Students in Floyd Bullard’s class learn about confidence intervals through an interactive activity. NCSSM's math instructors work each day to bring creativity, adaptation, technology, and student-centered teaching to the classroom.
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On a cool spring morning, Floyd Bullard and Chris Gann stand side by side overlooking a class of students working groups of three on the putting green of Hillandale Golf Course. Some crowed with the success of their putts, others moaned with disappointment; all were manufacturing and collecting data for use in Bullard’s Advanced Probability Modeling course. “It’s funny they are so disappointed because if they actually made all of their putts, this activity would be useless,” Gann joked.
After taking shots from various distances and noting whether or not the ball went in, students took their data back to the classroom. There, they would generate functions predicting their individual likelihood of making a putt at any given distance. The hands-on nature of this field trip and the corresponding assignment represent one of the core missions of NCSSM’s math department — a creative approach to mathematics.
“It’s a lot of fun. It’s a new way to actually collect data,” one student said. “I don’t think we are the best golf players out here,” her groupmate chimed in.
Creativity in Mathematics
For NCSSM’s math instructors, creative inspiration can be found in the everyday. “It really comes from our own geekiness,” said Math Instructor Philip Rash. Rash collects data on operating measure like RPM, MPG, and distance traveled for his truck. Based on his own fascination with numbers, he decided to bring that data into class and have his students analyze it.
“You just hear something that you as a person, not even as a teacher, think ‘that’s sounds cool, I wonder if I could turn that into a problem.’ You try to find a way to share that excitement that you have with your students,” said fellow Math Instructor Taylor Gibson.
While many students vocalize a preference for math because of its rule-bound surety, instructors say that the reason they love math, and love teaching math, is just the opposite. “Math is not rigid, there can be multiple approaches. It’s a creative process, it’s sometimes uncomfortable, it’s messy,” said instructor Tamar Avineri.
A Student-Centered Approach
Creativity in the department extends beyond the realm of simply generating problems. It fuels the student-centered approach that math department faculty say is the core of their mission.
“This was an awesome test,” Instructor Christine Belledin announced to her BC Calculus class. “No,” she corrected herself, “this was not an awesome test. You guys did awesome on this test.”
NCSSM’s math instructors think about their words strategically. When they ask questions of their students, instructors consider not only finding the right answer, but developing a deep level of understanding based on timing, wording, and personal relationships.
“When you ask a question makes such a huge difference,” says Belledin. “We ask big questions at the beginning and let the kids think about what they would do to solve a problem. Timing is a huge part [in the learning process] that allows students to either just mimic what you’re doing or think for themselves,” she went on, citing what she considers to be a unique facet of the NCSSM teaching model.
Instructor Taylor Gibson considers his personal history of interactions with a given student when it comes to asking the right questions. “When I think about what questions I ask students, the things that might come through my mind are my experience with their ability in the course, have I worked with them before?” Gibson says of his process. “It might seem to an outsider that I just walked up to Forrest and asked him this question that’s kind of obvious but there’s a lot of intentionality behind that question. ‘Where do I want that question to bring the student?’”
In an almost symbiotic way, instructors are stimulated and challenged by the questions they face from students as well. “They keep me on my toes, making me think hard,” said Avineri. A key facet of the student-centered approach is cultivating an experiential learning environment rather than a passive one. Students are not expected to sit back and take notes of everything an instructor says or writes on the board. Instead, they are engaged in activity during class, actively questioning the process and often following along on their laptops.
Instructors say that responding to the students’ questions is a major part of what kept the job fun and challenging. Students may bring up questions to which instructors do not know the answer, and an opportunity for instructive collaboration arises. Or, an instructor may know the answer, but chooses to guide the student so that they reach the conclusion on their own.
Technology in the Classroom
In Dan Teague’s Finite Mathematics class, students are typing lines of code into a software application called NetLogo. This software allows students to set up the turtle problem, a scenario that describes points, or “turtles,” in a box behaving as either “cowards” or “heroes.” Each turtle randomly chooses another to be its “friend,”, and another to be its “enemy.” Hero turtles want to be between their enemy and their friend. Coward turtles want to hide between their friend and their enemy. After the scenario is set up, students run it on their own computers and observe how the turtles behave, clumping and swirling around the screen. “It’s turtles all the way down,” Teague said.
While teachers are challenged by students’ questions, and students are challenged by course material, both are aided by the use of laptops in the classroom. All students bring laptops into the classroom, and instructors say the use of technology allows them to delve more deeply into concepts, diversify how concepts are illustrated, and make math more equitable.
Software-based lessons are more engaging, instructors say, and help foster the interactive and exploratory environment that allows students to learn how to tackle problems instead of simply following directions. “Students get to visually see what’s happening,” said instructor Forrest Hinton. “They get to manipulate data points. You hear conversations and debates and people asking, ‘what if?’”
Having computers in the classroom also makes the incorporation of multiple learning modalities fast, easy, and equitable. Not only do they make teaching in a variety of learning styles at once possible, they can also eliminate lots of tedious work. Problems that used to require students to do pages and pages of calculations can now be aided by the use of technology, making math more accessible for students who can grasp the concepts, but might struggle with repetitive and finicky calculations.
Lifelong learning
NCSSM’s math instructors all have different backgrounds and reasons they choose to teach, but share a certain similarity. “I think all of us are lifelong learners,” said Hinton. “We like asking questions and thinking about something new course or a new problem. [With teaching] every day you get a new challenge or a new problem so you really get to expand your horizons and work with super smart creative kids who are doing the same thing.”
Hinton’s previous work in a think tank led him to understand how often quantitative analysis is used with an agenda and when he teaches, this is something he thinks about. “We want our students to be critical and skeptical and precise,” he said.
“We want them to use their powers for good,” Belledin chimed in. After teaching through a Teach for America program for two years, Belledin returned to graduate school. Only then did she realize that teaching was her passion all along. “My favorite part of grad school was teaching my classes,” she said.
“One thing I didn’t realize before I started here,” said Avineri, “is the collaborative department, that we get to work with each other and learn from each other.” Part of what makes the job so rewarding for her, she said, is the dual challenge of teaching and learning new math all at the same time. She has had the chance to teach course material that she had not taken before, offering her the opportunity to learn and grow as an instructor and a mathematician.
“I had teachers who changed a lot for me when I was in high school, getting me to be a critical thinker and all the things that I try to embody with my students now,” said Gibson. “And I thought, ‘what could be more fun than trying to do that with a group of kids?’’