How to learn high school mathematics well?
First of all, analyze the reasons and build confidence.
Many excellent students in primary and junior high schools are stumbling in mathematics for the first time when they enter high school. Many successful students in junior high school become losers in senior high school. The main reason is: 1. Learning is passive. 2. Learning is not allowed. 3. Basic attention is not enough. 4. Do not have the conditions for further study.
Therefore, to enter high school, we must establish correct learning goals and lofty ideals. Constructivism's view of mathematics learning is a direct negation of traditional mathematics education thought, especially the view of "giving and receiving".
Learning is not a passive absorption process. This is an active construction process based on existing knowledge and experience. Therefore, the best way to learn mathematics is to do mathematics, that is, to let students learn mathematics through problem solving that best shows their process of constructing knowledge.
Second, improving the efficiency of lectures is the key.
The essence of human cognition is the "construction" process of the subject. All knowledge is the result of our own cognitive activities. We construct our own understanding through our own experience, and conversely, our experience is influenced by our own cognitive perspective.
Mathematical understanding should be regarded as the product of interaction between subject and object, that is, the dialectical unity of reflection and construction. If we completely deny the existence of an objective world independent of thinking and think that the ultimate goal of cognitive activities should not be the pursuit of objective truth, it will inevitably lead to "extreme constructivism." In the actual mathematics teaching, we often find such a phenomenon that teachers always complain that students can't do the same exercises even in class when they have appeared in the exam.
According to the viewpoint of constructivism, the following analysis can be made: Constructivism holds that the essence of students' learning activities is that learning should not be regarded as a passive acceptance of knowledge given by teachers, but a social construction process based on students' existing knowledge and experience. We have obtained a new explanation for students' understanding or digesting the true meaning of mathematical knowledge. "Understanding" does not mean that students understand the teacher's original intention, but that learners have reinterpreted and reconstructed what the teacher said with their existing knowledge and experience, which can only show that students think they have passed it.
So it is not difficult for us to understand the "cruel" fact that what students learn is often not what teachers teach. For example, the most common performance in mathematics teaching is that although the teacher explains it clearly in class, the students turn a deaf ear; Mathematics exercises that teachers have analyzed in detail in class may still be full of mistakes in students' homework or tests; No matter how much teachers emphasize the significance of mathematics, students still think that mathematics is a meaningless symbol game, and so on.
Students' real "digestion" of knowledge is to correctly incorporate new learning content into the existing cognitive structure, thus making it an organic part of the whole structure. Mr. Ma Ming, a famous special math teacher in China, has a vivid metaphor: the faster the teacher throws knowledge, the faster the students forget it. Teaching more doesn't mean learning more. Sometimes teaching less means learning more. The reason is that students lack the active construction process of mathematical knowledge.
During students' study, class time accounts for a large part.
So the efficiency of class determines the basic situation of learning. We should pay attention to the following aspects to improve the efficiency of attending classes: 1. Preview before class can improve the pertinence of listening, and the difficulty found in preview is the science in the process of listening. 2. In the process of class, science should first make material preparation and ideological preparation before class. Pay special attention to the beginning and end of the teacher's lecture. The last point is to take notes. Notes are not records, but simple and concise records of the main points and thinking methods in the above lectures for review, digestion and thinking.
Third, do more problems properly and develop good problem-solving habits.
If you want to learn math well, it is inevitable to do more problems, and you should be familiar with the problem-solving ideas of various questions. At the beginning, we should start with the basic problems, take the exercises in the textbook as the standard, lay a good foundation repeatedly, and then find some extracurricular exercises to help broaden our thinking, improve our ability to analyze and solve problems, and master the general rules of solving problems. For some wrong-prone questions, you can prepare a set of wrong questions, write your own thinking and correct problem-solving process, and compare them to find out your own mistakes so as to correct them in time. Whether it is homework or exams, we should put accuracy first, and put the methods and ideas of bud solution first, instead of blindly pursuing speed or skills. Learning mathematics well is also an important issue.
Fourth, practice the practice of binding personal mistakes.
I give my classmates a formula: less mistakes = more pairs. If you make a mistake, no matter what mistakes you find, no matter how simple they are, they are included; I believe that once you really do it, you will be surprised to find that your mistakes can't be corrected once. On the contrary, many mistakes are made for the second, third or even more times! Looking at my wrong suit, alas, it's shocking. This is really a good place for self-reflection and a good way to improve your grades.
In any case, we should have a hard-working spirit in our study, but we should not only be hard-working, but also be good at learning and summing up, so as to get twice the result with half the effort. We should understand the causes of difficulties in mathematics learning, take correct measures, give full play to our main role, learn to analyze and study problems, thus cultivating creative thinking ability, and at the same time, we can improve our interest in learning mathematics and make ourselves more effective and smooth in high school.
The constructivist view of mathematics teaching is consistent with the essence of "let students learn mathematics through their own thinking" actively advocated by Chinese mathematics educators. In a sense, we think that no teacher can teach mathematics. A good teacher does not teach mathematics, but can inspire students to learn mathematics by themselves.
Good teaching is not to explain the content of mathematics clearly, but to explain clearly is enough. In fact, we often find that students in the classroom have never studied mathematics except themselves. Teachers must let students learn math by themselves, or do math with students; Teachers should encourage students to think independently and accept each student's different ideas of doing mathematics; Teachers should actively create problem-solving scenarios for students, so that students can guess through observation, experiment and induction, find out the rules, draw conclusions, prove and popularize them.
Only when students construct their own mathematical understanding through their own thinking can they really learn mathematics well. For example, when teaching Pythagorean Theorem, teachers ask students to cut, supplement, spell and gather figures. After personal observation and hands-on operation, the students found the quantitative relationship between the three sides of a right triangle. In this way, students not only know Pythagorean Theorem, but also are familiar with the idea of proving Pythagorean Theorem by area cut-and-fill method. More importantly, they cultivate students' mathematical thinking ability and habit of self-inquiry, and stimulate students' interest in learning mathematics.
One of the main shortcomings of traditional mathematics teaching is that it ignores the subjective initiative of learners and the fact that learners are the main body of the learning process. Teachers have become "sellers" of knowledge, and students are regarded as being free to paint white paper in various colors or put it into containers of various things at will.