American middle-class parents are also starting to roll up math? Is it blindly following the trend, or is it a "scientific chicken doll"?

Sports and events have long been a must for American parents. But in recent years, American middle-class parents seem to have begun to roll up on the math track. According to the New York Post, "Russian mathematics" has even become a mandatory item for many parents who want to win at the starting line on the climbing vine. So, what is the charm behind the popularity of this math cram school? What does it mean for math learning in the AI era?

Text, edited by Jennifer

If you ask what middle-class families in the United States are rolling up right now, the answer may not be what you think.

Friends who know about education in the United States must know that sports and activities are a must for North American parents, which is not the same as Asian, especially Chinese, parents like to work hard in cultural subjects.

But recently, this atmosphere seems to have changed with the explosion of "Russian mathematics".

The Russian School of Mathematics (RSM), a Boston-based educational and training institution, has been in the news frequently in recent years.

Recently, according to the New York Post, in order to improve the probability of children's success in climbing the vine and win at the starting line, more and more middle-class families in the United States are listing "Russian mathematics" as a mandatory make-up class for children.

Image source: RSM

This cram school, which features teaching "Russian-style mathematics", has quickly opened more than 70 branches in the United States, and the number of students has now exceeded 20,000.

A Silicon Valley engineer dad thought that this famous "Russian Math" might be affected by the Russian-Ukrainian war, but he didn't expect that cram school places were still hard to find.

"Full" on the registration website indicates that it is full

Another mother, who lives in Manhattan, New York, paid a lot of money to hire a Russian math teacher as a tutor for her preschoolers after she couldn't grab a place in the training class. On the "chicken doll" track, parents who are not poor in money can always find their own shortcuts.

Behind the popularity of Russian-style mathematics tuition schools in the United States, I am afraid that they cannot do without the strength of Russian mathematics.

Whether it is in the International Mathematical Olympiad or the Fields Medal that makes the Chinese people uncomfortable, Russia has a very eye-catching performance. In recent years, in order to compete for Russian mathematical talents, Huawei has simply set up a mathematical research institute in Russia to provide Huawei with a series of basic scientific research support.

So, what is the charm of this cram school and the Russian mathematics behind it?

"It doesn't hurt to learn more math"

Natalia, who attends a private elementary school, has been tutoring mathematics here since she was 7 years old. While her peers were still learning to ride bikes and play video games, Natalia began spending two hours a week thinking about the fundamentals of multiplication and algebra.

Her mother, Anna, is a data scientist and investor who graduated from Stanford University. Anna is very satisfied with the tutoring arrangements she gave her children, she believes that the mathematics learning content provided by the school is not enough, and her daughter with excellent math grades can learn more deeply.

"If she wants to be a doctor in the future, an engineer — math never hurts." Mathematics will increase her understanding of the world. ”

Natalia and mother Anna (front row, second from left and back row, first left)

Of course, there are various reasons for parents who send their children to tutor math.

Some parents hope that "children can maximize their mathematical talents, which is difficult to do with the school curriculum alone." "More parents are thinking that they are quite Buddhist – they want their children to really take an interest in learning math.

In fact, math tuition is not new. In the United States, there are not only many private tutoring tuition classes, but also online learning communities such as Khan Academy and AoPS, and now Xueersi also has a place in the parent circle.

Among the strong math learning institutions, why does RSM quickly capture the hearts of American parents?

An RSM campus

It is understood that RSM provides mathematics courses from kindergarten to 12th grade for middle-class families in the United States, covering all areas of mathematics, from basic knowledge to advanced mathematics, and can be enrolled as early as 5 years old.

Martha Gershman, head of outreach at RSM, said: "Mathematics is a good tool to shape children's thinking, and the sooner we learn the better, we tend to underestimate children's logical thinking and abstract thinking skills."

In terms of course content, RSM can provide learning content that is much faster than learning in school. For example, third-graders are exposed to the concept of algebra, which most American schools don't teach until ninth grade. This has also made some parents flock to it.

So, as more and more children flock to this Russian math tuition school, how has the children's math performance changed?

RSM co-founder Rifkin is not "modest" and even said, "Every time our campus opens to a new town, the number of math honors classes in local schools will soon grow significantly, especially at the high school level." ”

However, Steven Latendi, the head of the mathematics department at Newton South High School, said that although the proportion of students attending honors math classes at the school has increased from 20% to 30%, there is no data to suggest that this is thanks to "Russian mathematics".

Instead, he worries that the sheer number of students tutoring Russian mathematics could add pressure to parents, children and schools.

For example, among parents who send their children to Russian mathematics tuition schools, there are many situations that are driven by comparison and fear, worried that their children are at a disadvantage, so they blindly follow the trend;

In teaching, teachers also encounter some difficulties, such as when explaining a new knowledge point, they often find that a quarter of the students have already learned in advance in the cram school;

In addition, the gap in math achievement between students is widening, especially between rich and poor families, after all, not all families can afford the high tuition fee of $2,000 per week...

It remains to be seen how far "Russian math tuition schools" like this will develop in the future, and what impact it will have on middle-class families and local schools in the United States.

Russian mathematics tuition school, what is the charm?

So, is the Russian math tuition school more gimmick than the content, or far beyond expectations, can it really become a "baby pushing artifact"?

Based on some news reports and real feedback from parent groups, Bund Jun found that Russian math tuition classes have the following characteristics:

1. Focus on logical reasoning, not the calculation process

On the RSM website, some specific topic cases are given. Here's what students will encounter in their second- and third-year classes:

In such a question, the child is not expected to calculate the answer, but uses the result of question A to solve problems B and C and reasoning about the problem at an abstract level. In the classroom, teachers also mainly rely on guiding students to observe for themselves and explore the differences between these numbers.

In the process of solving problems, children will probably discover the rules by themselves:

634 - 182 = 452

635 - 182 = 452+1 ；

635 - 181 = 452+1；

Next, the teacher will help students express their ideas in algebraic language, replacing the numbers 635 and 182 with symbols A and B, and reasoning out A - (B - 1) = (A - B) + 1. In this way, children in the third and fourth grades of primary school naturally came into contact with the idea of algebra.

This can also be seen in a major feature of Russian mathematics learning - more attention is paid to guiding children to logical reasoning, even young children, pay attention to the training of abstract thinking.

For example, when children have solved some basic additions and subtractions, they will usher in an open mind.

triangle + circle = 12;

triangle + triangle = 16;

So, triangle = ? Round = ?

Children will use simple reasoning to conclude that triangle equals 8 and circle equals 4.

However, the teacher is not satisfied with the answer in this step, but will make the student think further: "Why did you start with the triangle first?"

Next, through thinking about such problems, children will learn about the principle of solving unknown equations in advance.

According to MIT historian of mathematics, Slava Grovich, "The Russian way of teaching is to make sure that every student, when doing a math, understands why they do it, not just learn how to do it." This, he believes, can help children learn math more easily and better.

2. Do not exclude brushing questions, but the topic setting is very important

So, will Russian mathematics tuition schools allow students to brush up on a large number of questions?

A parent of a fifth-grade child in a private school in the United States shared that his child studied math at RSM for about 2 hours once a week, and practiced homework about 30-40 questions each time.

She found that the content and form of these topics were very flexible, and she paid more attention to logical thinking training, which children liked very much. When doing questions online, although the calculation questions seem very complicated, children do not need to calculate the result, just drag the mouse to move the decimal point to determine the number of digits.

In addition, the learning progress of Russian mathematics tuition classes is much faster than that of private schools, making children progress quickly.

Some parents feel that compared with AoPS (famous mathematics online learning community in the United States), which is more aimed at competition students, Russian mathematics practice questions, although there is a certain amount of brushing questions, but it is actually exercising children's logical thinking ability, and pays attention to fun.

Itina, a teacher who writes the math course materials, says that just as playing an instrument requires practice, math inevitably requires some practice. But it must be understood that children can only learn mathematics well if they are emotionally engaged.

"If wishful thinking is given boring questions to kids, they'll say, 'I don't understand, I hate it,' and walk away."

3. Start with difficult problems and bring students to the level of abstract thinking as quickly as possible

"In American schools, it starts with simple problems and then gradually solves difficult problems; When I was in school, the curriculum was a puzzle at the beginning, and then we would brainstorm. An engineer who immigrated to the United States from the Soviet Union to work in software development in Silicon Valley said. In 2020, he also founded an online tutoring platform in the United States that offers "Russian mathematics courses".

Sinking mathematical concepts, which represent abstract thinking, to the primary school level is probably the most distinctive point of Russian mathematics tuition schools.

RSM founder Inessa Rifkin believes that mathematics is the best tool for thinking and reasoning. Children should be brought to the level of abstract thinking as soon as possible, introducing them to algebra and geometry as early as possible, not just solving arithmetic.

RSM two founders

This is also why, in the Russian mathematics tuition school, children in the third and fourth grades begin to contact and learn algebra; Kindergarteners may learn geometry problems by putting together geometric "princess castles".

Of course, in this process, the teacher needs to guide the child to figure out the basic principles behind the mathematical concepts, rather than cramming and memorizing formulas.

According to Martha Gershman, head of outreach at RSM, the early development of abstract thinking is actually very important. And early math education should not underestimate children's abstract thinking ability.

Martha Gershman shares at the TED Talk

She believes that habitual withdrawal and self-doubt are the biggest obstacles to a child's learning mathematics compared to thinking about difficult problems.

When a child encounters a challenge, if instead of blurting out "this is too hard, I won't", but "Well, let me think...", it is equivalent to a good start in the mathematical journey.

In the era of AI, how do we learn mathematics?

If because of the above characteristics, Russian mathematics tuition schools have exploded in the circle of middle-class parents in the United States, then American parents are really at the forefront of "scientific chicken dolls".

Do not pursue specific calculations, but let children give full play to their logical thinking and reasoning ability;

Jump out of specific topics, ask more questions, and exercise at the level of abstract thinking;

Through repeated practice and problem solving, develop a mindset that is willing to explore and challenge...

Such a concept of learning mathematics reminds Bund Jun of the educational method that Luo Boshen, the head coach of the United States and tenured professor at Carnegie Mellon University, has always advocated - more important than the learning of mathematical knowledge, is the cultivation of mathematical thinking.

With the advent of ChatGPT, Professor Luo bluntly said that question-based learning for the purpose of exams will have no advantage in the era of artificial intelligence. No one is better at "brushing questions" than AI, and as educators, we must learn to change the way of education and cultivate children's ability to use their brains and solve problems.

Professor Luo Boshen

In traditional teaching, the teacher often makes a demonstration first, tells students the solution ideas of a certain question type, and then allows students to practice the same question type several times. Such a teaching method of "emphasizing exercises and thinking lightly" cannot be exercised by mathematical thinking.

"When you're faced with a hard problem and no one tells you what to do, you have to be creative and then figure out how to solve it. If you just listen to the method taught by the teacher in class, or just do some simple and repetitive problems, this is not exercising mathematical thinking and creativity. ”

So, how to learn mathematics to cultivate and exercise children's real thinking ability?

1. In math learning, don't be afraid of the "slow" in front of you

In order to promote mathematics education, Professor Luo often has some programs to teach elementary and junior high school students to exercise their thinking. In class, he doesn't tell students what to do. Instead, he asks the students to explore on their own, with each writing down their ideas on the board.

"Even if no one person can come up with a complete solution at once, students will see the various ideas on the blackboard and think that certain ideas can be combined to solve this problem."

Therefore, the same problem often gets completely different solutions in different classes. Instead of passively learning mathematical knowledge and skills, students participate in brainstorming and contribute their own thinking.

Even if it involves trying a lot of mistakes or going around in circles in the process, he believes that this is a very necessary mental exercise process. Whenever you solve a difficult problem, it is helpful not only to face similar topics, but even to face very different topics.

He advised students that instead of doing 10 questions without asking for solutions, it is better to slow down and thoroughly understand 1 question.

Just like Professor Luo's daughter, she has always been slow to do problems in elementary school, and sometimes a topic can be thought about for more than an hour. But Professor Luo never pushes him, because what matters is that the child is really trying to think about the problem compared to the answer to a question.

Professor Luo's daughter is doing mathematics, source Luo Bo Shen Weibo

And the longer and deeper a child thinks about a certain problem, the more she will naturally learn. In the future, after her knowledge expands and deepens, the speed of doing questions will be raised at once.

Today, Professor Luo's daughter has won a series of mathematics competition awards in addition to enjoying mathematics learning.

2. In mathematics learning, time and patience are very important

If a child has to face a very heavy homework and his free time is crowded out, he will not have time to patiently ponder a difficult problem or explore more of his potential.

In the end, I learned a lot of bits and pieces, and soon I forgot about it, not to mention how it helped improve my personal thinking.

In addition to lack of time, future mathematics learning must also overcome the utilitarian mentality. In order to cope with the exam, many teachers and parents will insist on letting their children brush as many questions as possible and master more problem-solving routines. As long as you can do the right topic, it doesn't matter if you know half and don't ask for a solution.

Such a utilitarian learning attitude is very detrimental to helping children develop a passion for exploring mathematics when they are young, and it is also detrimental to the cultivation of a "growth learning mentality".

3. Cultivate a growth mindset and build confidence in mathematics

Whether or not you have a growth learning mindset has a great impact on a child's mathematical performance.

Carol Dweck, a professor at Stanford University, studied the behavior of thousands of children and found that children have two learning mindsets: "fixed" and "growing".

Under fixed thinking, students believe that qualities such as intelligence or talent are fixed, and they tend to believe that only talent can create success;

Under a growth mindset, they believe that they can develop their abilities through hard work, which fosters a love of learning and allows them to learn from their mistakes rather than be crushed by them.

Professor Dweck said that having a growth mindset was a major determinant of whether they could excel in the subject.

Those children with a growth mindset are not afraid of the challenges in front of them when facing mathematical problems, and even if they fail, they will not have self-doubt and lose confidence in mathematics learning.

The establishment of a growth mindset needs to give children positive encouragement, guide children to be interested in the process of thinking about mathematics and solving problems, and enjoy it, rather than focusing on scores and results.

As Professor Luo said, brushing questions will become history. To overcome the utilitarian mentality, spend time and energy, and truly cultivate children's mathematical thinking is the right way to learn mathematics.

Resources:

(Swipe up and down)

1.How ‘Russian Math’ Became a Must-Have Extracurricular for Overachieving Parents

2.Why Thousands Of American Parents Are Sending Their Kids To 'Russian Math'

3.The new way rich parents are paying to get their kids into the Ivy League

4.Changing Your Math 'Mindset' Can Boost Your Math Performance

5.Masha Gershman: What Can We Learn From The Russian Approach To Math Education?