Math Connections Take Students Far

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.

Ms. Risbrough works with one of her calculus students. Image courtesy: Katherine Risbrough.

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.

Students in Ms. Risbrough's class map out language and processes to better understand shapes and limits in functions. Image courtesy: Katherine Risbrough.

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.

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 education@jpl.nasa.gov.