一、要循序渐进，打好基础

First, step by step and lay a solid foundation.

苏步青教授认为：学好数学要打好基础是一个根本问题。著名数学家陈景润说：“我觉得在学习上没有捷径好走，也无‘秘诀’可言。要说有，那就是刻苦钻研，扎扎实实打好基础，练好基本功。…要打好艰实的基础，循序渐进”；“学习没有别的方法，就是要循序渐进”。

Professor Su Buqing believes that a good foundation for learning mathematics is a fundamental problem. Chen Jingrun, a famous mathematician, said, "I don't think there are any shortcuts or"secrets"in learning. To say that there is, that is to study hard, lay a solid foundation, and do well in basic skills. We should lay a solid foundation and make progress step by step.

为什么数学学习必须循序渐进，打好基础呢？

Why should we learn mathematics step by step and lay a solid foundation?

苏步青教授指出：“学习这东西，是有规律的，必须由浅入深，由易到难，由低到高，循序渐进”，数学家王元指出：“不断地抽象是数学的特点之一，…学习数学时不断会碰到新的抽象概念，…学习数学首先要弄清一个个的概念。否则脑子里难免一盆浆糊”。他又指出：“学数学最怕的是吃夹生饭。如果一些东西学得糊里糊涂，再继续往前学，则一定越学越糊涂，结果将是一无所获。所以不要怕学得慢，一定要学得踏实”。

Professor Su Buqing pointed out that "learning this thing is regular, must be from shallow to deep, from easy to difficult, from low to high, step by step." Mathematician Wang Yuan pointed out: "Continuous abstraction is one of the characteristics of mathematics,... When learning mathematics, you will always encounter new abstract concepts. To learn mathematics, we must first understand the concepts one by one. Otherwise, it's hard to avoid a paste in the brain. He also pointed out: "what is most afraid of learning mathematics is eating sandwich rice." If something gets confused and continues to learn, it will surely become more and more confused, and the result will be nothing. So don't be afraid to learn slowly. You must learn to be practical.

这里所说的打好基础，主要指：要学好数学基础知识（包括数学概念、定理、法则、公式等）；练好基本技能（如运算技能、画图技能、数学语言技能、推理论证技能等）；掌握基本数学思维方法。

By laying a good foundation, we mean: to learn the basic knowledge of mathematics (including mathematical concepts, theorems, rules, formulas, etc.); to practice the basic skills (such as computing skills, drawing skills, mathematical language skills, reasoning and demonstration skills); to master the basic mathematical thinking methods.

关于循序渐进，华罗庚先生指出：“循序渐进决不意味着在原有水平上兜圈子，而是要一步一步前进，而且是要尽快地一步一步前进”。

Regarding gradual progress, Mr. Hua Luogeng pointed out that "gradual progress does not mean to circle at the original level, but to move forward step by step, and to move forward step by step as soon as possible".

怎样循序渐进，打好基础呢？

How to proceed step by step and lay a solid foundation?

首先必须重视数学基本概念、基本定理（公式、法则）的学习，在理解上下工夫。在这一点上，要向老师学习，看老师是如何分析一个概念的。

First of all, we must pay attention to the basic concepts of mathematics, the basic theorems (formulas, rules) of learning, in the understanding of the effort. At this point, we should learn from the teacher and see how the teacher analyzes a concept.

其次要熟练地掌握基础。华老指出：“我以为方法中最主要的一个问题，就是‘熟能生巧’。搞任何东西都要熟，熟了才能有所发明和发现”。陈景润强调：“读书不能只满足于懂，而要弄得烂熟”，他非常赞赏鲁迅先生搞文学创作总结的四句话：“静默观察，烂熟于心，凝思想，然后一挥而就”。

Secondly, we must master the foundation skillfully. "I think the main problem in the method is" practice makes perfect. " Everything must be cooked and ripe before it can be invented and discovered. Chen Jingrun emphasized that "reading should not only be satisfied with understanding, but also be familiar with it." He appreciated Lu Xun's four words in summarizing his literary creation: "silent observation, mature in heart, condense thought, and then a wave of it."

怎样才算熟练地掌握数学基础呢？

How can we master the mathematical foundation skillfully?

其一是要把最主要的、最基本的东西，在理解的基础上牢牢地装在自己的脑子里，做到应用时能呼之欲出，信手掂来；

One is to hold the most important and basic things firmly in one's own mind on the basis of understanding, so that they can be used freely.

其二，要既准又快。首先要准，就是要理解得准确，要算得对，证得对，在此基础上还要快，别人十分钟想出来，我5分钟、6分钟就完成了。对证明题还要做到逻辑过程不多不少，准确精练。

Second, it must be accurate and fast. First of all, to understand accurately, to calculate correctly, to prove correctly, on this basis, but also faster, others think out in 10 minutes, I finished in 5 minutes, 6 minutes. There is not much accuracy in the proving process.

怎样才能达到熟练掌握呢？

How can we master it?

其一，要反复学习，反复思考，用心记忆。

First, we should learn repeatedly, think over and remember.

其二，对重要的知识要做细致的“支解”和“综合”工作。

Secondly, we should do meticulous "disintegration" and "comprehensive" work on important knowledge.

其三，要适当多做练习，达到运用自如。要强调的是，做练习要自己下苦工夫想，不轻易问人，对较难的题目做完之后，要多做支解、综合、反思、总结工作。

Third, we should do more exercises to achieve the best use. It should be emphasized that we should work hard to think, not ask people easily, and do more work of explanation, synthesis, reflection and summary after finishing the difficult questions.

其四，注意经常复习，总结提高。

Fourth, pay attention to reviewing regularly, summarizing and improving.