossed the line at the same time and going the same speed. Then later I asked

This graph shows the size of the Universe at each time for the uniform expansion model. Sketch the curves for the accelerating and decelerating universes. Remember that all curves must go through the current Universe  and all curves must have the same slope at that point because the slope is the Hubble Constant. Label the curves accelerating and decelerating.

If the Universe expands at a uniform rate, right now is had its current size.

The students spent about 15 minutes on the worksheet. I’m happy to report that 103 of 115 (or 90%) of the students correctly chose C) older on this post-activity clicker question

If we discover the Universe is expanding at an accelerated rate, it means the Universe is

A) younger than 14 billion years
B) 14 billion years old
C) older than 14 billion years

Interpreting formulas and graphs

When you pose a question to students about a non-trivial concept, and they get it wrong, it’s not obvious where the error occurred, which step they missed or misunderstood.

Every now and then, though, you find a “diagnostic” question that clearly discriminates between the people who have a certain morsel of knowledge and those who don’t. I found one of these questions in the #astro101 class I’m working on.

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