Overcoming math anxiety doesn’t mean math isn’t hard, or that you’ll become a math genius overnight. What matters is that your feelings about the math experience change.
The term “math anxiety” was defined by Sheila Tobias, who, as provost at Wesleyan College, found that girls at the school avoided taking math or other math-intensive subjects such as physics, chemistry, or economics. She opened a clinic and interviewed hundreds of college students, and in 1976 she published an article in a women’s magazine that she expanded into a book entitled Overcoming Math Anxiety. She said that many girls were told that “girls can’t do math,” or, to put it another way,”they’re either good at numbers or good at words, but they can’t be good at both.” If a father says to his daughter,”Your mother always can’t keep an account,” it’s making her “learned helplessness,” so the term “math anxiety,” which has something to do with feminism, means how men make women lose power and make girls unable to compete fully in school. Tobias believes that boys also have math anxiety, but math anxiety affects girls more.
However, what does “math anxiety” mean? According to psychologists today, if you’re doing a math problem and you’re feeling physically uncomfortable or worried about getting the right answer-you may have some level of math anxiety. It can have many levels, it is defined as the face of math problems feel nervous, worry, or fear. If a student has math anxiety, he will choose to take as few math classes as possible, which will limit his later education and career choices. Parents with math anxiety also pass on this feeling to their children. A 2012 survey in 34 countries found that 59 percent of juniors said they feared math classes would be difficult, and about a third felt nervous while doing math homework. Interestingly, those with poor math scores were less worried about math, while those who were good at math were more anxious. In 2018, a British survey found that more than three-quarters of children with math anxiety scored normal or higher on math tests.
To be honest, I think most people are a little nervous about math, afraid of doing something wrong, afraid of not solving a problem, afraid of not understanding a concept. As long as someone in the parents ‘group throws out a “Mathematical Olympiad Problem” for Grade 2 and Grade 3 of primary school, I will be nervous. It’s as if mathematics were supposed to do it, to get you nervous, your brain focused, and your brain spun. Despite the “multiple intelligences theory” of educational experts, people still attach great importance to logical-mathematical intelligence.
Barbara Oakley, born in 1955, was in seventh grade when her father lost his job and the family moved to a poorer school district and she met a bad math teacher. Mathematics along by addition and subtraction to the logic of multiplication and division solemnly climb, directly to the beauty of mathematics in heaven. But if you happen to miss a step in a logical sequence, mathematics won’t forgive you. Barbara’s math grades had deteriorated, and she didn’t know anything about science. Fortunately, she was interested in history and culture, especially language. That meant that her language intelligence was very good. Graduated from high school, Barbara joined the army, got the chance to go to the university of Washington to learn Russian, after graduating from college, awarded the rank of second lieutenant, accept the training of radio, cable and telephone switching system, she finished the training with the bottom of the grade, and then went to the west, as a communications platoon leader. Barbara later realized that her career was in jeopardy, saying,”If I stayed in the military, I’d be second-rate with my bad skills.” If I leave the army, what can I do with a degree in Slavic language and literature? Basically, I would compete with millions of people who also have a BA degree for entry-level secretarial jobs.”
After retiring from the military, Barbara returned to Washington University to study communications engineering. ‘It’s a process of reshaping the brain,’ she said. Later she went to the Antarctic station work, and read the master’s, doctor, as a professor at the university. She wrote a book, A Mind for Numbers, translated domestically as The Way to Learn, with an interesting subtitle: “How to Master Math and Science, Even if You Fail Algebra.” She described her experience as failing math and science in high school, starting trigonometry at the age of 26, believing that she had no chance of studying science and engineering, and that her poor math grades made her “self-handicapping.” Barbara’s book is about learning methods. She says that solving mathematical and scientific problems is often more complicated and laborious than thinking patterns involving language, because mathematics is more abstract and encrypted. For example, the idea behind the plus sign is abstract, and the multiplication symbol symbolizes repeated addition, which is a kind of “encryption.” But math has the advantage that it’s much easier to figure out the basic concepts of math than to learn subjects that require rote learning. In her book, she refers to the “set effect,” which is a common stumbling block to students ‘homework. Simply put, your idea is far from the actual solution, but you can’t throw away your old wrong idea, accept or generate a new idea that will solve the problem. “Set effect” is what we often say “stupid” or “don’t understand.”
When I was reading this book, there was a doubt that Barbara’s poor math grades might have something to do with her frequent moving, which probably affected her studies. I also have a doubt, that is, a person is not good at mathematics when he was young, but as the mind becomes mature, will it begin to understand? Is language learning and translation useless for mathematical thinking? Can’t multiple intelligences help each other?
A man named Jason Wilkes, who wrote a book called Burning Math Books: Reinventing Mathematics, said that he got a C in elementary algebra and a C in trigonometry. He hated the words sine and cosine. Middle school math was autocratic and boring to him. When he was nearing graduation from high school, he was glad he never had to take math classes again. In his senior year in high school, Wilkes was flipping through a calculus textbook in the bookstore. The language was plain-straight things are easier to deal with than curved things, but if you put them big enough that every small part of the curved thing looks straight, you have to imagine, zoom in, solve the problem at the easier microscopic level, and then shrink back, and you’ve solved the problem. Wilkes said he was fascinated by the idea. He found calculus easy, but the basics of calculus, such as algebra, trigonometry, and logarithms, were difficult. He found calculus interesting: the derivative of the volume of a sphere was its surface area, and the derivative of the area of a circle was its circumference. The book opened his eyes, and he went to the math department, got a master’s degree in mathematical physics, and then a doctorate in evolutionary psychology.
There are many stories like this: A young man with a strange skeleton comes across a secret book like “Buddha’s Palm” in a bookstore, and then opens the door to the world of mathematics. I can conveniently speak two.
In August 1959, 14-year-old Hou Shida followed his father around the bookstore when he saw a book called Gödel’s Proof, which contained many tempting graphs and formulas. “I had to buy Gödel’s Proof because I had an intuitive feeling that it was destined to be related to me.” Hou Shida went home and read a book.”From the beginning to the end, this book resonated with my passion. I began to indulge in the thinking of truth and falsity, paradox and proof, mapping and reflection, symbolic operation and symbolic logic, mathematics and meta-mathematics, the mystery of the creative leap of human thought, and the mechanism of intelligence.” Hou Shida’s father was a physics professor at Stanford University and had won a Nobel Prize. He knew the author of Gödel’s Proof, and it didn’t take long for the two families to get together. Hou Shida later studied mathematics and got a doctorate in physics.
Tell me one more. In 1971, 16-year-old Lee Smalling was in high school. He was interested in politics and rock music. His teacher thought he was not smart enough and advised him not to take advanced math courses. To prove his teacher wrong, he finished high school math in his freshman year and became interested in architecture in his sophomore year. In his senior year, his favorite rock band broke up, his girlfriend broke up with him, he flunked chemistry, didn’t take physics, and he wanted to drop out. On the evening of reading the book, Smalling said,”It came to my mind that if I couldn’t do anything else in my life, I might be a theoretical physicist.” Because physics is more stable and broader than love.
Will these two stories inspire elementary and middle school students to learn math and physics well? Psychologists say, no, such stories can create “math anxiety.” There are so many myths surrounding mathematics that it makes people anxious about mathematics. The myth of mathematics is nourished by mathematical genius, as if only the chosen ones are “mathematicians,” and if you get scared when dealing with numbers, you feel like you’re not a mathematician, and then conclude that you’ll never like mathematics. You see, Hou Shida’s father is a physics professor, Yang Zhenning’s father is a mathematics professor, Smalling wanted to learn physics when he was admitted to the Department of Architecture, they are geniuses. Psychologists say the first step in overcoming math anxiety is to remind yourself that math doesn’t belong to geniuses and that anyone can do at least some math and let go of the pressure to help ease your anxiety. Mathematics, in other words, of course, belongs to the genius, but you learn a little math is five hundred years ago in primary and secondary schools, you should at least do it.
Psychologists also say that, unlike the humanities, math is often seen as a right or wrong discipline, which creates stress. Stanford University has a free online course,”How to Learn Math.” There’s a mind-style exercise that requires you to do 18×5 in your head. Everyone will solve this problem in a slightly different way. Experts recommend that taking the time to try and come up with several different ways to solve a simple math problem will help you shake off the right or wrong mindset and begin to enjoy the math problem-solving process. When math is taught as an open-ended problem, and different ideas and even mistakes are valued, students don’t have as much anxiety.
Psychologists, it seems, have found plenty of excuses for learning difficulties. However, Jason Wilkes’s Burning the Math Book also mentions teaching “the wrong” things. He said that mathematics courses at all levels, from elementary school to postdoctoral, are missing an important link, that is, the description of the vague and chaotic creation process. If we do not talk about the creation process of mathematical ideas, students will not be able to appreciate the elegance and beauty of mathematics.”We have to write textbooks like telling stories, so that the characters in the books are stumped and do not know where to go next.”
Paul Lockhart is a mathematician who taught at the University of California, Berkeley. He became interested in mathematics at the age of 14. It was not the school math class that inspired him, but the extracurricular reading that fascinated him. He had been dissatisfied with school education, and then he wrote a book called “A Mathematician’s Sigh,” and then really went to a K12 school in New York to teach mathematics.
Lockhart resented the storytelling of mathematics. The beauty of mathematics, he said, was that it had nothing to do with everyday life. Schools in order to let the child learn to calculate the circumference of a circle and the area of a circle, will make up a set of Mr Circle and Mrs Area of dialogue, but this is the most boring story. A good mathematical story comes from the history of mathematics. To make circles clear, we must tell about the efforts made by humans to measure curves in the history of mathematics. We must tell about the method of exhaustion.
The idea is challenging. Children understand the concept of geometry and edge, will know that there are three sides of the triangle, quadrilateral has four sides, know the pentagon hexagon and even regular dodecagon is seventeen sides, but a circle has a few sides? This is a difficult problem, in general, we in order to save trouble, will say that the circle has an edge, but the edge is a curve. It’s hard to explain to a child that if you think of an edge as a line segment, then a circle has countless edges, and the more edges a polygon has, the closer its shape, circumference, and area are to a circle. So, we can see the circle as a regular polygon composed of countless line segments, the circle is a kind of conceptual graphics. If you explain to the child, the child can understand?
Lockhart said to tell the area and perimeter of the circle, is about to speak the sotheby’s, Archimedes and exhaustion method in the history of mathematics. Eudoxus was an ancient Greek mathematician in 400 BC. One of his important contributions to mathematics was the establishment of the rigorous method of exhaustion and the use of it to prove some important quadrature theorems. In ancient China there are cutting circle for the mathematical thought, is to use the area of the circle inscribed polygon to infinite approximation circle area. But the exhaustion method, cutting circle, involves the concept of limit and infinitesimal, if along this line of thought, will talk about calculus.
At this point, it can be seen that Lockhart’s educational philosophy has certain dangers. You want to follow him to learn mathematics, cope with the high school entrance exam even will be a problem, but if you are interested in mathematics, willing to get more fun in mathematics, the Lockhart is a very good teacher. Lockhart believes that there are a lot of problems in primary and secondary school mathematics class, let the child write down a pile of formulas and theorems, and then constantly do the questions, this kind of mechanical education can not let the child appreciate the beauty of mathematics, a good way of education is to let the child in mathematics problems, from one problem to another problem, from which to develop mathematical thinking and mathematical skills. To test his teaching philosophy, he also wrote a book called Measurement: A Love Song to Mathematics, which starts with basic concepts such as size and shape and goes all the way to differential equations.
Could a teaching method like Lockhart’s make more children like math? I felt that math textbooks were still geared to the abilities and mental development of most students, and Jason Wilkes’s Burning Math Books: Reinventing Mathematics and Lockhart’s Measurement: A Love Song for Mathematics were more suitable for extracurricular reading.
What do mathematicians think about math anxiety? American mathematician Steven Strogatz says math has nothing to do with speed. Many mathematicians are slow, and smart people can solve simple problems quickly, but they spend a lot of time solving more difficult problems. When it comes to math, once you accept that the answer is not fast or slow, you relax. Another mathematician, Uri Treisman, noticed that many students failed calculus classes at the University of California, Berkeley. After investigating, he found that students with good grades often talked to each other about math and did their homework together, which he called collaborative learning. According to Treisman, it is useful for students to discuss math problems together. Even if you’re not a student, make math a shared experience where you need to learn a basic math principle and then teach it to others. Mathematicians suggest parents flip through elementary or middle school math books, watch math lessons online, and then coach your child to solve the problems. Collaborative learning can improve your “self-efficacy” in mathematics. Often, if we’re bad at math and our self-efficacy is low, this memory will follow you. Redoing homework, practicing math you’re good at now, or helping others learn can all help make math more interesting and reduce anxiety. Of course, overcoming math anxiety doesn’t mean math isn’t hard, or that you’ll become a math genius overnight. What matters is that your feelings about the math experience change.