Tag: teaching

Six-legged spiders

Here’s a quiz for you: what’s wrong with these pictures?

Black widow spider
Black widow spider
Advent calendar
Pyramids 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.

And you’d be right.

The November 25, 2011 edition of the Guardian carried the story, “Your moons are rubbish, astronomer tells Christmas card artists.” The offending advent calendar shows the Moon in the waning crescent 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:

  1. “Oh, puh-lease! It’s just a picture on a calendar! Gimme break, you grinch!”
  2. “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.)
  3. “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 brief encounter with iclicker2 ranking tasks

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:

  1. 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.”
  2. 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.
  3. Think about the common mistakes students make on this question and work out the rankings. And write those down, along with the corresponding mistakes.
  4. 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?

Thanks, Mr. Barsby

Today, October 5, is World Teachers’ Day 2011. My twitter stream is full of people sharing stories about their most memorable teachers. I can’t even finish reading the first sentence of any of these stories without thinking of my teacher, John Barsby. I don’t know if I ever properly thanked him for what he did for me. One blog post is far from enough but it’s a start.

Mr. Barsby, or JTB as we called him amongst ourselves, was my high school math teacher. I went to St. John’s Ravenscourt, a private school in Winnipeg, MB. (Thanks, Dad, by the way, for sending me there instead of River Heights and Kelvin.) There were about 80 kids in my Grade 8, enough for 3 classes. For math, they divided the kids into 2 “regular” classes with excellent teachers, I’m sure, and 1 “advanced” class for the kids who held promise in math. Or something. That was Mr. Barsby’s class. And I was in it.

This happened each year so I was lucky enough to have JTB every year, from Grade 8 until Grade 12. When I think back to high school, this class was my cohort, the group of close friends and familiar friends with whom I got through high school.

I don’t have time to describe all the things that happened in that classroom. One, I’ve got a meeting in 45 minutes and 2) high school was a long time ago and I’m turning into an old fogey, according to my daughter. But two things not just float to the surface of my memory, but jump from my memory whenever I think about JTB.

Ants by ceoln on flickr

He taught us about positive and negative numbers using red ants for positive, say, and black ants for negative. Whenever they meet, they eat each other. Red ants plus red ants means lots of red ants. Black and black: lots of black. But put red and black together and the total number of ants goes down. And what is good for red ants? Taking away some black ants: that double-negative is a good thing.

To this day, when I see one of my kid’s addition and subtraction exercises, in my mind I see what it looks like when you kick over an ant hill. Ants, red ones and black ones, scurrying about, adding and subtracting, until all the reds or blacks are gone and we’re left with just the sum.

That was how he taught us math, from positive and negative numbers right through to the 1st year University of Manitoba calculus course he somehow managed to teach us at our school. He used analogies and everyday experiences so we didn’t get bogged down in the mechanics of math. He taught us concepts.

[At this moment, I have to take a break cuz I’m gettin’ all teary-eyed. Happy tears, but still… Damn.]

Here’s what else I remember and it’s what I’m most thankful for. Even then, way back in Grade 8, I asked a lot of questions. Not stupid questions (“Mr. Baaaaarby, did you forget to square the 3 in the top line…?”) Well, maybe as many of those as the next kid, but the ones I remember were different. From what I know now, I was asking questions that made me more expert-like. Sense-making questions, which in math are often “push it to the limits and see if it still makes sense.” Like, when N gets really large, does the perimeter of an N-gon turn into the circumference of a circle? It does? Oh, cool.

I clearly remember some not-so-great moments when I’d toss out another of these. My classmates would groan, “Oh great, another question from Peter…” I could have stopped asking. I almost did. But I distinctly remember talking to my dad about not knowing what to do, and how he told me to tell my classmates, “to go suck eggs!” and keep asking questions. And I never, NEVER remember Mr. Barsbsy groaning or giving me the slightest hint of annoyance. In my head, I don’t remember any of his answers to questions but I still feel the comfort, the warmth (help me out here, I’m a science nerd with very little practice writing about feelings…) with which he welcomed and addressed my curiosity.  It’s the same feeling I’ve always had with my Dad (thanks again, Pop!).

I still ask questions. A lot of them. One of my role models is Simplicio from Galileo’s Two New Sciences. Simplicio asks a lot of questions of the wise and learned Salviati. Good questions. I like to think it’s almost like he knows what’s coming and asks just the right question at just the right time to help Salviati explain his discoveries. There’s a great line where Salviati says something akin to, “Ah, yes, excellent.  Let me just draw a diagram here in the dirt…” (I’ll update when I find it. Help me out?)

You see, I’m no longer afraid to ask those questions, the ones I suspect (or know) that other people have but are embarrassed to ask, or the ones I know (or suspect) will help the expert spit out a concept in a way the audience will get it. I’m quite happy to play the naive fool and put up with the occasional, “Oh no, here he goes again…” But I pick my questions carefully and thoughtfully. Just the right question at just the right time.

For the ability to ask think up those questions and the guts to ask them, thanks, JTB. You, too, Pop.

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