Classroom Stories

Classroom Stories: Light as a Wave

By Stacy Palen

Typically, I lecture about light as a wave by showing students images of waves and describing wavelength, frequency, and velocity. Then I tell them that wavelength and color go together; that light of a particular color has a particular wavelength.

However, when we would get to the Light and Spectra activity, it was clear that they had not fully internalized this information. Given that I’m not lecturing at all this semester, I invented a short activity (which can be accessed by clicking here) that unpacks this relationship a bit.

The activity uses an LED light tower that I happen to have. You can find this specific one here, but the activity could be adapted for use with spectral tubes or images from the internet.

I cannot darken the room this semester, so being able to adapt this activity made it indispensable. I also could not use the spectral tubes for my students because they simply weren’t bright enough to see. I wound up using the online images from the light and spectra lab. Without this activity students would not have been able to use their spectrum glasses in the classroom at all!

Oh, and in case you were wondering, no, it doesn’t work to try to project the spectrum tubes using the document camera.

Despite the difficulties in using the online images, student performance on the light and spectra activity was better than in the past. They also seem to have acquired a clear understanding that color and wavelength are related.

You can check out the activity yourself by clicking here!

 

 


Classroom Stories: More Ruminations on a Theme: Fermi Warm-Ups

By Stacy Palen & John Armstrong

This week, we have a guest post from a colleague at Weber State University. John Armstrong is also teaching in the inadequate classroom. He is experimenting with a way to fill the time while he figures out what’s changed about the A/V situation since the last class two days ago… 

Thanks to some intermittent multimedia issues in my new “temporary” classroom, I’m forced to get creative with the first ten minutes of class every day. So, I start by giving a Fermi problem to my students. I ask the question and they can work on the answer while I jiggle cables and try turning things off and on again.

Physicist Enrico Fermi was famous for posing seemingly unsolvable questions that he would then proceed to solve with a few back-of-the-envelope calculations. The most famous of these—how many piano tuners are there in the city of Chicago—requires some educated guesses about population, the popularity of pianos, and the diligence of their owners, but you get surprisingly close to the “correct” answer without knowing much of anything.

In astronomy, this tool has been leveraged in the Drake Equation to estimate the number of civilizations in our galaxy, proving that even when you can’t know some of the parameters you need to measure, you at least have a framework for study. The first three terms of this equation—the number of new stars formed in the galaxy, the number of these stars that form planets, and the number of Earth-like planets in each system—were largely unknown when I started my studies in the mid-nineties. They now have pretty good estimates. We are now on the verge of an estimate of how many planets can evolve life, which is something that could happen in the next decade or so.

But when I reached this point in my class, going from a simple Fermi problem to the Drake Equation seemed like a heavy lift.

I’ve always started the semester with a formal activity on estimating the number of pebbles in a jar. We measure the volume of the jar, remove a few pebbles and systematically measure their volumes, and then divide the two. The amount of agreement between the groups is surprising.

But thanks to my A/V woes, I’ve started asking a question every day. How much does the mass of humans increase each year? How far does a bumblebee travel in a day? How much food energy do you consume in a year? And each day, more and more students seem to dive in. Better yet, some of them have come in after doing some of their own estimations. How many bricks are in their house? How much electricity do they consume every year? 

The answer to the last question turns out to be surprising: It’s about ten times the amount of energy that you eat in food.

While I’ve always seen the value in Fermi problems, their routine application is giving my students extra practice and increasing their numeracy. And they also seem to be sparking my students' interest in their own questions.

I can’t wait to get to the Drake Equation!

—John Armstrong


Classroom Stories: Another Way to Do the Phases of the Moon

By Stacy Palen

The phases of the Moon are one of those topics that has been extensively studied by the astronomy education research community and is well-known to be more complex than most people think. There’s the change of perspective from Earth-view to space-view. There are multiple motions at once (the rotation of Earth and the Moon, and the revolution of the Moon around Earth). There’s the issue about light rays always traveling in straight lines and not bending. It’s complicated.

Last week, I pulled an old phases-of-the-Moon activity out of the archives, which can be accessed by clicking here, for my students to complete in addition to the activity, “Studying the Phases of the Moon” from the Learning Astronomy by Doing Astronomy workbook. This is not an appropriate activity for Learning Astronomy by Doing Astronomy because it requires students to have Styrofoam balls that have been colored black on one half. (I can’t make the classroom dark, so I can’t use the traditional “balls-on-sticks” approach.) But one thing that I like very much about this activity is that it leads them to figure out how to (approximately) tell time by the Moon, which means that I can ask them a question about it on my zombie-apocalypse midterm—insert evil laugh here!

The activity also asks them to consider the phases of other objects, such as the phases of Earth as seen from the Moon, or the phases of Deimos as seen from Mars or Phobos. Carrying the concept of phases away from Earth seems to help cement the idea that this is a phenomenon that is all about the relative location of the light source and the observer.

I followed this activity the next week with the “Studying the Phases of the Moon” activity from the workbook. I was interested to notice that students finished the activity in record time and were much better prepared for it. The two activities worked well together to really build their picture of how the phases of the Moon actually occur.


Classroom Stories: Energy and Kepler’s Laws: A Surprise for Me about Where the Difficulty Lies

By Stacy Palen

Recently, my students worked on the “Working with Kepler’s Laws” activity from the Learning Astronomy by Doing Astronomy workbook. In this activity, students learn about ellipses, consider the “simple” version of Kepler’s second law (a planet travels faster when nearer to the Sun and slower when farther away), and run some numbers for Kepler’s third law: P2=a3. To my surprise, Kepler 1 and Kepler 3 brought almost no questions from the students (aside from “Am I doing this right?”). It was Kepler’s Second law that brought the most substantive questions.

Over and over they asked “Yes, but WHY does it go faster when it’s closer?”

I used this question as the basis for a whole new activity.

Approaching this question as an energy problem, I had the students throw a ball straight up in the air and make pie charts representing how much kinetic energy, gravitational potential energy, or thermal energy the ball had at various points in its trajectory. Then they threw the ball to a friend and made similar pie charts (in this case the velocity is never zero, so the kinetic energy is also never zero). Then I had them consider a planet in orbit around the Sun and make a third set of pie charts.

Wow! This was so much harder for them than I expected!

First, it turned out that pie charts are a concept that most (but not all) of my students have in common. Who knew?

Second, we ran into the issue about where to put the “zero” of gravitational potential energy. This information was in the Background section, so it was invisible.

Third, we faced our biggest issue: Convincing students that when they threw the ball straight up into the air, the ball had zero speed at the apex of the trajectory. That alone was a 20-minute conversation!

Finally, even though I told them to describe what happens to the ball between the moment after it left their hand to the moment before they caught it, many students turned all the energy into thermal energy. I’ve edited the activity to try to correct these problems and will use it again in the fall in search of perfection.

Despite these problems, I was very happy about the conversations that I overheard as I moved around the room. Some students were completely unfamiliar with the conservation of energy. They made progress simply by learning how the energy transformations occur for a ball thrown in the air!

Other students rocked that part but were stuck when the questions about orbits showed up; this was often because they drew the Sun at the center of the orbit instead of at a focus. What a great opportunity to correct this problem!

Finally, some students spent a very long time arguing about whether they needed to account for energy lost to thermal energy in our current Solar System.

Overall, I was pleased by what I learned about how they think about energy as well as how well they grappled with this material. And I’ve now set them up to have a spark of recognition when they learn about planet migration later in the semester. This activity is a work in progress, but I will definitely try it again!

You can access the activity by clicking here!


Classroom Stories: Classroom Calculators

By Stacy Palen

Here’s the thing: all students have a calculator in their phone. And for a long time, I've thought, “They should use the calculator in their phone so they know how to use the calculator in their phone!” But here’s the other thing: a lot of those calculators are terrible. They don’t all do the order of operations the same way. They don’t all have the same “buttons” on them. They don’t all use the same notation. Therefore, any time I have students do any math at all in the classroom, I spend most of the time running around and helping them figure out how to put the “times ten to the” into their calculator. iPhone calculators are pretty good, but Samsung calculators don’t have the same functionality. Students must painstakingly type “(3 X 10 ^ 8)” rather than “3EE8.” That may not seem so bad, but if they forget the parentheses, the calculator doesn’t see their input as one number. So, if the problem includes division, the student is stymied. In addition, students' having their phone in their hand is distracting to the point of incompetence.

This semester, I had the idea to invest in a classroom set of calculators. I found a fairly simple solar-powered calculator that I could buy for less than $7, and I begged the chair of my department to use some of our lab fees to buy 60 of them.

When we have an activity involving a math problem, I invite students to borrow one, and I use the document camera to show them exactly how to punch things into the calculator. For Kepler’s Third Law, I show them how to square a number and how to take a cube root. For multiplying powers of 10, I show them how to put in “3 X 108” so the calculator interprets it as a single number (3EE8 or 3EXP8).

So far, this has been revolutionary. I spend far less time helping students with their calculators and far more time helping them think about their answers. Students can now help each other with the calculators, too, and they don’t need to wait for me to come around to them. Generally, this seems to be helping them be more patient.

Even for the many students who have their own favorite calculator, they sometimes don’t know how to use it for our specific purpose—it’s set up for stats, for example. While they have the option to borrow a calculator or use their own, I still spend some time helping these students find the “EE” or “EXP” key for scientific notation, but if they otherwise know how to use the calculator, they seem to remember this new function more easily. Looking back, I estimate that I could have bought only half as many calculators for the 70 students in the room, and even fewer if they work in pairs.

As I go along, I’m compiling a list of calculator instructions that I can print and tape to the cover. I may make a large poster of this information, instead, which might work better once we are back in our usual teaching space.

I have been pleasantly surprised by how much easier it is to manage the classroom when all my students have the same tool. In retrospect, it seems obvious that this method would be easier, but it took me nearly 20 years to think of it…


Classroom Stories: Teaching the Seasons in Inadequate Classroom Space

By Stacy Palen

Last week, we continued our struggle with the lack of AV equipment in our temporary teaching space. In order to teach the seasons in this space, I rewrote an old activity that used an overhead projector and a piece of cardboard with a hole cut out to help students understand why the angle of incidence matters.

Not having an overhead projector or cardboard handy, it occurred to me to have the students use their cell phone flashlights and the hole punched in their Learning Astronomy by Doing Astronomy workbook pages to accomplish the same purpose.

I always feel chuffed when I think of some new way to solve the problem!  

I very much liked the way students interacted with this activity.

In Part A, they have to assemble some of their own real-life knowledge about seasons on Earth. In Part B, they have to hold the WRONG idea in their head as if it were true, which is especially challenging! In Part C, they identify and explain the correct explanation. In the final part, they apply their understanding to seasons on Uranus and test their ability to extend their knowledge to a new situation.

It took most students about 25 minutes to do this activity.

When I teach it again, I’ll probably modify some of the language in Part B to make it even more clear that I expect them to write down things that they know are wrong.

This activity may eventually make its way into Learning Astronomy by Doing Astronomy because I’ve now figured out how to do it with no extra equipment!

You can access the activity by clicking here!


Classroom Stories: Teaching in the Trailer, or "This Will Have Been a Good Time"

By Stacy Palen

In my family, we have a saying, “This will have been a good time.” We use it to refer to upcoming events that will be stressful and potentially awful, but that we will remember fondly once they have passed. For example, when my snake-phobic husband and I went to the Amazon: he didn’t enjoy the trip while it was happening, but afterwards, he was glad to have experienced it. The whole time we were planning the trip, we kept repeating, “This will have been a good time.”

For years, I have taught Introductory Astronomy in the planetarium. This is a difficult space to work in because the chairs are comfy, the light levels are low, the board and projector space is limited, and working in groups of three or more is really difficult. The chairs don’t turn; the students have those little desks that lift out of the chair arm for them to write on; and it is almost impossible to get in and out of a row in the middle of class. If I want to access the computer, I have to go to the back of the room. It’s awkward, but I got used to it, and I figured out how to do both active learning and lecturing, even in this difficult space.

This semester, the planetarium building is being renovated so that we will have heating and cooling that actually work. That’s the plan, anyway. Don’t ask me why they couldn’t do this renovation over the summer. Figuring out the decisions of Facilities Management is above my pay grade!

My astronomy class has been moved into a “portable”—a double-wide trailer in the parking lot, which was furnished the day before classes started. The layout of the classroom is awkward, with students facing perpendicular to the long axis, and the computer being stationed in one corner. It’s like teaching in a hallway. The first week of class, none of the A/V equipment was working, so there were no projectors. During the second week of class, some of the A/V equipment worked, but intermittently—something about the HDMI cables, aspect ratios, and temporary equipment being incompatible with the University standards. I don’t expect this system to be stable for at least another week or two. I could complain about this (more!), or I could see it as an “opportunity” to try something new.

So now, I have jettisoned my long-time methods and materials, and I’m experimenting. I’ve reorganized the whole class to involve lots of mini-activities that can be done quickly in larger-than-usual groups, with lots and lots of peer instruction. For my students, there is really no choice but to read the textbook before they come to class, because it’s really not possible for me to lecture at all.

Today, we’ll negotiate the “points” restructuring, and my students will get to have a say in how much weight each component will have in their final grade. Now that we’ve done a few of the longer activities from Learning Astronomy by Doing Astronomy, a few homework assignments, and a few of the mini-activities, my students have a better sense of how much value each component should have. I’ve explained the experimental nature of what we are doing, and they are mostly cheerful about it.

This entire situation has got me going back and resurrecting things that I did a long time ago, such as using parts of Understanding Our Universe and Learning Astronomy by Doing Astronomy in ways that I haven’t before (it never occurred to me to tear the activities apart and do them over multiple days), seeking out new ideas and activities, and oh … let’s call it “innovating” … at breakneck speed. I expect a lot of this to be a mess, some of it to be useful in the long haul, and some of it to appear in future textbooks. It’s definitely a situation that “will have been a good time.”


Classroom Stories: Practice at Being Afraid

By Stacy Palen

In my other life, I train horses and riders. This means that I routinely deal with actual life-threatening situations like runaway horses and bad falls. Even non-life-threatening situations such as broken bones, giant bruises, bumps, cuts, and scrapes can seem routine to me but be scary for others.

Because of this background, I sometimes struggle to really understand and empathize with students who literally fear math and have an obvious physiological response to being asked to do it.

Recently, I came across a Facebook post by equestrian Denny Emerson about fear that helped crystallize my thoughts about this.

Two things you should know about Denny: First, Denny is as famous in the horse community as Tom Brady is in football. Second, his sport is more dangerous than most horse sports, as the horses race cross-country on uneven ground over solid fences that don’t come down. It’s not unheard of for people to die doing this sport at the highest levels.

Here’s part of what he had to say:

 

But we all experience things that create the exact flight or fight response as actual extreme danger that are not actually dangerous.

Case in point----Denny Emerson, age 9, is cowering in Miss Gibson's Four Corners School 4th grade math class, trying to remain invisible, as students are handed a piece of chalk, and asked to solve problems on the black board, in front of the whole class. As his name gets called, Denny is suffering the agonies of the damned, just as if he was about to be hurled into a pit of writhing cobras.

Which is another way of pointing out that the fear we so often experience is not actually in direct proportion to the danger we are in, but it feels that way.

So, then, it follows more or less logically, that one way to alleviate being paralysed by fear is to avoid, if possible, real danger, and to try to become better prepared to face challenge that only feels like true danger. Like arithmetic.[1]

 

Denny went on to talk about how to condition yourself and your horse to deal with fear, but I made a note in my mind of what he had to say here.

It resonated with me because a week or so before that, I heard the familiar whine of “When am I ever going to use this in real life?” from one of my students. (I refrained from pointing out that she was in astronomy class…practicality isn’t really the point.)

Denny’s answer is one that I’ve tried to articulate for a long time, and one of the best that I know: “it’s practice.”

Mathematics is not actually dangerous. AT ALL. But for some students, it feels that way.

Good. That makes it an opportunity to practice being afraid while holding it together and getting the job done anyway.

It’s practice at a tool they need in order to find success in the world.

Come to think of it, this may have been what my parents meant when they told me to do hard things I didn’t like because “it builds character.”

I probably won’t tell my students that—it sounds a lot like a curmudgeon's “get off my lawn” rant. But I may spend some time talking to them directly about how this practice can help them in other adrenaline-laden situations.

 

 

[1]Emerson, Denny. Tamarack Hill Farm Facebook Page. “More thoughts about fear, and how to live with the reality of fear without being a slave to fear” Facebook, November 23, 2018. https://www.facebook.com/permalink.php?story_fbid=10155572672270947&id=109161715946


Classroom Stories: Vera Rubin Tells The Story

Dark Matter
Image credit: NASA/JPL-Caltech/ESA/Institute of Astrophysics of Andalusia, University of Basque Country/JHU

By Stacy Palen

I was poking around, looking for something completely different when I came across this nice little vignette from "Physics Today" published in 20061. It’s the story of the discovery of dark matter, told by Vera Rubin herself.

The story is mostly accessible to introductory students, with only a little bit of stretch required in the single paragraph that describes circular velocities and flat rotation curves. Hilariously, she includes an "exercise for the reader.” (Well—hilarious to me, and probably you, but students won’t get it.)

If your students have already learned about galaxy rotation curves, they will be able to follow the paragraph. If not, it’s fine if they skim over it—they won’t lose the plot.

The descriptions of observing at the telescope, and the trouble of moving the spectrograph from one location to another really gives a nice feel for how hard it was to get this done the first time.

I’m not entirely sure what I’m going to do with this story in my classes yet, but I found it charming, and think it will capture the interest of some of my students who struggle to connect to this material. I’ll at least share it with them through the LMS so that students who are interested can read it.

If you come up with a plan to use it, tell me about it in the comments!

                

1 Unfortunately, the biographical information published with the article is out of date. Vera Rubin passed away at the end of 2016.


Classroom Stories: Psychology and Underrepresented Groups

C98R91 (1)
B.O'Kane / Alamy Stock Photo

By Stacy Palen

This week in Physics Seminar, we had a psychologist come and talk to us about a number of studies that indicate how stereotypes impact the performance of underrepresented groups. Generally, this refers to women and minorities (although other categories also intersect). The take-home message is that when underrepresented groups enter an environment in which they are the minority, they show a physical autonomic nervous system response. Really—heart rates and sweaty palms and all!

Dealing with this “fight or flight” response taxes their working memory, and they do not perform as well. Several other cleverly designed studies have investigated “stereotype threat” and have shown that when the stereotyped group is engaged in a task in which they are stereotypically bad, they are extremely sensitive to signals that confirm the stereotype.

For example, these groups will have a stronger negative reaction to a poor score on a first exam, and they are more likely to see that score as a signal that people like them are not “meant” to study science.

This is all very fascinating, but the speaker went further and gave us some concrete examples of specific interventions that help level the playing field. Interventions such as in-class discussions about the contributions of women in science may be obvious, but others were less obvious.

For example, one study had women engineering students wait briefly in an office full of items that evoke the male stereotype of an engineer (Star Trek posters dominated by male faces, gaming consoles, piles of soda cans, etc.). A second group waited in a very similar office which had slightly different posters (still science fiction, but less firmly associated with the male stereotype). This room also lacked the pile of soda cans and had an abstract picture of a flower on the wall.

Shockingly, the difference in performance on a subsequent math test was statistically significant, with the women who waited in the stereotype-evoking office performing more poorly. (Men’s performance was not affected.)

Astronomers are lucky. We have lots of examples of a diverse population contributing to our understanding of the universe. Highlighting those examples has been shown to improve performance by those who identify with the specific groups mentioned.

Conversely, highlighting the accomplishments of the majority group negatively impacts performance for the underrepresented group.

Interestingly, the majority group is not impacted in either case because they are not carrying the distracting mental burden of stereotype threat into the classroom!

The take-home message of these kinds of studies is that no matter how well the test instrument is designed, and no matter how much or how well the student knows the material, there are external factors affecting performance. These factors can be lessened by specific (small) interventions, like hanging up a different poster, highlighting diverse scientists, or intervening after an exam to point out that “this material is hard because it’s hard, not because you aren’t good at it.”