How-to: Using Grading Rubrics

By Stacy Palen

There is a tension for every professor between giving detailed feedback and keeping up with the workload. I suppose it’s possible that there is a “unicorn” professor out there somewhere who never struggles with this, but I haven’t met them!

Using a rubric can be helpful, because a rubric can add clarity to your expectations and cut down on the grading workload.

A rubric is a written explanation of your expectations for an assignment. Rubrics are most commonly applied to large projects or presentations, but they can be just as useful for the weekly homework assignment or in-class activity.

Using a rubric means that both you and the student are on the same page about what’s required. In science, we often consider our assignments to be quantitative and objective, so that the grading is likewise quantitative and objective.

But students may not see it that way; even if the assignment is quantitative, students may not know what makes a proper quantitative answer. Are you a professor who cares about complete sentences and units and showing all the work? Or do you only care about the answer?

It’s a fair point that students have questions about this, especially in an introductory course where they are not “plugged in” to the culture of your specific Department.

I typically post the rubrics for assignments on the LMS or course website, and also in the syllabus. Then when students ask me questions about why they lost points on an assignment, I’ll refer them to the rubric.

In some semesters, I have printed out the rubric for the first assignment, writing directly on it, so that students could see how the rubric was applied. That’s probably a good idea, but I’m not always able to get it done.

The level of detail included in the rubric depends on the assignment. For example, I will have different rubrics for short-answer homework questions than for in-class lab activities.

Exams, which in my class involve drawing pictures, writing paragraphs and solving puzzles, do not fit so neatly into a rubric category. But I find that by the time I reach the midterm, the students already have an idea of my expectations.

I have colleagues who have written holistic rubrics for their entire course. That is, they have written down in clear terms what an “A”, “B,” or “C” in this course means. For example, a “B” may mean that the student has completed 14 of 15 homework assignments with a grade of 80% or better, plus two exams with a grade of 75% or better, plus read and commented on two articles in the course discussion board. An “A” might mean both higher scores AND more articles read.

Some professors have gone so far as to then turn that rubric into a “contract” with the student, where the student can state up front at the beginning of the course that they intend to aim for a “C.” They often do.

I divide my grading rubrics into two parts: a part that is applied separately to each question, and “collective marks” that apply to the whole assignment. In the next two blog posts, I will explain how I use rubrics to grade for content knowledge, and how I use them to grade for “meta” qualities that span multiple parts of the assignment. I will also explain how I use rubrics to cut down on my grading workload.

There are endless other examples of rubrics and how to use them on the internet. Many of them come from K-12 teachers, who frequently use rubrics in their grading. Your students may be more familiar with the concept than you are!

Stay tuned for Part 2, “How-to: Grading Content” next Friday.


Classroom Stories: Thoughts on Missing the First Day of Class

By Stacy Palen

Establishing a classroom culture of intention (including routing attendance, handing things in on time, showing up promptly, and so on) starts on the very first day. Students take their cues from me: is this a professor who cares about these things or not?

Because of this, I have always avoided missing the first day (or two!) of class.

Unfortunately, the winter American Astronomical Society meeting almost always overlaps with the first week of class at Weber State University. I usually don’t go to the meeting. But this year I had obligations that put me in a bind, and I felt I needed to be at AAS during the first full week of January.

This meant missing the first day of class in all three of my spring semester courses. What to do?

Somewhat hesitantly, I put together an assignment for each class that I broadcast on Canvas the week before. I made an announcement so that students would know they were supposed to do it instead of coming to class, and then hoped for the best. I promised that I would grade this assignment before we met in class for the first time.

It worked out better than I expected.

The Introductory Astronomy assignment had two parts. Part A was a basic list of vocabulary words like “planet,” “planetary nebula,” and “universe,” that students were asked to look up and define in one or two sentences. Part B asked students to read the syllabus and then answer a few questions.

Part A gave me insight into what students know, what they don’t know, and, especially, what they think they know but don’t!

Students believe they know what planets, stars, and solar systems are, so they did not look up those answers but instead just wrote down what was in their head. These definitions were generally incomplete. For example, the definition of “planet” could easily have described an asteroid.

More difficult terms like “planetary nebula,” they actually looked up. The students were more likely to be correct about the topics they didn’t know as well.

That’s interesting.

Part B actually allowed me to skip talking about the syllabus during our first in-person class time, except to answer one or two questions about textbooks and the bookstore. This feels like such an improvement that I may institute this assignment every semester!

The mechanics of the assignment were a little bit tricky.

First, I had to convince Canvas to open the course ahead of the official University start date, which I did in “Settings.” I know I was successful because one student turned the assignment in on the Friday before classes started.

Second, in order to keep my promise to have it graded before the second meeting time, I had to have students hand in the assignment on Canvas.

In previous years, this would have been a show-stopper, because I despised typing in comments on assignments handed in via Canvas. But there is new functionality to write on assignments using a tablet, which makes the grading experience much more like giving feedback on paper.

I did get them almost all graded (except for four!) by the time class started on Wednesday. I felt it was really valuable to me to walk into class already knowing something more about their background than I typically do.

And skipping the syllabus discussion? Priceless.


Video: Stars Orbiting the Black Hole at the Heart of the Milky Way

This fun little video came across my computer screen not long ago:

It comes from the European Southern Observatory and contains 20 years of observations of the galactic center of the Milky Way.  Over this period, about 20 stars have been observed to travel in small orbits, moving quite quickly at some points in their orbits.

Near the center of the screen, one star makes a complete orbit over the duration of the clip and it is very clear when the star is farthest and closest from the focus of its elliptical orbit. Even though the focus is a black hole and not another star, let’s call the furthest distance apastron, and the closest, periastron.

The star moves quite quickly during periastron and just like comets in our own Solar System, which spend most of their time far from the Sun where they travel more slowly, this star spends most of its timer far from the black hole.

Notice that nothing is visible at the focus of this orbital ellipse.  Yet, there must be a great deal of mass there, to pull a star around in an orbit with a period of only 20 years.

Students can use these data to calculate the mass of the black hole at the center of the Milky Way Galaxy.  We show them how in Learning Astronomy by Doing Astronomy; Activity Number 29.  This video makes a great supplement to that activity!


Reading Astronomy News: The Little Spacecraft that Could: the Kepler mission is over.

By Stacy Palen

Summary: The Kepler mission, after at least one resurrection, has finally come to an end. During its 9.5 year “lifespan,” Kepler discovered more than 2,500 planets around other stars and changed our minds about how common planets actually are.

Article: https://www.sciencenews.org/article/planet-hunting-kepler-space-telescope-dead?fbclid=IwAR0iYMK2_9-tbCgb91JxpFVpLR9MCOgRpC7BxodF69P45Hhtq2_trWv4_4I

Questions for Students:

1. Study the graph of Exoplanet Discoveries. The yellow dots show all the planets discovered by Kepler. Compare the sizes of these planets with those discovered before and after Kepler.

Answer: Kepler discovered smaller planets than those discovered before or after.

2. Study the graph of Exoplanet Discoveries. This graph shows that very few planets have been discovered with orbital periods smaller than one day. Why might this be?

Answer: This is as close as a planet can get, even to a small star, and still be in a stable orbit.

3. Study the graph of Exoplanet Discoveries. This graph shows that few planets have been discovered with orbital periods larger than about 300 days. Why might this be?

Answer: This could be a selection effect. Kepler uses the transit method to detect planets, but planets with large orbits are much less likely to cross in front of the star; our line of sight must lie exactly in the plane of the orbit to see the planet transit. The idea that this is a selection effect is supported by the observation that planets with long periods have been detected by other methods (the blue and gray dots), but not by Kepler.

4. Prior to the Kepler spacecraft, the percentage of stars with planets was unknown. Now that Kepler has completed its mission, do astronomers think this number is large, with many stars having planets or small with few stars having planets?

Answer: This percentage appears to be close to 100%. “…astronomers have used Kepler’s exoplanet haul to predict that every one of the hundreds of billions of stars in the Milky Way should have at least one planet on average."

5. Comment on the impact of the Kepler mission on the Drake Equation.

Answer: The second term in the Drake Equation is the fraction of stars with planets. This term is now quite likely to be nearly one, whereas before the Kepler mission, its value was only speculative.


How-to: Patience, Growth Mindset, and Mathematics

By Stacy Palen.

I have a TON of math-phobic students in my classes. I teach at an open-enrollment university, where the majority of students test into Developmental Math. Many of these students have such poor math skills that they are enrolled in Math 0950, which begins with counting and the number line and culminates with percentages.

We have no structure here to make sure that these students pass their quantitative literacy classes before they take astronomy.

I feel quite strongly that everyone can do basic math. More importantly, everyone should. If their numeracy does not improve, these students will be taken advantage of by banks and credit card companies and salespeople and loan officers with every major (or not so major) purchase, all the rest of their lives.

I can make an argument that is compelling to myself that the financial crash of 2008 was caused in large part by people who did not understand how to calculate mortgage payments. So the lack of numeracy in the population has larger implications than just whether they score well on an astronomy exam.

Because I don’t want to send the students out the door like lambs to the slaughter, but I simultaneously don’t want them to hate me, I’m always on the lookout for tips and tricks about learning things that are hard.

Ages ago, I learned about the “growth mindset.” That’s the idea that success comes from working hard at things, rather than innate talent.

Focusing on growth mindset turns out to be particularly useful for underrepresented groups, who for better or worse don’t see the talent route as available to them. People in underrepresented groups often internalize this. They think: if people “like them” were “naturally good” at x, more people like them would do x.

When you want to encourage students, it’s hard to think of a quick motto that encapsulates all this. And it’s not always obvious how to make use of the idea that maybe students just need more practice to feel proficient.

This is why I recently took note of this article in the New York Times, about learning patience.

The author of the article makes the point that “patience, the ability to keep calm in the face of disappointment, distress or suffering, is worth cultivating.”

I could instantly see how a more patient person would do better with mathematics than a less patient person, especially if they had learned to fear math. There’s a lot in the article about how to interrupt the function of the amygdala, which is the part of the brain that stimulates that frantic, impatient reaction to everyday frustrations like slow-moving cashiers or slow-loading web pages. Or calculator malfunction. Or algebra. It’s worth a read.

But the thing that caught my eye was this motto: “Train, don’t try.”

Mathematics is not a matter of sheer willpower: just trying harder will not make you numerate! Instead, students need to systematically practice problems of gradually increasing difficulty -- repeating as necessary -- until their ability grows and develops, just like a muscle would.

This is why I insist that they do math in my class, and it’s why I start them doing it during lab time when I (and their peers) can give them pointers on their technique and their methods.

So I’m going to try the experiment of explicitly pointing out the connection between developing patience and developing math skill. And I will encourage my students to “Train, don’t try.”

I bet I will have to try it more than once to get it right.


How-to: The Last Choice, A Questioning Strategy for Your Astro 101 Lecture

By Stacy Palen.

Often, in-class questions are presented as a binary choice: “Does the star grow, or does it shrink?”

I always couch these as, “How many of you think the star grows?" Wait for hands. "How many of you think it shrinks?" Wait for hands. "How many people think that 9:30 in the morning is an unfair time to ask that question?" (Wait for hands.)

The last choice, though it may seem frivolous, is really important.

I try to make these last choices light-hearted and a little bit funny. For example:

  • “How many of you were asleep just now?”
  • “How many of you were thinking about lunch?”
  • “How many of you were thinking about puppies instead?”
  • “How many of you wish we would just get to black holes already, and stop talking about nuclear fusion?”

You get the idea. The light humor helps them stay focused and makes it clear that I expect them to put up their hand for every question at some point, even if it’s the silly last choice. I expect them all to participate, every time.

The last choices -- and the way students react, by laughing or groaning, for example -- help me figure out where they are in their heads.  Do I have their attention? Are they feeling confident to take a risk and make a guess? Are they actually listening to me at all? Were they really thinking about puppies?

I often don’t interpret that response in the moment. After class, while I’m walking back to my office and putting my notes away, I’ll think about what was happening in the classroom right at that time when I asked the last question.

Was there a better way to explain before I asked the question? Had I been talking too many minutes in a row? And so on. I might make a note in my lecture notes about a sticky concept, or an analogy that worked particularly well. This reflection afterwards helps me improve for next time.

Most importantly, the last choice gives students an “out.” It is an acknowledgement on my part that they might not know the answer, and that’s OK. I expect them to go ahead and guess sometimes! Giving the last choice makes it clear the question is not a referendum on how smart they are. I am genuinely asking the question because I am trying to figure out what they have understood so that I can help them.

Really, that’s what the last choice question is all about: it’s a less intimidating way for them to say, “I don’t know.”

The last choice helps students to stay focused because they know there will be a moment when they can answer honestly, and often it will come with a laugh.

A closing note on classroom technology: Sometimes I use “clickers." Sometimes I use a piece of paper divided in 4, with A, B, C, D written on each square; students fold the paper to show me the letter of their answer. Sometimes I just have them put up their hands, because the question is an extemporaneous one that just happened naturally in the course of my lecture. In this post, I talk about the questioning strategy as though it applies to extemporaneous questions. But of course, you could use this strategy for a planned questions, too.


Current Events: We've Landed on Mars! Again!

By Stacy Palen.

As of this writing, InSight has just landed successfully on Mars!  This mission is a little bit different from other recent missions: InSight (short for Interior Exploration using Seismic Investigations) is a lander, not a rover. Because it’s in the news, this is a great opportunity for a brief in-class discussion!

 

Insight-landing
This illustration shows a simulated view of NASA's InSight lander descending on its parachute toward the surface of Mars. Credits: NASA/JPL-Caltech

InSight is designed to investigate the interior of Mars: the crust, mantle, and core.   

A seismometer will measure surface vibrations, which will be used to determine the size of the core, the thickness and structure of the crust, and therefore the thickness of the mantle as well. These same measurements will be used to measure how frequent and how powerful the tectonics are on Mars, as well as the frequency of meteorite impacts.

Heat flow measurements will be taken using a probe that is hammered 5 meters (16 feet) down into the surface. These measurements will be used to determine the temperature of the interior. All of these measurements will lend insight (ha!) into the formation and evolution of Mars.

Radar soundings back and forth to an orbiting spacecraft will be used to measure the wobble of Mars on its axis, which in turn is affected by the structure and composition of the core.

The InSight lander is the result of many technical advances. It’s the first lander to pick up and place instrumentation from the top of the lander onto the surface of the object being studied.

The plan is for InSight to place its seismometer on the surface of Mars, then place a heat and wind shield directly on top of the seismometer. The lander needs to make these placements autonomously, something that has never been done before.

In another major technological advance, InSight arrived on the Martian surface through a complex series of steps involving parachutes and retrorockets. The successful operation of these kinds of tools is a pre-requisite for future human exploration. Just InSight's successful landing represents a major step forward in the study of Mars.

 

Insight-on-mars
An artist’s rendition of the InSight lander operating on the surface of Mars. Image Credit: NASA/JPL-Caltech

Discussion questions for students may be wide-ranging:

  • How does this mission connect to earlier discussions about the formation and structure of planets? (Hooray for final exam review!)
  • Why do we care about the structure of Mars? What implications might a study of the geologic properties of Mars have for future Mars exploration?
  • Do you expect the meteorite impacts to be frequent (more than one per day) or rare (less than one per sol)? Why?

And here are some quick “Google It and Think” questions for small groups:

  • How long did it take for this mission to get to Mars? What factors determined this “flight” time?  What challenges would humans face due to this travel time on a trip to Mars?
  • How many spacecraft, rovers, and landers are currently functioning on Mars? Why is Mars a unique target for missions like these?
  • There are three separate stages for the entry, descent, and landing sequence. What are they?  What problems can you think of that might have occurred in each stage? What steps did the engineering team take to make these problems less likely?

Reading Astronomy News: Astronomers Spot One of the Oldest Stars in the Entire Universe

By Stacy Palen.

Summary: A red dwarf star in the Milky Way barely contains any heavy elements at all. Its age is estimated at 13.5 billion years.

Article: http://www.astronomy.com/news/2018/11/red-dwarf-is-one-of-the-oldest-in-the-universe.

Questions for Students:

1. Why does the lack of heavy elements imply that the star formed very soon after the Big Bang?

Answer: Because since the Big Bang, stars have been making heavy elements and returning them to the interstellar medium. Young stars have more heavy elements than older stars.

2. Why do astronomers think there must have been at least “one ancestor” before this star formed?

Answer: Because it has some heavy elements in it.

3. How is the birth of this small star connected to the first generation of stars, which were probably ALL very massive?

Answer: Supernova explosions from those first stars could trigger the formation of smaller stars.

4. Where would this star lie on an H-R Diagram?

Answer: This star, because it is a very small red dwarf, would lie at the lower right on a H-R diagram.

5. This star is one-seventh (about 0.15 times) the mass of the Sun. Which of the following is a reasonable main sequence lifetime for a star with that mass?
a. 10 million years
b. 100 million years
c. 1 billion years
d. 10 billion years
e. 1 trillion years

Answer: e.

6. Astronomers can confidently state that all stars like this one (with similar mass) are still around, and none have died yet. Why can they state this so confidently?

Answer: Because 1 trillion years is a lot longer than the age of the universe.


Classroom Stories: Calendars, Leap Years, and Graphs

By Stacy Palen.

Discussing the calendar can bring a “science and society” learning objective into the astronomy classroom.

Lunar Calendars

Islam, for example, uses a lunar calendar. The resulting gradual drift of holidays and festivals such as Ramadan through the seasons opens discussion not only to the use of calendars, but also to the earliest observed crescent phase that marks the beginning and end of the fasting month.

Asking students to imagine, and then explain, how Ramadan differs when it is celebrated in different seasons, can give students a better appreciation for why seasons and calendars matter. When we discuss the lunar calendar, Muslim students often raise their hands to add stories of Ramadan, such as waiting for the first observation of the crescent moon that signifies the end of the fasting period.

A few years ago, a Muslim student, Kimi, would come to intro astronomy class wearing traditional attire and veil. Kimi was quiet until we reached this discussion of the calendar. She stepped in to talk about the meaning and practice of Ramadan. This talk, in turn, transformed the views of other students, and they welcomed hearing about her experience.

Later in the year, Kimi had some problems in her neighborhood. Her car was broken into, and her door was vandalized. Kimi stayed after class to explain that this was why she was late that day. Three other students waited to walk with her across campus and offer moral support. We do teach more than astronomy in the astronomy classroom.

The Gregorian Calendar

Students find it surprising that the date of a long-ago event does not tell you precisely how many days ago it happened. This is due to the number of days in a year (365.25) not being an integer. A random error occurs because early calendars did not take the fraction of a day into account, so they needed adjusting once in a while. Students are often surprised to hear this.

For example, in 1582, when the calendar changed from Julian to Gregorian, 10 days were deleted: Thursday, October 4 was followed by Friday, October 15! The Gregorian calendar was invented to correct the systematic errors, so that the random adjustments were no longer necessary.

Explaining the Gregorian calendar is cumbersome: every fourth year is a leap year, except if it's a centennial. The only exception to this is if the centennial is divisible by 400. The effect can be difficult to visualize.

800px-Gregoriancalendarleap_solstice.svg

Image created by Wikipedia user BasZoetekouw using Astrolabe data and used under Creative Commons Attribution 3.0 Unported license.

This graphical representation shows how the date of the summer solstice changes over the course of 400 years. This graph shows that the summer solstice moves 1/4 day later each year, until the fourth year, when it resets to, almost, the original date. As time passes, those almost errors accumulate, until they add up to just about one day after 100 years.

That “just about” error accumulates until it adds up to a full day after 400 years. And then the leap day is skipped.

Asking students to visualize how far the blue line would rise without the leap-year reset helps them understand that the date of the summer solstice would change significantly, by nearly a month, over the course of just one human lifetime. A visual representation of the effect helps students grasp a difficult concept with ease.

Image retrieved from: https://commons.wikimedia.org/wiki/File:Gregoriancalendarleap_solstice.svg


Classroom Stories: Establishing a Common Vocabulary

by Stacy Palen.

Sometimes, you do a thing in class, and you think, “Why did I never do that before?!” That happened to me this semester, when for the first time, I gave my introductory astronomy students a first assignment in vocabulary building.

This was basic, absolutely basic. I gave them a list of astronomical objects. Then, I told them to go to the library, look at an introductory astronomy book, and find a description of each object. The objects included: planet, meteor, comet, star, nebula, galaxy, and so on. 

I asked my students to rewrite each definition in one or two sentences, and then to hand in their definitions in during the second class. I did not give my students anything “tricky.” No words like dwarf planet or energy.

The assignment was a simple census of the Universe: what’s out there, and how can we talk about it?

The assignment was a bit of a desperation move. Often, my students are not prepared for class on day one, but I hate to waste the opportunity to establish a good homework habit by waiting until the second week. This seemed like a nice compromise that would get them engaged with the material, even if they didn’t have their book(s) yet.

Most students did not go to the library (of course). But two of them did, which sort of shocked me. And all of them completed the assignment in its entirety. It took me only a few minutes to grade because every student gave reasonable working definitions of the objects. I was not looking for detail.

But since then, the real magic has happened in classroom discussion.

For many students, it’s been a long time since they thought about space, and they've forgotten a lot of what they knew. For another group, they never learned about these objects to begin with. And for others (the most difficult group), they think they know what these objects are, but they are mistaken.

In Utah, astronomy appears in the 3rd and 6th grade core. Therefore, unless their high school made a special effort to offer an astronomy class, my students may not have talked about space at all since 6th grade. That’s a long time to ask anyone to hold onto unused knowledge.

This semester, I’ve noticed the advantage of our common vocabulary when talking about physical laws. For example, when I talked about orbital motion, I was able to say, “These laws govern the behavior of all kinds of orbits, from planets to comets to stars orbiting the center of the galaxy to extrasolar planets. We will use these laws over and over again.”

And students had an idea, from the census that they took in their vocabulary assignment, how broadly I was applying those laws. The feedback from students -- in the completely non-scientific form of nods -- was more positive than past feedback had been.

Before, I felt that my students were not sufficiently amazed by the universality of physical law. Now that we have a common vocabulary in place, I sense that they better understand my own amazement, and that in turn helps them develop a deeper appreciation for our Universe.