The new mathematics curriculum plays a fundamental role in students' understanding of the relationship between mathematics and nature, between mathematics and human society, and its scientific value, application value and cultural value, improving their ability to ask, analyze and solve problems, forming rational thinking, and developing their intelligence and innovative consciousness. At the same time, mathematics quality is the basic quality that citizens must possess, so mathematics, as a tool discipline, plays an increasingly important role in social and economic development. Under the new curriculum reform, how to deal with the teaching and learning of mathematics has become a wide topic.

First, based on the new textbooks, seriously study the curriculum standards, stand on the whole, and grasp the depth of teaching from a global perspective.

Judging from the whole set of teaching materials, the requirements of teaching and learning are not in one step, but in stages, levels and angles. The new textbook pays more attention to students' cognitive rules and students' interest in learning. Therefore, we should strengthen the research on new teaching materials, so as to change the original mode of teachers' minds, find new problems, adopt new methods and strategies, break old rules and find more reasonable teaching methods. Only in this way can we grasp the depth of teaching. Only in this way can we solve the problem of class hours. Of course, we should base ourselves on new textbooks, and we should not be completely confined to new textbooks. Some places can be supplemented appropriately, and transitional knowledge can be added according to the actual situation of students to make a good connection between junior high school and senior high school.

For example, "inequality" is a common tool to solve mathematical problems. Whether to teach some simple inequalities (such as "unary quadratic inequality" and "simple fractional inequality") before set operation is the biggest problem in this chapter. The new curriculum requires that set is only used as a language to learn, and students will learn to use the most basic set language to express related mathematical objects. Developing the ability to communicate in mathematical language is not an equivalent deformation of a set, nor is it a deeper operation of a set. Therefore, we should grasp the "language" teaching of set in teaching. If we really want to talk about the solution of quadratic inequality and simple fractional inequality, we must control the difficulty and depth, otherwise the class will become a problem again.

For example, the order of function and mapping in the new curriculum is different from that in the old textbook, so the teaching of function concept should start with the specific function and descriptive definition of function that students have mastered in the compulsory education stage, guide students to contact their own life experience and practical problems, and try to enumerate various functions, so as to construct the general concept of function and mapping.

For example, in the new curriculum, the concepts of maximum and minimum values of functions are further defined in the old textbooks. Therefore, in addition to grasping the requirements of curriculum standards (monotonicity application and information technology application), the maximum value problem of quadratic function in closed interval can be expounded and popularized here, but it is necessary to avoid too complicated and too skillful extension of such problems, and at the same time pay attention to avoiding the related range problems in old textbooks.

For example, in the power function part of the textbook, it is clearly stated that only a= 1, 2,3,0.5,-1 are discussed, and a=-0.5 appears in the review reference question (a). Therefore, we believe that, on the one hand, in the teaching of power function, the images and properties of power function should not be generalized to the general situation, which will increase the burden on students; On the other hand, it is necessary to strengthen the application of information technology in teaching and reduce the burden on students;

In the teaching of function application, we should first guide students to experience that function is a basic mathematical model to describe the changing law of the objective world, and to experience the close relationship between exponential function and logarithmic function and the real world and their role in depicting real problems. Secondly, we should use the teaching of function application to communicate the relationship between modules, so that students can understand the organic connection between knowledge. For example, the standard requires judging the existence of a quadratic equation and the number of roots by combining the image of quadratic function, so as to understand the number of zeros and roots of the function. According to the image of specific function, with the help of calculator, the approximate solution of the corresponding equation is obtained by dichotomy, which makes some preparations for the following algorithm learning.

For example, the system structure of solid geometry content has been greatly reformed. In the past, we used to study points, lines and surfaces, and then study their geometry, following the principle of part to whole; Now we should start with the overall feeling of space geometry, and then study the points, lines and surfaces that constitute space geometry. This arrangement is helpful to cultivate students' spatial imagination and geometric intuition, reduce the difficulty threshold of solid geometry learning, and improve students' interest in learning solid geometry.

Because there is no knowledge about points, lines and surfaces, the study in this chapter cannot be based on strict logical reasoning, which is very different from the previous textbooks. Teachers should pay full attention to this point in practical teaching, that is, the intuition of solid geometry.

For example, according to the requirements of the Curriculum Standard, we should learn analytic geometry first and then trigonometry. In this way, how to deal with the measurement problem in analytic geometry in the new curriculum arrangement, we think there are two advantages: on the one hand, we should strengthen the cultivation of students' algebraic operation ability. Considering that students' algebraic knowledge and ability to solve equations need to be improved in compulsory education stage, the ability to discuss the relationship between lines by algebraic method can improve students' ability to deal with mathematical problems by algebraic method; On the other hand, we should strengthen the application of Pythagorean theorem. In this chapter, all the measurement problems are dealt with by Pythagorean theorem, so that students can further feel the power of Pythagorean theorem. After repeated consideration, we intend to break through the tradition and teach in the order given by the curriculum standard.

This kind of problem needs to be further studied in the new textbook in order to make appropriate treatment.

Second, strengthen the comparative study of old and new textbooks.

For example, through the comparative study of Math 2, we deeply realize that it has the following characteristics:

(1), in terms of content arrangement, by studying the curriculum standards and comparing the new and old textbooks, we find that the preparation content of solid geometry in the new curriculum Math 2 embodies the principle of from whole to part, from concrete to abstract, while the content in the old textbook follows the principle of from part to whole. At the same time, in terms of content difficulty requirements, Mathematics II is less difficult than the old textbook, which is also reasonable.

(2) Highlight "mathematical inquiry" and "mathematical culture". From the introduction of questions, exploration and discovery, reading and thinking, some examples and exercises in the textbook, we can easily find this feature of Math 2.

(3) The selected materials are close to the reality of students' life, which stimulates students' interest in learning mathematics and consciously establishes mathematics consciousness in life.

For example, in Section 4.2, the relationship between the position of a straight line and a circle is cited. On the way back to Hong Kong along a straight line, a ship received a typhoon forecast from the Meteorological Observatory: the typhoon center is located 70 kilometers to the west of the ship, and the affected area is a circular area with a radius of 30 kilometers. It is understood that the port is located 40 kilometers north of the typhoon center. If the ship does not change course, will it be affected by the typhoon?

Review the reference questions in this chapter: Question 7 in Group A: Senior One 1 Class (1) ordered a three-layer cake for the Chinese New Year. If the outer layer of the cake is evenly wrapped with cream with a thickness of 0. 1cm and a density of 0.7 g/cm3, how many grams of cream will the whole class eat?

These materials reflect the real life of students well. We believe that students' application consciousness and practical ability will be further improved by learning Math 2.

(4) Pay attention to the integration with information technology.

For example, in textbooks, it is mentioned in many places that using information technology to explore mathematical problems, such as Exercise 3. 1, Question 6: If the straight line L passes through the point (0,-1), then the straight line L and the line segment connecting A( 1, -2) and B (2, 1) are always. Exercise 3.2B Group 6: Draw a straight line L: 2x-y+3 = 0 with information technology tools, take some points on the plane, measure their coordinates, substitute the coordinates of these points into 2x-y+3, find its value, and observe what the law is; Exercise 4. 1B the third group: it is known that the ratio of the distance from point m to two fixed points O (0 0,0) and A (3 3,0) is 1∶2. Firstly, information technology is used to explore the trajectory of point M, and then its equation is solved. Chapter 4 Review Reference Question Group B, Question 6:

It is known that the circle C: (x- 1) 2+(y-2) 2 = 25 and the straight line L: (2m+1) x+(m+1) y-7m-4 = 0.

① Verification: the straight line L passes through the fixed point;

② Using information technology, judge when the chord of the straight line L with circle C is the longest and the shortest. And find the value of m when the chord length is the shortest and the shortest length.

In the reading materials, insert the column of "Information Technology Application" as needed.

Through the integration with information technology, it is beneficial to improve students' ability to explore, discover and solve mathematical problems and to help students understand the essence of mathematics.

(5) Setting columns such as "thinking", "observing" and "exploring" in each section according to the needs in the teaching materials, and arranging the content with students as the main body of learning, is in line with the concept of the new curriculum. It is conducive to students' independent and cooperative learning, and realizes the transformation of teachers' teaching and students' learning. Moreover, the content of "reading and thinking" interspersed in the textbook can well reflect the history of mathematics.

(6) A footnote is added to the textbook, which makes a lot of reference to the basic mathematical thinking methods of solving problems.

For example, the side note of the judgment theorem of parallelism between lines and surfaces: The theorem tells us that the parallelism between lines can be deduced, which is a common method to deal with the spatial position relationship, that is, the parallel relationship between lines and surfaces (spatial problem) is transformed into the parallel relationship between lines (plane problem); After the example 1 ends, it is pointed out that if a straight line is to be proved to be parallel to a plane in the future, it can be concluded that the known straight line is parallel to this plane. This kind of treatment is conducive to improving students' autonomous learning ability, so that they can not only learn mathematics, but also learn mathematics.

Through the study of this module, we expect that the difficulties encountered by teachers and students mainly include: it is not easy to grasp the depth of teaching and learning; Many books for students' extracurricular tutoring do not meet the requirements of curriculum standards; The overall arrangement of content coverage is too wide and the contradiction between large capacity and less class hours; Students' learning styles and methods can't meet the requirements of the new high school curriculum; Students' ability to solve mathematical problems by using information technology is relatively weak.

The overcoming method we intend to adopt: 1 overcoming the difficulty has been mentioned above; Regarding the second difficulty, it is mainly to recommend good study materials to students; In overcoming the third difficulty, we should mainly grasp the essence, key points, difficulties and keys of teaching content, correctly grasp the teaching depth, carry out targeted teaching, and cultivate students' ability of independent learning and inquiry; The fourth difficulty can be overcome mainly through lectures on learning methods, introducing the ways and methods of autonomous learning to students, introducing the characteristics of high school mathematics and the learning methods that should be adopted, and vigorously carrying out research-based learning activities; To overcome the fifth difficulty, it is mainly to use spare time to strengthen the training of students' ability to use mathematical software, especially to let students learn to use geometric sketchpad.

Third, study the arrangement system of new textbooks.

Compared with the old textbooks, the arrangement system of the new textbooks has changed a lot. How does this change affect teaching and learning? This is also one of the difficulties encountered in the implementation of the new curriculum. So is it necessary to adjust and integrate the textbook system in specific teaching (such as compulsory 1, 2, 4, 5, 3 or 1, 4, 5, 2, 3)? We think it should be done anyway. In view of the changes of the system, the reasons for system adjustment and content addition and deletion are deeply analyzed, so as to better grasp the requirements for knowledge points. Because the textbook itself has a large capacity and the task of classroom teaching is heavy, it is necessary to make the main points, difficulties, methods and ideas thorough and clear without increasing the extra burden on students as much as possible, so that students can clearly understand and accurately grasp the methods and ideas.

However, for some knowledge in the later modules of the new textbook, such as the basic operation of sets, the definition domain of function definition and the solution of value domain, inequality needs to be solved. We consider making some adjustments to the solution of inequality and explaining it in advance in order to better apply knowledge. For example, in the teaching of "Function and Equation", the "algorithm idea" is infiltrated, so that students can gradually get familiar with the drawing method of algorithm flow chart, and thus better carry out the preliminary teaching of compulsory 3 algorithm.

Fourth, correctly grasp the selection and explanation of examples and exercises.

First of all, the explanation of examples should pay attention to standardization and formatting, especially where students are prone to make mistakes. Following their feelings is often the key to the topic. For example, when students prove that the function f(x)=x3+ 1 is the increasing function on R with the monotonicity definition of the function, after making the difference, they often use X 1

Secondly, we should pay attention to the combination with information technology when explaining examples. For example, compulsory (1)P35 Example 4: Known function y=2/(x- 1), x? [2,6], find the maximum and minimum value of the function. When explaining, you can use information to make function images (Excel or geometric sketchpad), so that students can have an intuitive experience, and then guide students to strictly prove the definition of monotonicity of functions, thus solving problems.

Third, the choice of exercises focuses on pertinence, and difficult questions are not selected. Select exercises that can reflect the main knowledge points, methods and ideas of the textbook, and adjust some exercises in the textbook according to the students' knowledge structure. For example, the last question in the "B" group of the review questions in the second chapter of the compulsory (1), because the students have not learned physics knowledge, should be dealt with after speaking. In short, the topic must be in line with the students' cognitive scope.

Five, the "thinking" and "exploration" of the new textbook.

"Thinking" and "exploring" in the new textbook are obvious differences between the old and new textbooks. The "thinking" and "exploring" in the new textbook not only help students to deepen their understanding of knowledge, but also help students to find problems, explore problems, analyze and summarize, which embodies the mathematical exploration and cultural value. We intend to use the time of collective lesson preparation to discuss these problems in depth and strive to do our best in teaching.

Six, not only to teach students to solve problems, but also to teach students to "ask questions".

This is not only one of the important ideas of the new curriculum, but also another major problem faced by teaching under the new curriculum, which embodies the value orientation of mathematics curriculum reform in senior high school.

Case: Regarding the history of the Sino-Japanese Sino-Japanese War of 1894-1895, the history lessons in China and Japan are as follows:

The China Students' Union raised the following questions: When the Sino-Japanese Sino-Japanese Sino-Japanese War of 1894-1895 broke out, what was the fuse, and what unequal treaties China signed after the Sino-Japanese War of 1894-1895; However, the Japanese Students' Union raised a question: Based on the history of the Sino-Japanese War of 1894-1895, when do you think the war between China and Japan will break out in modern times, under what background, and in what ways should Japan prepare and strengthen to defeat China? From the above problems, we can see the value of the problem and its influence on students' future development.

"It is more important to ask questions than to solve them." The report "Problem Center & Value Orientation of Mathematics Curriculum Reform in Senior High School" made by Confucius, a middle school affiliated to Qufu Normal University, Shandong Province, provides us with theoretical basis and operational methods to solve this problem in future teaching, which needs to be practiced in teaching.

Seven, change ideas, strengthen ideas and improve teaching methods.

Because the new curriculum should embody the basic ideas of the times, foundation, selectivity and diversity, so that different students can learn different mathematics and get different development in mathematics. Therefore, as a teacher, we should first change our ideas, fully understand the ideas and objectives of mathematics curriculum reform, and our role and function in curriculum reform, that is, we should not only be the imparting of knowledge, but also be the guide, organizer and collaborator of students' learning, just as "it is better to teach people to fish than to teach people to fish".

While changing ideas, actively explore ways to improve teaching. Teacher affiliated high school of south china normal university Hualuo introduced us to a very good and practical method:

(1) Strengthen independent exploration: "ask" in "doubt", "seek" in "exploration", "realize" in "mistake" and "learn" in "use";

(2) Strengthen cooperation and communication: classroom discussion, group communication and teacher-student communication;

(3) Strengthen the application of mathematics: pay attention to life examples and introduce popular nature; Strengthen the essence of mathematics and advocate experimental application;

(D) Strengthen the sense of innovation: pay attention to cultivating students' new ideas, new ideas and innovative ability.

For example, in the image and nature part of logarithmic function, students can compare the image and nature of exponential function, and students can cooperate to make the image of function, so that students can observe, compare, analyze and summarize its nature, thus cultivating students' independent exploration ability. For example, in the textbook "The History of Function Development", we plan to arrange qualified students to find relevant information from the Internet, and other students can find information in the reading room, so that students can learn to collect and sort out information.

For example, the nature of logarithmic operation: loga (m n) = logam+Logan, which we think is too sudden for students to accept. We intend to choose the following explanation, let students calculate first: log2 16, log22, log28, and ask: Can you find out the relationship between these three logarithms? Students can easily find log2 16 = log. Further questions, how does the relationship between real numbers in the equation make it easy for students to find real numbers 16=2×8? Further question: can it be summarized as a general case: loga (m n) = logam+Logan? Does this generalization hold? Arouse students' curiosity and make them think about how to prove it. At this time, the teacher can guide appropriately. This not only solved this difficult problem, but also laid the foundation for later natural proof.

Another notable feature of improving teaching methods is to strengthen the application of information technology. The textbook clearly points out that information technology should be used in teaching. For example, you can draw images of specific exponential functions with the help of calculators or computers to explore and understand the monotonicity and special points of exponential functions; Can draw the image of specific logarithmic function with the help of calculator or computer, and explore and understand the monotonicity and special points of logarithmic function; The approximate solution of the corresponding equation can be obtained by dichotomy with the help of calculator, which embodies the requirement of strengthening the integration with information technology.

Eight, students' learning guidance

Under the new curriculum reform, mathematics is rich in content, abstract and theoretical. After students are promoted from junior high school to senior one, they first encounter functions with strong theory, and there are many practical problems that are unfamiliar with the actual situation, which make some students feel uncomfortable and cause learning difficulties. How to make students adapt to the study of high school mathematics as soon as possible, in addition to solving the problem of the connection between junior high school and senior high school, the guidance of learning methods is obviously particularly important.

1, preview before class to improve the pertinence of the lecture. Because the classroom capacity of high school is much larger than that of junior high school, it is also more difficult. Therefore, the difficulties found in the preview are the focus of the lecture. At the same time, it can make up the old knowledge that is not well mastered in the preview, reduce the difficulty in the lecture process, and help improve the thinking ability and self-study ability.

2. Do a good job in reviewing and summarizing after class. Including timely review after class, unit review and unit summary, chapter summary, and learning experience and feelings. (Learning Weekly)

3, do five to: (1) Ear to: that is, listen attentively to the teacher's introduction to the new lesson, prepare for the study of this lesson, listen to the teacher's questions and how to guide thinking and exploration, how to analyze and summarize, and also listen to the students' questions and answers to see if it is enlightening. (2) Eyes: Look at the teacher's blackboard writing on key and difficult points in class. Gestures and actions deepen the impression of key points. (3) Mindfulness: that is, thinking attentively, keeping up with the teacher's mathematical thinking, and analyzing how the teacher grasps the key points and solves problems. (4) Oral: that is, under the guidance of the teacher, take the initiative to answer and participate in the discussion, and exercise their mathematical language expression ability. (5) Hands-on: that is, record the key points on the basis of listening, watching, thinking and speaking.

For this reason, we believe that in teaching design, we should fully consider the characteristics of mathematics and students' psychological characteristics, take into account the learning needs of students with different levels and interests, and use various teaching methods and means such as information technology to guide students to study actively and let them learn to think independently, explore independently, practice and cooperate.

Nine, strengthen the handling of student information feedback

The quality of students' lectures and homework directly reflects their mastery of knowledge. Analyze and summarize students' problems after class and homework in time, correct them in time, let go of any problems of students and any unclear knowledge points, conduct unit and chapter tests in a unified way, summarize students' problems in a unified way, add these problems in future tests, reprocess them, or through questionnaires.