The Teacher-Centric Universe (or, Galileo Would Be Ashamed)

My first year out of college, 22 years old and glimmering with hubris, I taught 9th-grade Earth Science. I’d last studied the subject myself in 8th grade, which made for a fun year, if “fun” can refer to wildly inaccurate lectures about glaciers.

When we arrived at the unit on astronomy—a topic I’d actually explored in college—I felt the exhausted, wild-eyed relief of a shipwrecked man crawling onto dry land. All right! Finally I could teach them something, not just spit back stuff I’d learned from their textbook like a mother bird offering regurgitated food. We began with the age-old debate of geocentrism vs. heliocentrism.

Geocentric models of the solar system put Earth at the center, with the sun and planets all orbiting around us. That’s how ancient Greeks saw the world.

The heliocentric model, meanwhile, places the sun at the center. At one point, the Catholic Church clung so tightly to the geocentric model that they put Galileo under house arrest for espousing heliocentrism. How dare he correctly propose that we’re not the center of the universe!

With my kids, I wanted to get past the historical scandals. I wanted to talk about data, predictions, and the nature of science.

Since antiquity, people have watched the planets. To the naked eye, they look just like stars, but with two differences. First, they don’t twinkle. And second, while the stars hold a fixed pattern from night to night, the planets drift. They wander across the sky, moving against the backdrop of stars. That’s what “planet” means, in fact—wanderer.

How did people explain this? Well, they imagined a universe with the Earth at the center, the stars in the distant background, and planets orbiting around us.

But this model had a problem. Each planet usually moves one direction, but sometimes it doubles back, reversing course for a few weeks, and then continuing on its original path. This is called retrograde motion, and it blew Greek minds. Why would planets do that?

Ptolemy had a solution. “The planets don’t orbit us in a simple fashion,” he said (though probably not in those precise words, and definitely not in English). “There are roller coaster loops in their orbits. That explains why they seem to move backwards.”

This theoretical invention helped, but the planets dance a very funny dance. To fully explain their motion, Ptolemy needed further tweaks. He proposed loops within loops. His model grew dauntingly complex. But it successfully predicted the motions of the planets, so for a thousand years, his book stood as the definitive text on planetary astronomy.

Enter Copernicus. He offered a much more elegant way to explain retrograde motion. It’s not that planets are orbiting us. It’s that we’re both orbiting the sun. Retrograde motion occurs because we’re orbiting at different speeds. Mars, for example, orbits the sun more slowly than we do. So when we’re at this point, Mars will seem to move one way.

But then, later in the year, we’re passing Mars, so it seems to move the other way.

And still later, as the orbits continue, Mars resumes its original direction in our sky.

Yes, Ptolemy’s geocentrism can predict the planets’ motion. But Copernicus’s heliocentrism has the same predictive power, and it’s far more elegant to boot. It’s what scientists call parsimonious.

I explained all this to my Earth Science class, pretty sure I was nailing it. “These kids will make great scientists, thanks to me!” I gloated mentally. Then Kenny—often the only one brave enough to speak up in that vacuum-quiet class—chimed in with a question.

“How did those old Greek people even know the planets existed?” (Kenny always had a way with words.) “They couldn’t see them, could they?”

“You… they… of course they could,” I said, blinking.

“Did those dudes have telescopes?” Kenny asked.

“No,” I said. “Planets are… you can just… see them. They look like stars, but they change position in the sky from night to night.”

“OHHHHHH!” the whole class exclaimed, and my heart sank. Here I was, contrasting theoretical frameworks to explain the movements of the planets, while my students didn’t even know that they’re visible from Earth. You don’t see much of a night sky growing up in Oakland.

In that awful moment, I realized I’d lost them. The whole class. I was like a general who’s been marching ahead with his nose in the air, and then looks up to realize that his army is nowhere in sight.

The problem wasn’t just that I relied too heavily on lecture, or that I launched into advanced material without checking my kids’ basic understandings. On a deeper level, I was applying the wrong model of the classroom. I was committing an error even graver than Ptolemy’s.

The class doesn’t revolve around me. Each student follows his own orbit around something that sheds a light far brighter than I do, and exerts a pull far greater: the content itself. As they trace their own elliptic paths around the material, their progress might appear to me like retrograde motion. But that doesn’t mean they’re caught in backwards loop-de-loops. It just means I’ve got to work to see the whole system through their eyes. A class isn’t teacher-centric. It’s truth-centric.

And for the first time in my teaching career, but certainly not the last, I realized that Galileo would be ashamed of me.

Thanks for reading! If you like stories about my stumble-walk of a teaching career, you might enjoy 0.999… and the Debate that Repeats Forever and The Anxieties of Hermit Crabs.

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22 thoughts on “The Teacher-Centric Universe (or, Galileo Would Be Ashamed)

  1. I loved the “general with the nose up” analogy. I shudder to think of similar mistakes I’ve made. I could just imagine having that “uh oh” moment as I was reading this post.

    What are some ways we can help the people who haven’t hit the dry land yet do this better?

    • Thanks! That analogy was originally going to be the title of the post, until I had too much trouble drawing it…

      The way I see it, there are a few key forms of evidence on the class’s state of mind and level of understanding: (1) Written assessments, like HW/quizzes/exit tickets/diagnostics; (2) Conversations/observations with students during class; and (3) One-on-one conservations/tutoring with kids outside of class time.

      If the first two forms of evidence aren’t cutting it, then I tend to lean more heavily on the third. A one-on-one conservation, without time pressure, can reveal a lot (not just about that student in particular, but the class as a whole).

  2. Creative: No, the planets are large enough to show visible disks, so while they do twinkle when the “seeing” is bad, it’s not nearly as large an effect.

    Ben: Way too late now, but Galileo was not excommunicated, and Copernicus’s heliocentric circular-orbit theory was only somewhat simpler than the standard theory (it still required epicycles, just not so many). That may be why it didn’t see much early adoption: few thought that a simpler but counterintuitive theory was sufficiently compelling. In fact, no amount of superimposed circular motions can ever be equivalent to elliptical motion, so the epicycle research program was doomed from the start.

    • Ah, thanks. I’ll change “excommunicated” to “put under house arrest.”

      I didn’t realize Copernicus still needed epicycles! Circles aren’t so good, I guess.

      Am I right in thinking that both of the foci of our elliptical orbit lie inside the sun?

      • A quick search seems to reveal that the answer is “no.” One of the foci is inside the sun (the sun in fact “orbits” it, or wobbles around it, depending on one’s favored choice of words), the other lies some distance outside of it, and has no physical significance.

  3. A friend of mine who teaches HS physics and astro told me about teaching about solar eclipses, and how many of his students claimed that seeing the moon in the sky during the day was impossible. They’d apparently somehow never noticed it! (He made a note to take them outside on the next clear day during which the moon was visible — some of them were apparently pretty surprised! They really hadn’t believed him!)

    I think the reason for this might be similar to the reason that your students were unable to understand how one could track the motion of the planets against the stars — if you live in most cities, the night sky isn’t much too look at, and the sky in general I think falls out of one’s attention. Even if you see the occasional object, it isn’t clear enough, and there aren’t enough other objects around it, to really make sense of what the ancient astronomers were doing…

    Our assumptions about what we our students know, about what their experiences of the world are like, are sometimes violated in quite dramatic ways!

    • That’s pretty stunning. And it helps explain why we so often run into the obstacle of, “Man, why didn’t that lesson connect with them? I really thought they’d enjoy learning this.” As you say, our assumptions about their mental landscape can be wildly inaccurate.

  4. I find it stunning how just when I’m having a crisis of faith (in myself, my students, schools, education in general, etc.) you always seem to have a post that addresses exactly the issue I’m having.

    I have been teaching 8th grade pre-algebra for a few years and this year, I was given 8th grade geometry as well. I do AMAZINGLY well with the geometry kids. They are engaged and curious and enjoy coming to class.

    The pre-algebra kids seem to like me well enough, but their progress has been minimal. I’ve tried different styles of teaching from lecture and worksheets to activities and projects to inquiry-based with minimal differences.

    I am reading this blog post possibly in a way you didn’t intend. I need to remember that my students have so many things going on in their lives that most of it has nothing to do with me.

    While teaching is the center of my working universe, my class isn’t even remotely close to the center of theirs.

    Thank you for this.

    Keep up the drawings! I’m only able to do one a day. I’d love your feedback

    relearningtoteach.blogspot.com

    • Hey Justin, thanks for reading! I’m glad you find resonance in these posts.

      The lesson you’re drawing maybe isn’t the one I was focusing on, but it’s certainly a worthwhile moral. Our classes occupy just a small part of our students’ lives. To understand their behavior and progress inside the classroom often requires understanding what their lives are like outside of it, and accepting that our role is limited.

      I like your blog a lot, too. “Terrible at my job” is obviously an overly harsh epithet for yourself, but I know the feeling, that hard-to-shake glass-half-empty sensation that the things we do right are dwarfed by the things we do wrong. I still can’t hit that level of candor when I write in the present tense, hence all my stories about “my first year teaching” or “back when I was in college,” when in reality, all those anxieties and errors persist to the present day.

      • When I began the blog at the beginning of this year, I WAS terrible at my job and had only just come to realize it. I was putting all of my failures on the kids and never on myself.

        I’m getting much better as I reflect on things, but I’m not where I want to be. Yet!

        I think it’s so important for us to remember that even though we exist in the bubble that is our room and we are alone facing those kids, we aren’t alone unless we want to be. There are thousands of teachers out there who are facing the same issues. Some are being overwhelmed, but some are succeeding and we have to stick together.

        This job is WAY too hard to go it alone.

        Keep up the good work and the bad drawings! :-)

  5. You might be amused to read that one of my physics professors rewrote Ptolemy’s Almagest using modern arguments. In Copernicus’ time, the geocentric model was simpler and actually more accurate than the heliocentric model — it took some time for observations to catch up. Also, there was no model of physics which could adequately explain how the Earth could move without us feeling it, so the rejection of geocentrism involved the rejection of quite a lot of physics without any replacement.

    http://farside.ph.utexas.edu/books/Syntaxis/Syntaxis.html
    and the discussion in Paul Feyerabend’s “Against Method”

    • Cool! And strange. It’s interesting learning from you and John Cowan about the shortcomings in Copernicus’ model. The historical transition from geocentrism to heliocentrism is obviously a more subtle and less strictly observation-driven story than the one I tried to feed to my students.

  6. “a more subtle and less strictly observation-driven story”
    I wouldn’t feel too badly about this. One of the things that I’ve learned over twelve years of homeschooling is that many things I thought I knew from school were in fact simplified and redacted for easy digestion. You can’t teach upper level Astrophysics to most twelve year olds. You can lay the foundations for that work, though, and it sounds like you got a good start on that.

  7. Ben

    First things first: great site, I’ve founded it somehow and now I’m a regular visitor.

    I’m glad Alex and John have pointed to some less known facts of Copernicus-Ptolemy conflict. You might be surprised that the number of epicycles in Copernicus model is unknown. Different people have different opinions about – ‘De revolutionibus…” was more a program than finished model. If you like you might look for very good methodological explanation of paradigmas change in “Why Did Copernicus’s Research Programme Supersede Ptolemy’s?”, written by Imre Lakatos and Elie Zahar in 1974.

    The Galileo’s process also wasn’t as simple as it show school books. Basically the Church wanted to keep helicentrism as a hypothesis, Galileo wanted to teach it as a fact. In early XVII century helicentrism was unproveable, so it is debatable who was right. Good analysis of Galielo’s affair you might find in G. V. Coyne, M. Heller & J. Źyciński (eds). The Galileo Affair: A Meeting of Faith and Science. Proceedings of the Cracow Conference, May 1984 – I’m afraid it may be difficult to get. But it’s worth reading for somebody interested in XVI/XVII century science and relation between science and religion in this period.

  8. Pingback: Friday links: math with bad drawings, the rejection that wasn’t, holiday caRd, and more | Dynamic Ecology

  9. In the lower grades, in some schools with lower-income kids or with special ed kids,, teachers have to check to see if the children have a clear understanding of the meanings of the prepositions in the English language. Clearly they must have that knowledge in order to read effectively, but they also REALLY need to know the exact meanings of the prepositions (under, beyond, within, etc) in order to have a chance of understanding science content.

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