The inhabitants of Pittsburgh could not find a sensational store, because in fact it is in Connecticut. However, this did not stop the comedians from accepting the news at face value and believing that this is a real tablet allegedly actually placed in the institution by the cashier, who was sick of the fact that some know-it-alls are arguing with him about the final sum. And so it was?
Actually, there is nothing like this (you can read about this story as a confirmation). But on the whole this explanation is quite plausible. Cashiers in our day do not know how to make calculations in the mind, do they?
On the other hand, who generally knows how to count? Mathematics is too complicated. Only those who work with numbers know how to make calculations in the mind.
This statement, again, is incorrect. Wrong, but popular? Well, it could well be.
In any case, Denise Legran regularly faces his confirmation in restaurants and shops. For example, during hangouts with friends, at times when you need to fold to pay bills or give a tip. "Everyone is frightened by any need to solve any problems," she says.
Even before the cash registers turned the calculation of discounts into a click on several icons, it often helped the sales staff count the total amount of purchases. And doing this, she always wondered: "How do they find their money? How are the budgets planned? "
But Legrand is just one of the very people who work with numbers. She directs the Center for Aid for Mathematics at the University of Arkansas in Little Rock and teaches mathematical analysis at the Faculty of Mathematics and Statistics at the University. And she, by the way, often remains discouraged by the reaction of people who find out about her profession: "Are you a mathematics teacher? Never loved mathematics. "
" I do not think that I ever even met a man who would confess to me that he likes mathematics, "she sadly reports.
Sam Lohorn, a young graduate of the Arkansas University in Little Rock with a bachelor's degree in mathematics, is puzzled by the fact that the lack of skills to work with numbers provokes a respectful reaction in society: people are almost bragging about each other about this.
" How often do you hear people say "I can not read, I hate to read"? "He asks.
"At the same time to say" I hate mathematics "is a perfectly acceptable thing for a society," agrees Legran
Meanwhile, the demand for professionals in the field of exact and natural sciences around the world is growing. That's where new jobs appear. To meet the need for qualified personnel, "many governments and private organizations are improving approaches to teaching science and are promoting training aimed at improving the mathematical skills and academic skills of students and workers," write researchers at the University of Chicago in a report published in February The current Directions in Psychological Science.
Similar efforts, they write, are usually aimed at accelerating and improving the flow of more mathematical and Auchnogo material. However, as a result of the analysis of data from the International Program for the Evaluation of Educational Achievement of Students in 64 Countries, in which 15-year-old students passed math, science and reading skills, researchers concluded that concern about solving mathematical problems was "fear of mathematics "- has a rather big influence on the ability of students to learn the exact sciences and something must be done with this.
In other studies it was revealed that the need to take tests in q Fraud intensifies the experiences of students, but the excitement about mathematics stands apart. For example, some studies have shown that the pulse of the subjects increased at the mention of mathematics, while no other reaction was observed with other objects.
Even successful mathematicians are exposed to this fear enough to make mistakes. Anxiety about mathematics leads to a decline in academic achievement in its development, the researchers say.
Working with such fears is one of the missions of Legrand as director of the Center for Assistance in Teaching Mathematics, which provides individual and group classes to students of any level and any department. Speaking as teachers of the center, students are offering other students help with homework, improving teaching skills, preparing for tests and generally working on popularizing mathematics.
This laboratory on the fourth floor of the building of engineering technology and science at the University of Little Rock – a set of lighted Fluorescent lamps and computer-equipped rooms. In the center there is both a "loud part" for group classes, and a "quiet side" for work or games in silence. There are a lounge, toys, sofas, white lecture boards and inspirational slogans.
Here are examples of some of them:
- Failure happens only when a person drops his hands.
- Tetris's example teaches us that errors accumulate in the 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 must be erased," Legrand shares his thoughts on this matter
Lochorn volunteered to work as a volunteer teacher in the center during his studies at the university. In addition, he also taught on a fee basis in several centers of Mathnasium. He and Legrand see certain patterns in the thinking of adults who did not like mathematics. Here are some of them:
- The error is tantamount to stupidity.
- Mathematics is the memorization of formulas.
- People are divided into those who have a "mathematical mindset", that is, who are good at working with numbers, and all the others.
- Success means getting the right answer. There is only one sure way to get the right answer.
All these settings are very harmful, say mathematicians, and they suggest that they stop thinking in this way.
Failure is also good
The center's 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, do work immediately, invest time in it.
They also advocate the right psychological attitudes:
"You need to fail," says Lohorn . – Unsuccessful attempts are part of the learning process. It's very useful to be in a situation where you need to ask yourself: "Damn, what did I do wrong?" That's when you are going with the thought and it turns out something in the spirit: "Yeah, I did not see the whole situation, I did not notice that nuance , Did not have a holistic view of what was going on. ""
Failures are a tool. Free your mind from prejudice in order to learn from your mistakes.
In addition, "remembering is not the goal of mathematics," Legrand says. "The main thing is to understand the process." Of course, knowing, or at least knowing the formula, can help, but as soon as students begin to understand why the formulas work, they can begin to alter them at their own discretion.
Remembering formulas will not help you start thinking more logically.
"People quite naturally associate mathematics with numbers," says Lohorn. "They think it's the science of numbers." However, in practice, it is more the science of regularities. I believe that the human brain is created for mathematics.
For example, we could not walk, if not the fitness of the brain to search for patterns. We are created in order to search for patterns. We love them and do not like chaos. "
And by the way, according to Legrand, neither she nor Lokhorn 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 material checks before giving a lesson. However, the main idea here is that the need to work on your level of mathematics does not make them losers.
"Having communicated with most mathematicians," says Lohorn, "you will see that if you are not a person obsessed with yourself, he will always tell you something like" I need to work on So-so or so-and-so. "
Like other subjects, mathematics has its own special vocabulary and grammar, which differs from the standard one. Legrand emphasizes that good performance in it requires patient reading, as well as in other subjects.
But mathematics differs from other subjects in the sense that some of its concepts are built on others. It is not necessary for a student at the Faculty of History to know the history of Arkansas in order to be able to read about the history of Little Rock. In mathematics, on the contrary, it is impossible to learn trigonometry without first learning to count fingers and toes, and surrender from the dollar. Each new subject adds a set of skills to your piggy bank, which will be required in the future.
Legran does not define success as getting the right answer. Success lies in enlightenment from an understanding of how this answer comes about.
"People say:" Algebra will never come in handy! ", But that's not the case," she says. – The point is to learn to think. You learn how to process information. "
And by the way, as noted by Lohorn:
"One of the things I say to laboratory visitors is:" You do not have to memorize absolutely everything you've ever been taught. " Yes, we hope that you will remember all these nuances, but it 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, traffic signs, instructions, subtitles, and other very different kinds of texts. But how often do you have to perform any complicated mathematical operations to solve problems? The average person does this infrequently. "
From this follows two conclusions:
- Problems with remembering the formula of a quadratic equation does not mean that you do not have the ability to "work with numbers."
- To strengthen mathematical skills, use them more often.
A great way to do this is to use gaming methods.
Learning should always be fun
Use applications to play math games, even designed for children. Play on your computer, smartphone or any other mobile device.
- The free Bedtime Math application (bedtimemath.org) offers a fascinating format for presenting facts with subsequent test questions of varying complexity. One of the problems told about the use of goats instead of lawn mowers. The application offered you to watch a video about how 800 goats were plucked the lawn of the National Laboratory. Lawrence in Berkeley.
- Euclidea Geometric Constructions (euclidea.xyz) will be more complicated, another free application with its own web version. His tasks are based on the classical problems of construction using a ruler and a compass and are divided into 120 levels of complexity from simple to very, very complex.
- Coloring books with mandalas are positioned as a good means of comfort for adults. "You can create your own mandala options using the ruler for drawing and compass," says Lohorn. "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 from all levels – from kindergarten to college.
- Legrand notes that dancing 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, sort of puzzles that require the use of advanced mathematics skills without the need for advanced mathematics as such.
- The Wall Street Journal has a weekly column Varsity Math, which publishes entertaining mathematical problems
- Another interesting column with similar problems was for a long time conducted by Martin Gardner for Scientific American. The site Martin Gardner Puzzles collected some of the best of them.
- And also look for a video on YouTube about the origins of "hexaflexons" by Gardner. Here's a cool example.
If you did not succeed with everything else, just go back to pampering with folding and unfolding hexaflexes.