It’s not
about
the right
answer
after all
A math professor walks into a second grade classroom (really, no joke.) Benton Duncan, chair of the North Dakota State University mathematics department, comes bearing strips of paper, narrow and long. He takes the two ends of a strip to make a loop. But instead of folding one end over the other to make the kind of simple loop used in a construction-paper garland, Duncan matches both outside ends, resulting in a twisted loop. It’s a Mobius strip — a mathematical phenomenon with no inside or outside. The circle of 7-year-olds, a little puzzled, a little uncertain, make one themselves.
Duncan then cuts down the center line of one of the strips. Now it’s a longer strip with two twists. The kids try it and then do it again, this time twisting more. Smiles, shared loops, hands in the air. “Look at mine.” “It’s cool.” “Show me again.” Next they cut the many twisted strips down the middle. “Let’s see what happens now,” says the professor. The kids agree to try it, curious, engaged, lots of loops, little hands. Patterns begin to emerge, and more complex questions.
This is not the elementary math class of my youth, the 1960s. That summons memories of sitting in rows of metal desks, penciling answers on endless and repetitive worksheets, the mimeograph paper, damp and aromatic, white with sky blue numbers. Something different is happening here. There’s excitement, exploring, thinking in new ways, experimenting, questioning, laughing, sharing.
Members of the mathematics faculty at NDSU are, in fact, spending lots of time in elementary classrooms. Take Maria Alfonseca, for instance. She’s visited kindergarten where she asks students imagination-capturing questions: How many 5-year-olds would it take to reach the moon if everyone held hands? Or Jessica Striker who visited her own child’s class one day where she and the kids counted M&Ms of different colors and discovered there were hundreds of combinations of colors and patterns possible.
There’s a good reason mathematicians are venturing off campus. They understand mathematics not only as a tool that can be fun. They understand it as the tool that allows us to think deeply about the world around us. Duncan and his colleagues want the world to benefit from more people who have those kinds of mathematical skills. “It’s simply not about what you’re learning this year in math class,” says Duncan. “It’s not even about adding, subtracting, multiplying or dividing. It’s about where you can be, the kind of thinker you will become, if you stick with it, keep learning, keep accumulating math skills.”
That’s worth a whole lot of M&Ms and Mobius strips and lines of kindergarteners that reach the moon. As Duncan sees it, everything exciting about the future is about the thinking skills kids learn in math: space travel, global communication in a digital world, politics, environmental issues. “All innovation,” he says, “all invention and new thinking will come from thinkers who are literate in math.”
Research shows that by the third grade a student’s relationship with math is solidified — and it’s very difficult to change that trajectory. Unlike other academic subjects, math education is absolutely cumulative. It builds on itself, year after year, concept after concept. If students miss one major concept, say fractions, for instance, they are almost certain to fall behind and not catch up, not ever. In fact, missing key concepts, by fourth grade, means learning nothing at all in subsequent math courses.
Back when I was a student, I was confused by fractions and didn’t know how to ask the right questions to move me toward understanding. Perhaps some laughter and three-dimensional tools, collaboration, and discussion would have helped. I still feel a certain anxiety when faced with percentages. As I talked to Duncan, I began to have a different sense of my “math allergy” as I have called it over these decades of numerical apology and shame.
Indeed, many people suffer from what John Allen Paulos, a Temple University math professor and author, calls innumeracy — the math equivalent of not being able to read. On national tests, nearly two-thirds of fourth graders and eighth graders were not proficient in math. More than half of U.S. fourth graders taking the 2013 National Assessment of Educational Progress could not accurately read the temperature on a neatly drawn thermometer. And adulthood does not alleviate our quantitative deficiency, Paulos reports. A 2012 study comparing 16- to 65-year-olds in 20 countries found that Americans ranked in the bottom five in general numeracy.
I’m a freelance writer, a poet, and a therapist. My lack of math skill has become, by mid-life, a part of my identity. In college, I chose programs that did not require college algebra: political science, English. Eventually, I entered a master’s program in clinical counseling that required a course in statistics. Thanks to helpful fellow students and a generous and understanding instructor, I passed, barely. Now I understand that my professional fate likely had its roots in early elementary school, my career path, in part, sculpted by fourth grade.
“I’m used to it,” says Duncan. “I hear it on airplanes all the time. So many people are afraid of math, dislike math. Once they hear I am a math professor, the stories begin.”
Duncan himself spent his elementary and high school years in southern California. “Back then I wanted to be everything,” he says, “an architect, a city planner, a writer.” He majored in astrophysics at New Mexico Tech and soon discovered that you could choose math as a profession without having to be a high school teacher, something he didn’t see himself doing. “I was honestly looking for a cheap college education that was “mathy,” says Duncan. Next came a master’s and Ph.D. from the University of Nebraska and a yearlong commitment to NDSU that has turned into eleven years and counting, tenure, and the department chairmanship.
Duncan sees mathematical illiteracy as a symptom of our education system’s approach to math education — teaching that too often focuses on finding a specific answer rather than on how to think about complex questions. “When early math learning is reduced to an answer-seeking exercise,” says Duncan, “it’s easy for students to get lost in the symbols and formulae and leave all meaning behind, to fall behind and stop learning.” Those students become adults on airplanes who hate math, fear math, feel math incompetent. And they are.
Math as a way of thinking and exploring and inventing isn’t part of math class until college sophomore or junior curriculum. “Then we finally get to the good stuff,” says Duncan, “math as a tool that leads to innovation and invention, new ideas and new theories and new solutions.”
Students who make it through higher-level high school math, advanced algebra, calculus, physics, and to the second year of college almost always had a teacher somewhere in their early educational biography who loved math, could teach concepts and transfer their love of math — and the possibilities that math opens up to their students. “Sadly,” says Duncan, “the reverse is true, too. For people who don’t like math, there is often a teacher in their history who empathized with their math struggles instead of offering support and sympathy.”
While we tend to think of empathy as a good thing, in this sense empathy sounds like: “I know math is difficult. I don’t like it either.” Students need math sympathy which sounds like: “This is difficult and you can do it. Just stick with it. Here’s another way to look at it.”
Duncan wants more math teachers who can sympathize and teach through students’ struggles, who can model their own love of math and belief in math as a powerful way to think and affect the world.
Games and video games can be part of that, hands-on experiments, M&Ms and trips to the moon. “I’m fine with the gamifying of education,” says Duncan. “I’m in favor of anything that keeps building students’ math skills and supports them reaching years 14 and 15 (sophomore and junior years of college) of their math education, where knowing math concepts really changes how you can think about everything.”
In a Washington Post article, educational writer Moriah Balingit says, “Everything around you is a combination of the arts and some form of math, technology and engineering.” Duncan agrees. Math is that fundamental to understanding the world and creating a better future.
Duncan’s commitment and passion about the possibilities within the mysteries of math, have gotten me thinking. I’m starting to imagine the world of numbers and word problems and equations anew, as something alive somewhere that could be exciting and rewarding to explore. And suddenly I see that people who work at NASA and in Silicon Valley are just like me, except for one thing: They learned math, they likely love math, and they know how to use it to explore and expand the world we share.
The elementary school visits by Duncan and his colleagues may be the largest endeavor of its kind locally, but nationally and globally, efforts to increase math skills among children have been growing since at least 1998 when the Mathematics of Science, Art, Industry, and Culture began sponsoring a series of interdisciplinary mini-conferences and festivals highlighting and celebrating mathematical connections in the different fields. “What we’re doing is not new,” says Duncan. “Larger more organized versions exist around the world.” Still the NDSU math department is doing its part.
Duncan’s concerns around kids and math and the future do not include the international race in test scores. “I’m not moved by all the press that says students in China and other countries are ahead of American kids in math,” says Duncan. “They might be ahead in the kind of education that makes math about seeking the right answer to a problem, but that’s not what math means to me. And it’s not the kind of math that is going to change the world. I’m interested in the kind of thinking that math competency creates, the kind of thinking that leads to a cultural willingness to go deeper, to think about knowledge and beliefs in ways that create new knowledge, innovation, and possibility.”
In fact, the brightest possible future will include kids all over the world learning that kind of thinking. Solving the big problems we share with all our fellow earth dwellers — water issues, food insecurity, environmental issues, space exploration, robotics role in the future, privacy, and more — depends on it.
So how about a mathematician for president? “Absolutely,” says Duncan. “In math you can’t get away with sloppy thinking. I want the people in charge to think clearly, logically, critically, creatively, and originally. That’s math.”
Carol Kapaun Ratchenski is a counselor in private practice in Fargo, a fiction writer, poet and storyteller. A North Dakota native and graduate of NDSU, she also is on the North Dakota Humanities Council board of directors.
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