Problem solving like a physicist

In my role in the Carl Wieman Science Education Initiative at the University of British Columbia, I am often “embedded” in an instructor’s course, providing resources, assistance and coaching throughout the term. This term, I’m working with an instructor in a final-year, undergraduate electromagnetism (E&M) course.

The instructor has already done the hard part: he recognized that students were not learning from his traditional lectures and committed to transforming his classes from instructor-centered to student-centered.  Earlier, I wrote about how we introduced  pre-reading assignment and in-class reading quizzes.

This course is heavy on the math. Not new math techniques but instead, math the students have learned in the previous 3 or 4 years applied to new situations. His vision, which he shared with the students on the first day, was to introduce some key concepts and then let them “do the heavy lifting.” And by heavy lifting, he means the algebra.

The vector for this heavy lifting is daily, in-class worksheets. The students work collaboratively on a sequence of questions, typically for 15-20 minutes, bookended by  mini-lectures that summarize the results and introduce the next concept.

We’re making great strides, really. After some prompting by me, the instructor is getting quite good at “conducting” the class. There are no longer moments when the students look at each other thinking, “Uh, what are supposed to be doing right now? This worksheet?” It’s fine to be puzzled by the physics, that’s kind of the point, but we don’t want students wasting any of their precious cognitive load on divining what they should be doing.

With this choreography running smoothy and the students participating, we’re now able to look carefully at the content of the worksheets. Yes, I know, that’s something you should be planning from Day 1 but let’s face it, if the students don’t know when or how to do a worksheet, the best content in the World won’t help them learn. Last week’s worksheet showed we’ve got some work to do.

(Confused guy from the interwebz. I added the E&M canaries.)

The instructor handed out the worksheet. Students huddled in pairs for a minute or two and them slumped back into their seats. You know those cartoons where someone gets smacked on the head and you see a ring of stars or canaries flying over them? You could almost see them, except the canaries were the library of equations the students are carrying in their heads. They’d grasp at a formula floating by, jam it onto the page, massage it for a minute or two, praying something would happen if they pushed the symbols in the right directions. Is it working? What if I write it like….solve for….Damn. Grab another formula out of the air and try again…

After 10 minutes, some students had answered the problem. Many others were still grasping at canaries. The instructor presented his solution on the document camera so he could “summarize the results and introduce the next concept.” The very first symbols at the top-left of his solution were exactly the correct relationship needed to solve this problem, magically plucked from his vast experience. With that relationship, and a clear picture of where the solution lay, he got there in a few lines. The problem was trivial. No surprise, the students didn’t react with “Oh, so that’s why physics concept A is related to physics concept B! I always wondered about that!” Instead, they responded with, “Oh, so that’s how you do it,” and snapped some pix of the screen with their phones.

Scaffolding and Spoon-feeding

We want the worksheets to push the students a bit. A sequence of questions and problems in their grasp or just beyond, that guide them to the important result or concept of the day. Here’s what doesn’t work: A piece of paper with a nasty problem at the top and a big, blank space beneath. I’ve seen it, often enough. Students scan the question. The best students dig in. The good and not-so-good students scratch their heads. And then bang their heads until they’re seeing canaries.

There are (at least) 2 ways to solve the problem of students not knowing how to tackle the problem.  One is to scaffold the problem, presenting a sequence of steps which activate, one by one, the concepts and skills needed to solve the nasty problem. The Lecture Tutorials used in many gen-ed “Astro 101” astronomy classes, and the Washington Tutorials upon which they’re modeled, do a masterful job of this scaffolding.

Another way, which looks the same on the surface, is to break the nasty problem into a sequence of steps. “First, find the relationship between A and B. Then, calculate B for the given value of A. Next, substitute A and B into C and solve for C in terms of A…” That’s a sequence of smaller problems that will lead to a solution of the nasty problem. But it’s not scaffolding: it’s spoon-feeding and it teaches none of the problem-solving skills we want the students to practice.  I’ve heard from number of upper-level instructors declare they don’t want to baby the students. “By this stage in their undergraduate studies,” the instructors say, “physics students needs to know how to tackle a problem from scratch.”

This is the dilemma I’m facing. How do we scaffold without spoon-feeding? How do we get them solving nasty problems like a physicist without laying a nice, thick trail of bread crumbs?

Fortunately, I have smart colleagues. Colleagues who immediately understood my problem and knew a solution: Don’t scaffold the nasty problem, scaffold the problem-solving strategy. For a start, they say, get the instructor to model how an expert physicist might solve a problem. Instead of slapping down an elegant solution on the document cam, suppose the instructor answers like this:

  1. Determine what the problem is asking. Alright, let’s see. What is this problem about? There’s A and B and their relationship to C. We’re asked to determine D in a particular situation.
  2. Identify relevant physics.  A, B, C and D? That sounds like a problem about concept X.
  3. Build a physics model. Identify relevant mathematical relationships. Recognize assumptions, specific cases. Select the mathematical formula that will begin to solve the problem.
  4. Execute the math. Carry out the algebra and other manipulations and calculations.
    (This is where the instructor has been starting his presentation of the solutions.)
  5. Sense-makingSure, we ended up with an expression or a number. Does it make sense? How does it compare the known cases when A=0 and B goes to infinity? How does the order of magnitude of the answer compare to other scenarios? In other words, a few quick tests which will tell us our solution is incorrect.

Wouldn’t it be great if every student followed a sequence of expert-like steps to solve every problem? Let’s teach them the strategy, then, by posing each nasty problem as a sequence of 5 steps. “Yeah,” my colleagues say, “that didn’t work. The students jumped to step 4, push some symbols around and when a miracle occurred, they went back and filled in steps 1, 2, 3 and 5.” Students didn’t buy into the 5-step problem-solving scheme when it was forced upon them.

So instead, for now, I’m going to ask the instructor to model this approach, or his own expert problem-solving strategy, when he presents his solutions to the worksheet problems. When the students see him stop and think and ponder, they should realize this is an important part of problem-solving. The first thing you do isn’t scribbling down some symbols. It’s sitting back and thinking. Maybe even debating with your peers. Perhaps you have some insight you can teach to your friend. Peer instruct, that is.

 

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One Earth, one sky: the power of Twitter

This post was inspired by the beauty of the night sky and the interactions that followed down here on Earth.

A couple of nights ago, Venus, the Evening Star, hung a few degrees below a spectacular, 3-day old crescent Moon. I hesitate to paste in a photo here because it just won’t capture the breath-taking, awe-inspiring beauty of the evening sky. Like I often do when there’s a break in the clouds — something we Vancouverites try to take advantage of — I tweeted an alert to my followers

Down on Earth, people started retweeting my alert, forwarding it to their twitter communities. And people did look up, in Vancouver, Vancouver Island, Edmonton, and Winnipeg, sharing their experience with me and others through twitter @replies and mentions. Like a good tweep, I tweeted one last invitation to keep the conversation going (my apologies for missing a few RTs: that darn “Twitter doesn’t always show your RTs” bug)

Mission accomplished, I thought to myself.

It took someone outside my circle of astronomy friends to point out what had happened. (Thank-you, Marie-Claire @mcshanahan!) She wrote back

She made me remember what Twitter has done for “backyard astronomy,” a hobby so rewarding it can pull you off the couch and into your backyard and neighbourhood park just for a chance to glimpse something you’ve seen a hundred times before. In sharing our experience on Twitter, we connect with others around the World doing the same thing. I knew that at that moment, @LuckyStrz was standing outside in Winnipeg with one, freezing, un-gloved hand tapping away on her phone. I tried to sum up that feeling with

Her reply was one of the nicest and most-rewarding I’ve received:

This is the magic that Twitter has brought to astronomy. People around the World simultaneously look up at the night sky and share their experiences. Timezones, borders, politics, age, race, gender — none of that matters. We’re one Earth, one sky.

That’s a powerful phrase. Certainly not one I coined. It might have been @ThilinaH and @ObervetheMoon. Or @unawe. Maybe it was @VirtualAstro with his amazing, viral #meteorwatch. I’m not sure. But I am sure that if you’re on Twitter and start following these folks and the backyard astronomers in your community (in Canada, follow @rasc; in the US, check out the Night Sky Network) you, too, can experience breath-taking, astronomical events and heart-warming, global connections. And standing outside in your slippers or Sorels in the dead of winter, you need all the warming you can get!

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The astronomy of Chinese New Year

Chinese New Year occurs on January 23 this year. The fact that we even have to announce the date reveals that it changes each year. That’s because the date for Chinese or Lunar New Year depends on how the annual cycle of the Earth orbiting the Sun interlocks with the roughly monthly cycle of the Moon orbiting the Earth. The event that lights the fuse on the celebrations is the December solstice.

There are some parts of the Northern hemisphere where it doesn’t get very cold in the winter, like Vancouver where I live. But talk to anyone living just about anywhere else, and they’ll tell you through chattering teeth, that December 21 is the middle of freakin’ winter, not its beginning, as our Western calendars proclaim.

On Western calendars, winter begins in the Northern hemisphere on the December 21 solstice, not when it starts to get cold out.

In other words, those freezing cold days on the Prairies in November? Fall, not winter. Changing the name doesn’t make them any warmer.

The ancient Chinese astronomers and calendar-makers knew their hot from cold, though, and recognized the December solstice is the middle winter, just like March is the middle of spring, June is the middle of summer and September is the middle of fall:

In Chinese tradition, the December solstice occurs in the middle of winter.

Chinese New Year marks the end of winter and the beginning of spring, the transition from dreary blue to vibrant green in the diagram above. Now the Lunar Cycle comes into play. Each season — winter, spring, summer and fall — is roughly 3 months long so there’s about a month and a half from the solstice to the New Year.

Or a lunar cycle and a half.

Here’s how it works: take note of the Moon’s phase on December 21 and let the lunar cycle play out. Last year, for example, there was a new Moon on December 24, 2011, a few days after the solstice. So began the last lunar cycle of the year which finishes on Monday, January 23, 2012, Chinese New Year.

Depending on the Moon’s phase at solstice, the date for Chinese New Year can vary by about a month. This year, we’re pretty close to the earliest possible date. For next year, though, there are new Moon’s on December 11, 2012, on January 11, 2013 (the end of the middle, winter solstice cycle) so that Chinese New Year won’t be until February 10, 2013.

If all this dependence on the phases of the Moon seems a little archaic and superstitious, let me ask you a question: When are Canada Day and Independence Day?

No brainers: July 1 and July 4.

What about Halloween? October 31. D’uh!

Okay, smarty-pants, when’s Easter this year?

Er, um, just a sec while I… [google google google] … Sunday, April 8, 2012.

You see, the phase of the Moon also plays a part in determining the date for Easter, which is defined as the first Sunday after the first full Moon after spring equinox. This year, the Moon is pretty close to new at the equinox and there won’t be a full Moon until Friday, April 6.  Easter occurs that Sunday, April 8. The fact that the most important date in the Christian calendar depends on the phase of the Moon, and that preparing for Easter depends on predicting those phases far in advance, are reasons why the Vatican has had an observatory for more than 250 years.

There is long and prestigious history and tradition of Chinese astronomy and time-keeping. I’ve only scratched the surface here, and my sincerest apologies if I’ve misrepresented that tradition through my over-simplification or just plain got-it-wrong-edness. In any case, be sure to take a moment next Monday to wish your friends a hearty Gung Hei Fat Choi!

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Motivation for pre-reading assignments

Image: chain by pratani on flicker (CC)

For the next 4 months, I’ll be working with an instructor in an 4th-year electromagnetism course. If you’ve taught or taken a course like this, let me just say, “Griffiths”. If you haven’t, this is the capstone course in E&M. It’s the big, final synthesis of all the electricity and magnetism and math and math and math the students have been accumulating for the previous 3-1/2 years. This is where it all comes together and the wonders of physics are, at last, revealed. It’s the course all the previous instructors have been talking about when they say, “Just learn it. Trust me, it will be really important in your future courses…” That’s the promise, anyway.

The instructor came to us (“us” being the Carl Wieman Science Education Initiative) because he wasn’t happy with the lecture-style he’s been using. Students are not engaging, if they even bother to come to class. He’s trying to use peer instruction with clickers but it’s not very successful. He wants to engage the students by giving them worksheets in class but he’s not sure how.

So much enthusiasm! So much potential! Yes, let’s totally transform this course, flipping it from instructor- to student-centered! Yes, and I purposely using the word “flipping” with all its baggage!

Hold on there, Buckaroo! One thing at a time. Changing everything at once rarely works. It takes time for the instructor to make the changes and learn how to incorporate each one into his or her teaching.

So, we’re tackling just a few things this term. The first is to create learning goals (or objectives) so we can figure out how to target our effort. In talking with the instructor, I learned there are very few new, mathematical techniques introduced in the course. Instead, the course is about selecting the right sequence of mathematical tools to distill fundamental physics out of the math describing E&M. That led us to this draft of one of the course-level, big-picture goals:

While you are expected to remember basic relationships from physics like F=dp/dt and λ=c/ν, you do not have to memorize complicated formulas we derive in class because a list of formulas will be given. Instead, you will be able to select the applicable formula from the list and know how to apply it to the task you’re working on.

The biggest change we’re making is the introducing effective pre-reading assignments. Oh sure, the instructor always said things like “Pre-reading for Lecture 1: Sections 12.1.1 – 12.1.3” but that’s not doing the trick. More and more of my colleagues are having success with detailed, targeted reading assignments. Rather than the “read the whole thing and learn it all” approach, we’re going to help the students learn (ha! Imagine that!):

Reading assignment (prior to L1 on Thu, Jan 10)
==================

Read Section 12.1.1. Be sure you can define an "inertial reference frame"
and state the 2 postulates of special relativity.

Review Section 12.1.2 (these concepts were covered in previous courses)
especially the Lorentz contraction (iii) and write out the missing steps
of algebra at the top of p. 490 that let Griffiths "conclude" Eqn (12.9).
Be sure you can explain why dimensions perpendicular to the velocity are
not contracted.

Read Section 12.1.3. Look carefully at Figure 12.16 so you're familiar
with the notation for inertial frames at rest (S) and inertial frames in
motion ( S with an overbar )

Now comes the hard part: getting the students to actually do it. It’ll take effort on their part so they should be rewarded for that effort. A reading quiz, probably in-class using clickers, worth marks could be that reward. (An online quiz we can use for just-in-time teaching might be even better but one thing at a time.) A straightforward quiz-for-marks promotes sharing answers (that is, cheating) and clicking for students not there (that is, cheating). I don’t want them to participate for that sole reason that they’ll be punished for not participating. I’d rather use a carrot than of a stick.

How do we present the pre-reading assignment as something the students WANT to do? Here’s a chain of reasoning, developed through conversations with my more-experienced colleagues. It’s addressed to the students, so “you” means “you, the student sitting there in class today. Yes, you.”

link 1: Efficient. You have a very busy schedule full of challenging courses. You want to use your E&M time efficiently.

link 2: Effective. We want the time you have allocated to E&M to be effective, a good return on your investment.

link 3: Learning. We recognize that many of the concepts will be learned when you do the homework. But rather than using class time to simply gather information for future learning, what if you could actually learn in class? Then you’d better follow along in class and you’d already be (partially, at least) prepared to tackle the homework.

link 4: Engagement. We’re going to create opportunities for you to learn in class through engaging, student-centered instructional strategies. But you need to be prepared to participate in those activities.

link 5: Preparation. To try to ensure everyone has neighbours prepared to collaborate and peer-instruct, we’re asking you to complete the pre-reading assignment. It will also save us from wasting valuable class time reviewing material that some (most?) of you already know.

link 6: Reward. This takes some effort so we’re going to reward that effort. If you do the readings as we suggest, the reading quiz questions we ask will be simple, a 5-mark gimme towards your final grade. Oh sure, you’ll be allowed to miss X of the quizzes and still get the 5%. Those marks are for getting into the habit of preparing for class, not a penalty for being sick or not being able to come class. The quizzes are also continuous feedback for you: if you’re not getting 80% or more on the reading quizzes, you’re not properly preparing for class. Which means you’re not link 5, 4, 3, 2, 1.

The big message should be, your effort in the pre-reading assignments will help you succeed in this course, not just with a higher grade but with better grasp of the concepts and fewer all-nighters struggling with homework.

Is it all just a house of cards? I don’t think so. And I’ll find out in the next few weeks.

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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.

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