text/Sun Lingjun
Children who wait for parents to feed them will not grow up, and students who wait for teachers to teach them will not learn well. Without waiting or relying on it, students who take the initiative to prepare will be invincible in the examination room.
For mathematical formulas and theorems that need to be proved, before the teacher explains them, use the winter and summer vacations to preview them in advance. Just like the previous lecture on independent learning and internalizing concepts, combine formulas and theorems, read the text thoroughly, and thoroughly understand the text content of the introduced formulas or theorems. Literary meaning, understanding the ins and outs of formulas or theorems, and laying a solid foundation are very critical for subsequent mathematics learning.
Mathematical formulas, generally speaking, include two categories. One category has no derivation process. For formulas without a derivation process, it is important to strengthen memory, and it is even more important to understand the relationship between the various elements in the formula, to have in-depth understanding, and to apply it flexibly.
Another type of formula or theorem, with a specific derivation process, and even a variety of proof methods . For example, Pythagorean theorem definition: In a right triangle on the plane, the sum of the squares of the lengths of the two right-angled sides is equal to the square of the length of the hypotenuse. If the lengths of the two right-angled sides of a right triangle are a and b, and the length of the hypotenuse is c, then it can be expressed in mathematical language: a²+b²=c². There are more than 500 ways to prove it.
For theorems or formulas that have a derivation process, on the basis of familiarity with the text and a deep understanding of the text introduction, you must dare to try and derive it independently in advance. Regardless of whether it can be deduced or not, after the derivation is completed, opening the text to compare similarities and differences, and thinking about revisions will be of great benefit to understanding the theorem or formula. Repeated operations, comparative analysis, and repeated revisions are more conducive to a thorough understanding of the ins and outs of the theorem or formula.
Of course, it is not enough to be satisfied with this. It would be better if you can repeat it in your own language or teach a few classmates. Teaching for the sake of learning is the most effective!
Concepts (definitions, theorems) and formulas are the basis and cornerstone of learning mathematics. Only by truly understanding them thoroughly can you learn mathematics well in a down-to-earth manner.
From now on, whenever you see a formula or a theorem that needs to be derived, you must study it as mentioned above and thoroughly understand the ins and outs of the formula or theorem. Over time, by doing your best, you will develop a good learning habit that will benefit you throughout your life.
has a weak foundation and the earth is shaking. You must not start learning with a little knowledge, otherwise, the result will be that the more you learn, the more difficult it will be, until you can no longer go on, or even give up completely. You know, when you reach this point, you give up not only your studies, but probably your life as well.
