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

What do you mean by that, again?

Oh sure, trust me to turn a fun Twitter #hashtag into a posting about education. Well, sorry, I filter everything I read and experience through my education filter (or my will-my-kids-have-a-meltdown? filter).

I’ve been reading my tweeps #tweetmy16yearoldself messages on Twitter, thinking to myself, Geez, that kid was way more with it than I was. Like my #spacetweep friend @Zarquil, who tweeted

#TweetYour16YearOldSelf Honestly, you’ve got it all figured out already. Listen to your own heart and don’t put so much reliance on others.

Or my math teacher friend @ptruchon who wrote to himself,

Thanks for spending so much awesome time learning the guitar. I wouldn’t have time now, and I’m still enjoying it. #tweetyour16yearoldself

And then my education friend @janniaragon tweeted something that I’m paraphrasing from memory because the tweet was a couple of days ago and it’s slipped off the timeline.

“slim-leg jeans, black hair with bangs, t-shirt from [somebody’s] concert”

You see, @ptruchon and @Zarquil are tweeting TO their 16 year-old selves, sending a wise message back in time. But @janniaragon is tweeting ABOUT her 16 year-old self, a 140-character snapshot of herself back then. That’s the way I interpreted #tweetyour16yearoldself and I’m wasn’t keen to recall and share those awkward years.

Different people have completely different interpretations of the word “tweetyour16yearoldself”, producing completely different responses. Just like I see in undergraduate physics and astronomy classes every day! The instructor says an important word which sits, in his or her mind, at the pinnacle (or is that “apex”, @ptruchon?) of a pyramid of background knowledge and concepts. But the students interpret the word in a different way and attach none of the background the instructor assumes is there. Or worse yet, attach a different background and then struggle to hang the instructor’s version of the concept on scaffolding that isn’t there.

The biggest offender in my field is “theory”. To astronomers, physicists, scientists in general, “theory” is the pinnacle of science. Why, if you produce even one outstanding theory in your career, you’ve made a valuable contribution to the field. But to students, “theory” is often a vague guess, a stab-in-the-dark. Actually, let me quote from a new astronomy textbook, “Investigating Astronomy – A Conceptual View of the Universe” (W.H. Freeman and Co, coming soon) by @caperteam and @rogerfreedman. They say it much better than I can:

In everyday language the word “theory” is often used to mean an idea that looks good on paper, but has little to do with reality. In science, however, a good theory is one that explains reality and that can be applied to explain new observations.

It’s all about interpretation. Instructors, be sure to share the pyramid of background knowledge behind key words when you use them. And students, interrupt your instructor and ask, “What do you mean by that, again?”

We're all on the same team

I work at a huge institution. In 2009, there were more than 45 000 students and 10 000 faculty members at UBC, and enrollment continues to climb. We’re split into a handful of Faculties and Schools and many Departments.

With that many faculty members, it’s no surprise that people in different departments are doing the same things. And sometimes there’s mild hostility (or more) as different departments compete for bums-in-seats, grants, recognition and so on.¬† Sometimes there’s a feeling of, “Why are you doing that for them? They have their own people” as if we’re giving away our department’s secrets.

And that’s too bad.

Which is why I’m so glad to be working and collaborating and sharing with a couple of colleagues who don’t live in my building.

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