Here’s a quiz for you: what’s wrong with these pictures?
Black widow spiderAdvent calendarPyramids at Giza
Did you find anything wrong? Surely you noticed the black widow spider has only 6 legs, not 8. Here’s the original – I amputated one leg with photoshop for the pic above. If you rolled-over the pyramids picture and saw the reference to National Geographic, you might suspect the pyramids are in the wrong locations. Not in this picture, though: there’s nothing wrong it. (source)
What about the picture from the advent calendar? If you’re at all familiar with this blog and my passion for teaching astronomy, you might have guessed I’m going to tell you about the Moon and its incorrect phase.
As astronomer Peter Barthel correctly points out, this phase rises around 3:00 am and sets around 3:00 pm. No matter if this Moon is rising, setting or somewhere in between, you’re not going to find people caroling in the town square. The artist got the wrong phase. In fact, Barthel has done much more than point out this one flawed calendar. In an article submitted to the journal Communicating Astronomy with the Public, he finds errors in artists’ depictions of the Moon in everything from Dora the Explorer to Christmas wrapping paper, from the Netherlands to North America.
The responses to the Guardian story, and its offspring like this Globe and Mail piece, seem to fall into three camps:
“Oh, puh-lease! It’s just a picture on a calendar! Gimme break, you grinch!”
“Oh, c’mon! Everybody know the Moon cannot be in the waning crescent phase in the evening!” (I suspect the Guardian reporter might fall into this camp because he writes, “[t]he phases of the moon are easy to grasp.” As someone who teaches astronomy and studies astronomer education, let me tell you, for the vast majority of people, they’re not.)
“Oh, dear. Another case of scientific illiteracy.”
Me? I’m in Camp 3. Why can’t an artist do some fact-checking before drawing the Moon? Does the artist think to himself, “I wonder if that’s the right phase? Ah, screw it, whatever.” I doubt it. It’s more likely a lack of recognition that the phases of the Moon follow a predictable, understandable pattern. That is, most people don’t even realize you can ask a question like, “when does the waning crescent Moon rise?”
Or worse yet, there’s a distinct possibility that people (yes, now I’m talking about more than this one, particular artist — the problem is widespread) are completely unaware of the Moon, other than the fact that we have one. Why, just recently a colleague said to me, “I have no idea about phases. I never look at the Moon.”
Which brings me back to the six-legged spider. If you bought a book for your kid with a six-legged spider, you’d see the error. Would you draw in a two more legs? I would. Even your kid would see the error and tell you the book is rubbish. Why the difference between spiders and the Moon, then?
“Because spiders are something everyone sees every day.” Uh-huh, like the Moon.
“Because spiders are icky and gross and awesome. And the Moon is, like, science-y. Boooorrrring…” Damn.
What do I think we should do about it? I’d like people to learn some astronomy, sure. More than that, though. I want people to think scientifically. I want to live in a world where people have the awareness (and freedom) to stop and ask, “Really? Are you sure about that?”
That’s a tall order so let’s get on it. We can start by modeling scientific awareness for our kids, students, friends. Show them it’s okay to be passionate about math. Show them it’s okay to step off the sidewalk onto the grass to look at a bug or an interesting stone. Read them stories that engage their brains. Don’t buy books, wrapping paper or calendars with incorrect science. And if you accidentally do, don’t laugh it off with a “whatever…” It only takes one or two of those for kids to learn the science is dumb and only grinches point out mistakes. Instead, take the opportunity to talk with them about how we should always be curious about how things work.
A society of scientifically-literate people? That’s a world I’d like retire in.
My boss, Carl Wieman, likes to describe what we do as “looking for the pattern of how people learn science” (as he does in this video.) And the places to look are classroom studies, brain research and cognitive psychology. I certainly agree with the first place – that’s teachers and teaching. And research like this, that and this other thing about how the brain physically changes while you learn in very cool – that’s science. But cognitive psychology? I’ve been a science geek since, well, since before I can remember anything else, so I really haven’t been exposed to psychology and those other disciplines they teach on the “Arts” side of campus.
Carl says it’s important, though, and I trust him, so my colleagues and I read a cognitive psychology paper for our CWSEI Reading Group “What College Teachers Should Know About Memory: A Perspective From Cognitive Psychology” by Michelle D. Miller (College Teaching, 59, 3, 117, (2011)). Here’s a link, if you have access from where you’re clicking.
The paper is a nice summary of the models of memory. Short term, long term, working memory, ecological (or adaptive) memory. Here’s my interpretation. Every bit of information that’s stored in memory is accompanied by “cues”. Think “tags”, like the ones that accompany this blog post. When you see the cues, you recall the memory, just like finding blog posts by clicking on a tag. Without the tags, finding posts means paging through the archive. With a tag, you can zero in on the post. And the more tags on the post, the easier it is to find. Same with memories: the more cues linked the memory, the easier it will be to recall later.
Not all cues are created equal, though. As Miller puts it,
[u]nderstanding the role and importance of cues enables a richer and more accurate understanding of why people remember — and forget — what they do. (p.119)
Miller carefully crafted descriptions of the kinds of cues that trigger recall, so while I’m cutting them into a list and adding some bold, these are Miller’s words (p. 120):
Here are what I believe to be the cues that trigger us to “tag” information as being survival-relevant:
sensory impact, termed vividness: Concrete information that comes accompanied by sound, visual qualities, even tactile sensation tends to be more memorable than abstract information. Visual information is particularly salient to human beings, so that anything that can be visualized tends to be particularly memorable.
emotional impact is another cue that incoming information warrants long-term storage. Consider situations that relate to survival in a “natural” setting—a sudden danger, a new food source, encountering an enemy—and all would come accompanied with an emotional “charge.”
relevance to one’s own personal history is another indication that information will be useful in the future
structure and meaning—the ability to interpret information and put it into context—helps us distinguish useless background clutter from information that we need to keep
personal participation, as contrasted with passive exposure. This will come as no surprise to those familiar with the “active learning” trend. If we watch someone else do something, that activity may or may not be relevant to us, and it we will likely opt not to form a detailed memory of it. However, if we ourselves carry out the action, there is a greater likelihood that we will need to learn from and recall that experience later. We may also encode a richer set of cues when we are actively involved, which increases the likelihood of retrieving the information later.
Don’t you love it when you read an article that concisely and explicitly describes all those things you feel, in your gut, are important? It’s times like this that make me re-evaluate my naive and, frankly, prejudiced view of psychology, “C’mon, how can you possibly know how humans work?” “Oh, like that, ” he says, sheepishly. “Um, thanks. That’s cool!”
The week my colleagues and I read this paper, I was preparing the next activity for an introductory, general-education astronomy course I work on. This activity, like the others I’ve written and am sharing through the Astro Labs page on this blog, is a chance for “Astro 101” students to get some hands-on interaction with astronomy. Up next was the activity on black holes, especially spaghettification.
“Spaghettification”?
Talk about a made-up word, huh. Not by me, mind you. Chat with any astronomy instructor and you’ll find we all know exactly what it means because it’s the perfect word to describe what happens if you fall into a black hole.
<astronomy lesson>
A black hole with the mass of the Earth would only be about the size of a grape. Imagine it this way: if you could pack together and compress the entire Earth down to the size of a grape, the force of gravity would be so strong curvature of spacetime would be so high that not even light, traveling outwards as the speed of light, could escape.
That describes trying to get out a black hole. What about falling in? Let’s imagine you’re 2 metres tall and your lying on your back with your feet 2 metres from the black hole and your head 4 metres from the black hole. You can see it down there, between your feet, a little shiny grape a couple of metres away. It’s okay to think classically here, for a moment. Gravity is very strong but, being an inverse square law, it drops off quickly: your head is 2 times farther from the black hole than your feet so the force of gravity is only 1/4 as strong. What do you suppose happens when the black hole pulls 4 times harder on your feet? They get ripped off, that’s what. Your body gets stretched out as your feet accelerate towards the black hole, leaving your knees, hands, chest and head behind. This difference-in-forces is called a tidal force because these same kinds of forces occur in the Earth-Moon system where the Moon yanks on the water on Earth’s near-side and leaves the far-side water behind, giving us the tides. Newton worked that one out for us, more than 300 years ago.
The force of gravity between the Moon and the water on the near-side of the Earth is stronger than the force between the Moon and the more distance, far-side water. Earth's watery skin is deformed, giving us the tides. (Graphic: Peter Newbury CC)
Meanwhile, back at the black hole, the hapless astronaut is being pulled down a little funnel that ends up on the grape-sized black hole. Happy astronaut one second, long and skinny piece of spaghetti the next. Spaghettification, baby!
</astronomy lesson>
Ouch, that’s gotta hurt! LOL. Yeah. But how do we get Astro 101 students to remember it a month from now on their exam? Play-Doh, that’s how. Our activity progresses from setting up the phenomenon of tidal forces, to sample calculations demonstrating tidal forces are real, to recreating the spaghettification of a Play-Doh astronaut.
An astronaut falling into a black hole, before spaghettification......and after!
Here’s where the part about memory comes in. Students are potentially reluctant to play with Play-Doh. This is University. We’re not Children anymore. Teaching assistants and instructors are equally reluctant to ask students to play with Play-Doh. “Why,” they wonder, “should I?”
Because, I tell the teaching assistants who, if necessary, relay it to the students, it will help you remember. Playing with Play-Doh, stretching the poor astronaut’s legs, often pulling them right off his body, and squishing the Play-Doh into to a narrow strip, is tactile. And emotional – you just ripped his head off, dude! It gives relevance and a physical structure to those calculations. And it takes personal participation – oops, I just pulled his leg off!
Good in theory but how about in practice? The activity ran. The teaching assistants sold it. The students did it. All of them! Now we just have to see if they (1) learned anything and (2) can remember it. For (1), one of the questions they answer at the end of the activity is, “In your own words, describe what happens to the astronaut. Why do you think it’s called ‘spaghettification’?” Here’s one student’s answer, typical of many I thumbed through:
as the astronaut falls toward the black hole, feet first, its body stretches as it nears the black hole. the closer body parts (feet, then hands) stretch faster and fall faster than the head and body. It’s called spaghettification because the legs and hands stretch elongate like spaghetti.
Yep, I’ll take that. Would have been nice to see the word “tidal” in there but he did make the connection between closer and faster. For (2), we’ll be sure to put something on the final exam that tests this material. I’ll let you know in 4 weeks.
As my pop likes to say, “learn by doing.” Let’s update that to, “remember by doing.”
As I’ve mentioned before, the folks at i>clicker lent me a set of the new i>clicker2 clickers. I had a chance to try them out this week when I filled in for an “Astro 101” instructor. I sure learned a lot in that 50 minutes!
(image: Peter Newbury)
Just to refresh your memory, the i>clicker2 (or “ic2” as it’s also called, which is great because the “>” in “i>clicker2” is messing up some of my HTML) unit has the usual A, B, C, D, E buttons for submitting answers to multiple-choice questions. These new clickers (and receiver and software) also allow for numeric answers and alphanumeric answers. That last feature is particularly interesting because it allows instructors to ask ranking or chronological questions. In the old days, like last week, you could display 5 objects, scenarios or events and ask the student to rank them. But you have to adapt the answers because you have only 5 choices. Something like this:
Rank these [somethings] I, II, III, IV and V from [one end] to [the other]:
A) I, II, V, III, IV
B) II, I, IV, III, IV
C) IV, III, IV, I, II
D) III, I, II, IV, V
E) V, II, I, III, IV
These are killer questions for the students. What are they supposed to do? Work out the ranking on the side and then check that their ranking is in your list? What if their ranking isn’t there? Or game the question and work through each of the choices you give and say “yes” or “no”? There is so much needed to get the answer right besides understanding the concept.
That’s what’s so great about the ic2 alphanumeric mode. I asked this question about how the objects in our Galaxy appear to be moving relative to us:
The alphanumeric mode of the ic2 allows instructors to easily ask ranking tasks like this one about the rotation of the Galaxy.
(Allow me a brief astronomy lesson. At this point in writing this post, I think it’ll be important later. Oh well, can’t hurt, right?)
The stars in our Galaxy orbit around the center. The Galaxy isn’t solid, though. Each star moves along its own path, at its own speed. At this point in the term [psst! we’re setting this up so the students will appreciate what the observed, flat rotation curve means: dark matter] there is a clear pattern: the farther the star is from the center of the Galaxy, the slower its orbital speed. That means stars closer to the center than us are moving faster and will “pass us on the inside lane.” When we observe them, they’re moving away from us. Similarly, we’re moving faster than objects farther from the center than we are, so we’re catching up to the ones ahead of us. Before we pass them, we observe them getting closer to us. That means the answer to my ranking question is EDCAB. Notice that location C is the same distance from the center of the Galaxy as us so it’s moving at the same speed as us. Therefore, we’re not moving towards or away from C — it’s the location where we cross from approaching (blueshifted) to receeding (redshifted).
As usual, I displayed the question, gave the students time to think, and then opened the poll. Students submit a 5-character word like “ABCDE”. The ic2 receiver cycles through the top 3 answers so the instructor can see what the students are thinking without revealing the results to the students.
I saw that there was one popular answer with a couple of other, so I decided enough students got the question right that -pair-share wouldn’t be necessary and displayed the results:
Students' answers for the galaxy rotation ranking task. The first bar, EDCAB, is correct. But what do the others tell you about the students' grasp of the concept?
In hindsight, I think I jumped the gun on that because, and here’s what I’ve been trying to get to in this post, I was unprepared to analyze the results of the poll. I did think far enough ahead to write down the correct answer, EDCAB, in big letters on my lesson plan. But what do the other answers tell us the students’ grasp of the concept?
In a good, multiple-choice question, you know why each correct choice is correct (yes, there can be more one correct choice) and why each incorrect choice is incorrect. When a student selects an incorrect choice, you can diagnose which part of the concept they’ve missed. The agile instructor can get students to -pair-share to reveal, and hopefully correct, their misunderstanding.
I’m sure that agility is possible with ranking tasks. But I hadn’t anticipated it. So I did the best I could on the fly and said something like,
Good, many of you recognized that the objects farther from the center are moving slower, so we’re moving toward them. And away from the stars closer to the center than us.
[It was at this moment I realized I had no idea what the other answers meant!]
Uh, I notice almost everyone put location C at the middle of the list – good. It’s at the same distance and same speed as us, so we’re not moving away from or towards C.
Oh, and ABCDE? You must have ranked them in the opposite order, not the way I clumsily suggested in the question. [Which, you might notice, is not true. Oops.]
[And the other 15% who entered something else? Sorry, folks…]
Uh, okay then, let’s move on…
What am I getting at here? First, these ranking tasks are awesome. Every answer is valid. None of that “I hope my answer is on the list…” And there’s no short-circuiting the answer by giving the students 5 choices, risking them gaming the answer by working backwards. I know there are lots of Astro 101 instructors already using ranking tasks, probably because of the great collection of tasks available at the University of Nebraska-Lincoln, but using them in class typically means distributing worksheets, possibly collecting them, perhaps asking one of those “old-fashioned” ranking task clicker questions. All that hassle is gone with ic2.
But it’s going to take re-training on the part of the instructor to be prepared for the results. In principle, there are 5! = 120 different 5-character words the students can enter. Now, of course, you don’t have anticipate what each of the 119 incorrect answers mean. But here are my recommendations:
Work out the ranking order ahead of time and write it down, in big letters, where you can see it. It might be easy to remember, “the right answer to this question is choice B” but it’s not easy to remember, “the correct ranking is EDCAB.”
Work out the ranking if the students rank in the opposite order. That could be because they misread the question or the question wasn’t clear. Or it could diagnose their misunderstanding. For example, if I’d asked them to rank the locations from “most-redshifted” to “most-blueshifted”, the opposite order could mean they’re mixing up red- and blue-shift.
Think about the common mistakes students make on this question and work out the rankings. And write those down, along with the corresponding mistakes.
Nothing like hindsight: set up the question so the answer isn’t just 1 swap away from ABCDE. If you had no idea what the answer was, wouldn’t you enter ABCDE?
I hope to try, and write about, some other types of questions with my collection of ic2 clickers. I’ve already tried a demo where students enter their predictions using the numeric mode. But that’s the subject for another post…
Do you use ranking tasks in your class, with ic2 or paper or something else, again? What advice can you offer that will help the instructor be more prepared and agile?
