A probe into mathematics teaching in senior high school.
1, about the existing problems
1. 1 Students cannot accept high school textbooks with large capacity and strong difficulty. In junior high school mathematics, the content of junior high school textbooks is simple and popular, and it is easier to have fewer questions. It is easy for students to master the context of mathematical knowledge, and the description of concepts in textbooks is relatively simple, some mathematical theorems are not proved at all, and the connection between textbooks is slow. The content of high school textbooks is extremely abstract, focusing on the study, calculation, theoretical analysis, logic and abstract knowledge presentation of variables and letters. Such as set, mapping, function and many other abstract concepts. In the first year of high school, there are many symbols. The textbook of definitions and theorems is extremely strict, with the characteristics of high starting point, great difficulty and large capacity. In recent years, with the adjustment of textbooks, junior high school textbooks have been greatly reduced, and senior high school textbooks are also decreasing. However, due to the restriction of the college entrance examination, teachers can't and dare not reduce the difficulty, which directly leads to the fact that the difficulty of mathematics teaching in senior high schools has not been reduced at all. To be sure, the adjusted high school textbooks have not reduced the difficulty, but become more difficult. The first year of high school is short, the mathematics capacity is large, and the teaching progress is extremely fast. It is not surprising that students can't adapt to high school mathematics study.
1.2 students can't adapt to the connection of some knowledge points in junior and senior high school curriculum standards. Junior high school mathematics curriculum standards require a simple understanding of some knowledge, and senior high school textbooks are not properly supplemented. Some junior high school students should only have superficial knowledge or only know one conclusion. How the conclusion came from, what questions to answer with the conclusion, and the ways and means to answer it are unknown. There are some knowledge that senior one students often encounter in class, which they have not learned. For example, the discriminant of a quadratic equation in junior high school, the relationship between roots and coefficients, and the visualization of quadratic functions solve many problems of quadratic inequalities. The curriculum standards are not high, and students have been exposed to simple knowledge points, which makes high school learning particularly unacceptable. Some teachers have no choice but to make up, which takes up a lot of time. In order to complete the teaching task, they have to speed up. It leads to the tragedy that junior high school mathematics knowledge is not mastered and senior high school mathematics knowledge is left behind.
1.3 students can't adapt to the teaching methods of senior high school teachers quickly. The content of junior high school textbooks is small, the difficulty is small, the requirements are not high, and the teacher's teaching progress is not fast. Some key and difficult points were repeatedly explained, practiced many times, and broke through one by one. Some teachers have taken pains to practice in order to make students get good grades in the senior high school entrance examination, and some problems have reached the point of perfection. As a result, some students lost their enthusiasm for learning mathematics, and students appeared. Value knowledge over ability? 、? Pay more attention to examination papers than books? This mistake. When students enter high school, the teaching materials have large capacity, high requirements, fast progress, wide information and deep difficulty, not to mention the key and difficult points. The new curriculum standard high school teaching inspires and guides students to think and answer by setting guidance, questions, traps and changes, pays attention to the infiltration of students' thinking methods, cultivates students' thinking quality and ability, and advocates students' autonomous learning. It is very difficult for the newly enrolled senior high school students to adapt to this teaching form and keep up with the teacher's lectures, which seriously affects the study of mathematics.
1.4 students did not adjust their psychology and learning methods in time. Everything freshmen face is new: new environment, new textbooks, new classmates, new teachers and new groups. Students must have an experience from strangeness to familiarity. The intense and cruel senior high school entrance examination entered the ideal high school study. Some students are relaxed, not nervous after entering school, and carefree. Some students have heard the information about how difficult it is to learn high school mathematics before the middle school entrance examination, and they have a psychology of staying away. Some abstract concepts in senior high school mathematics, such as mapping, set and non-planar straight line, make students at a loss and affect the learning quality of freshmen. Junior high school teachers explain in detail and students are skilled in training. After training, they are familiar with concepts, formulas and questions. As long as you sit right, you can get good grades in the exam. Students revolve around the teacher, completely obey the teacher, and do not pay attention to independent thinking and induction. High school students need to sum up and master mathematical thinking methods because they have more learning contents and less learning time. Senior one students are still learning mathematics with the learning method of junior high school, which has caused great learning resistance, and the homework assigned by the teacher on that day is difficult to complete. There is no time to preview and review, which seriously affects the improvement of learning quality.
The tutoring materials of the new course 1.5 are not perfect. The new curriculum reform has been going on for several years, and there are many supplementary teaching materials in the book market. These supplementary textbooks are in the same strain as the old textbooks, and some of them are just adjusted in order. The content can be said that the sound of the waves is still the same, and it does not reflect the concept of the new curriculum standard, which makes teachers and students raise objections to learning mathematics well.
2. About several countermeasures
2. 1 Grasp the students' learning situation and make effective connection. At the beginning of the first year of senior high school, a freshman symposium was held to investigate students' entrance scores and conduct relevant tests to understand students' learning foundation, learning habits and the characteristics of junior high school math teachers' lectures. Study the syllabus and teaching materials of junior and senior high schools, master the knowledge system of junior and senior high schools, find the best connection point of junior and senior high school knowledge, teach students in a targeted way and make effective connection.
2.2 Stimulate students' interest in learning and achieve psychological cohesion. Teachers must play an active role emotionally and psychologically, and interest is a necessary condition for effective activities. To make students learn mathematics well, we must stimulate their interest in learning mathematics, use multimedia teaching methods, stimulate their desire to learn mathematics, establish their confidence in learning mathematics well, pay attention to the cultivation of good study habits, encourage students to question boldly, be brave in innovation, study independently, advocate inquiry learning, and let students adapt to high school mathematics learning, and succeed every time. Teachers should affirm praise and encouragement in time to achieve psychological cohesion.
2.3 On the cohesion of teaching materials. In the teaching of senior one, we should focus on the basic knowledge, rather than overemphasizing the difficult problems, partial problems and college entrance examination questions, so that students can accept and like mathematics, complete the study of mathematics knowledge, practice the new curriculum concept and adopt it in teachers' teaching. Low starting point, small gradient, more practice, hierarchical? Review the old knowledge of junior high school, learn the new knowledge of senior high school, and realize the connection of junior high school and senior high school textbooks.
2.4 On the convergence of teaching methods. Senior high school mathematics requires students to establish strict concepts through observation, analogy, induction, analysis and synthesis, and the teaching methods must be well connected. Give full play to the leading role of teachers, highlight students' subjectivity, let students explore independently, cooperate and communicate, truly understand and master mathematical knowledge and mathematical thinking methods, and gain experience directly in mathematical activities.
2.5 Guidance on learning methods and cultivation of good study habits. We must embody the concept of student-oriented. Completely change the way of learning, and advocate students to communicate with each other and actively participate under the guidance of teachers. Stimulate students' imaginative thinking, encourage students to speak enthusiastically in class, cultivate students' good study habits, strengthen the guidance of learning methods and improve teaching quality.
2.6 On cultivating students' mathematical thinking quality. Teachers must pay attention to strengthening students' thinking training, carrying out effective thinking activities, abandoning thinking inertia and connecting students' ability to analyze problems.
Author: Zhang Yuxin Work Unit: Huaide No.1 Middle School, Gongzhuling City, Jilin Province.
The second exploration of mathematics teaching in senior high school
First, the status of high school mathematics teaching
At present, in the teaching practice of high school mathematics, students mainly adopt the tactics of asking questions and memorizing, so as to cultivate students' ability to solve problems independently, collect various questions for students to practice, and memorize the methods of solving problems, and then mechanically imitate their own problem-solving routines when encountering similar problems, instead of looking for solutions themselves. Teachers, on the other hand, use traditional classroom teaching methods to tell students all the different types of mathematical exercises and specific solutions. In the long run, students lose their initiative and enthusiasm in mathematics learning, which greatly affects the cultivation of students' independent problem-solving ability and innovative thinking ability. Once you encounter a topic type that you have never touched before, you will become helpless. Therefore, under the advocacy of the new curriculum standards, both teachers and students need to actively change their concepts and pay attention to the cultivation of problem-solving ability, so as to improve the effectiveness of mathematics teaching in senior high schools.
Second, cultivate students' ability to solve problems
First of all, consolidate the teaching of basic knowledge and provide the necessary guarantee for students to solve problems independently. Find students by analyzing the internal relationship between knowledge and ability? Solve the problem by yourself? The cultivation and effective improvement of students' ability mainly depends on two factors: first, teachers accurately grasp the overall knowledge base and skill state of students in actual teaching; Second, on this basis, for students? Solve the problem by yourself? Ability training, providing necessary knowledge and skill preparation. Therefore, in the actual teaching of senior high school mathematics, teachers not only need to fully grasp students' knowledge through various channels, but also need to take effective measures to build a bridge between old and new knowledge for students. Bridge? Attach importance to the teaching of students' basic knowledge and skills, and provide intellectual support for students to learn new mathematical knowledge and solve new mathematical problems. At the same time, in teaching, teachers need to pay attention to the accumulation of knowledge and help students to classify and sort out knowledge, thus creating good conditions for them to analyze and solve problems independently. Secondly, create problem situations to guide students to find problems independently. Actively cultivate students? Solve the problem by yourself? Our primary task is to let students find problems and ask questions independently in their studies. The problem is the origin of thinking, any thinking process points to a specific problem, and the problem is also the basis of creation, and all creation starts from the problem [1]. In the teaching practice of high school mathematics, create a? Problem situation? It is equivalent to establishing a good learning environment, which can effectively stimulate the initiative and enthusiasm of the majority of students, and take the initiative to find problems without children's independent thinking and discussion. Therefore, in mathematics classroom, teachers need to pay attention to students' learning. The nearest development zone? Implement a comprehensive grasp and create some on this basis? Problem situation? Enable students to? Jump? You can find and ask questions independently. What if you are right? Geometric series? When teaching this knowledge, the teacher can create it like this? Problem situation? One day, in the race between the hare and the tortoise, the tortoise was 65,438+0 kilometers ahead of the hare, but it was known that the speed of the hare was 65,438+00 times that of the tortoise. When the rabbit catches up with 1km, the tortoise also has the prospect of110 km. When the rabbit catches up with110km, the tortoise advances1100km; The rabbit arrived at11000 km, and the tortoise went forward11000 km. Q: What is the distance between the rabbit and the tortoise in the same period? Can rabbits catch up with turtles? By creating this form of problem situation, students can observe the characteristics of series, and then introduce the concept of geometric series, stimulate students' interest in learning, and guide students to find corresponding problems and ask questions. Finally, cultivate innovative thinking and explore new mathematical thinking methods for students? Solve the problem by yourself? Provide conditions. In the process of learning mathematics in senior high school, innovative thinking is an important part of analyzing and solving problems, and plays an important role in developing students' intelligence. Therefore, in the actual teaching of high school mathematics, teachers should actively cultivate students' innovative thinking, encourage students to make bold guesses, and thus ask questions [2]. At the same time, teachers also need to actively encourage students to explore new mathematical thinking methods, and master and apply them comprehensively, so as to truly understand the essence of mathematical learning and apply them to the solution of practical mathematical problems, so as to effectively cultivate and improve the whole mathematical problem-solving thinking ability, and then cultivate students' mathematical thinking ability. Solve the problem by yourself? Ability.
Three. Concluding remarks
As a basic applied subject, mathematics requires students to have strong imagination, logical thinking ability and reasoning ability. However, in the actual learning process, because students lack the ability to solve problems independently, students generally think that mathematics is difficult to learn and are unwilling to learn mathematics, which leads to? Tired of learning? Psychology. Therefore, in the teaching practice of high school mathematics, teachers should pay attention to students' learning. Solve the problem by yourself? Ability to fully cultivate, so as to effectively improve students' ability to solve mathematical problems, and then improve the learning effect [3].
Author: Feng Chunrui Work Unit: Education Bureau of Huating County, Gansu Province
Research on Mathematics Teaching in Senior High School Part III
1 Several Problems in Senior High School Mathematics Teaching
1. 1 pays too much attention to students' autonomous learning and ignores the guiding role of teachers.
In the process of high school mathematics teaching, enriching students' learning methods can make students study better and lay a good foundation for their lifelong learning and development. In addition, in the actual teaching process of high school mathematics, the role of teachers is seriously ignored, and students' autonomous learning is overemphasized. Due to the lack of teachers' role, students' cognitive level just lingers in the same place, which leads to classroom teaching. The teaching process is the unity of students' independent construction and teachers' guidance. When students encounter difficulties, teachers should guide students to think, and when students' thinking is narrow, teachers should broaden their thinking. In short, the guidance of teachers is an important prerequisite to ensure the directionality and effectiveness of students' learning.
1.2 The teaching classroom lacks positive education for students.
The new mathematics curriculum in senior high school strongly respects personality differences and students' learning, and encourages students to actively participate. Learning difficulties, poor students give timely praise and self-confident encouragement, but this does not mean that students blindly praise. Full recognition and encouragement of praise and criticism. On the one hand, we should be good at discovering students' bright spots and ideas, and give timely and appropriate praise and encouragement to let students play; On the other hand, students' wrong opinions clearly point out that fuzzy mathematics problems should be clarified.
1.3 The role of teachers in the teaching classroom is not balanced.
The new mathematics curriculum requires students to actively observe, practice, guess, reason, verify and communicate mathematics teaching activities. Students' learning style, reading, practice, independent exploration, cooperation and communication, etc. It is teachers who guide, cooperate and promote and become the leaders of classroom teaching. The new curriculum advocates democratic, open and scientific courses, emphasizing? Teachers are courses? . This requires teachers to become not only the implementers of the curriculum, but also the builders and developers of the curriculum. The fundamental difference between the new curriculum and the old curriculum is that the new curriculum requires cultivating students' innovative spirit, promoting students' personality development, emphasizing students' feelings, guiding students to put forward their own opinions and making them masters of mathematics learning, which is not only the transfer of traditional teaching methods, but also the transfer of teaching. However, in actual learning projects, due to students' cognitive limitations and individual differences, various unexpected problems will inevitably occur, so teachers must give full play to their leading role. Teachers should evaluate and correctly handle students' experiences in time, learn more, and understand and understand the relationship between the universal values of multiculturalism. In addition, in the new curriculum, too much emphasis is placed on respecting personality differences and learning from students, encouraging students to actively participate, exaggerating the incentive function of praise, ignoring the guidance of error correction, cultivating students' self-confidence and affecting their physical and mental health.
2 Some problems in the teaching content of mathematics in senior high school
2. 1 The teaching content is difficult.
Under the new curriculum concept, we use one of the textbooks of People's Education Edition. Compared with the old textbooks, it seems that the difficulty is reduced, but some new contents have been added, and these difficult parts have been greatly increased. In my opinion, the new curriculum textbooks are compiled in full accordance with the actual situation of urban key high school students, regardless of rural students. For example, the early content of the algorithm involves the knowledge in computer language, and the logic is highly knowledgeable, abstract and professional. These contents are difficult for rural students to learn, because of regional differences, they do not have enough computer knowledge, or even no such knowledge. The content of the new mathematics curriculum is divided into five modules, five compulsory modules in senior high school and two elective modules. With the increase of teaching content, teachers blindly pursue teaching progress in order to complete teaching tasks. Sometimes, the content of a class for two or three hours has not been practiced, digested and consolidated, which makes students understand incompletely, even the knowledge they can remember is not understood or understood deeply, which will definitely not solve the problem and will inevitably increase the difficulty of learning.
2.2 The teaching process did not give full play to the guiding role of teachers.
In practical teaching, students' learning autonomy is emphasized, while teachers' active guidance is ignored. Some teachers think that the new curriculum is to give full play to students' initiative and let them learn independently, while ignoring teachers' necessary and vague active guidance and students' preparation of mathematics knowledge, which reduces the effectiveness of classroom teaching.
2.3 Under the background of new curriculum reform, the practical function of teaching materials has been diluted.
In the new curriculum requirements, in senior high school mathematics teaching, we should make full use of various resources to complete the expansion, extension and combination of teaching AIDS, and integrate them into students' real life. However, due to teachers' individual differences and understanding of curriculum resources, in teaching practice, teachers of teaching resources unilaterally develop teaching content that they have not fully mastered, and the teaching content is generalized or even blurred. Faced with this situation, teachers should make rational use of modern teaching methods and make full use of teaching books. According to the characteristics of teaching content, give full play to the auxiliary role of computers and carefully apply multimedia courseware to achieve the best teaching effect.
2.4 excessive emphasis on computer and information technology teaching
With the increasing popularity of information network technology, computer-aided teaching and information technology are important means to modernize mathematics education. For example, in the teaching process of mathematical geometry in senior high school, proper teaching courseware and sufficient multimedia-assisted teaching methods can achieve better teaching results. It can be seen that computer teaching plays a very important teaching auxiliary role in the process of high school mathematics teaching. Therefore, in the current classroom teaching of senior high school mathematics teaching, the use of computer information technology has become the main teaching means, and whether it is overused can be ignored. No matter how good the teaching of computer technology is, we can't rely on multimedia network for everything, such as basic arithmetic, imagination, logical reasoning of students' mathematical activities and mathematical proof. So I think it is best to grasp the balance between information technology teaching and traditional teaching, and pay attention to effective integration and fusion.
3 Conclusion
To sum up, there are still some shortcomings in the process of high school mathematics teaching, and it is necessary to further strengthen the solution of teaching problems, provide a good learning environment for teachers and students to teach and learn, and avoid the recurrence of these shortcomings as much as possible.
Author: Wang Junmin Work Unit: Pingchuan Middle School, Baiyin City, Gansu Province