This is a blog about teaching introductory astronomy, curated and primarily written by Dr. Stacy Palen of Weber State University.
Want to share suggestions or strategies for engaging students in Astro 101? Join us in the comments!
This is a blog about teaching introductory astronomy, curated and primarily written by Dr. Stacy Palen of Weber State University.
Want to share suggestions or strategies for engaging students in Astro 101? Join us in the comments!
By Stacy Palen
LIGO has been busy, and a newly released graphic summarizes many of the exciting discoveries the detector has made in concert with Virgo, its European counterpart.
Summary: Since 2015, the LIGO/Virgo collaboration has detected gravitational waves—ripples in spacetime caused by rapidly accelerating massive objects—from 10 stellar mass binary black hole mergers and one binary neutron star merger. Black holes and neutron stars are both forms of stellar remnants—the final stage of stellar evolution that a star enters when it has burned through its entire fuel supply. This graphic provides a great jumping off point for discussions about masses in the stellar graveyard.
1. Consider the final masses of the black hole mergers (larger blue circles). What is the smallest merged mass?
Answer: About 19 solar masses.
2. Consider the masses of black holes that have been detected in X-rays (EM Black Holes, in purple). What is the largest black hole mass that has been detected this way?
Answer: About 23 solar masses.
3. Estimate the average mass of the black holes that have been detected in X-rays.
Answer: About 10 solar masses.
4. Estimate the average mass of the black holes that have been detected in gravitational waves.
Answer: This average looks to be about 25 solar masses.
5. Astronomers make the claim that they are detecting a “new population of black holes” with gravitational waves---—that is, that the type of black holes they are detecting now are different than the ones they were detecting before. Based on your answers to questions one through four, explain why they would say this.
Answer: Even though the two groups of black holes overlap in mass, gravitational waves are detecting more massive black holes, on average, than were detected with X-rays in the past.
6. Compare the number of EM black holes to the number of black holes (before merging) discovered with LIGO/Virgo. How much has LIGO/Virgo contributed to the total sample of known black holes?
Answer: LIGO/Virgo has nearly doubled the number of black holes that have been observed.
7. Is it reasonable, then, to compare the two populations (the pre-merger black holes from the LIGO/Virgo data and the X-ray black holes)?
Answer: Yes, statistically speaking, we know of about the same number of objects in each case.
8. Consider the masses of Neutron stars (yellow). What is the largest neutron star mass that has been detected with light (EM)?
Answer: About 2.1 solar masses.
9. Consider the masses of Neutron stars (yellow). What is the average neutron star mass that has been detected with light (EM)?
Answer: About 1.5 solar masses
10. Theorists predict that we would not expect to observe neutron stars with masses above about 2.14 solar masses. Are these observations consistent with that prediction? What do you think astronomers are wondering about the post-merger object resulting from the merger of two neutron stars?
Answer: The neutron stars observed with light are consistent, but the outcome of the neutron star merger is a little bit too massive. As of this writing, astronomers are still trying to figure out the form of that post-merger object. It could be a black hole, a neutron star collapsing to form a black hole, or a stable neutron star. More data are needed!
Using Trade Books in an Introductory Physics Course
I regularly teach PHYS 1010: Elementary Physics, at Weber State University. I didn’t choose the course name; at your school, it might also be called Conceptual Physics or Descriptive Physics. Regardless, it is a physics course with no math prerequisite (and therefore very little math content), primarily taken by students to fulfill a General Education breadth requirement.
There are challenges for the instructor. Some students have profound difficulty with proportional reasoning. Others sign up for the course after taking an Advanced Placement calculus-based physics course in high school, specifically because they are looking for an easy course.
The standard texts are approachable and conversational but might also seem patronizing—at least they do to me. Typically, there are between 90 and 100 students in my course. What to do?
I want the course to provide a meaningful experience for all students, while being faithful to the catalog description and General Education mission by presenting a survey of topics in physics and physical science.
I’ve made my course reading-intensive, because I believe in the transformative power of reading in any discipline. To get an A in my course, students have to, among other requirements, read two trade books.
The first trade book is something I choose for the whole class to read together. Most commonly, I’ve used American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer by Kai Bird and Martin Sherman. It’s an excellent book, a Pulitzer Prize winner that I recommend to anyone. It’s also a 600-page (not counting notes and references) serious work, arguably the most scholarly biography of Oppenheimer to date.
It’s not a book a lot of my students would choose on their own. It includes many physics topics we talk about in the class and is a great springboard for discussing issues of science-and-society in the 20th century.
We read it in sections and take one day every other week from class as “book club day” to discuss a section of the book. Before we discuss the book, students take a short-answer reading quiz. If they don’t pass the reading quiz, they can come meet with me and, by discussing the book with me, convince me that they’ve done the reading.
The only real requirement is that they read the book.
In the in-class discussions, a different group of students participates enthusiastically as compared to a “regular” day of class. The discussions have been some of my most memorable days in the classroom in my 20-year career.
Once the students get over the “Yes, we are going to read this whole thing” on the first day of class, a surprising number enjoy it and I get more positive than negative comments on my evaluations about the reading.
I had one student tell me that she started reading again because of my class.
Beyond the book we read together, in order to get an A, students need to read another trade book from a list of ~10 that I provide.
Here is the list of books that my students currently have to choose from:
Selections cover a variety of the people and issues from science in the last century and include a diverse group of authors and subjects. I break the class up into smaller groups for a separate book club discussion for each book in the last week of class.
Grades in my class are based on reaching benchmarks in various categories.
To get an A, a student needs to average 75% or better on my (physics) quizzes and tests and read both of the trade books. They get a B, but no better, if they don’t read the second book. They can’t do better than a C without doing the reading.
This all makes for a reasonable balance between making every student do something significant and giving every student a reasonable chance for a good grade.
The reading-intensive General Education science course has been as successful as anything I’ve tried in the classroom, in my obviously biased opinion. I love to talk about it with my colleagues.
Have you tried something similar with your students? Let us know in the comments!
By Stacy Palen
In the last two posts, I explained what a rubric is and why they are useful. In the prior blog post, I explained how I use the first part of the rubric to guide me as I assess content knowledge in each question. In this post, I will explain how I use “collective marks” that apply to the whole assignment.
I first heard of collective marks in the sport of dressage. In this sport, the horse and rider complete a test consisting of 25-40 movements, which are each scored individually against a rigid standard of perfection. At the end of the test, the horse/rider pair are scored on four different and more subjective standards, such as “effectiveness of the rider” and “harmony.”
These collective marks might be loosely summarized as “sure, it was technically perfect, but did they make it look easy?”
I use collective marks for all the things that I care about that are not technically astronomy, such as spelling and grammar. But I also include here other features of the assignment that may appear in question after question, like units or neatness or labels on graphs.
It is tedious and time-consuming to keep writing “units” or “complete sentences” after every question. Grading these items collectively allows me to focus on the content in my first pass through the assignment. Then, I leaf through the pages again to recall my general impression of the “beauty” of their performance. I scale the collective marks to be worth about 10% of the student’s grade on the assignment.
For example, if the assignments are all worth 100 points:
For each assignment, 10 of the points will come from the “collective marks,” determined by the neatness, clarity, and other aspects of the work that are taken as a whole.
10: Excellent: You remembered to use units on every measurement or calculation. The assignment is neat and easy to read, with correct spelling and grammar and complete sentences! All mathematical steps are included, and all the graphs and tables have labels, with units! You are a rock star!
9: Very good: There are one or two minor flaws of spelling or grammar. However, all of the numbers have units.
8: Good: There are three or four minor flaws. I could find all of your work, but it was disorganized and a bit sloppy.
7: Fairly good: There is a major flaw (forgetting units or a label) or a combination of 5 or 6 minor flaws.
6: Satisfactory: There is a major flaw and several minor flaws.
5: Marginal: There are two major flaws and several minor flaws; I could barely read your writing.
4: Insufficient: There are several major flaws; I could not read your writing on many of the answers or had to hunt through your papers for the answers.
3: Fairly Bad: I could not find some of the answers, and the work is very sloppy. There are major and minor flaws. Please visit the writing center for a reminder on spelling, grammar, and sentence construction.
2: Bad: I couldn’t read your writing, and the spelling and grammar were poor. The work is sloppy, but it appears that you attempted every question in the assignment.
1: Very bad: You have made no effort to show respect for your own work, or for the time your professor will require to grade it.
0: Not performed
Giving collective marks takes very little time, once I’ve graded the content.
Depending on how many students I have (and how far behind I am in my grading!), I may circle the flaws (such as spelling errors) on their assignment. But I don’t stress about making sure to catch every flaw or giving a correction. I just make a circle and move on.
Before I started using collective marks, I felt conflicted about grading for things like spelling. It seemed wrong to just ignore bad spelling or messy papers, but at the same time, I didn’t feel I had adequate time to correct every student’s grammar.
Collective marks let me do that in a way that lets students know I care, and I notice, but then puts the student back in the position of learning how they should have spelled “gallactic.”
I also find that collective marks reward the students who take the time to carefully write out their assignments, check their spelling, or make careful drawings. I have been known, on rare occasions, to give 11/10 for collective marks, because a student shows such diligent care.
Using collective marks saves me time, makes my grading more consistent, and rewards students who are careful and thoughtful in their work.
Give them a try and let me know how it goes!
By Stacy Palen
In the last post, I explained that a rubric is a written explanation of your expectations and intentions, and why they are useful in clarifying expectations and simplifying grading. 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 this blog post, I explain how I use the first part of the rubric to guide me as I assess content knowledge.
I assign short-answer homework problems, which sometimes include math, each week. I also assign one in-class hands-on exercise each week. Students in my class take two exams each semester, each of which involves a variety of problem types. It’s useful for me to separate the content knowledge from the over-arching skills, like writing complete sentences, including all the details of a graph, and so on.
For example, I often grade short-answer homework questions out of 3 points, using this very basic rubric:
The answer to each question will be graded out of three points:
3: Excellent: Exactly right! Well done!
2: Satisfactory: Well, you kind of had the right idea...
1: Fairly Bad: You wrote something down.
0: Not attempted
This rubric is tightly focused on the content of the answer to this question. There is nothing here about complete sentences, units, handwriting, or even clarity of thought. This is very fast to do, and by the time I get to the bottom of a stack of 120 assignments, I’ve seen all the answers and recognize on sight whether this particular answer should get a 2 or a 3. I will use this rubric for short-answer and mathematical answers, and sometimes for sketches.
I need a more detailed rubric for some pictures, and all graphs. It is appropriate to have more points available for these types of answers than for the answers to short-answer questions because it takes a lot of time to produce a high quality sketch or graph. Personally, I care deeply about graphs because I place graph-reading near the top of all the life skills a student might learn in an introductory science class. An educated person needs to know how to read a graph, if only so they can plan for retirement! I have a separate rubric for graphs. This rubric helps to remind students about the parts of a graph that matter:
For each graph, you will be graded out of 5 points:
5: Excellent: The graph is clear an dwell-presented. Axes are labeled with units, and there is a legend if more than one thing is plotted.
4: Good: The line fits are slightly in error and don't fit the data as well as they could. Constraints have not been applied correctly; some graphs must have lines that pass through 0,0, for example.
3: Satisfactory: The data are plotted correctly but the line fit is inappropriate or missing. Alternatively, there is a line with no data to constrain it.
2: Insufficient: Major or many components are missing, such as an axis or axis label.
1: Very Bad: Seriously? You wasted my time turning this in?
By using these rubrics to grade for content, I free myself from having to agonize over how many points to give for an answer that is mostly correct but poorly worded. I can give the benefit of the doubt for answers that seem right but leave me not entirely certain that I know what they meant. I can give students a little bit of credit, even if I can’t completely read what they have written. And I don’t have to worry here about spelling, units, or grammar. I have collective marks for all those issues, which I’ll talk about in the next post.
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.
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.
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.
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!
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.
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.
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.
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:
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.