Teacher Feature | May 31, 2022
Math Connections Take Students Far
A Los Angeles math teacher gets students engaged with connections to science and exploring the human side of math, such as how leaders inspire change in their communities.
Katherine Risbrough has been teaching high school math for almost 10 years. She began her teaching career in the Hickory Hill community of Memphis, Tennessee, where she taught everything from Algebra 1 to Calculus and served as a math coach for the district. Five years ago, she came to Los Angeles to teach Integrated Math and Calculus at Synergy Quantum Academy High School.
Outside of math, Ms. Risbrough is also a superfan of college football and never misses a game at her alma mater, the University of Southern California. Her fandom for making the game is rivaled only by her love of Harry Potter, having been to every midnight book and movie release.
I caught up with Ms. Risbrough to find out how she gets students excited about math, and I learned about a new strategy she used this past year: bridging math and science by teaming up with the AP Physics teacher. Her cross-discipline curriculum focused on helping students make connections between subjects and got them engaged as they returned from more than a year of remote learning.
Math can be intimidating for students and it can be difficult to keep them engaged. How do you get your students excited about math?
Sometimes it's easier said than done, but math needs to be as hands-on and discussion-based as possible. We use a lot of the calc-medic curriculum, which is application and discovery first followed by a whole class discussion to share ideas and cement new learning. When students have to speak and defend a hypothesis or an argument, they are practicing mathematical reasoning, which is a skill they can take into all STEM coursework. I avoid lectures as much as possible. We also do a lot of flipped classroom learning (videos at home and practice in class), group work, use technology, and do activities that get students moving around the classroom.
I believe that learning mathematics should be a collaborative, exploratory process and that every student already has the skills necessary to become a successful mathematician. It’s my job to give them opportunities to show off and strengthen those skills, so that they can be just as successful with or without me present to help them.
This year you’ve introduced some interesting projects to make your class more interdisciplinary. Tell me a bit more about that.
I’ve really focused on keeping the math contextualized by being sure the content is interdisciplinary. For example, over half of my AP Calculus students are also taking AP Physics. This year, in particular, I was sure to coordinate with the physics teacher to see how we could align our curriculum in kinematics with what we were doing with integrals and derivatives. This began with students doing JPL’s additive velocity lesson in their physics class to set the stage for how calculus ties together acceleration, velocity, and displacement.
Both classes are so challenging for students, but when they see how strategies in one class can help lift them in another, it’s almost as if they are getting to see two different strategies to solve the same problem. Designing challenges that could be solved with both physics and math gave the students an ability to approach problems from either side. At first, they were pretty intimidated to see their two most challenging classes teaming up, but the end result was some incredible student projects and dramatic improvement in their ability to graph out relationships.
I also kick off new units by making connections to students' own life or even their future careers. They need to know the “why” beyond just, “because you’ll be tested on it.” We try to talk about STEM historical figures and current leaders (specifically mathematicians and scientists of color) as often as possible. For example, I use clips from the movies "October Sky" and "Hidden Figures" to set the stage and then lead into projects about rocket trajectories and elliptical orbits.
This year, in calculus, we started the year with the idea of “Agents of Change” and looked at thought leaders such as veteran astronaut Ellen Ochoa and climate scientist Nicole Hernandez Hammer and how their work relates to “instant rates of change” and “average rates of change” in calculus. Then, I had students think about moments of change in their life, and how that instant can be carried forward to a make a long term change in their careers and communities.
Coming back from COVID-19 and more than a year of remote instruction, how are your students adjusting to being back in the classroom?
Our students missed out on so many social and academic opportunities because of COVID, but they aren’t letting that stop them. The biggest struggle was starting off the school year and getting back into routines. Because of the demographics of our students, there have been more absences than usual, as many of our students help support their family at home. Many parents struggled to keep work through the pandemic, and a lot of my students work outside of school or take care of their siblings. The effects of caring for their families while still trying to focus on applying to college has really taken a toll on students.
I’m fortunate that so many kids are comfortable and open sharing feelings of increased anxiety, responsibility, or worry over the past two years. I believe it's important that my classroom and our group first and foremost be an escape from that space rather than an added stress. Their success in math – even a rigorous AP math class with a breakneck pace – comes from me being there for them as a person first and a teacher second. We focus so much on “catching them up” that we forget to take some time for them to process all they have had to manage.
As we move toward graduation, what is one story of success that you will take away from this year?
Honestly, it's the success of my students. They have jumped into AP Calculus after 1.5 years of distance learning and the social-emotional learning burdens of Covid, and have done amazing work. They are thoughtful, persistent, and often learning multiple grades worth of skills within one calculus lesson. I guess I'm a small piece of that, but all that I've really done is give them space to explore, discuss, and learn. It's what they've done with that space that has been the best thing to watch!
Looking for ways to bring NASA STEM into your classroom or already have a great idea? The Education Office at NASA's Jet Propulsion Laboratory serves educators in the greater Los Angeles area. Contact us at firstname.lastname@example.org.
Ion Propulsion: Using Spreadsheets to Model Additive Velocity
Students develop spreadsheet models that describe the relationship between the mass of a spacecraft, the force acting on the craft, and its acceleration.
Time 30-60 mins
Explore a collection of standards-aligned math lessons with links to NASA missions and science.
TAGS: Teachers, School, Classroom, Instruction, K-12, High School, Math, Calculus, Physics, Algebra, Lessons, Resources
Teachable Moments | October 31, 2016
When Computers Were Human
In The News
This week, we celebrate the 80th anniversary of the Jet Propulsion Laboratory. JPL was founded long before it became NASA’s premier center for robotic exploration of the solar system – and even before the agency existed. In fact, JPL started as the test-bed for some of the earliest rocketry experiments (thus the name “Jet Propulsion Laboratory”). There were a number of factors that conspired to change JPL’s focus from rocketry to space exploration. The Space Race and the resulting formation of NASA were two major factors. But also, with its growing expertise in launching rockets to new heights, JPL was anxious to take its experiments even farther. So in 1957, when the Soviet Union won the first leg of the Space Race by placing Sputnik, the first artificial satellite, into Earth orbit, JPL was called into action. A few months later, NASA launched the JPL-built Explorer 1, which became the first U.S. satellite.
Soon, the challenge was to land on the moon – and JPL was once again called to the task. Landing on another planetary body had never been accomplished so, understandably, it took a few tries to get things right. JPL’s first attempts at a moon landing with Rangers 1 through 6 all failed for various reasons. Some of the spacecraft flew very near the moon only to miss it by a few hundred kilometers; others met their mark only to have onboard cameras fail. Ranger 7 was the first mission to successfully land on the moon and transmit data, capturing images 1,000-times better than those obtained by ground-based telescopes. It wasn’t a particularly soft landing; rather it was a purposeful crash landing, capturing images along the way. But everyone at JPL was thrilled to have hit their target and returned usable data. These data, and those collected by subsequent missions, made possible NASA’s later human missions to the moon.
At the same time it was launching the Ranger lunar missions, JPL had also set its sights on venturing even farther into space and began launching a series of missions called Mariner to Venus, Mercury and Mars. It wasn’t long before JPL’s specialty became creating robotic spacecraft to go not just to the moon, but also where no one had gone before.
Learn more about the history of JPL and the U.S. space program in the video series below. And explore the interactive timeline.
How They Did It
What’s often not known is that all the early rocket experiments and later missions to the moon and beyond wouldn’t have been possible without a team at JPL known as the human “computers.” Most of these human computers were women who either had degrees in mathematics or were simply very good at mathematics. Over the course of time, these women not only performed hundreds of thousands of mathematical calculations crucial to the U.S. space program, but also eventually became some of the first computer programmers at NASA.
In the early days of space exploration, the best mechanical computers were large (the size of a room) and not particularly powerful. Human capabilities were much more powerful for many tasks, including the rapid calculations needed for trajectory analysis and verification, as well as the graphing of data points on trajectories, which made a spacecraft’s path easy to see.
One of the human computers’ main tasks was computing the planned trajectories, or paths, for a spacecraft based on the vehicle weight, lift capacity of the rocket, and the orbital dynamics of the planets.
When a spacecraft is launched, it begins sending telemetry signals back to Earth. These signals tell engineers information about the spacecraft’s location and health. But this information isn’t perfectly straightforward. It arrives as a bunch of numbers that need to be combined in formulas along with other constantly changing parameters (such as velocity, vehicle mass and the effect of gravity from nearby bodies) in order to reveal the spacecraft’s actual location. Before there were computers (as we know them today) to do these calculations, human computers would feverishly calculate the exact location of the spacecraft as the telemetry came in and compare that to the planned trajectories. Their calculations would reveal whether the spacecraft was on target.
Doing the calculations required to get Explorer 1 into orbit was no small task. Calculating the trajectory for a Ranger crash landing or a Surveyor soft landing on the moon was even more challenging. Once humans were destined to be on board for the Apollo missions, the stakes were even higher. Fortunately, JPL had set the stage developing the techniques – and calculations – necessary to land a robotic spacecraft safely on the moon.
Why It’s Important
Today, JPL continues setting the pace for exploration of the solar system using robots to go where humans hope to venture one day, such as Mars. Though trajectory computations are now done using modern day computers, humans are still required to do trajectory analysis and mission planning. Every mission is different, and with new techniques comes new simulation equations that must be developed and computations that must be performed during actual mission events to ensure success. But even now, nothing is fail-proof. Lots of variables can and do influence spaceflight. Arriving safely on another planet millions of miles away isn’t easy or taken for granted, but when things go right and we achieve a safe landing, it is definitely cause for celebration.
When launching to another planet, we want to take the most efficient route, using the least amount of rocket fuel possible. The early human computers quickly discovered that launching when two planets are closest and using a lot of rocket fuel for the job isn’t the best plan.
Use this fascinating bit of history as a real world, advanced algebra and physics lesson with students in this standards-aligned activity that has grades 9-12 calculate the next launch window to Mars!
Let's Go to Mars! Calculating Launch Windows
Students use advanced algebra concepts to determine the next opportunity to launch a spacecraft to Mars.
Time 30 mins - 1 hr
- Meet JPL engineer Sue Finley – Finley started at JPL in 1958 as a human computer and still works at the laboratory.
- Women at JPL website
- JPL History
- JPL 80th Anniversary Article
- JPL Timeline
- JPL 80th Anniversary Video Playlist
- JPL 80th Anniversary Printable Calendar
- Mars in a Minute Video Series
- Stomp Rockets Activity
- Basics of Space Flight Tutorial
TAGS: Women in STEM, JPL Anniversary, History, Human Computers, Launch Windows, Algebra, High School, Women at NASA