Everyone in the theater applauded as the credits rolled at the end of the movie, Hidden Figures, and for good reason. It is an amazing, humorous, educational, inspiring and important movie. It is a film that every educator and math student should see. This true story of the contribution of three black women to NASA’s launching of John Glenn into orbit is full of so many positive messages about math, science, patriotism and social justice that I am compelled to share my perspective as a high school math teacher. Here are my reflections from this incredible movie.
On Math
Math is More Than Computing.
Yes, a team of nearly twenty African-American women was known as “the computers,” because in the days before calculators, computation was done by hand. However, the movies’ three protagonists, Katherine Johnson, Dorothy Vaughn and Mary Jackson, were all given assignments for which the math went far beyond simple computation. They had to visualize geometrically, draw graphs, generate equations, assign units, assess another’s work, creatively program and, yes, solve lots of problems. Much of the work that was glorified in the movie was the application of mathematics, not calculation with mathematics. In fact, the director the Space Task Group, Al Harrison insisted:
“This isn’t about plugging in numbers, this is about inventing the math.”
Intellectual work is valuable.
Several times in the movie there was reference made to the “work” done by the various NASA personnel.
Dorothy reference the number of people needed to run the new IBM: “We’re going to need a lot of manpower to program that beast. I can’t do it alone. My gals are ready. They can do the work.” *
Al Harrison in response to a politician’s inquiry: “That’s the math we don’t have yet, gentlemen. We’re working on it.”
Ruth (Katherine’s colleague) on Katherine’s last day on the Space Task Group: “You did good work around here.”
Al Harrison after John Glenn was returned safely to earth: “Nice work, Katherine.”
Dorothy instructing the other women in reference to Katherine re-computing John Glenn’s critical re-entry coordinates: “Alright, give her space. Let her work.”
The work referenced here is the kind of work that educators are called to teach in the 21st Century classroom. We math teachers are currently implored to replace meaningless busy work with relevant intellectual work.
Math put humans into space.
Katherine upon being questioned about how she knows that one type of rocket is needed over another:
“What’s there tells the story if you read between the lines. The distance from launch to orbit is known. The Redstone mass is known. The 
Mercury Capsule weight is known. And the speeds are there in the data…. The numbers don’t lie.”
That says it all.
The movie got the math and the science right.
Hollywood has a track record for flunking math and science in movies, however, in this one, they earn a stellar score.
Katherine as an 8-year old child prodigy: “If the product of two terms is zero, then common sense says at least one of the two terms has to be zero to start with. So, if you move all the terms over to one side, you can put the quadratics into a form that can be factored, allowing that side of the equation to equal zero. Once you’ve done that, it’s pretty straight-forward from there…”
Stafford: “The Atlas Rocket can push us into orbit. It goes up. Delivers the capsule into an elliptical orbit. Earth’s gravity keeps pulling it, but it’s going so fast that it keeps missing the Earth – that’s how it stays in orbit.”
A+, Hollywood.
On Math Education
All need to be encouraged to check their work.
When Katherine Johnson was asked by her new boss to check the work of the lead engineer, Paul Stafford, Mr. Stafford balked. In response to his objection, Harrison gave a speech about the importance of the task, and that no one is above having his or her work checked.
“Do I need to remind everyone…that we are putting a human on top of a missile and shooting him into space? It’s never been done before. And because it’s never been done … everything we do between now and then is going to matter: it’s going to matter to their wives, their kids, I believe it’s going to matter to the whole damn country. So this Space Task Group will be as advertised. And America’s greatest engineering and scientific minds will not have a problem with having their work checked.”
Yes, those engineers had to check their work because the boss said so, but the boss also gave them the reason why… because getting the answer right is important. If NASA engineers needed to be reminded of this on occasion, then so do our math students.
Much of the math that launched John Glenn into space is taught in high school.
Yes, the characters in the movie mentioned things like the Frenet Frame and the Gram-Schmidt, but many of the terms used and the equations shown in various scenes would be recognized by students in high school math classes across America.
Paul Stafford: “We need to move from an elliptical orbit to a parabolic path.”
Katherine: “On any given day, I analyze the manometer levels for air displacement, friction and velocity and compute over 10,000 calculations by cosine, square root and lately Analytic Geometry.”
Our math students should know that they are actually learning rocket science!
There is opportunity for everyone in STEM fields. (Science, Technology, Engineering and Mathematics)
The three women portrayed in Hidden Figures were specialists in three different STEM fields: Mathematics, Engineering, and Programming. These are all fields in which we have a shortage of American citizens earning a degree, to the point that much of the classified work in this country is being done by people who have citizenship from other countries. The STEM community sees this as an issue and would very much like to see more Americans pursuing careers in these fields. With the typical STEM job offering twice the annual earning of a non-STEM job, there is a huge opportunity for economic advancement for low-income students entering these vocations. If they are not choosing this on their own, then we educators should be doing more to encourage and support their election of these endeavors.
On Equity
The oppressed are not victims.
Hidden Figures is very much a story about victory over oppression, not victims of oppression. The victory was achieved by the heroines changing themselves, changing others, and changing the system…
In order to adapt to economic change, we must improve ourselves.
When Dorothy Vaughn finds out that the new IBM computing machine means that the human computers will be obsolete, she not only makes moves to position herself well in the new age of computers, she encourages her friends to do the same.
“It’s not going to matter soon. This IBM’s going to put us all out of work… Only one thing to do: learn all we can. Make ourselves valuable. Somewhere down the line a human being’s going to have to hit the buttons… We have to know how to program it. Unless you’d rather be out of a job?”
Dorothy then goes to the public library and checks out a book on Fortran (one of the original programming languages). She even reads it aloud to her sons on the bus, as a mother’s lesson in overcoming adversity.
This message is extremely relevant in the political climate today. Many jobs are being lost to automation and changes in the global economy. The promise of today’s politicians to “bring those jobs back,” is equivalent to thinking that the emergence of the information age, represented in the film by the IBM machine, could have been prevented in order to maintain the human computing jobs. It is equally as silly to think that anyone today can stop the evolution of the job market. Instead, we educators should be teaching students, and ourselves, to do as Dorothy did, and adapt to the new 21st Century economic environment.
They were strong women not just smart women.
These three women were more than simply a mathematician, engineer and programmer; they were wives, mothers and daughters. Katherine Johnson was a single, widowed mother who had to raise and support three children. Mary Jackson was a married mother who held down a job and attended night school. It takes internal strength to balance that kind of life.
They were brave women not just strong, smart women.
The three heroines each had a moment in the story in which they spoke truth to power. In the engineering lab, the courtroom, and the office. In each case, their courage effected change.
Black men are not thugs.
The two primary black male roles in the movie, the husbands of Katherine and Mary, were not the gangsta and drug-addict that is too often the portrait of black men in movies. Jim Johnson and Levi Jackson were both strong, family-oriented men of solid character.
Prejudice and Discouragement are sometimes found in your backyard.
The women of Hidden Figures were not only dealing with racial bigotry, but they faced sexism as well, even from their own friends. At the first meeting with her future husband, Katherine’s suitor puts a huge foot in his own mouth:
Jim Johnson: “Aeronautics. Pretty heady stuff. They let women handle that kind of- … I was just surprised something so taxing…”
video clip
Levi Jackson (Mary’s Husband commenting on her desire to become a NASA engineer): “All I’m saying, don’t play a fool. I don’t want to see you get hurt. NASA’s never given you gals your due, having another degree won’t change that. Civil rights ain’t always civil.”
Both men came around to offer full support of their ladies’ dreams, after their wives stood strong to their convictions. Sometimes the battles for equity must be fought in our homes and communities, not only against “them.”
Prejudice is sometimes harder to see now.
We no longer have colored bathrooms, colored bus seats, colored drinking fountains or colored coffee pots, but we do have colored schools and even colored classrooms. We know that schools are just as segregated now, as before Brown vs. Board of Education. The inequity in funding and support for the black schools means segregation by opportunity, which is more criminal than segregation by race. The roster of my own class of “at-risk” students is 90% populated by students of color, while those same groups of students make up only 54% of the school population. When I brought this to the attention of the administration, they were genuinely unaware, but instantly concerned. Statistics like this, which exist on paper, are harder to see and less humiliating, but actually more dangerous than a “coloreds only” sign. Therefore, we educators need to be more vigilant in exposing these numbers and in changing the practices and policies that they represent.
The Powers That Be must be part of the change process.
As much as the three heroines are rightfully credited with impacting change in NASA’s practices regarding women and blacks, we need to also recognize those members of power structure that aided them in their cause: Space Task Force Director Al Harrison who gave Katherine access to classified data and high level meetings, Astronaut John Glenn who went out of way to greet the black female computers and insisted that Katherine do the calculations on his re-entry, Polish engineer Karl Zielinski who encouraged Mary to seek her engineering degree, IBM Technician Bill Calhoun who gave Dorothy the opportunity to program the new technology and her boss, Vivian Michael, who promoted her to Supervisor.
People of all ethnicity and gender can contribute.
This story was about more than whites and blacks sharing the same bathroom. It was about the talents and contributions of people of all backgrounds. Katherine makes this very point in the first meeting of her and her future husband.
Katherine: “So, yes…they let women do some things over at NASA, Mr. Johnson. But it’s not because we wear skirts…it’s because we wear glasses.”
Racial equality is pragmatic as well as moral.
This important story of Johnson, Jackson and Vaughn is about more than women or blacks receiving a fair shake. It is about how one of the crowning achievements of America may not have been accomplished without them.
Vivian Mitchell (Dorothy’s Supervisor): “Seems like they’re gonna need a permanent team to feed that IBM.”
I don’t want to question Al Harrison’s sense of social justice, but his tearing down of the “Coloreds Only” bathroom sign was as much an action of practicality as it was a display of righteousness.
Harrison “Go wherever you damn well please. Preferably closer to your desk.”
His primary purpose was to get an American into orbit, not to get a black woman to urinate next a white one, but he saw that the path into space traveled through an integrated restroom. Katherine knew it also traveled through an integrated boardroom. She was being kept out of key meetings, because of her gender and race, when she knew that her work was being hindered by the locked door. She stated her case for inclusion to her boss, not on a basic of equality, but on a basis of practicality.
Katherine: “I cannot do my work effectively without having all of the data and all of the information as soon as it’s available. Indeed to be in that room, hearing what you hear.”
When Harrison has to stand for her presence in the meeting, he did not say, ‘We need more black women in these meetings.’ Instead, he claimed,
“This is Katherine Goble with our Trajectory and Launch Window Division. Her work is pertinent to today’s proceedings.”
One of the strongest points of the movie is that prejudice not only harms the oppressed, but it hinders all of us. Equity does not only make America more fair, it makes America better.
On American Patriotism
Black history is American history.
The story of Hidden Figures is not the only story of African-American mathematicians and scientist who have made terrific contributions to our nation. In fact, those lists are long and distinguished:
America always struggles to live up its ideals, but those ideals are America.
The names of the two spacecraft highlighted in the film are named Freedom and Friendship. These names seem a bit ironic when contrasted to the social controversies of the time. Many blacks and women in the ‘60’s would not have considered America to be friendly or free, however, gender and racial equity made huge strides towards these American values during that time period.
Mary: “I’m a Negro woman. I’m not going to entertain the impossible.”
Zielinski (engineering colleague): “And I’m a Polish Jew whose parents died in a Nazi prison camp. Now I’m standing beneath a space ship that’s going to carry an astronaut to the stars. I think we can say, we’re living the impossible.”
Mary would be happy to know that over 50 years later, not only are women of all ethnicities being allowed to become engineers, they are being actively recruited for such a career, and we in the public school system are being charged with raising them up. Again, this is not a matter of equality; it is a matter of practicality. America needs more engineers, and any antiquated systems of injustice will keep us from achieving our technological potential, and from reaching our highest ideals of Friendship and Freedom.
* All Quotes from Hidden Figures Screenplay by Allison Schroeder and Theodore Melfi, May 12, 2015 (Based on the book Hidden Figures by Margot Shetterly).
I’ve heard Steve Leinwand say that it is unprofessional to ask teachers to change more than 10% a year. It is also unprofessional to ask them to change less than 10% a year.
How do you quantify professional growth?
When faced with a challenge, the fixed mindset brain “goes cold.” It literally shuts down.
However, when faced with the same challenge, the growth mindset brain “fires up.” It knows that more is being asked of it, so it kicks into high gear to meet the challenge, rather than duck it.
I also saw an interesting take on the Snowball Activity. Students write down one comment and one question about a topic (notice and wonder), then wad up their papers and throw them around the room. Each student picks up a “snowball” and adds another comment and question. This is done again, until there are three of each. After the fourth toss of the snowballs, the students do not write, but instead debrief publicly as the teacher summarizes the comments and questions on the board. This is a strong way to have ALL students reflect on learning.
We started by surveying the audience on 
He explained that you start with “something to be modeled,” (noticed he did not say a real-life situation) and then you create an abstract representation of it. This is a back-and-forth process of verifying the accuracy of the model’s description of the something as well as the “thing” that we want to do with it. (Use rocks to keep track of the sheep). So the audience was responses were spot on… collectively. Yes, modeling is Representation AND Application, but not necessarily just Representation OR Application. Furthermore, Edmond wanted to make it clear that modeling does not have to apply to only “real-world” examples. He claims that when we discuss the transformations of a family of functions, we are also modeling… using an abstract representation to “do something” to the original parent function.
Big Take-Away = 
The San Francisco USD Mathematics Teaching Toolkit: Changing the Practice Along with the Content — Glenn Kenyon & Kathy Bradley (
The Math Projects Journal 