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STEM in the Middle School
Middle School STEM subjects help our active learners take their problem-solving skills to the next level.
Sixth graders study life science and physical science, including air quality and other relevant local topics. Seventh grade covers earth science and physical science, and students travel to the Teton Science School in Jackson Hole, Wyoming, to learn about the ecosystem and outdoor exploration. Eighth grade presents a survey of physical sciences and scientific processes with an emphasis on hands-on experimentation, analytical thinking and problem solving, and development of technical communication skills.
Middle School math topics range from pre-algebra to geometry. Students hone problem-solving strategies through mathematical investigations. They analyze real-life situations and study how those situations can be modeled by linear, inverse, exponential, or quadratic relationships. Recognizing patterns, defining and manipulating variables, collecting and graphing data, and predicting outcomes are all central to the curriculum.
Sixth graders take Foundations of Computer Science, which culminates in the design of a game or an interactive story. STEM electives available for seventh and eighth graders include Computer Science, Robotics, and Make Club.
Middle School STEM Activities
Our Middle School has an average class size of 16 students. Every child is well-known and supported in the ways that best meet their needs.
Every day on the Lincoln Street Campus, students walk past a bulletin board displaying the award-winning Annual Report story “Computer Science for All at Rowland Hall.” The bold headline is a lofty aspiration that is becoming a reality, one class at a time.
“We’ve always known this was an area that we wanted to grow,” said Director of Technology Integration Christian Waters. “We feel that increasing opportunities for students in computer science and robotics is in line with the strategic priority to prepare students for an ever-changing world.”
There is an argument that coding is a new literacy skill everyone must have, along with reading, writing, and arithmetic.—Christian Waters, director of technology integration
And in today’s digital world, no matter what fields students want to go into, an understanding of the basics of computer science is not only an asset—it’s a necessity. “There is an argument that coding is a new literacy skill everyone must have, along with reading, writing, and arithmetic,” said Christian.
Knowing this, Rowland Hall has made recent investments in our computer science offerings, which are already making a difference across divisions, including in the Middle School. This year’s hiring of the division’s first full-time computer science teacher is one substantive proof of the school’s commitment to growing the program, and the Middle School team is taking advantage of the opportunity to offer classes students haven’t always had access to before. This year, they are building robots made of LEGO bricks, designing games, and coding their own websites. Next year, there will be even more opportunities, like application design, expanded robotics offerings, and a maker class.
And students are discovering a passion for the subject—even if they were unsure what to expect when they began. Eighth grader Emery L. thought she was signing up for a mechanical engineering course, so was surprised when it was software engineering. Now, though, she’s passionate about creating with code. “I enjoy the problem solving,” she said. “The more you learn, the more tools you have to work with, and eventually you can put them all together and create something big and impressive.”
Eighth grader George J. sees the possibilities as limitless when it comes to what he can do with his growing knowledge of computer science. He also said it has changed the way he views the world. “I like looking at websites and knowing how they were built, and knowing I could build something similar,” he said. “If I see a problem in the design, I know I could fix it."
The number of students discovering a passion for computer science in the Middle School is expected to increase in coming years, due largely to the exposure they are getting in the Lower School. Starting in kindergarten, Rowland Hall students are introduced to STEM and robotics principles, and starting in second grade, all Lower School students take computer science as part of their curriculum. Students also have access to more resources, including an all-new TREC (technology, robotics, engineering, coding) lab, which is home to multiple 3D printers and has plenty of space for students to build, experiment, and explore.
“Not only are they building skills and knowledge, but they are also building interest,” said Director of Curriculum and Instruction Wendell Thomas. “In a couple of years, the students coming into the Middle School will have significant experience, and we will be able to offer them next steps and challenges.”
I enjoy the problem solving. The more you learn, the more tools you have to work with, and eventually you can put them all together and create something big and impressive.—Emery L., class of 2027
Introducing these skills and knowledge earlier also means more students are invested in computer science and see themselves as a part of the field—an important step in fulfilling the school’s goal of bringing computer science to all. “We realize that, like schools across the country, we still have work to do to ensure girls and people of color are represented in our computer science classes,” said Christian. “Everybody should be able to see themselves as successful in computer science and robotics.”
It's a plan Emery supports. Even though she’s not currently taking computer science this semester, she is continuing the work she started in the fall on her own time, learning various code languages and continuing to work with computer science teacher Jon Poll on projects. She enjoys the challenges the subject presents and the opportunities her experience will bring in the future. “In any job, tech is always present,” she said. “If you have these skills and abilities, there will be a way to apply them in any career that you choose. Even if it’s a minuscule part, there still is something to do with it.”
Wendell agreed, noting that the future of computer science in the Middle School, as well as the school as a whole, all comes down to fulfilling our vision to prepare students to make a difference in today’s world. “People the world needs need to understand how computers work and how they can be used,” he said. “We are doing that at Rowland Hall.”
Teacher Sara Donnelly knows that the best way to help her eighth graders grasp scientific concepts is to connect their studies to authentic learning experiences. As a result, she’s always on the lookout for projects that transform science topics into “aha!” moments for students.
“I want them to see science as something that’s familiar, part of their lives, and useful—and not intimidating,” she said.
This year, she kicked off this approach by introducing students to the study of waves, or transfers of energy. An essential component of the study of physics, waves help scientists understand physical phenomena, and they can be found in many forms in our everyday lives, from the sounds we use to communicate to the lights we use to see.
“One of the reasons I start with waves is they offer a more qualitative experience and are more visual,” said Sara. This makes them especially useful for building scientific understanding and skills in middle schoolers: depending on students’ abilities, they can observe waves in a variety of ways, such as by listening to music or by observing colors made by light. These real-world practices, explained Sara, also help them learn to apply knowledge through unbiased observations, as well as practicing accurately recording data.
The eighth-grade waves study is divided into three subunits (wave properties, sound waves, and light waves), and examines what waves are, the types of waves, how waves travel, and how, with different materials, waves can be sped up, slowed down, or amplified. The kids quickly picked up on the concept: during a Middle School dance that took place during the unit, Sara said students were commenting on the need for more absorbent walls in the gym. Students also discovered that waves were the reason behind some of their day-to-day experiences—eighth grader Sophia H., for instance, noted that the unit helped explain odd noises she’d heard: “I found out that sound waves traveled through vibrating particles, which definitely explained some of the weird sound phenomena that I have experienced in the past,” she said.
I want [students] to see science as something that’s familiar, part of their lives, and useful—and not intimidating.—Sara Donnelly, eighth-grade science teacher
The students also enjoyed opportunities to set waves’ paths in order to better understand them. In November, they demonstrated light behavior and the law of reflection via mirror mazes. And in December, in culmination of all they learned in the first unit of the year, they designed models of their ideal concert experiences, a project centered around how both light and sound waves can affect how a person experiences an arts event.
“They were really excited about it,” said Sara. “Eighth grade is a great opportunity for students to use their creativity, apply their understanding of something, and take it to a more abstract way of showing their understanding.”
For the project, students were divided into teams and tasked with designing 3D models of concert venues, complete with speakers and lights marked with the directions of their waves. Students had to think through how the movement of sound and light would affect the audience’s experience: Where should speakers be placed for optimal sound quality? How will sound travel around the venue? How does the shape of the stage, or the seating, affect sound? How do light and color mix? What building materials will produce the best results? How do you manage accessibility for all attendees? In addition to a writing papers outlining each choice and its scientific justification, students presented their models to their peers, incorporating 30-second clips of songs that complemented their venue designs—choices varied and included Offenbach’s “Can-Can,” 21 Pilots’ “Stressed Out,” and AC/DC’s “Thunderstruck.” It was a unique, and fun, way to tie together what they had learned.
“It was an interesting unit and I expanded upon my knowledge of waves quite a bit,” commented student Kendra L.
The project was a great way to build students’ confidence as scientists while also preparing them for new challenges: since returning from winter break, the eighth graders have been immersed in a new unit around forces in motion—a more challenging topic that’s stretching their learning through studies around acceleration, friction, and inertia. And just like in the waves unit, Sara is incorporating activities—including one titled “How Slow Can You Roll?” in which students work to slow the movement of a ball—that bring learning to life while building skills like how to communicate effectively, how to work well with others, and how to use sound data to solve problems.
“I want them to be able to reason through different theories as to what a possible solution might be, and to avoid jumping to conclusions,” said Sara. “The unit is building up their skills to be good scientists and good observers who ask questions and design solutions.”
Editor's note: This piece is republished from Rowland Hall's 2020–2021 Annual Report.
This story won silver in the 2021 InspirED Brilliance Awards (magazine feature article writing category).
Computer science impacts our daily lives, but its workforce falls woefully short when it comes to reflecting national racial, ethnic, and gender demographics. Solving that problem starts with K–12 education. The subject’s proponents at Rowland Hall are ensuring equity is programmed into the curriculum—and the curriculum gets the attention it deserves—building toward a computing-literate society where everyone has a seat at the table.
During hybrid learning one February afternoon, about 40 Rowland Hall faculty, staff, and upper schoolers—some working from home, others from the Lincoln Street Campus—gradually populated a Zoom room. It started off as a standard pandemic-era Upper School class, but 20 minutes later, it looked more like an avant-garde digital dress rehearsal. Students unearthed accessories from family members’ closets and Halloween costumes past: a cowboy hat, a pair of aviation goggles, a leopard-print scarf. They cloaked themselves in masks, feather boas, heavy makeup, and oversized sunglasses.
Director of Arts Sofia Gorder and her dance students comprised half of these creative camouflagers, but despite appearances, it wasn’t prep for one of their performances. It was an open workshop held by teacher Ben Smith ’89 and his Advanced Placement Computer Science (CS) Principles class to show the Upper School community how facial-recognition technologies work and how they can be harmful, particularly for underrepresented groups.
One dance student, Mena Zendejas-Portugal ’21, wore a pink wig with bangs that covered her eyes. She used makeup to draw decoy eyes on her cheeks, below the magenta fringe. Mena and her peers smirked at their laptop cameras as a web-based program used artificial intelligence (AI) to guess their ages and genders.
Before Mena wore her disguise, the program vacillated between misidentifying her as a 13-year-old boy and a 12-year-old girl. After Mena changed her appearance, ironically, the program’s guess came closer to the reality: it classified her as a 16-year-old female.
“It wasn’t a surprise how the AI read me since I have a rounder face along with short hair,” said Mena, one of the leaders of the student Justice, Equity, Diversity, and Inclusion (JEDI) Committee. “It’s just a confirmation for the thought of AI being built around stereotypes and constructed beauty standards that aren’t applicable to everyone.”
Algorithms permeate our daily lives, and flawed coding can have devastating real-world consequences, from wrongful arrests to housing discrimination. Ben educates the Rowland Hall community on these problems, and ensures his CS students are equipped to solve them.
Algorithms permeate our daily lives, and the type of flawed coding that Mena experienced can have devastating real-world consequences, from wrongful arrests to housing discrimination. Ben educates the Rowland Hall community on these problems, and ensures his CS students are equipped to solve them. “If these students are going to become leaders in technology, they need to have this perspective,” Ben said. “You can't ask people to have an interest in a career and not prepare them for the future ramifications of that.”
Ben has long given students space to discuss JEDI issues but formally added it to his CS curriculum during the 2020–2021 school year. And at Rowland Hall, the marriage of CS and social justice is a natural development: the school prioritized science, technology, engineering, and math (STEM) in the 2014 Strategic Plan, and during the past school year, longtime JEDI work escalated as a priority.
February’s facial-recognition workshop—Drag Vs. AI by the Algorithmic Justice League, which “combines art and research to illuminate the social implications and harms” of AI—helped a cross section of upper schoolers see firsthand why this work matters: “By just learning CS and not looking behind the scenes, the future could be less inclusive than we envision,” Mena reflected. Indeed, AI researcher Joy Buolamwini, a Black woman, launched the league after personally experiencing algorithmic discrimination in her work. In one project utilizing generic facial-recognition software, the program failed to detect Joy’s face until she wore a white mask. In another, she had to ask a lighter-skinned friend to stand in for her. We can solve these problems, Joy posited in a 2016 TED Talk with over 1.4 million views, by creating more inclusive code. Teams must be diverse and driven to create “a world where technology works for all of us, not just some of us, a world where we value inclusion and center social change.”
This ethos fuels Ben’s work. The Rowland Hall alumnus, now celebrating 20 years as a faculty member at his alma mater, started teaching CS in 2015 and shifted to teaching that subject exclusively two years later. From day one, he’s made it his mission to diversify CS, a field “plagued by stark underrepresentation by gender, race, ethnicity, geography, and family income,” according to CS advocacy nonprofit Code.org. The US needs more—and more diverse—computer scientists, and efforts to broaden that workforce need to start in K–12 schools. Computing jobs are the top source of all new wages in the US and they make up two-thirds of all projected new jobs in STEM fields, Code.org touts, making CS one of the most in-demand college degrees. And exposure before college makes a difference: students who learn CS in high school are six times more likely to major in it. Among traditionally underrepresented groups, the likelihood is even higher: seven times for Black and Latinx students, and 10 times for women.
Ben currently relies on one-to-one recruitment to grow CS enrollment among those underrepresented populations. He read a book around 2014, during graduate school in instructional design and educational technology at the University of Utah, that sparked his professional goals: Stuck in the Shallow End: Education, Race, and Computing by Jane Margolis. The book chronicles the lack of access to CS courses for Black and Latinx students—and addresses how to change the system. “It was just one of those eye-opening moments,” he said. “There’s no logical reason—except institutional bias—for why computer science education looks the way it does today … It’s incredibly unjust.” Since then, Ben has prioritized combating what he calls the most glaring equity issue in education today. He collaborates with other schools and organizations that are trying desperately to expand CS opportunities, and works diligently to build an equitable CS program for Rowland Hall. “With Rowland Hall's support, I’m committed to a future where all computer science courses have a student population that mirrors the demographics of the school as a whole.”
Building Curriculum from the Ground Up
Fortunately, Ben isn’t starting from scratch when sixth graders meet him in Foundations of Computer Science, a required class since 2016. Since Christian Waters stepped into the role of director of technology integration in 2013, he has crafted an arsenal of computing lessons to captivate the full spectrum of beginning and lower schoolers. Christian teaches at least one unit of digital citizenship, coding, and robotics to every lower schooler. Kids engage in hands-on activities like programming colorful toy robots and building wearable tech comprised of LED lights affixed to felt. They also get the space to think big and consider computing’s real-world applications, like furthering one of the United Nations Sustainable Development Goals. How might they use computing, for example, to remedy a problem like overcrowding or a lack of affordable and clean energy?
Christian draws curriculum from dozens of expert educational resources, including the Robotics Institute at Carnegie Mellon University, Children’s Innovation Project, and Code.org. “We've built something that is really relevant, and the best combination of the best materials and resources,” Christian said. “It's not a curriculum that is sold in a big box that you wheel into a classroom, and everyone has to do it the exact same way. It's tailored to the needs of Rowland Hall and relevant to our goals and our objectives.”
Thanks to ongoing collaboration between Christian and Ben, Rowland Hall’s CS curriculum is also vertically aligned: “We're preparing students for Advanced Placement Computer Science A Java in a way they never were before. Students in the Middle School are learning about objects, classes, functions, and variables,” Christian explained. “It's thanks in part to how we're building up from the Beginning School.”
One example of vertical alignment and mission-centric curriculum: Christian uses a Code.org activity where lower schoolers train a computer to recognize facial expressions—broaching some of the same issues upper schoolers examined in their February workshop. The crux of the Lower School lesson, according to the educator: “How do we distinguish between facial features and whether someone is happy or sad or excited, and is that even ethical to do that?” Students exercise their critical-thinking skills and confront questions involving how these programs work, and how to ensure they’re as ethical and unbiased as possible. “Ultimately what students get is that there is a lot of subjectivity in how we humans train computers,” Christian said.
A Group Effort
Part of attracting younger and more diverse students to CS—and, down the road, reducing bias in code—entails continual, widespread exposure. Christian has not only integrated CS into classrooms, he’s also created community-wide opportunities to rally around computing and engineering. He organizes three annual events that are now synonymous with STEM culture on the McCarthey Campus: the beginning and lower school Family Maker Night in the fall, the school-wide Hour of Code in the winter, and Lower School Maker Day in the spring. “These events are designed to demystify technology and making,” Christian said. “All students can see themselves as computer scientists, coders, makers, roboticists, engineers.”
These events and the school’s CS curriculum as a whole are dominated by collaborative group work that occasionally reaches across subjects and divisions. Before the COVID-19 pandemic, Ben Smith's Advanced Placement Computer Science Principles students collaborated annually with Tyler Stack's fourth graders to make an app that helps young students learn math. Upper schoolers worked in groups to devise and test app concepts on the lower schoolers and use their feedback to improve app design. For Katy Dark ’21, it was a highlight of Rowland Hall’s CS program: “The thing that will stick with me the most is using new interfaces to help people.” It’s a fitting favorite memory for Katy, who in 2020 became the first Rowland Hall student to win the top national award from the Aspirations in Computing program, sponsored by the National Center for Women & Information Technology (NCWIT). She won, in part, for her efforts tutoring students and developing a coding club at Salt Lake City’s Dual Immersion Academy, a bilingual Spanish-English charter school she attended during her elementary years.
The app project is a prime example of group work that can encourage underrepresented populations to pursue CS, according to Dr. Helen Hu, a Westminster College computer science professor whose work examines how educators can improve diversity in CS. “In industry there's something called agile co-programming, which is people working in groups,” said Dr. Hu, also the parent of a Rowland Hall ninth grader and seventh grader. “This is actually an important skill in computing—being able to work with others.” While some students love computing for computing, she added, a lot of others love it because of what it can do, “because of the problems you can solve, because of the impact you can have,” she said. “By doing both, by emphasizing these other parts of computing, you're helping both types of students. The students who love to code, still get to code. The students who love coding to solve problems are getting to do that. We know that students aren't going to learn it as well when you just teach it at the level of, ‘Where does the semicolon go and where do parentheses go?’”
Alex Armknecht ’20, a 2019 Aspirations in Computing regional award winner who’s now a CS major at Loyola Marymount University (LMU), appreciated learning CS at a more holistic level. “I loved the CS classes at Rowland Hall and they were consistently my favorite classes throughout high school,” she said. “I loved the way Mr. Smith taught and allowed us creative freedom … his class is the main reason I am majoring in CS. I learned the importance of asking for help, creativity, and collaboration, which all have been helpful to me in my college CS classes.”
During her senior year, Alex also participated in another shining example of collaborative group work in CS: the Upper School’s For Inspiration and Recognition of Science and Technology (FIRST) Tech Challenge Robotics team. The team started off strong in its inaugural 2019–2020 year and has continued to evolve, Ben said: “It’s expanded the opportunities for young women to become leaders, compete, and see how other girls across the state are involved with technology and engineering.”
During the 2020–2021 school year, juniors Irenka Saffarian and Tina Su stepped into unofficial leadership roles that bode well for the near future. Both have taken Advanced Placement CS A and are great coders, Ben said, and they pushed hard for the team to make it to the national semifinals in the FIRST Global Innovation Awards. Rowland Hall was the only team from Utah and one of only 60 teams internationally to make it that far. “Our theme right now is take it to the next level,” Ben said. “We realize we are right on the verge of getting to that level where we’re really competitive—where we actually compete with the best teams in the state.” And Irenka and Tina, Ben said, are committed to getting the team there. They embody the enthusiasm that Ben and Christian hope to cultivate across the school. “I hope that the future of taking computer science courses at Rowland Hall is increasingly coming from a place of excitement and interest and, ‘I cannot wait to use this skill in anything that interests me,’” Ben said. “It's not about a kid sitting in a basement all alone typing on their computer. This is about groups of people making exciting and interesting and really impactful decisions, and everyone needs to be at the table.”
Progress Made, and the Work Ahead
We are talking more about it, not just because it's zeitgeisty, but because technology has a lot of ground to make up here. We see ourselves as trying to help kids recognize that.—Christian Waters, director of technology integration
While Katy, Alex, Irenka, and Tina are recent success stories, Christian and Ben readily acknowledge that Rowland Hall isn’t exempt from racial and gender disparities. But the school is perpetually working “to change that from the ground up,” Christian said. Thanks in part to schoolwide training, JEDI values are ingrained in how Rowland Hall instructors design and teach tech-related classes. “We are talking more about it, not just because it's zeitgeisty, but because technology has a lot of ground to make up here. We see ourselves as trying to help kids recognize that.”
Ané Hernandez, a junior who took AP computer science and robotics as a sophomore during the 2020–2021 year, appreciated the heightened JEDI focus. Ané’s parents are both engineers and she’s been interested in CS for as long as she can remember—the winner of a 2021 Aspirations in Computing regional honorable mention loves the art of programming. Ané, who is Mexican American, has also long been interested in JEDI issues and advocating for more equity and representation, including through Rowland Hall’s student JEDI committee. She found it compelling to see how two of her passions, JEDI and CS, are related. "As technology is rising, racial, gender, and socioeconomic problems still exist," Ané said, "so they're just becoming interwoven."
While she’s grateful for how the JEDI units have furthered her passion for CS, she hopes her school also uses this momentum to self-reflect on, for instance, how to make CS more accessible to lower-income schools and communities. And that sort of community outreach isn’t unprecedented at Rowland Hall. In summer 2015, and in two summers that followed, Rowland Hall hosted a nonprofit Hackathon centered around teacher training. “That was a way that we contributed to a culture of learning and growth in our community,” Christian said. Educators from local public and independent schools convened on the Lincoln Street Campus to learn coding skills and how to use certain tools, like 3D printers and Arduino robots. The technology team helped cover some of the costs, Christian said, and teachers could earn state licensing credit for attending. Ben's resume is also flooded with conferences and workshops where he’s trained his peers. “It’s great for me to show a group of 15 or 20 educators how to teach a curriculum,” he said, “and then I can show them that I have a classroom with a majority of female students, and that I've been able to recruit and build, and that this is possible.”
These sorts of efforts could expand in the future. Rowland Hall is seriously considering ways to increase CS opportunities and spaces, and plans could solidify as early as the 2021–2022 school year. Christian and Ben are drafting a CS strategic plan that involves integrating CS with other subjects, training teachers, and expanding current classes. And Christian, Ben, and Director of Curriculum and Instruction Wendell Thomas are starting a CS task force and have asked others to join: one or two teachers from each division, Dr. Hu, and Sunny Washington, a startup COO and CEO who also serves on the board of Equality Utah. One of the task force’s first actions will be to provide feedback on the strategic plan draft.
For now, Christian and Ben’s work to recruit more—and more diverse—CS students is paying off. Since 2014, 19 Winged Lions have earned a collective 25 awards from the Aspirations in Computing program, including one win (Katy’s) and two honorable mentions at the national level. Rowland Hall also won The College Board’s 2019 and 2020 Advanced Placement Computer Science Female Diversity Award for achieving high female representation in our AP CS Principles class. Dr. Hu lauded the achievement. “That's pretty impressive," she said—especially for Utah. "There are some states where they have tens of teachers who received this. We have three. I think that speaks to how difficult this is in the state."
Ben, Christian, and the faculty and staff who support them remain focused on graduating good citizens armed with the tools to make tech work for all of us, not just some of us.
Ben, Christian, and the faculty and staff who support them remain focused on graduating good citizens armed with the tools to make tech work for all of us, not just some of us, as Joy Buolamwini so wisely said. Recent grad Katy is now attending Trinity College in Dublin, Ireland, and majoring in law—possibly cyber law. Anna Shott ’16 emailed Ben in December 2020 to share that she’d be joining Microsoft as a program manager the following year. “Your class truly influenced the path I chose, and I cannot thank you enough for sparking my interest in computer science,” wrote Anna, a University of Southern California grad who also worked as a K–12 CS camp counselor on her college campus. And current student Ané said what she learned in AP Computer Science Principles—that an algorithm can decide whether someone is granted a loan, for example—was a game-changer for her. “This experience has made me want to not only major in computer science, but a specific realm of computer science that maybe deals with AI and diversifying participants and coders so that there isn't such a large bias.”
Alex also plans on working in CS, another testament to Ben’s teaching: “I decided I wanted to go to my college when I met LMU's chair and professor of computer science and he reminded me of Mr. Smith,” she said. “I would not be a computer science major if it weren't for him. He pushed me to work my hardest, to try new things, and provided me with lots of opportunities.”
This sort of feedback keeps Ben laser-focused on boosting equity in CS at Rowland Hall and beyond. “I won’t pretend that it didn’t bring a tear to my eye,” he said. “It’s certainly fuel for the work that I do and it reminds me that it's worth doing. I could sit back on a curriculum and just deliver, and do fairly well at it. But this is beyond that. The work is more than what I teach—it’s who I’m teaching to.”
In mathematics, students learn the definition of an equation: a statement that shows the values of two mathematical expressions are equal (for example, x – 5 = 10).
But math teachers, including Garrett Stern, who teaches in the Middle School, want students to understand that an equation isn’t just numbers and letters on a page. “An equation,” said Garrett, “relates to an image on the graph.”
For many of our math students, this piece of algebra art represents their pinnacle achievement in middle school math.—Garrett Stern, math teacher
These images can take a variety of forms—such as lines, parabolas, and circles—which, when placed together on a graph, can do something exciting: they can create art.
To help illustrate the visual beauty in mathematical equations, Garrett has for the past six years assigned his students the task of creating their own algebra art using the Desmos graphing calculator, a free resource used by educators around the world. Every year, he’s found that Rowland Hall students are able to produce inventive, and often very impressive, works of art.
“For many of our math students, this piece of algebra art represents their pinnacle achievement in middle school math,” said Garrett.
At an April 15 student assembly, Garrett highlighted algebra art as well as recognized the accomplishments of this year’s crop of artists. He was joined by three students, Rebecca M., Jojo P., and Erika P., who created some of the most outstanding pieces in this year’s unit. Below, these students share their algebra art experiences with the Rowland Hall community.
“Star Destroyer” by Rebecca M.
Rebecca’s drawing of a Star Destroyer is one of this year’s most complicated pieces. In fact, the Star Wars fan’s subject was so detailed that Garrett said he initially attempted to talk her out of it.
“I tried to dissuade Rebecca from trying her idea,” he remembered, “but she rejected my advice.”
Rebecca—who was inspired to tackle the Star Destroyer after viewing an algebra art drawing of an AT-AT, or All-Terrain Armored Transport, that now-junior Dillon Fang created when he took Garrett’s class—admitted that, although she was able to complete her chosen subject in the end, the process of creating the Star Destroyer was very challenging.
“I was quite confident going into this project, but my confidence began to dwindle after doing some equations,” she said. Rebecca especially remembers the difficulty of creating the ship’s bridge. “It has many small pieces that you don’t think about until you have to trace it with algebra equations.”
Rebecca said the time-consuming three to four weeks it took to complete her project required a lot of patience and resilience—but that it was worth it because it taught her she can do difficult things.
“I am super proud of it. I would gladly do it again,” said Rebecca. “I managed to push through and made a really cool design.”
“Simplicity” by Jojo P.
Jojo loves line drawings, especially of people, and discovered that she could successfully recreate the curves of a traditional ink-and-paper line drawing in the online Desmos format—an accomplishment that caught her math teacher’s attention.
“What impresses me most about Jojo's piece is the stylish curvature,” Garrett said.
But creating her project wasn’t easy. Jojo remembers feeling far behind her classmates in the early days of the assignment.
“I didn't really know how to make the equations,” she said. “In the beginning, all I had was about five lines, when everybody else had way more done. I was scared I would be behind.” Instead of panicking, however, she persisted, figuring out the equations she needed and building on her skills as she moved from long lines and wide curves to nail and flower details, which she said were definitely the hardest part of the drawing.
“When it was finished, I felt proud,” Jojo remembered. “I felt awestruck because I didn't think I could do anything like this.” It’s clear that the experience built her confidence in a way that will continue to benefit her.
“The project was challenging, but it showed me, as a mathematician, what I actually was capable of,” Jojo said.
"Ornate Owl" by Erika P.
Garrett chose to highlight Erika's piece at the assembly because she managed to include texture—although she said that hadn’t been her original plan.
“I wanted to create an owl because owls are my favorite animal, but I hadn’t planned on making it so detailed,” Erika explained.
After experimenting with equations for the owl’s body, beak, talons, and eyes, Erika said she felt like she needed to add more to her drawing and started on what turned out to be its most complicated component: feathers.
“I had to try out multiple numbers in order to get the feathers—which were created out of parabolas—to be thin and long enough to look good if I consistently spread them throughout the wings,” she said. The feathers alone took Erika over two hours to complete, and are just one example of the experimentation she had to do to create a piece that she was proud to turn in.
“The hardest part was getting shapes and lines to line up and intersect, as well as experimenting with equations to get shapes that looked at least somewhat realistic,” she remembered. “I just had to jump into it.”
Now, Erika said, she can’t imagine her drawing without those detailed additions, and she’s proud she challenged herself.
“I was glad I decided to add detail because I was thinking about submitting the work before then, but it just didn’t feel like a finished piece,” she said. “After finishing, I felt quite accomplished!"
Altogether, this year’s eighth-grade class created 75 pieces of algebra art. Below are some examples of their work (click each square to see the artwork larger on Desmos).
“Our students deservedly feel proud of their achievements,” said Garrett. “They ambitiously attempted challenging images, embraced sophisticated equations, attended to detail, and, above all, persevered.”
On March 5, Rowland Hall eighth grader Sophie Zheng learned that she had earned an inaugural Maryam Mirzakhani AMC 10 Award for her January 30 performance on the American Mathematics Competition (AMC) 10 exam, an optional test designed to promote the development and enhancement of problem-solving skills for students in tenth grade and below.
The inaugural Maryam Mirzakhani AMC 10 Award was awarded to only 149 young women out of 36,000 AMC 10 competitors across the United States.
Named after the late Maryam Mirzakhani—an International Mathematical Olympiad gold medalist and the first woman honored with the Fields Medal, the most prestigious award in mathematics—this prize was given to only 149 young women out of 36,000 AMC 10 competitors across the United States. Sophie was one of six top-scoring female students in the Mathematical Association of America’s (MAA) Intermountain Section, which covers Utah and part of Idaho.
Earning the Mirzakhani award feels extra special to Sophie, who grew up around the campus of the Institute for Advanced Study in Princeton, New Jersey, when Mirzakhani was a faculty member at neighboring Princeton University.
“Winning the award makes me feel like I’ve truly met her now,” said Sophie.
In addition to earning her the Mirzakhani award, Sophie’s score on this year’s AMC 10 also qualified her for the American Invitational Mathematics Examination (AIME), the next level of AMC competition. Sophie was one of four Rowland Hall students, and the youngest, who took the AIME this year. Upper School math teacher Adella Croft, who proctors AMC exams at the school, wasn’t surprised to learn of Sophie’s accomplishments. She believes that anyone who watches her work can see her passion.
“One of the things that I think characterizes Sophie is just the sheer joy she takes in doing mathematics,” Adella said. “She has so much fun with it; she makes it look effortless.”
I enjoy the exhilarating moment when an equation starts fitting together into a sudden revelation.—Sophie Zheng
This may, in part, be tied to how mathematics knits together Sophie’s love for both the creative and the analytical.
“I have always seen myself as an artist, taking on piano, drawing, and origami, but now math is a new aspect incorporated into my life,” she explained. “I enjoy the exhilarating moment when an equation starts fitting together into a sudden revelation. I find math hidden in nature’s beauty: recursion in the trees, the curve of bird wings. These intricate mathematical patterns can also bring a whole new inspiration and style when creating art and origami.”
Her passion for mathematics at such a young age both underscores Sophie’s promise in the field and serves as an inspirational example of girls’ strength in STEM. The MAA hopes that publicizing such examples will encourage more girls to get involved with opportunities like competitive exams. Here at Rowland Hall, Sophie is already doing her part to encourage others in math—she’s a charismatic leader who happily mentors peers in class and at Math Club meetings, Adella said. Sophie added that this support works both ways: Rowland Hall offers a welcome and hardworking family that has supported her journey—one that she hopes will echo Maryam Mirzakhani’s.
“I hope in the future to not only be recognized among females, but in the whole community of competition math, as she was,” Sophie said.
We can’t wait to see what else you achieve, Sophie. Congratulations on this exciting and impressive accomplishment!
For three hours on March 11, four exceptional Rowland Hall mathematicians—juniors Zach Benton and Yuchen Yang, freshman Zach Klein, and eighth grader Sophie Zheng—were in the Eccles Library, focused on the 15 problems that made up this year’s American Invitational Mathematics Examination.
The AMC 10 and AMC 12 are optional mathematical exams designed to promote the development and enhancement of students’ problem-solving skills. Each test is 75 minutes long and consists of 25 multiple-choice questions. The AMC 10 is offered to students in 10th grade and below, while the AMC 12 is offered to students in 12th grade and below. AMC 10/12 qualifiers are invited to take the AIME, a three-hour exam that consists of 15 questions, with each answer an integer number between 0 to 999.
Known to test takers as simply the AIME, this exam is offered to students who excel at the American Mathematics Competition (AMC) 10 or AMC 12 exams (see sidebar). According to the Mathematical Association of America (MAA), which creates the AMC exams, approximately the top 2.5 percent of scorers on the AMC 10 and the top 5 percent of scorers on the AMC 12 qualify to take the AIME.
“The fact that we had four students from Rowland Hall take the AIME is extraordinary,” said Upper School math teacher Adella Croft. In fact, this is the largest number of AIME qualifiers in Rowland Hall history. (It’s also worth noting that Nathan Zhou, who took the AIME at Rowland Hall on March 11, attended the school last year and was coached with the other qualifiers.)
“The AIME is about mathematics beyond the classroom, about kids’ ability to be creative,” Adella explained. “And it’s typically non-traditional problem-solving—it’s very clever, sometimes even humorous. It’s cool.”
The MAA points out a variety of exam benefits, from helping students develop positive attitudes toward analytical thinking and mathematics that can assist in future careers, to challenging them with interesting questions that align with what they’re learning in school. But to be prepared for this level of competition, students must be willing to devote hours outside of class to studying topics like number theory, set theory, geometry, and probability. Rowland Hall students also meet weekly for Math Club and with coach Hiram Golze, one of Adella’s former students and a one-time USA Mathematical Olympiad qualifier (the Mathematical Olympiad is the next level of competition for top AIME scorers). Adella likened these preparatory measures to violin soloists who devote hours each day to mastering their instrument. “This is like taking math to the level of an artist,” she said.
And it’s that devotion to mathematical proficiency that truly motivates these students. While earning as high a score as they can on the AIME is always a goal, it’s clear there’s much more to the experience than that. These exams, taken by some of the brightest young mathematicians in the world, are extremely difficult—in 2006, for example, 22,764 students sat for the AIME and earned an average score of 2.741 out of 15 points (and only four students had a perfect score that year). In 2019, the average score was 5.87. But rather than discouraging them, the difficulty drives the Rowland Hall students toward their individual bests, helping them sharpen problem-solving skills, embrace hard work, and enjoy pursuing knowledge for its own sake—skills that will serve them for life.
It is a persistence exercise. They do it in absolute silence and isolation, pitting their mental faculties against each problem.—Upper School math teacher Adella Croft
“It is a persistence exercise,” said Adella. “It’s too bad it’s not a spectator sport because these are as competitive performers as any. They do it without an audience. They do it in absolute silence and isolation, pitting their mental faculties against each problem. They’re resilient, they’re passionate, they’re driven, they’re fearless.”
And they’re also not letting social distancing stop them. Each week, the students are meeting virtually for tutoring and for Math Club—amazingly, as a bigger group.
“It’s growing!” Adella said, noting that after she sent an email to students about ways to participate in Math Club during distance learning, she received several replies from kids who were interested in joining for the first time.
“Beyond finding a way, it’s spreading. It’s infectious in a good way,” she laughed.
Due to COVID-19, the MAA has put an indefinite hold on all aspects of the AMC program, including postponing until further notice competitions and the scheduled grading session. We will update this story with news as it becomes available.
In the meantime, if you’re curious about what the AIME looks like, visit Art of Problem Solving. They create test prep resources for math exams and offer a collection of past AIME questions and answers.
Top photo, from left, standing: Yuchen Yang, Nathan Zhou, Sophie Zheng, Zach Klein, and Hiram Golze. From left, seated: Adella Croft and Zach Benton.
After years of watching CSforAll Summit videos online, Rowland Hall alumnus and computer science teacher Ben Smith ’89 is elated to attend the national conference in person: the third-annual event is happening October 21–23 here in Salt Lake City, at the University of Utah.
In conjunction with the summit, CSforAll asks participants to make a specific commitment to support the ultimate goal of “making high-quality computer science an integral part of the educational experience of all K–12 students and teachers.” Accordingly, Rowland Hall is committing to increase girls’ participation in computer science to more closely mirror the school's demographics.
Read on for a Q&A with Ben about that commitment, the summit, and why this matters to Rowland Hall.
Who from Rowland Hall is attending the CSforAll Summit?
I’m going with Chief Information Officer Patrick Godfrey and Director of Technology Integration Christian Waters. It’s Rowland Hall’s first time sending anyone. The summit was originally held in the Obama White House for the first few years, and now it travels to a new city each year. This is a great opportunity to have this event in our hometown, very close to the school.
The summit is the one place each year that focuses on equity, inclusion, and access to CS for all students, a goal that Rowland Hall and the computer science program have been dedicated to for quite some time.—Computer Science teacher Ben Smith ’89
Why are you excited to attend the summit?
I’m a member of the CSforAll teacher community, and I watch the announcements and videos coming out of the summit each year. The summit is the one place each year that focuses on equity, inclusion, and access to CS for all students, a goal that Rowland Hall and the computer science program have been dedicated to for quite some time.
Why did we set a broad commitment, as opposed to a narrow one (for instance, “launch a coding camp”)?
We wanted a commitment that each division and each teacher could adopt, even if the method by which they accomplish it varies based on circumstances. Perhaps one division could pursue integrating CS into all science and math classrooms, thereby reaching all students, while another one might make a concerted effort at recruitment strategies, and another might reconfigure the course offerings or schedule to accommodate CS for all students.
What do you hope to get out of the conference that will help us reach our goal?
I hope to hear from people about structures, innovative strategies, and methods for making our commitment possible. There are some important topics at the conference, such as "Teaching Ethics and Social Impacts of Computing in K–12 CS," "Building a Supportive Pathway for Girls in CS, Engineering, and Beyond," and "Inspiring Engagement through Popular Culture and Media."
What has our male/female CS participation looked like in the past several years?
We’ve tracked participation in tech and CS classes in the Middle School and Upper School for six years. In both divisions, we’ve moved the needle for girls participating in CS classes closer to our school demographics (which are roughly 50/50), with the Middle School reaching a high in 2017 of 40 percent participation by girls. This year, the Advanced Placement CS courses in the Upper School have 60 percent girls—a majority for the first time at Rowland Hall. We still have challenges with the competing interests of sports, theater, dance, and music on students’ schedules, as CS is not a required course. What’s impressive is that we’ve been able to consciously and successfully close the gap for girls, though we still need to look at students of color and other demographic factors.
Add anything else you think is important.
Rowland Hall's CS, engineering, and STEM program has grown immensely in the last six years, and we’re on the precipice of changes and adoption at all divisions.
Last fall, Rowland Hall first graders tackled a mystery in the science lab: how could two islands on either side of the world have the same tree growing on them?
As part of a unit on seeds and trees, students suggested an explanation for this phenomenon, and then followed clues to determine whether their explanation was plausible. Carly Biedul—who served as the long-term science substitute teacher during Kirsten Walker's maternity leave and continues to teach the first- and second-grade science labs—was impressed with the students' engagement. "It was awesome to see how the first graders kept changing their answer the more and more they learned about seeds," she said. She explained that this lesson taught students about more than seed dispersal: it showed them that it's okay if your first answer to a problem is wrong because scientific study entails gathering evidence and then refining your answer based on what you learn.
Kids are the scientists now, and teachers are the facilitators. —Molly Lewis, sixth-grade science teacher
Over the past four years, Rowland Hall has been examining and refining the ways we teach science, largely in service of the Strategic Plan's second goal: provide the Intermountain West's most outstanding math and science program. While division-specific and developmentally appropriate, these curricular changes all have one thing in common: students are spending more time in class—and hopefully outside class too—engaging in the behaviors of science. They are conducting more lab experiments, which involve asking questions, making observations, collecting data, and forming and revising arguments. Teachers are often using the universal framework of claim-evidence-reasoning to guide their lessons, which fosters the kind of critical thinking that students can apply in any field.
In kindergarten through eighth grade, Rowland Hall's science curriculum now aligns with the Next Generation Science Standards (NGSS),which emphasize inquiry-based learning and making connections across scientific domains. The vision outlined in the NGSSis one where students are empowered to lead their own scientific discoveries, and sixth-grade science teacher Molly Lewis wholeheartedly supports it.
"Kids are the scientists now," she said, "and teachers are the facilitators." Whether directing a lab experiment about human vision—having students identify the limitations of their eyesight in certain circumstances, such as a dark room—or exploring the relationship between the form and function of red blood cells, Molly is happy to let the students take risks and posit theories that might initially be ill-founded. "We're giving them meaningful context instead of just abstract ideas, and then teaching them the skills necessary to discover what's true or what they can prove."
In the Middle School and the Lower School, phenomena—like the trees and their traveling seeds, or fossils found in sedimentary rocks—are being used to draw students into the practice of inquiry. The Lower School also has several new units that integrate science and literacy, laying the groundwork for more in-depth experiments in the science lab. The Beginning School, meanwhile, builds foundational skills with activities such as daffodil painting and dissection.
For Upper School Science Department Chair Alisa Poppen, the skills and concepts learned through lab work are essential, and her department recently acquired some new sensors and probes necessary for proper data collection. Echoing Molly, Alisa said, "We are using labs to build models rather than simply confirm ideas. We are focused on the behaviors of scientists, and understanding that science is not a collection of facts but rather a series of practices."
We are using labs to build models rather than simply confirm ideas. We are focused on the behaviors of scientists, and understanding that science is not a collection of facts but rather a series of practices. —Alisa Poppen, Upper School science department chair
While the Upper School curriculum is focused on moving toward lab-based Advanced Topics courses—rather than using the NGSS as their guide—Alisa is thrilled at the prospect of students entering ninth-grade science with an excellent foundation in the claim-evidence-reasoning framework. Furthermore, she sees additional lab time creating an upswing in student engagement, much like Carly observed in first grade.
Teachers and administrators will continue to observe how students perform in science classrooms—and, like good scientists, they will refine their practices based on the data they collect. Ultimately, Rowland Hall remains committed to providing students with the best possible learning experience. New Middle School science teacher Melissa Sharp hopes that by increasing students' enthusiasm for science, their learning experience will carry over into after-school hours too. "I want them to get into the car and ask their parents about genetics, and say, 'Mom, let me see your thumb!'" she said. "Or they might watch football and think about concussions, wondering what is happening in terms of neuroscience."
What it boils down to for everyone teaching science at Rowland Hall, including Melissa: "I want students to embrace the identity of a scientist."