In Algebra 1, ninth grade students learn systems to solve systems

There was nothing particularly odd about the timed quiz that was taking place on a late January afternoon in Strub 115. Students in the Algebra 1 class were focused, their pencils were moving, the SMART Board was displaying their countdown clock. The teacher, Fran Smiland, walked around the room, wearing an easy smile as she wove between desks, looking over the students’ shoulders. It was only the moments of pause that seemed out of the ordinary really. When Mrs. Smiland arrived at a student, she often uttered a simple and nearly silent affirmation like “good job” or “you got this,” before she visited another desk. And sometimes students would engage her a little longer, in conversations too quiet to hear.
Paloma Murga ‘26, a student in that A Block, gave some examples of the sort of brief interactions that might take place between Mrs. Smiland and her students during a quiz like this. “You can ask questions,” Paloma explained, and Mrs. Smiland might nudge you “to look at something one more time.” This model of gentle encouragement was something Paloma found “much less stressful” from what she had encountered in the past. Mary Elizabeth Ryan ‘26 expressed her appreciation for this approach as well. As a rule, Mary Elizabeth enjoys math, but also said it was “a better class environment” from what she had ever experienced before, and added, “I love this class.” 

Mrs. Smiland has clear intentions in the way she models classroom behavior. “I am passionate about what I do, and I hope that I impart that to my students,” she said. “And my goal is to train my students to believe the best time to make a mistake is in the classroom.”
Although this is Mrs. Smiland’s first year teaching at Mayfield full time, she taught math in Mayfield’s summer sessions, while working as a math teacher to middle schoolers at Holy Family during the school year. Emily Goodell ‘99, Chair of Mayfield’s Math Department, saw the immediate value Mrs. Smiland could offer Mayfield as an Algebra instructor. Mrs. Goodell saw Mrs. Smiland as “a master in (her) discipline” but also someone who “would be really good with helping our ninth graders transition from middle school to high school.” And Mrs. Goodell admired the way Mrs. Smiland has been “building relationships with students,” and said “it's infectious…it's hard not to get excited when students are learning to love math.”

Since Mrs. Smiland taught at Holy Family for years—and as this tends to be one of the bigger feeder schools for Mayfield—several of her past pupils are current Mayfield students, including a handful in her ninth grade Algebra A Block. She enjoys seeing the familiar faces, but finds it easy to connect with the whole community. “Everybody's coming with different backgrounds and everybody has a different set of skills,” Mrs. Smiland said. “It's been fun for me to get them all to the same level.”  

Once Mrs. Smiland’s Block A Algebra finished their timed quiz, and enjoyed a short break, they launched into the activity Mrs. Smiland had planned for the day: “Systems of equations applying to real world problems.” 

In algebra, a “system” is defined as “a finite set of equations for which common solutions are sought.” Students in Mrs. Smiland’s class were in Unit Six at this point, and they knew the general mathematical principles. Isolate the variables. Figure out to eliminate or substitute. Don’t forget to distribute the negative. But instead of just solving a linear equation like: 3(10a + 4) – 2, students in this class were approaching a new challenge: applying the same algebraic principles to real life scenarios, like calculating speed, distance or time of moving objects. 

When the inevitable: “Ben paddles his kayak at 3 mph” question appeared on the SMART Board, and the class was asked to calculate the rate of the river current between his travel upstream vs. downstream, there were the expected audible groans and muddled expressions. But there were also a lot of smiles too. There was a feeling in the classroom that is hard to pinpoint—but missing the tension that so often comes when attempting a totally unfamiliar task.

Addison Thomas ’26 ventured to describe what makes Mrs. Smiland’s classroom environment so unique. “I love (her) teaching…I learn so much more in a loose and exciting environment, and she provides it every class.” And Addison made it clear she did not always feel this way in her math classes before Mayfield. “I haven't enjoyed math since elementary… because my old teachers did not show interest in my growth and I felt cornered and alone.” She added, “It is a relief to go to class, and not dread it at all.”  

Isabelle Buckwater ’26 praised Mrs. Smiland’s class “because we go at a reasonable pace when we learn the information,” but there will always be days in which students can’t absorb the entirety of material during class time. And Hannah Alfaro ’26 mentioned that Mrs. Smiland goes above and beyond in this regard. “She meets with us after school until we get the material,” Hannah said. “I really, really love having Mrs. Smiland as a teacher.”

Even the decorations on the walls of Room 115 give a sense of overall encouragement. Animated calculators pasted on and around the door detail each of the students’ “Matholution 2023.” These are their New Year’s resolutions as it relates to math, whether it be “studying for tests longer” to “being more organized in writing to-do lists.” They are gentle reminders of the positive steps students can continue to make every day. 
It doesn’t take long to realize there are so many other types of “systems” at work in Mrs. Smiland’s classroom, far outside of the algebraic definition. There is a system of building trust and bolstering confidence. A system that allows a safe environment to make mistakes. A system that celebrates a growth mindset at a personal and communal level. And all of this underpins the more overt output of the class. It is these social systems that empower students to go on to then tackle the mathematical ones.

Mrs. Smiland talked about how she had posted a picture of an ostrich with its head in the ground on her board on Back to School Night. She knew that students and adults alike can go to great lengths to avoid math. But she promised parents that she wouldn’t let their children go through her class with an avoidance attitude. “Even if they're not going to like math, they're going to face it and we're going to do it together,” Mrs. Smiland said. “We're going to work as a team to get that head out of the sand.”
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Established in 1931, Mayfield Senior School in Pasadena, CA is a Catholic, independent, college preparatory school for young women grades 9-12. Noted for its rigorous academic program, which includes 28 Advanced Placement and Honors courses, Mayfield’s curriculum is underscored by a philosophy of educating the “whole child,” which also encourages commitment to and excellence in the arts, athletics, community service and spiritual growth. The nurturing environment at Mayfield Senior School allows each student to flourish in an atmosphere of personal attention.