I recently spent two days camping and exploring on Cedar Mesa in southeastern Utah. It was really fun. Check out this shot from inside Gravel Canyon:

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It was also a spectacular place to look at the stars. From where I was camped at Gravel Crossing, I don’t think there was an artificial light source within thirty miles. As the stars first come out, Jupiter, Mars and Saturn are strung across the southern sky almost in a line. Beautiful.

For the last six months I’ve enjoyed teaching myself some basic astronomy. Before that, I could find the Big Dipper and the North Star, but that was it. Now, I’m familiar with all of the major constellations (except for a small slice of the sky that I still haven’t gotten myself up early enough to see). I can place all of the astrological signs in the sky and visualize their relationship with the sun — which is how they were chosen in the first place. I know how to find the planets, track the motion of the moon across the sky, and roughly tell the time of night using the constellations. It’s been a fascinating experience — both in coming to better appreciate the night sky, and as a view into my own learning.

Retrieval Practice

The biggest reason I’ve gained some proficiency has been a great deal of practice. I would estimate I’ve spent 30 hours stargazing over the last six months, divided between a variety of types of practice. Using a Planisphere to orient myself and identify stars, constellations, and other objects. Looking at the stars and identifying constellations from memory. Identifying constellations or individual stars on cloudy nights when only part of the sky is visible. Watching the stars come out at dusk and trying to predict where different constellations will be. Orienting myself based on the constellations (especially fun at dusk as the southern constellations come out first, so no North Star). Especially useful was showing others different constellations and talking about how to find them, especially the different astrological signs.


Mental Representations

But learning the night sky through memorization alone would be pretty staggering. I can probably identify, as either individual stars or parts of constellations, somewhere from 200-300 stars. To make this manageable, I use what Anders Ericsson calls mental representations. Instead of consciously retrieving each piece of information from memory, they are grouped together so that I can unconsciously see a set of information as parts of a coherent whole. I see individual stars as constellations. Orienting myself toward the night sky, I divide it into twelve sections, each corresponding with one of the astrological signs, and use these as landmarks. I visualize the stars as concentric circles rotating around the North Star. I can find the planets by associating them with the astrological sign whose arc of the sky they are in. I see subsets of the night sky in terms of their relationships — to find Hercules, I follow the curve of the Big Dipper to the bright star Arcturus (arc over to Arcturus), which is in the constellation Bootes. Adjacent to Bootes is the distinctive curve of the constellation Corona Borealis. Continue in that direction, and find Hercules. When I am stargazing, a large proportion of my thinking is around identifying constellations and connecting them with my larger mental representations of the night sky and the different relationships between objects, allowing me to build those representations at the same time as I exercise retrieval practice.


I made plenty of mistakes along the way. The Planisphere was my largest source of feedback as I reconciled my representations of the night sky with what was on the Planisphere. Sharing with others was helpful as well. Early on, I was mistaking the bright stars Castor and Pollux, the Gemini twins, with two stars in the constellation Cancer, and focusing on the wrong stars near Cassiopeia. A friend pointed out the discrepancies. I’ve also consulted sources on the internet for star stories to add some more context to the different constellations, often helping me to clarify what exactly I was looking for.

This process hasn’t been perfect. I make no claim that I have learned in any ideal way. I’ve made sense of things on my own terms. This is what I’m supposed to see when I see Taurus, the bull:


But instead, I see an upside down bull, running down and to the right, in profile. I still struggle with a mental representation of Virgo that is anything but a set of random lines in different directions. While I’ve become more and more familiar with the southern sky, where the astrological signs act as useful landmarks, I struggle with the northern sky and frequently have to check myself to find certain constellations. My mental representations are incomplete, and would benefit from more focused feedback and instruction to point to areas where my knowledge is lacking — likely including areas that I don’t realize my knowledge is lacking.

That said, this brings to light some questions about teaching math. Some folks argue about whether students should learn concepts or procedures first — but I was learning the concepts and memorizing at the same time, in a kind of iterative cycle, constantly going back and forth between the two. As I memorized more stars, they created a place to hang my mental representations, and as my representations became more complex, I had a greater capacity to assimilate new knowledge. I was able to give myself effective feedback by exploring and checking in most cases — but I am sure that some expert instruction could quickly fill in some holes and bad habits I’ve built. There has to be a balance.

Anyway, my point is just that this learning experience has highlighted the ambiguities of some debates that often seem to be portrayed in black and white. None of these questions have easy answers, they’re enormously dependent on context, and in many cases, it’s a both-and, not an either-or.

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