First, it is necessary to popularize mathematics more generally and concretely.
Everyone learns valuable mathematics, everyone gets the necessary mathematics, and different people get different development in mathematics. This concept has been put forward in the compulsory education stage, and it should be regarded as the most basic educational concept in the vocational education stage of high school. Due to the differences in individual development, students' ability to learn mathematics and their development in mathematics are also different. This basic idea truly embodies the basic viewpoint of people-oriented and student-centered in the new curriculum.
After three years of mathematics study in junior high school, students' mathematics ability has been initially differentiated. Most students who enter vocational schools are diverted from the senior high school entrance examination. Although the foundation of mathematics is uneven, it is generally poor, and the habits, confidence and ability to learn mathematics are not the same. So different students should be treated differently, as long as they can develop on the original basis. The content of the compulsory course of the new curriculum puts forward: meet the basic mathematics needs of future citizens and let students go further.
The role of mathematics in all walks of life has greatly proved that mathematics is an indispensable part of a person's quality, especially with the popularization of computers, mathematics has been closely linked with social life, so mathematics has become a part of personal life.
The new curriculum reform requires everyone to learn useful mathematics in mathematics teaching, and everyone should master the necessary mathematics, so that different people can learn different mathematics and get different development in the learning process. This is the so-called popular mathematics view. This requires us to:
(1) emphasizes application and practice, so that everyone can learn useful mathematics. In the usual teaching, we should not be limited to the knowledge in books. We should collect more examples of mathematics application in daily life, cultivate students' understanding and experience of mathematics application, let students practice mathematics extensively, learn mathematics from life, and then apply what they have learned to life.
(2) Emphasize the process and methods so that everyone can master the necessary mathematics. In the process of new curriculum reform, the past practice of seeking only the results without asking the process has been changed, and the examination of students' problem-solving process and methods has been strengthened. In the process of students' cooperative exploration, teachers don't tell students the answers directly, but let students get all-round development in the process of exploration through their wholehearted participation, personal practice and personal experience. For example, in our life, we need to enclose a vegetable field in the open space near the wall. The length of the fence is certain, and all students should master the necessary mathematical knowledge of how to enclose vegetable fields to maximize their area. Therefore, in the teaching process, the teacher should let the students think clearly about this problem. Through students' independent inquiry, let students understand the method of solving problems and let everyone master the necessary mathematics.
(3) Pay attention to individuality and development, so that different people can learn different mathematics and get different development in the learning process. The new curriculum requires us to let students speak freely, not to suppress students' personality, and to pay attention to the publicity of students' personality, so that students' personality can be fully and comprehensively developed. In the teaching process, because each student's hobbies are different, they have different feelings about mathematics. Different people have different orientations in emotion and values. Our teachers should respect students' different feelings about mathematics and pay attention to students' application of different solutions in solving problems. If they have a good foundation, they can make more positive demands and let them study and explore at a deeper level. If they have a poor foundation, they can achieve their goals as long as they understand the most basic problem-solving methods.
Second, let students feel the fun of mathematics in the teaching process
Einstein said that interest is the best teacher, so the most important thing is to stimulate students' interest in learning. Then, first of all, we should change their idea that mathematics is boring, and let them realize the fun and beauty of mathematics. Unfortunately, because our teachers don't realize the beauty of mathematics in the teaching process, the content of mathematics has removed the humanistic and historical facts in the process of mathematics development, and has replaced mathematics teaching with boring calculation and difficult reasoning.
1. Create scenes that students are familiar with and realize the assimilation and adaptation of knowledge.
Constructivism holds that everyone learns knowledge by incorporating new knowledge into the original knowledge structure in his own way, and teachers can change learning conditions, especially external conditions, to a certain extent. Teaching consists of teachers' arrangement and control of these external conditions. What is difficult is which situations students are familiar with and easy to accept. Most teachers have turned mathematics into pure mathematics, so students should create familiar situations. Always communicate with students to understand their thoughts and living conditions. At the same time, we should pay attention to extracting mathematical problems from the phenomena around us, obtaining information about production and life from newspapers and other media, and looking for problems related to mathematical knowledge from other disciplines. This practical mathematical scene not only contains rich mathematical ideas, but also embodies the essence and characteristics of mathematics. And because students are familiar with it, it is easy to attract students' attention and make them think positively.
2. Reflect the mathematical culture and strengthen the teaching of mathematical history.
The cultural purpose of the new curriculum is to convey the main factors of human culture. Mathematics is a subject developed for the needs of the development of human civilization. Its development depends on the development of the mathematical system itself and the objective needs of real life. In the development of mathematics, how many twists and turns and bizarre stories have happened, which makes people think deeply, enlighten and teach. Our mathematics teaching completely ignores the process of mathematics being discovered and created. It's just a bunch of conclusions and facts. What students see in the learning process is always so perfect, accurate and static mathematics. The historical and humanistic things in mathematics can also be said to be the most important things that have been omitted. This makes mathematics put on a cold coat, and it is understandable for students to stay away. Thus, interesting historical facts and stories in the process of establishing mathematical knowledge are infiltrated into teaching.
3. Practice math.
Practice is the only criterion for testing truth. The new curriculum advocates active and exploratory learning methods, and holds that students' mathematics learning activities should not be limited to acceptance, memory, imitation and practice, but also include self-study methods such as independent exploration, hands-on practice and cooperation and exchange. A basic feature of modern learning style is experiential, emphasizing physical participation and attaching importance to direct experience. For vocational school students, one of the reasons for poor mathematical foundation is the incomplete development of abstract logical thinking. Therefore, action-oriented teaching should be fully developed in the learning process, so that its action representation and image representation can play a full role and serve the formation of the highest level symbol representation. In this process, students realized how mathematics was discovered and created, and experienced trial, failure, failure and success in the process of creation, as well as the excitement and joy of success. Everyone practices his understanding of mathematics in his own way. This kind of mathematics will not only arouse their interest, but also be of great help to form their good world outlook and strong will. Therefore, doing mathematics in vocational high schools should become a very important form of learning mathematics.
Third, application is the soul of vocational high school mathematics.
Mathematics is an instrumental subject. It plays an important role in any subject. Some people even say that if a subject has not developed enough to be expressed by mathematics, then the development of this subject is still imperfect. Developing students' ability to solve problems with mathematics can be said to be the core and ultimate goal of curriculum reform in every country. For mathematics teaching in vocational high schools, due to the particularity of vocational education, we should pay attention to the reform of mathematics curriculum in vocational schools: some students entering vocational schools will face different requirements from different industries: some industries are closely related to mathematics, such as IT industry and electronic and electrical industry; In some industries, there are not many opportunities to use mathematics, such as tourism and business. And different industries pay different attention to mathematical knowledge. For example, the computer industry will have higher requirements for algorithms, while the business side will focus on profit and optimization. Other students who enter the university for further study will face different requirements in mathematics because of their different majors, but they all need to lay a foundation for their differences in vocational high schools to adapt to the future. Therefore, first of all, we should make a detailed investigation on the mathematical knowledge that each major needs at present and the mathematical knowledge that this major needs to develop further, so as to determine what vocational high schools must teach and what they can teach. For example, the application of four operations, linear programming and estimation in business. Optimization, calculus, probability statistics (estimation) and other mathematical knowledge. With the development of society and the continuous development and improvement of majors, new contents related to mathematics should also enter the teaching content in time. For example, there are seasonal discounts in shopping malls now, and some merchants discount the prices of elevation products. What is its actual discount rate? How to calculate the profit rate? How to use these business behaviors to analyze costs and prices? The relationship between sales prices enables students to figure out how to calculate profit and loss rate and discount rate. Another example is the combination and choice of various loan methods and repayment methods in society. Can students make a rational understanding and recognition of them? These are things that are closely related to everyone in real life. Others are related to specific majors. For example, when students majoring in computer science are studying arithmetic progression, we might as well guide them to start with the optimization of algorithms. If students of all majors know the specific contents of their major while studying mathematics, they can not only enhance their interest in learning mathematics, but also let them know their future careers, killing two birds with one stone.
In short, the implementation of the new curriculum has raised brand-new problems for all our teachers, and also pointed out the direction of our efforts, which is also a brand-new challenge. Therefore, the research on the reform of mathematics curriculum and classroom teaching in vocational high schools can only achieve good results if it is constantly explored and tried in practice.