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这不是
乐虎电子
正确的
回答
毕竟

A math professor walks into a second grade classroom (really, no joke.)本顿·邓肯, chair of the 乐虎电子 mathematics department, 带着纸条来了, 窄而长. 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, 邓肯在外线都能命中, 导致一个扭曲的循环. 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. 现在它变成了一条长一点的带两个弯道的长条. The kids try it and then do it again, this time twisting more. 微笑，共享循环，双手高举. “看看我的.“很酷。.“再给我看看。.” 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 回答s on endless and repetitive worksheets, 油印纸, 潮湿芳香, 白色和天蓝色的数字. 这里发生了一些不同的事情. There’s excitement, exploring, thinking in new ways, experimenting, questioning, laughing, sharing.

Members of the mathematics faculty at NDSU are, 事实上, spending lots of time in elementary classrooms. 以玛丽亚·阿方塞卡为例. 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 乐虎电子 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 乐虎电子 what you’re learning this year in math class,邓肯说。. “这不是 even 乐虎电子 adding, subtracting, multiplying or dividing. 重要的是你能在哪里, 你会成为什么样的思考者, 如果你坚持下去, 继续学习, 不断积累数学技能.”

这值很多M&Ms and Mobius strips and lines of kindergarteners that reach the moon. 在邓肯看来, everything exciting 乐虎电子 the future is 乐虎电子 the thinking skills kids learn in math: space travel, 数字世界中的全球通信, 政治, 环境问题. “所有的创新,他说, “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. 如果学生错过了一个重要的概念, 说分数, 例如, they are almost certain to fall behind and not catch up, 永远不会. 事实上, 缺少关键概念, 到四年级, 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 正确的 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. 当我和邓肯谈话时, I began to have a different sense of my “math allergy” as I have called it over these decades of numerical apology and shame.

事实上, many people suffer from what John Allen Paulos, 天普大学数学教授兼作家, calls innumeracy — the math equivalent of not being able to read. 在全国考试中，接近三分之二 of fourth graders and eighth graders were not proficient in math. 超过一半的美国人.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. 2012年的一项研究 16- to 65-year-olds in 20 countries found that Americans ranked in the bottom five 一般计算.

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, 我的职业道路, 在某种程度上, 四年级雕刻.

“我已经习惯了，”邓肯说. “我经常在飞机上听到这种说法. 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,他说, “an architect, a city planner, a writer.” He majored in astro物理 at New Mexico Tech and soon discovered that you could choose math as a profession without having to be a high school teacher, 一件他没想到自己会做的事. “I was honestly looking for a cheap college education that was “mathy,邓肯说。. 接下来是硕士和博士学位.D. 来自大学 of Nebraska and a yearlong commitment to NDSU that has turned into eleven years and counting, 任期内, 还有系主席.

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 回答 rather than on how to think 乐虎电子 complex questions. “When early math learning is reduced to an 回答-seeking exercise,邓肯说。, “it’s easy for students to get lost in the symbols and formulae and leave all meaning behind, 落后，停止学习.” Those students become adults on airplanes who hate math, fear math, feel math incompetent. 它们是.

Math as a way of thinking and exploring and inventing isn’t part of math class until college sophomore or junior curriculum. “然后我们终于谈到了好东西,邓肯说。, “math as a tool that leads to 创新 and invention, 新的想法，新的理论和新的解决方案.”

Students who make it through higher-level high school math, 高等代数, 微积分, 物理, 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,邓肯说。, “the reverse is true, too. 给那些不喜欢数学的人, 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. 我也不喜欢.” Students need math sympathy which sounds like: “This is difficult and you can do it. 坚持下去. 这是另一种看待它的方式.”

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&她去了月球. “我对游戏化没有意见 教育，”邓肯说. “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 乐虎电子 everything.”

在华盛顿邮报的一篇文章中, 教育作家Moriah Balingit说, “Everything around you is a combination of the arts and some form of math, 技术与工程.邓肯表示同意. Math is that fundamental to understanding the world and creating a better future.

Duncan’s commitment and passion 乐虎电子 the possibilities within the mysteries of math, 让我开始思考. 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, 除了一件事:他们学数学, 他们可能喜欢数学, 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, 但是在全国和全球范围内, efforts to increase math skills among children have been growing since at least 1998 when the Mathematics of Science, 艺术, 行业, and Culture began sponsoring a series of interdisciplinary mini-conferences and festivals highlighting and celebrating mathematical connections in the different fields. “我们所做的并不新鲜，”邓肯说. “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,邓肯说。. “They might be ahead in the kind of education that makes math 乐虎电子 seeking 正确的 回答 to a problem, 但这不是数学对我的意义. 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 乐虎电子 knowledge and beliefs in ways that create new knowledge, 创新, 和可能性.”

事实上, 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, 食品不安全, 环境问题, 太空探索, 机器人在未来的角色, 隐私, 更多的——取决于它.

那么让数学家当总统怎么样? “当然，”邓肯说. “In math you can’t get away with sloppy thinking. I want the people in charge to think clearly, logically, critically, creatively, and originally. 这是数学.”

Carol Kapaun Ratchenski is a counselor in private practice in Fargo, a fiction writer, poet and storyteller. 北达科他州人，毕业于NDSU, she also is on the North Dakota Humanities Council board of directors.

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