First, the basic quality of high school students' mathematics learning

Parents: What basic qualities should you have to learn high school mathematics well?

Teacher Wang of Mathematics: To learn high school mathematics well, students should have two basic qualities: one is the non-intellectual quality of mathematics; The second is the intellectual quality of mathematics.

Parents of students: Teacher, please explain in detail why students should have non-intellectual qualities in mathematics.

Miss Math: Yes. As a high school math learner, students should be a serious and responsible person, that is, honest, confident, patient, careful, persistent, dedicated and ambitious. Always observe and capture the information of yourself and the people around you as the basis for analyzing and solving problems. It is hard to imagine that an ignorant and careless student can take things to heart! Let alone use your brains to analyze and solve the problems you encounter! Are you qualified to learn high school mathematics well and stand in the forefront! If you want to learn math well, please be a conscientious person first! To learn high school mathematics well, students should have an honest heart, and honesty is very important for mathematics learning. Use negative examples to illustrate. For a senior high school student with his own semi-mature ideas, if he lacks honesty as the basic point of mathematics learning, it will be difficult to grasp and evaluate him effectively and practically from all aspects, and the methods and countermeasures adopted are likely to be misplaced or invalid. Because of this, students will try their best to cheat their parents at home, and they will try their best to cheat their teachers at school, and spend their energy on relatively minor aspects other than learning, so that mathematics may get worse and worse. Finally, it will step into a vicious circle of weakening interest in mathematics learning and lack of confidence. For some students, especially some unconscious students, parents and teachers need to cooperate closely here in order to find out clearly and prevent this situation from being nipped in the bud. To learn high school mathematics well, students should be persistent, enterprising and competitive. To make a simple analogy, a person can't climb the top of a wonderful show without perseverance and fearless endurance. What is needed here is perseverance (perseverance, patience,); In the process of climbing, I encountered all kinds of difficulties and obstacles, and I couldn't get the beautiful scenery of mountains and rivers. What is needed here is enterprising spirit; When a low mountain is climbed by many people, you should have the confidence and courage to climb a higher dangerous peak and have a romantic relationship with others. When you reach the top, you will have a feeling that "once you reach the top, you will see that other mountains are dwarfed under the sky". The feeling of taking pleasure in suffering, and the physical and mental gains of stepping into a higher realm and being unique. What is needed here is the spirit of competition, that is, firm confidence and lofty aspirations. Of course, in the specific climbing process, it is inseparable from the efforts and careful handling of various problems. This cycle for many times, your perseverance and competitive spirit will continue to increase, and your perseverance in doing things will become stronger in the future. Mathematics learning is like climbing a wonderful mountain, which requires students to have non-intellectual qualities such as honesty, self-confidence, patience, carefulness, perseverance, intention and ambition.

Parents: What do you mean by mathematical intelligence?

Mr. Wang: Generally speaking, to learn high school mathematics well, students should have a solid foundation of junior high school mathematics knowledge and ability, a relatively smart and organized mind, and good mathematical thinking quality. In every specific process of learning mathematics knowledge from teachers, students' intellectual quality is constantly improving, which requires students to feel and explore training with their heart. Because mathematics is a very rational subject, it requires students to have a strong rational foundation, and this rational "kingdom" can make students have more rational gains. The intellectual quality of mathematics needs students and teachers to gradually form and improve in the process of learning together, so I won't go into details here.

Second, the typical problems that students often appear in high school mathematics learning.

Student: As a senior one student, what problems should I pay attention to in my future senior high school mathematics study?

Miss Mathematics: To learn high school mathematics well, students should make a good connection between junior high school mathematics learning and senior high school mathematics learning, so as to make a good start for senior high school mathematics learning. It mainly includes the excessive cohesion in learning psychology and the excessive cohesion in learning methods.

Below, let's first analyze the psychological convergence of mathematics learning. Ignoring this surplus or having no strategy to deal with it will directly affect your mathematics study in the subsequent stage of high school. Students will face some new changes, among which we should focus on dealing with all kinds of psychological uncomfortable contradictions. For example, there was once a senior one student whose junior high school math study was among the best in his class. He heard a lot of praise from the teacher in his ear, and his heart was always full of success and joy, and he was very enthusiastic about math learning. When he was admitted to a provincial key high school, his role in the mathematics learning class changed with the change of the learning environment. When he entered school, his mediocre math scores failed to attract special attention from teachers, and his praise was unheard of in the past. Compared with his classmates, he has less psychological experience of his sense of success, which is similar to junior high school mathematics learning, forming a huge psychological experience contrast and naturally losing his heart. This kind of mentality will have a certain negative impact on his mathematics study and must be stopped as soon as possible. To solve psychological problems, we can pour out psychological "doubts" and "bumps" to teachers, parents or close classmates, relieve psychological pressure and let the mind return to a state of natural relaxation. Only in this way can we use our brains and find ways to correct our psychological disadvantages in mathematics learning. In fact, in the long river of life learning, you often encounter some new situations that are difficult to achieve, which requires you to actively adjust yourself and try your best to deal with it. This is a flexible way of doing things. When you cross this "bumpy" and look back, it is really a small thing in life, but to achieve great things, we must start from solving every small thing! By solving these small things rationally one by one, your psychological endurance and handling ability will be greatly strengthened, and eventually you will benefit a lot.

Let's talk about math learning methods. There is a big difference in mathematics learning between junior high school and senior high school. With the deepening of learning, students themselves play an increasingly important role in mathematics learning. In high school mathematics learning, students should pay attention to the following two phenomena. First, difficulties in daily study often occur. In the daily study of senior high school students, the tasks (homework) assigned by teachers in various subjects are based on the requirements of the subject and are not coordinated. These tasks are embodied in students, and if students want to finish them effectively in the limited time available in a day, all kinds of conflicts (contradictions) will be exposed. High school students are more reasonable and sincerely want to complete the teacher's task, but they often don't know about it when dealing with it, forming a more difficult situation than being in a dilemma. This is what we want to talk about in mathematics learning, which is very prominent among students with learning difficulties. If this phenomenon is not handled well, it will inevitably lead to a passive situation in senior high school mathematics learning over time. Secondly, the phenomenon of mathematical thinking substitution appears more and more frequently in mathematics learning. Substitution of mathematical thinking means that one's own mathematical thinking is replaced by others' mathematical thinking in the process of mathematical activities. In fact, from two aspects, in the process of mathematics learning, the substitution of mathematical thinking has both good and bad sides. On the one hand, the proper substitution of mathematical thinking can make the process of mathematical learning a "simple" process and improve the efficiency of producing new thinking results; On the negative side, if you don't handle it properly, your mathematical thinking will lose its independence and rely on others' mathematical thinking until your mathematical thinking dries up. For example, in mathematics classroom teaching, as soon as the teacher asks questions, some students have their own clear problem-solving ideas in a short time (for example, 3 minutes), while some students need a long time to find and complete their own problem-solving ideas (for example, 10 minutes). Comparatively speaking, these students are far behind in their thinking. By the time the teacher explained, this thinking gap in math class already existed. After the teacher explains the question, even if every student knows it, the gap in thinking process will also lead to the hidden thinking training gap behind the thinking result. The reason is that for the whole thinking process of the problem, students' thinking and teachers' thinking, which have independently completed the thinking process, should replace the unfinished part of students' thinking (that is, the mathematical thinking in the last 7 minutes). Over time, students who think slowly often give up halfway if they can't finish it. To put it more seriously, it's like someone took something from your "brain", which is much more terrible than someone unreasonably stealing and occupying some of your tangible property. After a long time, your brain will become an empty skull and your mathematical thinking will eventually dry up. Now, let's compare the following differences in the process of mathematics learning in junior and senior high schools. Junior high school math teachers are more considerate of students than senior high school math teachers. In other words, professionally speaking, there are more components of thinking substitution. Senior high school math teachers focus on guidance, leaving enough room for students to think. At the beginning of high school, students who are not good at analyzing new situations and new problems and are highly dependent tend to form an illusion that there are not as many "pointing tasks" to be completed in high school mathematics learning as in junior high school mathematics learning, which will cause some students who do not grasp the essence of things or look at problems in depth to be careless in mathematics learning-it seems that there are not so many learning tasks to be completed, but they are taken lightly. However, after a period of time, math learning will be very difficult. Therefore, a series of problems and many links, such as how to preview in math learning, how to stay ahead of the teacher's thinking in class, and how to reflect and consolidate after class, all need you to constantly adjust your learning methods according to your own characteristics and actual situation, and form a math learning method that suits you and works silently with the teacher. It will take some time to "run in" before it can gradually take shape.

Otherwise, if you don't handle it well, you will have all kinds of psychological confusion, and the confused mentality will affect the optimization of mathematics learning methods, and then many problems of psychology and learning methods will be intertwined, which will have some side effects on you and produce the phenomenon of "vicious decline" in high school mathematics learning.

Thirdly, the strategies to solve the problems encountered by middle school students in high school mathematics learning.

Parents of students: Do you have any strategies to solve the above-mentioned problems such as "psychological obstacles", "difficult phenomena" and "thinking substitution" in senior high school mathematics learning?

Miss Math: Yes, it's about the learning strategies of high school math. Its psychological strategy should distinguish which transcendence stage it is in, namely, the first transcendence stage, the transcendence stage of others and the second transcendence stage. When students are struggling in mathematics learning, they should first position themselves in the first stage of self-transcendence. Under the premise of various efforts, they are stronger than their own yesterday day by day and are ready to enter the stage of surpassing others. If they want to surpass others at this stage, it is naturally a bit overreaching, and their body and mind have to bear great blows and obstacles; When you have the ability and "capital", you enter the stage of surpassing others and can compete with others. If you succeed in surpassing others, that is, no one around you can compare with you, then you must enter the second stage of surpassing yourself and constantly improve yourself until you reach the peak! Of course, psychological strategies are not absolutely along this line. In addition, a smart and interested senior high school student should reasonably take up as many educational resources as possible from the math teacher, and will find opportunities to discuss key issues and key issues with the teacher in order to achieve rational and sound information. After a thing is handled well, he will have a deep psychological feeling and understanding. The strategic problem of its mathematics learning method is mainly reflected in that students should grasp several interrelated links in mathematics learning, namely, studying in advance (preview before class), listening to lectures in class, reviewing and consolidating, and reflecting and improving (self-testing and improving). Earlier, we mentioned how difficult it is for senior high school students to learn mathematics and how to deal with the problem of mathematical thinking substitution in mathematics learning. For the former, the students involved need to list the events in the difficult phenomenon one by one and arrange them in the order of events; Or distinguish between primary and secondary events and take the method of light and heavy counterattack to break through one by one. To do this job effectively, you must study in advance, so that when dealing with these difficult events, you can put them in a reasonable order or prioritize them condescendingly, so that you can handle them with ease. For the latter, you should study ahead of time and keep your mathematical thinking in a leading position (as far as possible ahead of other students and teachers), so as to maintain the independence and uniqueness of your mathematical thinking. Finally, the improvement of reflection in each link is discussed. This link will help you upgrade your knowledge of mathematical declarative knowledge and mathematical procedural knowledge to knowledge of mathematical strategies, grasp the essence and essence of the knowledge and methods you have learned, and let you jump out of the Wang Yang sea of knowledge in future mathematical learning.

The above is only from a macro perspective, through the form of dialogue between math teachers, students and parents, to answer some typical questions in high school math learning. Some specific knowledge problems in mathematics learning need to be solved reasonably and effectively by students in teachers' teaching and their own learning, forming a coordinated joint force and aiming at the goal of learning mathematics well in senior high school!

Teacher of Taiyuan No.5 Middle School: Wang Zhijun