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Basic but important physics questions: What does it mean to say Energy is conserved?

January 19, 2017

Ok, here’s a question I’ve been thinking a bit about. In my classes we learn about the principle of energy conservation as the idea that there is this fundamental quantity, energy, that we can account for in a system. If the system is completely isolated, this quantity doesn’t change, and when this system is interacting with its surroundings (via work, heat or radiation) we can account for the changes in the energy of this system.

But it’s gotten me thinking of a question I find myself asking a lot—”Is the energy of this system conserved?” I think most of my students hear that as “does the energy of this system stay the same?” But now I’m thinking that if my notion of conserved is “can be accounted for” then the answer to this question should always be yes (we can always figure out how to calculate the energy flowing in/out of the system), unless we’re working on problems dealing with the total energy of the universe and dark energy or something.

Wikipedia seems to say that a conserved quantity is constant along the trajectory of a system, and thus is sounds like for the system of a ball falling to the ground (where K is increasing), energy would not be conserved.

So if this is true, must I say something like the energy of the ball system is not conserved, but we can account for the change in the energy of the system by calculating the work done by the gravitational force? And is this an application of the principle of energy conservation?

My thoughts on seeing Hidden Figures

January 3, 2017

A few days ago, I finally got to see Hidden Figures at the theater, and I loved it. Here’s what I wrote on Facebook:


Before you read further, I encourage you to first read what this film meant to Refranz Daviz, an amazing educator, teacher of color, and leader of the EduColor Movement: Why Seeing Hidden Figures is Important.

Now that you’ve read Rafranz’s take as a teacher of color, I’ll share my perspective as a white, male science teacher, whose experience in science and life, in general, has been a very privileged one. In this post, I’d like to think about the lessons I learned from this film and think about how I can share those lessons with my students.

Warning: there are a few spoilers ahead. 

  • The enormity of obstacles, even when they are just bathrooms: separate but equal never is. As a child, I remember learning about “separate but equal” and seeing signs for a “colored” water fountain next to one for “whites only.” I knew this was wrong, but many of the images I remember seeing showed facilities that did look nearly “equal”
    Back then, I had a hard time understanding how this seemingly small difference could be a major spark of the Civil Rights Movement. But separate is never equal, and this film teaches that lesson in powerful ways. When Dorthy Vaughn goes to the public library to find a book on FORTRAN, she has to steal it from the Whites-only section of the Library. When Katherine Goble asks about the location of the bathroom after she has been reassigned to the all-white Space Task Force and figures out she has to walk half a mile to the colored restroom back in her old workplace. Watching her have to run this distance, in heels, in the rain, carrying stacks of calculations to check over, only to rush back to her desk to keep working, only to get yelled at by her boss. These examples make it clear that something as simple as the placement of a library book or bathroom can be a tremendous obstacle for advancement—when you have to spend half an hour trudging to the bathroom multiple times a day, you are going to have less time to work than the white male engineer across from you who just has to walk outside the office to find a bathroom.
  • The pervasive subtlety of systematic racism and sexism: What was most interesting to me was that despite all the moments of visible and invisible racism that the heroines faced in this movie, and deep impacts these events had on them, most of the white characters were completely unaware of the unequal society around them. The bathrooms for the white scientists were right around the corner. I learned from reading the book that NASA even provided on-campus dormitory housing for female employees—whites only, of course. When you get on the bus, there’s a seat waiting for you in the front, and your section of the library is stocked with every book you could want, including those that would allow you to advance your career. All of this creates an atmosphere that allows the white scientists (and the entire white community of Hampden) to live a life blithely unaware of all the intricate and mostly hidden ways society is structured to maintain their status and deprive blacks of the opportunity to gain equal status.
  • The incredible amounts of grace and restraint that Black Americans must display at every moment in order to simply exist in a white world: The movie is filled with moments where one of the protagonists endure a veiled insult or indignity from a white colleague, and must simply brush it off, to not cause a scene which would only draw a negative reprisal. The most powerful of these moments comes in the opening scene of the movie, which is in the trailer, and features the three lead characters trying to fix a broken-down car on the side of the road when a Virginia State trooper approaches. In this movie, there’s a great moment of comic tension where the officer says something like “NASA, I didn’t know they hired …” and Dorthy Vaughan quickly interjects “Women,” and manages to cajole the officer into providing the women a police escort to work. But throughout this scene, all I could think of was Sandra Bland, and how simply asking why she was pulled over set off a confrontation with the officer that resulted in her arrest and death in a Texas jail cell.
  • The many ways to be part of a movement: The movie also does a good job of depicting the many different ways in which blacks participated in the civil rights movements. Not everyone marched in protests; some, like Mary Jackson, petitioned the county to allow her to take advanced science courses at the all-white high school in town and went on to be the first black female engineer at NASA. The movie does a great job showing that it takes a spectrum of efforts to bring about change in society.
  • The power of privilege: There were many moments in the film where the privilege of the white characters in the film was overwhelming. Some, like the supervisor of the white computers, played by Kristin Dunst, go nearly the entire film unaware of their privilege and even overt acts of racism. The movie also sets some characters up with the opportunity to use their privilege for change; the director of the Space Task Force, played by Kevin Costner. After he yells at Kathrine Golble Johnson for her long bathroom breaks and then discovers her reasons, he rages as the “Colored Restroom” sign with a crowbar, desegregating bathrooms on the campus with the line, “We all pee the same color here.” The film makes it clear that it often takes someone with privilege to tear down the system of privilege.Often that person doesn’t even have virtuous motives like equality and justice. Sometimes, like this case, the boss just wants his employee to be able to spend more time behind her desk. For more on this, I found this article illuminating:
    When the women of ‘Hidden Figures’ needed The ManUpdate: I also read another interesting pieve in Vice, Space So White, that raises some good questions about why the screenwriters felt the need to add some scenes where the white boss character “saves” the black heroine from segregated bathrooms, and lets her into the control room during the launch. Neither of these incidents actually took place. 
  • A great picture of the early days of electro-mechanical computing, with some guidance for today: One of my favorite story lines is the work to install an “IBM” to take over many of the calculating duties from the human “computers”. The early history of computing seems to be on full display complete with punch-cards, oscilloscopes, racks of machines, green and white line paper for printers, and jokes about not being able to fit the equipment through the door. Here’s a machine that does 24,000 calculations per second and will likely make all human computers obsolete. But Dorothy Vaughn sees opportunity here; she realizes that we will always need people to program the computers, and so she grabs a copy of a book on FORTRAN (cleverly subtitled as the “language of the future”) and proceeds to teach her entire department the fundamentals of programming so that they are ready to jump right in and help when the opportunity presents itself. It seems to me that this is exactly the lesson we need in today’s world where robots and machines capable of performing legal discovery or reading x-rays makes us fear for the future of even highly skilled jobs like lawyers and radiologists.
  • Math in the movie: I mostly loved how math was portrayed in the movie, starting in the very first scenes where the young Katherine was sitting in the hallway and naming and mentally manipulating all the shapes she saw in a stained glass window, followed by a scene where she was asked to solve an algebra problem involving the product of two quadratics. Her explanation of her solution was thoughtful, clear and sounded just like a promising young mathematician should.Later in the film, there were a number of great discussions centered around mathematical problems. Katherine Johnson also talked about needing to “invent new mathematics”, which was a wonderful thing to hear in the middle of a scene. They talked about the “ancient” Euler’s method as a possible solution, and Katherine went back to her office and grabbed an old textbook to study it further, just as I would expect any good mathematician to do. The movie also made it clear that mathematics was about hard work and collaboration, not insights of genius.One of thing I really appreciated is how accepting friends and family seemed to be of the main characters’ love of mathematics, and didn’t paint them as freakishly abnormal because they understood mathematics and found enjoyment in it. The movie didn’t try to overplay up any sort of “nerd” angle for any of the characters, nor did it go all “A Beautiful Mind” with the math sequences where animated equations and mathematics were flying through the sky.

This was a great film. I think it’s a must see for every science teacher, and then I think our challenge is to figure out why these incredible women and their contributions to science were left out of our educations. We can also bring their stories back for our students. I think this is a film that can inspire children of any age, and I plan to show it to my 6-year-old daughter. This film also invites its audience to dig deeper and learn more about this history, and I think this provides a unique opportunity for science teachers. What if we were the ones who created a teaching guide and lesson plans that helped students to understand the history of human computers, how one goes about calculating the trajectory of a rocket launch, the changing demographics of NASA, and the challenges underrepresented minorities still face in the sciences today?

Lastly, and most importantly, I personally want to approach this work with a great deal of humility and a strong desire to help, not lead. This is not my story to tell, and I know there are many other women of color out there who are more than capable of leading the way on this. Here are a few I’ve found who are worth following:

Jedidah Isler is an astrophysicist, and she’s been tweeting about the film:

Jeanette Epps is a current NASA Astronaut:

Here’s a great discussion on periscope from Film Critic Rebecca Theodore about black women geniuses:



Let’s Start a Movement for Hidden Figures

December 11, 2016

I am over the moon (pun intended) excited about the upcoming release of the movie Hidden Figures.

I think this movie is a tremendous opportunity for science education—It’s a chance for us to teach the human side of science, along with a healthy dose of social justice. And it’s got me thinking about how we can make this a movement.

I must admit that until I saw a trailer for this movie a few months back, I did not know who Katherine Johnson, Dorothy Vaughn and Mary Jackson were, and that speaks to the inadequacy of my own education, as well my need to do better as a teacher who cares about making sure that all of my students see themselves as future physicists.

I can remember watching The Right Stuff, as a child, and for the following year, my dreams were of going to the air force academy and becoming a test pilot. I believe this movie has the power to inspire students and to challenge all of us to make our world more equitable and just so that each of us can live up to our full potential.

So how do we make this a movement? Here are some thoughts:

  • What if we organized school-wide trips to see the movie? This is easy for me as a boarding school teacher but were I back in teaching in day schools, I think many kids would have liked an invitation to meet me at the theater to see this movie.
  • What if we created a teacher’s reference guide? So far, I’ve seen a pretty cool contest to identify modern day Hidden Figures, and an effort by IBM to celebrate STEM role models, but there doesn’t seem to be a lot of resources our there for the teacher who wants to build a lesson or a unit around the film. The Wikipedia pages of Dorothy Vaughn and Mary Jackson seem rather sparse—and don’t begin to answer all the questions a student might have about this film like:
    • How Many Women were employed as “computers” by NASA in the 1960s?
    • How do you calculate the trajectory of a spacecraft like Apllo 11?
    • How does the math I’m studying now in (elementary/middle/high school) connect to this work?
    • How has the experience of women and under represented minorities working in science changed since the 1960s?

    What if some enterprising teachers tried to create some resources and lesson plans to support this film? We could start by just collecting some of the resources that are out there, like this great interview with Katherine Johnson.

  • What if we organized discussions? There are sure to be people who go to the movie who would like to talk about it more. This seems like a great opportunity for science outreach. Could we hold a meetup in January in our various towns to talk about the film? Could we advertise it at our local theaters? Could we organize virtual discussions?
  • Surely NASA sees that this movie might inspire a new generation of scientists and engineers—so might some NASA scientists and engineers be willing to host skype Q&A sessions with students?

These are just the first thoughts floating through my head. There are probably people out there who are working on this that are more closely connected to this film and these issues than I am as a while CIS male. If you know of anyone who is doing education outreach work for this film, please point me in their direction—I would love to support their efforts.

We are looking for a physics teacher

December 7, 2016

My school, St. Andrew’s School in Delaware, is looking for a full time physics teacher for 2017-18. St. Andrew’s is an outstanding coeducational 100% boarding school with excellent facilities, situated on 2500 acres of farmland, 1 hour from Philadelphia.

Here are a few other tidbits about this job and my school:

  • The culture of the school is unique, and really must be experienced to be believed. 310 students and 80 faculty living and working together to find deep joy in learning, working to make the world a better place, and to create a compassionate, caring community that rejects the culture of pettiness and cynicism that can often infect the traditional high school.
  • The school draws students from all over the world and is 100% need blind in its admissions. Nearly half of the student body receives financial aid, and the average grant is $42,000 (this is almost unheard of in the independent school world).
  • The school is led by a visionary headmaster, Tad Roach. To get a sense of what an incredible educational leader he is, I encourage you to read a few of his chapel talks.
  • The faculty are incredible. They are experts in their fields, deeply committed to the craft of teaching, collegiality and continuous improvement. I credit many of them with helping me to rekindle my interest in the humanities as a young teacher.
  • You’ll have a lot of autonomy. One of the luxuries of teaching in private school, and our school in particular, is that you are given a large amount of control over what and how you teach, yet at the same time, you’ll have a tremendous network of colleagues with with to share ideas and gain feedback.
  • You’ll have a great opportunity to shape the future of the science curriculum at our school. We use a modified version of the modeling curriculum in physics and chemistry, along with standards based grading, and very open to your ideas for how we can continue to experiment and improve science education for our students. You’ll be part of a vibrant and very collaborative department—we’re doing some very interesting work to create a longitudinal study of a subset of our students to help us define, measure and collect evidence of the skills we are trying to teach. We also have an amazing department chair.
  • You’ll even have a chance to help shape the future of our building, as we are in the early stages of planning for a major renovation of the science building.
  • Classes are very small, usually around 12 students, and a typical load is 3 or 4 sections.
  • You’ll have tremendous resources to support you in your teaching. The physics department has a special endowment to bring leading scientists to campus to deliver a lecture and speak to classes (past speakers have included Brian Green, Bill Phillips, Janna Levin, Jill Tarter, Stephon Alexander, Sean Carroll , and last year, Chanda Prescod-Weinstein. We also have resources to bring teaching experts to campus to observe classes and offer coaching, like Rhett Allain, Eugenia Etkina, and Andy Rundquist this year. Every summer, we run Physics Teacher Camp, bringing a group of physics teachers together to work intensively to discuss pedagogy and develop our curriculum. We have the resources to provide for almost any professional development opportunity you can imagine.
  • As a small school, we’re also very flexible. If you have interest in teaching another subject, this can likely be accommodated in the future. In my time here, I’ve taught multiple levels of physics, computer science, mathematics and worked as a college counselor. And I’ve seen colleagues who started in careers as classroom teachers grow into positions as department chairs, deans and even go on to become heads of other schools.

In short, the community is truly inspiring. If you’ve never considered boarding school teaching, you’ll be amazed by the connections you can form with students and the things they can accomplish when you encourage their interests outside the school day. This year, I’ve worked with a group of students to organize an Oxfam Hunger Banquet, am working with a young woman to design and paint a 10×10 mural in our science building to celebrate the beauty creativity and diversity of math and science, and am working with another student to create a campaign to change the culture of sleep at the school so that we set getting 8 hours or more hours of sleep each night as our most important priority.

This is a school that will help you to grow and discover new interests and talents, and build amazing connections with colleagues and students. You will often be amazed that you get paid to do be a part of this community.

Here’s the link to the job description. Please feel free to ask questions (confidentially) in the comments, and I’ll try to answer them or connect you with those who can.

Post 600: We’ve got work to do

November 10, 2016

Wow. It’s taken me almost 4 years to write 100 more posts on this blog. My previous milestones were:

500: May 23, 2012
400: Sept 27, 2011
300: July 13, 2011
200: February, 18, 2011
100: October 25, 2010

I think this is what one calls a “slowdown in output.” Blogging seems to have changed since those heady days when I somehow found myself writing 100 posts in one summer, and my life has changed even more as Maddie has grown, and we had our second daughter, Ada, back in 2015. These old posts remind me of happier, more innocent times, not unlike this photo from Tuesday afternoon, when my 6 year old had just pressed the button to vote for the first “girl President”, in her words.

IMG 9838

I see so much hope and optimism in the faces in this photo. I’m going to do my best in the weeks and months ahead to make sure we can all get back to that feeling. We’ve all got work to do.

Getting by on the day after

November 10, 2016

Tap, tap, tap… is this thing still on? It’s been a long time since I posted anything here, but it’s been a rough day, and I thought maybe firing up the old blog would be a cathartic release.

Like many of in America, I stayed up late last night and watched the results in total disbelief. No one saw this coming, how could we have missed this? I spent my Sunday canvassing voters in Philadelphia, I took my daughters to vote on Tuesday, and when she pressed the button to vote for the first female president, I was certain we would win.

As the results proved otherwise, the questions started popping up on Facebook and Twitter—what will I tell my children? What will I teach my students? And I watched as some really great answers came across my feeds—here’s a great piece on how to talk to kids, and @bowmananimal has one of the very best stats lessons I’ve ever seen focused specifically on how we could have missed this (seriously, if you teach stats, this is gold).

Once I figured out what I was going to say to my 6 year old daughter, I turned to my physics class, and struggled to think about what we were doing in there. How can we just be figuring out the energy momentum relation when it seems like so many more important things are happening around us.

Then I saw these tweets from Ben Lille, director of the awesome StoryCollider podcast

And I saw this post on the

In our class, we talk often about how important it is that you tell the full story of every number that you write, and this summer, I saw someone write about how every number you write in a science class represents a measurement, and when you write a measurement, you want to communicate 2 things:

  • What you’re measuring—this is why we include units
  • An idea of the uncertainty of the measurement

I decided to put together these ideas into a short slideshow to share the idea of measurement uncertainty and systematic uncertainty, and how even when you’ve got poll with a large sample size and a very narrow measurement uncertainty, your poll might still be invalid if one of the assumptions that underly the poll (like that every demographic of voters will turn out in equal numbers). And this is true of experiments as well—If you read graduated cylinders from the top of the meniscus, then all of your volume measurements will be slightly too large—and that’s why scientists work incredibly hard to identify and correct for systematic errors.

Lastly, we talked about inspiring Sagan quote:

Science is not perfect, it’s often misused.
It’s only a tool, but it’s the best tool we have.

I tried to add some nuance to this quote by talking about how science is a tool used by humans, and we bring a lot of baggage to science. We have unconscious biases, and these biases who gets to be a scientist, what experiments we choose to conduct, and even the data that we take. And sometimes these biases, mixed in with racism and sexism lead to some really horrible things done in the name of science. Ben Lille’s Science Needs a New Ritual is a great 2 page primer on this.

And then we did some physics problems, because there can be great joy in thinking about ideas, because unlike many of the other challenges we are now facing, these problems had solutions.

Turning PDFs into student portfolios

June 16, 2016

Our school has one of those amazing multifunction copiers that will scan to email. For the past few years, I’ve gotten in the habit of pulling the staples out of my assessments, and feeding the giant stack to the copier to create a big PDF. This has been great for keeping an archive of student work, but it’s also fairly cumbersome—to find an individual student’s work, I need to search the entire PDF.

I’ve often wished I could automatically split that one large PDF into a set of smaller PDFs, one for each student. And while I’m at it, it would be great if I could share that PDF with the student so that she could also see have an electronic archive of all her assessments.

With Google drive, this should be easy. I can use gClassFolder to build a folder system for my classes that includes one folder for each student that is shared between me and that student.

After some experimenting with Python and the pyPdf library, I’ve gotten pretty close to a solution, so I’m sharing it here with the hopes that you’ll be able to improve it further. I still need to add some code to have this program move the files into individual folders. I’ve also got a bit of code in this program that will email the PDF to each student.

So I’m posting this code on github with the hopes that you might find it useful, and think of ways in which I can further improve it. This code is very rough, and not well commented. It also requires that you install pyPdf, by typing this on the command line:
pip install pyPdf
PDFspliter python project

To run, this program requires a csv file titled “students.csv” that lists the students in the PDF in order, and the page number where the students’ individual PDF begins. The link will take you to a Google doc template that you can download.