Magicsniper for Chinese students in the United States

Sender: magicsniper (let's enjoy the WeChat in June), email area: Picture
Question: Re: the gap between Chinese College Entrance Examination and English college students' math questions
Mailing station: shuimu community (Sun Jan 23 13:12:49 2011), within the station

The myth of "Chinese student mathematics Nb" (zz)

They all talk about the mathematical basics of Chinese students.

China is only a medium school with good mathematics, and I will mention it when I arrive at the university.

There are huge differences between Chinese and foreign engineering higher education, especially in basic mathematics courses.

In China, first of all, it is the extreme accommodation of mathematical tools for middle school thinking.
In addition to basic calculus, Chinese engineering teaching materials like middle school students like to use scalar expressions.
Taking into account the size, ignoring the direction, and even the statement "skipping the negative number and not writing, only considering the size,
Avoid vector expressions.
At the beginning, mechanics courses in Europe and America used a large amount of matrix theory and linear space knowledge to force students to compare
Abstract thinking looks at problems from a relatively high point of view and abandons some bad habits in middle school thinking.

After that, I found that many Chinese students are wondering why foreigners are not familiar with the problem.
This is a complicated problem. Although many of them are the top leaders of Tsinghua, xigong University, or the first few.

This is another difference between Chinese and foreign engineering education.
We Cultivate the proficiency in solving simple problems. Excellent students are just a comparison of proficiency in solving simple problems.
High. We have a lot of conclusions on some common simple questions that require students to back up and come to these conclusions.
The proficiency of students determines

The test score.
Foreigners are wondering why Chinese students have come up with so many conclusions that they have not deliberately stressed. Most important
Chinese students think these conclusions are very valuable and profound. Foreigners think that...
It is obvious that tensor operations are far from being performed.

All in all, for a long time, "back-to-conclusion" education has killed students' reasoning ability and made them
Conclusion of excessive dependence.

For a simple example, in the theoretical mechanics course, we emphasize conservation of momentum and momentum.
The formula can solve many Chinese problems at once.
However, if a model is neither conservation of momentum nor conservation of momentum
Annoying. Because this is not a rule.
A foreigner doesn't care about this. I forget a page full of paper and tell you: I don't know anything about conservation of shit momentum or angular momentum.
Conservation, because a linear combination of its momentum and momentum is conservation.

And
Ta talked about some stupid questions that are frequently asked by Chinese students.
"How can the angular velocity calculate the vector? It's not a circle. The vector should be straight"
"When will the area become a vector? He was always regarded as a scalar in middle school"
"What is the difference between consistent continuity and continuity? What is the difference between consistent convergence and Convergence ?"
It is difficult to get rid of the shadow of Middle School logic, and it is a common problem for Chinese students to solve urgently.
Trap

After learning the Real-Time Function Change, Chinese students still naively believe that the derivation and points are inverse operations.
".
I have learned linear algebra for one year in China (well, some have only learned linear algebra for half a year), but I don't even know what a symmetric array can do.
Using orthogonal operators (this kind of students may have scored more than 90 points in the domestic linear algebra examination, and only one calculation in China
Determinant, feature vector

Of course, water ). When this content is involved in the class, I'm surprised to see it with a big mouth.
Only Chinese students.

Another one that exposes the scars of Chinese students,

Chinese students have no concept of "field". Their understanding of "gradient, rotation, and divergence" is only in the definition form.
Applications are particularly inskillful. Chinese students are very advanced in algebra and triangle Transformation
To make foreigners stunned.

The University has a strong tendency to reject advanced tools that contain great wisdom. Besides basic calculus operations
In addition, the mathematical thinking ability of Chinese students remains at the peak of middle school, or even worse.

Chinese students think that it is not obvious that the Gini inequality is a kind of skill. It is a patent of a few people, and they are afraid of it.
, Let alone the inequality between holder and minkovski. 99% of engineering students do not know the cosine inequality, and the remaining 1%
Another 99% won't be used. Foreign Teachers

The syllabus is based on the linear spatial thinking of the advanced architecture.
Inequality is simply as intuitive as "the sum of the two sides of a triangle is greater than the third side.

OK. There are too many examples. A joke about a convex function and the random exchange of extreme order, 80%
They are all made up by Chinese students. We will talk about institutional issues later.

Another example:

The things mentioned above are not the first thing I have found. Many people have complained before, including some domestic
Grant. Their response is to strengthen the teaching of basic mathematics courses, and change the "advanced mathematics" of engineering to "number of engineering courses ".
Learning analysis ". Good Mathematical Analysis

There is great wisdom, but now our "shanzhai culture" has taken effect again: who put your name in front of"
The word "engineering", so the mathematical analysis is superior to the advanced mathematics, the content is deleted and then deleted.
What is the difference between the numbers of different names.

Our batch-production talents claimed to have learned a few points. Even Cosi's convergence criteria were unknown, and the Division was point-by-point convergence.
And consistent convergence, claiming to have learned Fourier analysis, but will only set the formula, do not know the orthogonal of the trigonometric series, put
The TA is crazy. Her eyes

Chinese students are never famous for their mathematics level. The French and Hungary talents are.

Therefore, we must reflect on why Chinese middle school students are better at mathematics and physics than foreigners.
When I got to college, I was not only caught up, but also far beyond? What makes us more advanced?
Exclusive sense of thinking and advanced tools?

What is the leading role of our secondary education:

Through the sea of questions tactics, we allow students to repeatedly practice some of the more non-mainstream primary mathematics, but modern mathematics does not
Skills of interest (for example, the Auxiliary Line of junior high school ry, triangle full, etc., the trigonometric function algebra transformation of Senior High School,
How does one reduce the power and expand the angle ). Foreign countries will emphasize
Spatial knowledge, such as extending the concept of length to "modulo", and introducing triangular inequalities in other spaces.
It is a little abstract, but it seems useless to us, because these things cannot help us calculate the elliptic or parabolic
Line equations, and the college entrance examination depends on these. After Memorizing some conclusions, it seems that our middle school students are older.
It requires more mathematical skills for "Form operations. However, these skills will be quickly forgotten after the college entrance examination.
The advantage is gone, the disadvantage of abstract thinking is still there, and the habit of "form calculation" is still there, so "casually submit
It's not surprising that the order of limits is changed.

At the same time, Chinese middle school education only shows the ugly side of mathematics, not the beautiful side. Endless questions
Sea makes students get bored or afraid. After entering the university, students escape or resist the pressure of high school students.
Higher thinking and higher tools have become inevitable. In contrast, in foreign countries, existing concepts are being promoted in new spaces.
The similarities, connections, and differences of math can better reflect the nature of math and tell students that math is beautiful.
No matter how advanced the middle school mathematics skills are, they can only solve simple problems.
.
[Mentioned in the masterpiece of PTM :]
: The Chinese college entrance examination is coming out of the UK, and the university has to be overwhelmed.
: A freshman in the United States has a mathematics class equivalent to a sophomore in China,
: The first mathematics class in the United States is equivalent to the second year in China.
:...................

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Retreat
Attacking Xu rulin
Robbing grain and grass
Difficult for the primary

※Source: · Shui Mu community newsmth.net · [from: USA]

 

Buy one get one free, and then attach it to a student studying in Canada

 

Sender: blacklord (blacklord), email area: Picture
Question: Re: the gap between Chinese College Entrance Examination and English college students' math questions
Mailing station: shuimu community (Sun Jan 23 16:51:55 2011), within the station

I am a TA at a North American University and a high school student tutor.

1. High school students learn a lot of knowledge here, but they will use the simplest knowledge to solve many complex practical problems.
If they have lab courses in high school, they use various electrical components to make complex functional circuits. However, our high school courses do not
There is a pn.

2. North America's undergraduate students are much better than domestic students and have a low starting point. However, we were dumped when we graduated from undergraduate courses.
Far away

What I observed was the cause of the system. In China, except for public electives, most of the courses in China were fixed.
They are all mixed graduates, and students in North America have a lot of autonomy in selecting courses. After all, a class costs $1000 and they are more active in learning.
Nature and purpose

In addition, American students have a strong ability to solve practical problems. Teachers leave theories in their homework within the scope of the classroom, but they can solve the problems.
I found that foreign students will find uncommon solutions to the equation on the webpage/mathematics manual.
In comparison to homework, most Chinese students only use what the teacher taught in class.

 

[Mentioned in the masterpiece of PTM :]
: The Chinese college entrance examination is coming out of the UK, and the university has to be overwhelmed.
: A freshman in the United States has a mathematics class equivalent to a sophomore in China,
: The first mathematics class in the United States is equivalent to the second year in China.
:...................

--

※Source: · waterwood community http://newsmth.net · [from: Canada]