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Bringing math concepts to life through quilting


Like the other Blugolds in her project group, Nina Kriese never has been a big fan of mathematics.

Yet the UW-Eau Claire Spanish major is all smiles as she and her team share their project with their math class and answer their professor’s questions about geometric symmetry and patterns.

"This is the first math class that I’ve ever liked," Kriese of Red Wing, Minnesota, says after her group's presentation, as she eagerly begins work on her next class assignment.

Why the enthusiasm for her "Introduction to Mathematical Thinking" class?

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Dr. Simei Tong believes art can help her students learn math concepts.

Instead of teaching the class in a traditional way, Dr. Simei Tong, associate professor of mathematics, has students using a variety of mathematical concepts to create colorful fabric quilts.

"Mathematicians often say that math is beautiful, but sometimes students do not see it," Tong says. "So I thought that it would be great if I could use a different way to present it.

"It’s fun and active learning. Through the struggling, students build up confidence in themselves even if they never thought that they had that talent before."

The active learning is making a difference for students like Kriese, who says she finds herself paying far closer attention than she might otherwise during a more traditional math class.

Rachel Lundell agrees.

"It’s hard; there is a lot of problem solving," Lundell, a political science major from Mahtomedi, Minnesota, says of making the quilts. "Figuring out the design, cutting the pieces and then figuring out where it all goes is hard. But it's cool to see how we can bring the math we're applying to life through the quilts."

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Students use the math concepts they are learning to make fabric quilts during their math class.

It is also interesting to see how the math skills they are acquiring translate to the real world, says Angela Klinkner, a music education major from Cashton.

"I see patterns in things and think about how things are put together now," Klinkner says, noting that she comes from a family of quilters so she also is excited to talk with them about their projects.

The students are among the more than 50 freshmen and sophomores in two of Tong's Math 106 classes this semester who are creating quilts as part of their math studies. Each student designs and sews two quilts as part of a group project and two quilts on their own.

Through the quilt-making process, students learn about a variety of mathematical topics that require reasoning and critical thinking, such as number theory, geometric symmetry and patterns, fractals and chaos theory, coding theory, exponential growth models and graph theory, Tong says.

A well-crafted quilt requires mathematical accuracy and an understanding of multiple math concepts, Tong says.

For example, if students include star patterns in their quilt design, they must make sure the intersections meet and the points of the stars line up accurately.

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Community groups share their quilting fabrics, tools and talents with UW-Eau Claire math students.

To do that successfully students must accurately measure each geometric figure in their pattern, precisely cut each piece of fabric, plan space for a seam, and then sew it together exactly as designed.

In addition to learning math concepts, students also gain confidence and learn to be persistent when facing challenges, including challenges relating to mathematics, Tong says.

"This special experience is valuable because they learn how to cooperate with each other, and also learn how to figure out things that they never had experienced before," Tong says, noting that at least half of the students in the class have never sewn before or taken a design class. "When challenges happen, they need to change the design or change something else to make the project work."

While this is just the second semester that Tong has used the quilts as part of her math curriculum, she has long been interested in how educators can bring math and art together to help students learn.

For the last two years, Tong and art faculty members have worked together with students on math-art research, specifically the mathematics of geometry figures in quilting design.

Among the research collaborators is Li-Ying Bao, a professor of art and design, who teaches students how to use computer software to design images for their quilts, which Tong then helps them bring to life.

With support from the Office of Research and Sponsored Programs, faculty and students in math and art recently worked together to produce a textbook titled "Mathematics in Artistic Design: Bringing Projects to Life."

"This book contains six projects, which is the guidance for my Math 106 classes this semester,” Tong says. “It includes math topics: translation symmetry, reflection symmetry, rotational symmetry, tessellations, Fibonacci sequence and circles.”

Each project in the textbook includes definitions of a math topic, drawings to explain the concept, activities requiring students to demonstrate their understanding of the concept, an example of a quilt using the math concept, tips for creating a quilt that incorporate the concept, and questions to encourage students to reflect on how math and art intersect in their design.

The math-art research team that created the textbook includes Tong; Dr. Charles Bingen, assistant professor of mathematics; Roslyn Cashman, a senior art, graphic design, major from Black Earth; and Skyler Hanson, a mathematics major from Albert Lea, Minnesota.

The two pictures on the cover page of the textbook feature designs created by math and art students working collaboratively on quilt projects.

One design, representing the rotational symmetry and Fibonacci sequence, was produced by Alex Graham, a senior from Delafield who is graduating in December with an art degree, and Casey Grosshauser, a senior mathematics, actuarial science, major from Waunakee.

Cashman and Austin Angell, a senior mathematics major from Rice Lake, using 3D image and symmetry, created the second image.

The research team is currently working to get the textbook published.

While Tong teaches the mathematical concepts related to the quilts, community members and local quilting groups help make her innovative approach to teaching the class possible, Tong says.

It was her 91-year-old neighbor, Doris Kassera, who introduced her to quilt making, Tong says.

"She took me to get the tools and a sewing machine when I had no idea of sewing at all," Tong says. "I grew up in Shanghai, China, so I did not know how long is an inch or a yard. I learned everything from my friends in the community.

"I've enjoy making quilts and I am now passionate about connecting math with quilt pattern design and making. Four years after I started this new journey, I can teach my students mathematics by design and quilt making."

Now many of those same local quilters and artists are sharing their expertise — along with their fabric, tools and time — with the students.

They also offer tips and strategies, as well as critiques of the students’ creations, she says.

Members of the American Sewing Guild, Wisconsin Indianhead Chapter, Clear Water Quilters, and the Sewing Club at Sew Complete all have been key to the class’ success, Tong says.

"These groups are very supportive with everything that they can contribute, including all the fabrics, sewing machines and their time," Tong says.

Some of the quilts the students create in their class this semester will be part of the Chippewa Valley Art Quilting Exhibition, which will run from Feb. 9-March 7, 2018, in the Foster Gallery of the Haas Fine Arts Center.

"It’s amazing to see how beautiful these projects are even though about half of the students never had sewing or design before," Tong says.

Students can keep the individual quilts they create, providing them with a visual — and beautiful — reminder of what they learned in the class, Tong says.       

As the fall semester nears its end, Tong says she sees tremendous growth in her students' confidence, math skills and ability to work as part of a team.

"Most important is that our students get a chance to learn and practice math and art," Tong says. "They may find their true passion and talent for their life. Students are amazed to find out that they have talents that they never thought about before." 


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