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What should I do if my math foundation is too poor?
A friend asked: I have a poor foundation in mathematics. What should I do? Well, this is a rather general and difficult question. If you search online, you will find many answers. However, the answer is often the same, as we all know, such as: understanding basic concepts, trying to solve problems, and so on. I want to write something more operational in a responsible manner. If I were myself, I would browse all the contents in the textbook first. Then, I will spend a day in the bookstore looking for two or three review materials that can not only explain the knowledge in the book, but also have examples and answers. When browsing quickly, we mainly look at the general types of knowledge points and examples. As for the detailed answers to the examples, I can jump while watching. You can't understand the same knowledge as this teacher. If someone else said it, you might be inspired. So do books and review materials. You look confused and entangled in this book. Looking at it from another angle, you may seem much more relaxed. Browse a few review materials quickly, then choose the one you like to tell and typeset, and buy it. Maybe a few books are good, but don't buy them all at once. Be sure to buy only one. Eat this book thoroughly and buy another one when you still have time and energy. After buying a book, the first way to learn is to "read" the book. While reading, deduce formulas in your mind and calculate examples. It is best to read the whole book in a short time. If you are tired or can't finish reading, you can only read one or two examples after reading each knowledge point for the first time. If you still don't understand some questions, don't spend too much time revising them, make a conspicuous mark and skip to the next content. In a week or two, read the book again, focusing on the topics marked last time. How happy it would be if I found the marked questions easy to do this time! However, if you still can't do it, it doesn't matter. Don't spend too much time skipping. Before each reading, copy all the formulas in the book like calligraphy, and deduce the formulas in your mind while copying. After copying the formula, you will find it easier to read the review materials. After reading this book for five or six times, basically all the marked questions can be understood. If you still don't understand, ask the teacher and classmates. At this stage, you can choose some marked questions and work them out on paper without looking at the answers, or choose other exercises and work them out independently to test your level. According to this step-by-step method, most students will make progress. Unfortunately, however, this method cannot solve everyone's problems. Some students have made little or no progress, and even have no ability to study alone in this way. The reason for this situation is that some students' Chinese reading ability is poor, or some logical thinking ability is not enough, or other different specific circumstances. Although I advocate self-study and self-help in my study, the improvement of some basic abilities is a long-term process. If time is short, students still make little progress through the above methods. I think it is best to find a tutor and help themselves with external help. However, most tutors, that is, they can only do and talk about topics, and may not be able to analyze students' lack of knowledge and ability according to their performance, and take corresponding measures to improve them. Therefore, before choosing a tutor, it is best to communicate with the other party, talk about your own problems, let the other party talk about how you think it should be improved, and see if the other party is a flexible, thoughtful and capable tutor. Poor tutor, even if he can do the problem again, may not be able to teach others to do it, but it will hurt students' confidence in learning. In my opinion, a good tutor only needs one and a half hours to talk about the topic and teach students to do it. The rest of the time, he will tell students about several chapters, and then determine the progress and methods according to the students' understanding and feedback. Some knowledge may need to be repeated over and over again. Students suddenly realize that those impatient tutors may be crazy because of their slow response, and subconsciously pass on the label of being too stupid to students, but in fact, except for a few mentally handicapped people, most students with learning difficulties can learn well in the end with appropriate help. After imparting knowledge, we should focus on students' feedback in the next tutoring. Let the students retell some theorems in their own words, or let the students simply deduce the facts expressed by the theorems with graphs. Through these feedback exchanges, students can not only sort out and organize this knowledge in their own minds, but also start with some simple questions to improve their logical thinking ability. Why don't students understand a certain knowledge point? Why is a question wrong? Why can't a problem be worked out? These are all very useful information. Starting from these problems, we can find the real weaknesses of students hidden behind the problems. If you simply tell students the solution to a problem, it can only be a short-sighted approach of "treating the headache and treating the pain in the foot". Students may not do similar but slightly flexible questions in the future. Can you ask the school teacher for help instead of choosing a tutor? Teachers have to face dozens and hundreds of students. If you read a review material and find that there are many questions you can't do, you should ask the teacher. I'm afraid the teacher is too tired to explain to you. So when there are many questions that can't be answered, it is better to ask the teacher by self-study such as repeated reading. After most of the questions are finished, it will be better to ask the teacher when there are still a few questions that can't be answered. These are the two study options I can think of now. Considering that friends who ask questions are pressed for time, these two options are both methods that pay more attention to short-term curative effect and quick success. Perhaps for education, a better solution is how to prevent students from being uninterested in mathematics and how to avoid students' poor mathematical foundation, rather than waiting for problems to come out to solve. But this is a long-term and big project related to all aspects, so I won't say it here.