Knitting and crocheting require mathematical thought. A growing movement hopes to use these crafts to interest girls in the sciences.
By Holly Korbey
In the basement of the North Branch Library in Nashville, Tenn., on a recent Saturday, you could hear alternating murmurs of excitement and exasperation over the soft clicking of needles. A small group of kids were learning how to knit.
A 10-year-old carefully knitted a case for his iPod with multicolored fuchsia, green and blue yarn, while a more experienced teenager carefully counted rows to create a raised pattern of the letters “H” and “K.” Young knitters racked up rows that one day, with practice, might become something — a blanket, a scarf or even, someday, a sweater. A nearby grownup commented on how nice it was to see young people so focused on making something, remembering how her brother once carved beautiful crosses out of a fallen tree in her yard. “He was always good with his hands,” she said.
For many of today’s kids, “being good with your hands” often means texting at lightning speed. While the Maker Movement has increased awareness and participation in building, tinkering and making things, most American students don’t learn any kind of formal handwork in school. Home-economics-style sewing and handcrafts classes, as well as shop classes, have been pushed out of most schools to make room for more “academic” subjects like reading, math and science.
But knitting and academics, especially math, are more closely related than they first appear, and there’s a growing movement in certain math and science circles to bring the two together — not only to teach math concepts also but to address the startlingly wide gender gap in the fields of science, technology, engineering and math. As the number of women who choose STEM careers continues to drop, participation in knitting, especially among young women, continues to grow.
While the research is only in the beginning phases and no hard data is available yet, researchers are confident that knitting can be used to teach math concepts, and they are using the studies to figure out which concepts work best. They hope their findings will be used in the near future to convince schools that knitting a scarf or crocheting a sweater provides a unique opportunity for students to learn hands-on, problem-solving skills in a way that is fun and interesting. And they are hoping that bringing knitting into math class will alert girls to the career possibilities of STEM.
Researcher Melissa Gresalfi, an associate professor of math education at the Peabody College of Education at Vanderbilt University, says that textile arts like knitting can teach rich mathematical ideas that can be difficult for students to understand. Her KnitLab project, which includes afternoon workshops as well as week-long summer camps for kids, is part of a larger exploratory study into the overlap between complex mathematics, problem solving and textile arts like knitting and crochet.
Gresalfi expects that the four-year effort, supported by a National Science Foundation grant, will illuminate the usefulness of handcrafts to help students visualize and explore mathematical concepts. “We’re trying to say that the creation of textile designs becomes a resource that supports mathematical reasoning,” she says.
Gresalfi’s work is focused on middle school students ages 10 to 14. But she’s most interested in the girls — who have the highest math anxiety and lowest workforce participation in the science, technology, engineering and mathematics fields.
According to the National Girls Collaborative Project, female achievement in math and science remains strong throughout K-12 education, but drops off in college: though women earned 57 percent of all bachelor’s degrees in 2013, they only made up about 18 percent of computer science degrees, about 19 percent of engineering degrees and 43 percent of math degrees. And workforce participation by women in STEM fields is decreasing: only 11 percent of all physicists and nearly 8 percent of mechanical engineers, for example, are women.
Professor Sarah Kuhn, a psychologist and member of the Social Science Advisory Board for the National Center of Women and Information Technology at University of Massachusetts Lowell, thinks that, in part, women don’t flock to STEM careers because activities offered to them early on aren’t that exciting. “I was tired of trying to convince girls that robots were cool,” she said, commenting on STEM education trends that focus on robotics or what she called, “the ukulele flame-thrower.”
Last year, Kuhn gathered a group of engineers, professors and textile artists to launch the Lowell Tex project, developing STEM lessons for students using textile crafts like knitting and weaving. The finished curriculum will be taught for the first time this summer at the Lowell National Historical Park as part of their summer camp, in part to honor Lowell’s history as a textile center. Handcrafts, according to Kuhn, are “a STEM opportunity hiding in plain sight.”
While experts agree that knitting is a good STEM activity for everybody, it’s no secret that knitting is most popular among adult women — according to the Craft Yarn Council 29 million, or nearly one-fifth of, American women knit, and they make up 70 percent of all knitters. Since knitting and its one-hook cousin crochet, are activities inherently filled with “rich mathematical thinking and problem solving,” according to Gresalfi, one of the objectives of the KnitLab is to raise awareness that knitting is math.
At the KnitLab, Gresalfi and her research assistant, Kate Chapman, first teach kids to knit, and once they are proficient ask them to perform a series of knitting “challenges” that test their problem-solving abilities. One challenge involves having kids figure out how to make a knitted square made up of concentric squares of alternating colors. In another, young knitters design their own bag, and make decisions about how big it will be, an activity that includes important mathematical thinking about ratio and proportion.
KnitLab kids wear GoPro digital cameras around their necks to document their thinking. Later, Gresalfi and Chapman watch hours of video of kids’ hands solving problems, and analyze what they see: how do kids make decisions about the size of their bag? How do they go about predicting where the stripes in the knitted square will be?
The researchers have found that once kids master the logistics of basic knitting, they can quickly move on to the more complex skills of problem-solving and designing.
At its most expert levels, knitting illustrates in three dimensions math concepts that are often left to college-level abstract thinking. Physicist Richard Feynman once recalled overhearing two college women discussing the properties of analytic geometry, only to discover one was showing the other how to knit a pair of argyle socks.
A group of mathematician-crafters, nearly all of them women, has begun to explore the cutting edge and mathematical possibilities of knitting and crochet. Beginning in 2005, determined to raise awareness about the effects of climate change and pollution, sisters Margaret and Christine Wertheim at the Institute for Figuring in Los Angeles, created an entire coral reef made of crocheted organisms that uniquely blended art, science, math and craftwork. And Cornell University math professor Daina Taimina has become somewhat of a handcraft celebrity for her book, Crocheting Adventures with Hyperbolic Planes, in which she uses the exponential stitching technique available in crochet to create complex mathematical objects that are also beautiful to see and touch.
For Taimina, who was raised in Latvia where handwork is still taught in schools, the idea of a separation between crafts and math, or girls and math, seems unnecessary and even silly. She recalled how when she first introduced her crocheted objects to a college-level math class in America, one of her students, a male computer science major, called her “Betty Crocker.”
She admitted she didn’t know who Betty Crocker was, but soon understood the reference. She sees mathematics’ sexism problem to be a uniquely American one. Attending university in Latvia, Taimina said no one considered math and science to be male domains. She was part of an elite math program in which, out of 24 students, only three were men, she said. “So for me, when you say girls can’t do math, it’s like, ‘Oh really?’”
Yet Gresalfi has found through interviews that many expert knitters and crocheters often don’t know that they are using this kind of high-level math thinking. It’s within this mysterious meeting of craft, women and attitudes toward math that Gresalfi sees an opportunity to highlight the work that expert needleworkers do. “We’re working on a paper right now that’s demonstrating the rich mathematical thinking that expert crafters engage in. People don’t see it — crafters themselves don’t often see that math is what they’re doing,” she said. “But what we want to know is this: what is it about textile crafting that sustains deep, committed participation? And are they the same qualities that could sustain rich mathematical thinking? And why is this kind of mathematical work not part of math classrooms?”
Gresalfi said it takes three to four hours for a middle-schooler to learn to knit, and because of packed curriculums, most schools simply don’t have that kind of time.
Megan Schmidt, who teaches high school algebra and statistics in St. Francis, Minn., began crocheting her own hyperbolic planes — curving surfaces with no flat areas — and bringing them to class, saying they help students visualize math in action, and provide a sensory experience of touching and feeling. Schmidt said she’d love to teach her students to crochet, and thinks it would be beneficial to their math thinking. “If I had time, I would,” she said, “but it’s those darn standards!”
Gresalfi said knitting not only provides math opportunities for students, but other learning experience as well. Collaboration, multiple ways of thinking about a problem and mistakes are an inherent part of knitting. Mistakes are not just expected — they are invited, and handcrafters’ expertise is determined by how well they can fix mistakes. “If you look at how learning works, this is exactly what all the literature says you want in your robust math classroom,” she said. Introducing more hands-on learning to math classrooms means “we would gain a much richer group of people who are interested in this [math]. And we’re not dumbing down or watering down mathematics, we’re doing the things we should be doing.”
Kuhn said that knitting has also been found to be relaxing, which might do double-duty: teaching math concepts while simultaneously easing math anxiety.
Though the study won’t be completed until 2018, Gresalfi and Chapman have already taught more than 50 kids how to knit, and hope once this project is done, they can launch a new one in which they can test how knitting might be used in schools.
At the North Branch Library KnitLab, the 10-year-old had finished his iPod case. He was asked about his next project. “I think I’ll knit a case for my Harry Potter magic wand,” he said.