Some time ago, I watched a video on the headlines, mainly about a Chinese-American mathematician who discovered a new solution to the unary quadratic equation.
This mathematician' name is RoboShen, the head coach of the American team of the International Mathematical Olympiad, and he is a very good person. In 19 years, he discovered a new solution to an unusual unary quadratic equation, and then he was very excited, and then it was sent to youtube, which caused a great reaction, and in general, the reputation was mixed, some expressed support, some expressed opposition.
He has also come to China to introduce his method, which has not caused as much repercussions abroad. Let's first introduce Professor Luo's new method.
<h1 class="pgc-h-arrow-right" data-track="5" > Professor Luo's new method</h1>
For a unary quadratic equation, if it can be written in the form of (x-a)(x-b)=0, then obviously a and b are the roots of this unary quadratic equation, and Professor Luo's method is to convert an equation into the form of (x-a)(x-b) = 0.
Maybe some readers have to ask, isn't that just cross multiplication? What is the new approach? Don't worry, keep looking down.
Taking x²-8x+12=0 as an example, if you want to decompose it into the form of (x-a)(x-b)=0, then there is
a+b=8，ab=12
Usually our approach is to "dismantle and accumulate", that is, to find a way to split 12 into two numbers, so that their sum is 8, then can we "dismantle and accumulate"? Professor Luo's idea is "demolition and accumulation".
令a=4+u,b=4th
Substitute ab = 12, to get (4 + u) (4-u) = 12
16-u²=12.u²=4.u=±2
Substitute a, b gets two roots 2 and 6
The advantage of "dismantling and accumulating" is that for some of the more difficult to decompose univariate quadratic equations, "dismantling and accumulating" is difficult to try out, but "dismantling and dissipating" is relatively easy, such as the following equation.
x²-8x+13=0
For the above equation, cross multiplication is difficult to try, but if you use Professor Luo's method, it is not difficult.
a+b=8，ab=13
令a=4+u,b=4th.
Substitute ab=13 to get (4+u)(4-u)=13
16-u²=13.u²=3.u=±√3
The two roots of the equation are 4+√3 and 4-√3.
<h1 class="pgc-h-arrow-right" data-track="23" > the author's opinion</h1>
1. It does not make much sense for solving unary quadratic equations.
Although the second equation listed above cannot be decomposed by factorization using the cross multiplication method, it is very simple to use the matching method and the formula method is not difficult. There is a succession of hearings, and there are specializations in the art. In terms of some elementary basic operations alone, even famous mathematicians may not be able to match ordinary teachers or even students in the front line.
2, from the perspective of innovation, I have to admire.
Professor Luo once said in the video that many parents hope that their children can be the first, but if they only follow others, they will never be the first, and to be the first, they must walk in front of others and be brave in innovation!
3. Reflections on education
Under the baton of the middle and high school entrance examinations, domestic education tends to be a variety of "standard answers" and "optimal solutions", with "scores" as the goal, which greatly stifles students' ability to innovate. For example, a student once solved a problem in a less commonly used method, but after joint consultation between the teachers of the teaching and research group, it was finally decided to let the student use the standard method to solve it to avoid being deducted points in the middle school entrance examination in the future. Many times, teachers will say "Your method is right, but don't write this way during the exam...", and even some teachers will directly say "You can't write this way!" ”
The basics of all kinds of curriculum reforms are forms, and in their bones they are still test-oriented education, because the baton of the middle and high school entrance examinations is placed there, and you can't just jump around!
What do you think of Professor Luo's new approach? Comments are welcome in the comment area