Winning the "mathematical monster": it's not about numbers, but about learning to think
Recently, a tweet ran through the network, the content of which was the following: a mysterious tablet appeared in one of Pittsburgh's cookery with the following message to visitors: “Please refuse to discuss mathematics in the queue at the checkout.”
Residents of Pittsburgh could not find a sensational store, because in fact it is located in Connecticut. However, this did not prevent the humorists from accepting the news at face value and believing that this was a real sign, supposedly really placed in the institution by the cashier, who was tired of some know-alls arguing with him about the final amount. And so it was?
')
In fact, there is nothing of the kind (as proof you can read about this story). But in general, this explanation is quite plausible. Cashiers in our days do not know how to do calculations in the mind, is not it?
On the other hand, who in general today can count? Math is too complicated. Only those who work with numbers can perform calculations in their minds.
This statement is again incorrect. Wrong, but popular? Well, it may well be.
In any case, Denise Legrand regularly encounters his confirmation in restaurants and shops. For example, during parties with friends, in moments when you need to chip in to pay the bill or give a tip. “People are afraid of any need to solve any problems,” she says.
Even before cash registers turned the calculation of discounts into clicking on a few icons, she often helped sales staff with calculating the total amount of purchases. And while doing this, she wondered every time: “How do they count their money? How do you plan a budget? ”
But Legrand is just one of those very people who work with numbers. She leads the Mathematics Education Assistance Center at the University of Little Rock in Arkansas and teaches mathematical analysis at the University’s Department of Mathematics and Statistics. And, by the way, she often remains discouraged by the reaction of people learning about her profession: “Are you a math teacher? I never liked math. ”
Sam Lahoorn, a young graduate of the University of Arkansas in Little Rock with a bachelor's degree in mathematics, is perplexed that the lack of skills to work with numbers causes a respectful reaction in society: people almost do not brag about each other about this.
In the meantime, the demand for professionals in the sciences and sciences is increasing worldwide. This is where new jobs appear. To meet the need for qualified personnel, “many governments and private organizations are improving approaches to the teaching of exact sciences and promoting training aimed at improving mathematical and research skills among students and workers,” write researchers from the University of Chicago in a report published in February issue of Current Directions in Psychological Science.
Such efforts, they write, as a rule, are aimed at accelerating and improving the supply of more mathematical and scientific material. However, as a result of data analysis of the International Program for the Assessment of Educational Achievement of Students in 64 countries, in which 15-year-old students took tests in mathematics, science and reading skills, the researchers concluded that the concern about solving mathematical problems was “the fear of mathematics “- has a rather large influence on the ability of students to master the exact sciences and something must be done with this.
In the course of other studies, it was revealed that the need to take tests as a whole reinforces the experiences of students, but excitement about mathematics stands apart. For example, some studies have shown that the subjects' pulse quickened at the mention of mathematics, whereas with other subjects a similar reaction was not observed.
Even students who are successful in mathematics are exposed to this fear enough to make mistakes. Anxiety about mathematics leads to a decrease in academic performance in its development, the researchers say.
Working with such fears is one of the missions of Legrand as the director of the Mathematics Learning Assistance Center, which provides individual and group classes for students of any level and of any departments. Students acting as teachers of the center offer other students help with homework, improving their learning skills, preparing for tests and generally working on promoting mathematics.
This lab on the fourth floor of the engineering and science building at the University of Little Rock is a set of lighted fluorescent and computer-equipped rooms. In the center there is both a “loud part” for group lessons, and a “quiet side” for work or play in silence. There is a lounge, toys, sofas, white lecture boards and inspirational slogans.
Here are examples of some of them:
Lokhorn volunteered to work as a volunteer teacher at the center during his university studies. In addition, he also taught on a fee basis at several Mathnasium centers. He and Legrand see certain patterns in the thinking of adults, who do not like math. Here are some of them:
All these installations are very harmful, mathematicians consider, and suggest to stop thinking in this way.
Center teachers give students advice on ways to relax and calm, such as deep breathing. They emphasize that when solving problems it is useful not to postpone them until the last moment, to do the work right away, to invest time in it.
They also advocate correct psychological attitudes:
Failures are a tool. Free your mind from prejudice to learn from your mistakes.
In addition, “memorization is not the goal of mathematics,” says Legrand. “The main thing is to understand the process.” Of course, knowledge or, at least, the ability to learn a formula can help, but as soon as students begin to understand why formulas work, they can begin to redo them at their own discretion.
Memorizing formulas will not help you start thinking more logically.
And by the way, according to Legrand, neither she nor Lahorn were born with a “mathematical mindset”. They also need to study the subject and think with their heads. She, in particular, conducts the most thorough checks of the material before giving a lesson. However, the main idea here is that the need to work on their level of mathematics does not make them losers. They learned to enjoy the effort.
Like other subjects, mathematics has its own special vocabulary and grammar, which is different from the standard one. Legrand stresses that good academic performance requires patient reading, as well as in other subjects.
But mathematics is different from other subjects in the sense that some of its concepts are built on others. A history student doesn’t have to know the history of Arkansas to be able to read about the history of Little Rock. In mathematics, on the contrary, it is impossible to learn how to trigonometry without first learning how to count fingers and toes, and giving up the dollar. Each new topic adds a set of skills to your piggy bank that will be needed later.
Legrand does not define success as getting the right answer. Success lies in insight from understanding how this answer is made.
And by the way, as Lokhorn notes:
From this two conclusions follow:
A great way to do this is to use game methods.
Use applications for playing math games, even intended for children. Play on your computer, smartphone or any other mobile device.
If you didn’t work out with the rest, just go back to pampering with folding and unfolding hexaflexagons.
Residents of Pittsburgh could not find a sensational store, because in fact it is located in Connecticut. However, this did not prevent the humorists from accepting the news at face value and believing that this was a real sign, supposedly really placed in the institution by the cashier, who was tired of some know-alls arguing with him about the final amount. And so it was?
')
In fact, there is nothing of the kind (as proof you can read about this story). But in general, this explanation is quite plausible. Cashiers in our days do not know how to do calculations in the mind, is not it?
On the other hand, who in general today can count? Math is too complicated. Only those who work with numbers can perform calculations in their minds.
This statement is again incorrect. Wrong, but popular? Well, it may well be.
In any case, Denise Legrand regularly encounters his confirmation in restaurants and shops. For example, during parties with friends, in moments when you need to chip in to pay the bill or give a tip. “People are afraid of any need to solve any problems,” she says.
Even before cash registers turned the calculation of discounts into clicking on a few icons, she often helped sales staff with calculating the total amount of purchases. And while doing this, she wondered every time: “How do they count their money? How do you plan a budget? ”
But Legrand is just one of those very people who work with numbers. She leads the Mathematics Education Assistance Center at the University of Little Rock in Arkansas and teaches mathematical analysis at the University’s Department of Mathematics and Statistics. And, by the way, she often remains discouraged by the reaction of people learning about her profession: “Are you a math teacher? I never liked math. ”
“I don’t think that I ever even met a person who would confess to me that he likes mathematics,” she says sadly.
Sam Lahoorn, a young graduate of the University of Arkansas in Little Rock with a bachelor's degree in mathematics, is perplexed that the lack of skills to work with numbers causes a respectful reaction in society: people almost do not brag about each other about this.
“How often do you hear people say“ I can't read, I hate reading ”?” He asks.
“At the same time, saying“ I hate math ”is quite an acceptable thing for society,” agrees Legrand
In the meantime, the demand for professionals in the sciences and sciences is increasing worldwide. This is where new jobs appear. To meet the need for qualified personnel, “many governments and private organizations are improving approaches to the teaching of exact sciences and promoting training aimed at improving mathematical and research skills among students and workers,” write researchers from the University of Chicago in a report published in February issue of Current Directions in Psychological Science.
Such efforts, they write, as a rule, are aimed at accelerating and improving the supply of more mathematical and scientific material. However, as a result of data analysis of the International Program for the Assessment of Educational Achievement of Students in 64 countries, in which 15-year-old students took tests in mathematics, science and reading skills, the researchers concluded that the concern about solving mathematical problems was “the fear of mathematics “- has a rather large influence on the ability of students to master the exact sciences and something must be done with this.
In the course of other studies, it was revealed that the need to take tests as a whole reinforces the experiences of students, but excitement about mathematics stands apart. For example, some studies have shown that the subjects' pulse quickened at the mention of mathematics, whereas with other subjects a similar reaction was not observed.
Even students who are successful in mathematics are exposed to this fear enough to make mistakes. Anxiety about mathematics leads to a decrease in academic performance in its development, the researchers say.
Searching of decisions
Working with such fears is one of the missions of Legrand as the director of the Mathematics Learning Assistance Center, which provides individual and group classes for students of any level and of any departments. Students acting as teachers of the center offer other students help with homework, improving their learning skills, preparing for tests and generally working on promoting mathematics.
This lab on the fourth floor of the engineering and science building at the University of Little Rock is a set of lighted fluorescent and computer-equipped rooms. In the center there is both a “loud part” for group lessons, and a “quiet side” for work or play in silence. There is a lounge, toys, sofas, white lecture boards and inspirational slogans.
Here are examples of some of them:
- Failure happens only when a person gives up.
- The example of Tetris teaches us that mistakes accumulate with a mountain, and achievements disappear.
- The difference between genius and stupidity is that any genius has its limits.
- You are unique, just like everyone else.
“Some of them need to be erased,” Legrand shares his thoughts on this.
Lokhorn volunteered to work as a volunteer teacher at the center during his university studies. In addition, he also taught on a fee basis at several Mathnasium centers. He and Legrand see certain patterns in the thinking of adults, who do not like math. Here are some of them:
- Error is tantamount to stupidity.
- Mathematics is memorizing formulas.
- People are divided into those who have a “mathematical mindset,” that is, who are good at working with numbers, and all the rest.
- Success means getting the right answer. There is only one sure way to get the right answer.
All these installations are very harmful, mathematicians consider, and suggest to stop thinking in this way.
Bad luck too
Center teachers give students advice on ways to relax and calm, such as deep breathing. They emphasize that when solving problems it is useful not to postpone them until the last moment, to do the work right away, to invest time in it.
They also advocate correct psychological attitudes:
"You need to fail," says Lokhorn. - Unsuccessful attempts - part of the learning process. It is very useful to be in a situation where you need to ask yourself: “Damn, what did I do wrong?” Then you are going with the thought and you get something in the spirit: “Yeah, I did not see the whole situation, did not notice that nuance , did not have a holistic view of what was happening. ""
Failures are a tool. Free your mind from prejudice to learn from your mistakes.
In addition, “memorization is not the goal of mathematics,” says Legrand. “The main thing is to understand the process.” Of course, knowledge or, at least, the ability to learn a formula can help, but as soon as students begin to understand why formulas work, they can begin to redo them at their own discretion.
Memorizing formulas will not help you start thinking more logically.
"People quite naturally associate mathematics with numbers," says Lokhorn. - They think it is a science of numbers. However, in reality it is more like a science about patterns. I believe that the human brain was created for mathematics.
For example, we could not walk if it were not for the brain's ability to search for patterns. We are created to look for patterns. We love them and do not love chaos. ”
And by the way, according to Legrand, neither she nor Lahorn were born with a “mathematical mindset”. They also need to study the subject and think with their heads. She, in particular, conducts the most thorough checks of the material before giving a lesson. However, the main idea here is that the need to work on their level of mathematics does not make them losers. They learned to enjoy the effort.
“After talking with most mathematicians,” says Lokhorn, “you will see that if a person who is not obsessed with himself is in front of you, he will always tell you something like“ I have to work on this or that ”.
Like other subjects, mathematics has its own special vocabulary and grammar, which is different from the standard one. Legrand stresses that good academic performance requires patient reading, as well as in other subjects.
But mathematics is different from other subjects in the sense that some of its concepts are built on others. A history student doesn’t have to know the history of Arkansas to be able to read about the history of Little Rock. In mathematics, on the contrary, it is impossible to learn how to trigonometry without first learning how to count fingers and toes, and giving up the dollar. Each new topic adds a set of skills to your piggy bank that will be needed later.
Legrand does not define success as getting the right answer. Success lies in insight from understanding how this answer is made.
“People say:“ Algebra will never come in handy for me! ”, But that’s not the point, she says. - The point is to learn to think. You learn to process information. ”
And by the way, as Lokhorn notes:
“One of the things I tell visitors to the laboratory is:“ You don’t have to remember absolutely everything you have ever been taught. ” Yes, we hope that you will remember all these nuances, but this will not happen if you do not use them regularly.
You read all the time, right? We constantly have to read. Even if you do not pick up books, you still read the menu, road signs, instructions, subtitles, and other various kinds of texts. But how often do you have to perform any complex mathematical operations to solve problems? The average person does this infrequently. ”
From this two conclusions follow:
- Having problems remembering a quadratic equation does not mean that you do not have the ability to "work with numbers."
- To consolidate math skills, use them more often.
A great way to do this is to use game methods.
Learning should always be a joy.
Use applications for playing math games, even intended for children. Play on your computer, smartphone or any other mobile device.
- The free application Bedtime Math ( bedtimemath.org ) offers a fascinating format for presenting facts, followed by test questions of varying complexity. One of the tasks was about using goats instead of lawn mowers. The application offered you to watch a video of how 800 goats plucked out the lawn of the National Laboratory. Lawrence in Berkeley.
- More difficult will be Euclidea Geometric Constructions ( euclidea.xyz ) - another free application with its own web version. His tasks are based on the classic construction tasks using a ruler and compasses and divided into 120 levels of difficulty from simple to very, very complex.
- Coloring books with mandalas are positioned as a good sedative for adults. “You can create your own custom mandalas with the drawing and compass ruler,” says Lahorn. “This is a very useful thing if you are upset or worried.”
- Khan Academy ( khanacademy.org ) is a free educational website with videos and interactive games for students at various levels - from kindergarten to college.
- Legrand notes that dance and music are math in motion. So dance, play a musical instrument.
- Sudoku, KenKen, magic squares, chess and checkers can be called mathematics for recreation, such puzzles that require the use of advanced level mathematics skills without the need to know advanced mathematics as such.
- The Wall Street Journal has a weekly column called Varsity Math , which publishes entertainment math problems.
- Another interesting column with similar puzzles for quite a long time led Martin Gardner for Scientific American. The Martin Gardner Puzzles website contains some of the best ones.
- And also look at YouTube for a video about origami "hexaflexagons" Gardner. Here is a cool example .
If you didn’t work out with the rest, just go back to pampering with folding and unfolding hexaflexagons.
Source: https://habr.com/ru/post/404573/
All Articles