First, mathematics teaching based on the core quality of mathematics
What to teach and how to teach? This is the eternal topic of teachers' teaching. Teachers' mathematics teaching based on mathematics core literacy should first update their concepts. To cultivate and improve core literacy, we should not only rely on imitation and memory, but also need to understand and feel, and we should actively and consciously combine the concept of "student-oriented" with teaching practice. 1 Grasp the mathematics curriculum as a whole
Mathematics teaching is based on the core quality of mathematics, and the overall understanding of mathematics curriculum is the basis. High school mathematics curriculum is an organic whole. In order to understand the nature and concept of mathematics curriculum as a whole and grasp the goal of mathematics curriculum as a whole, it is especially necessary to understand the core literacy of mathematics as a whole, understand the content structure, main line, theme, key concepts, theorems, models, thinking methods and applications of mathematics curriculum as a whole, and design and implement teaching as a whole. For example, take a chicken and a rabbit in the same cage. In primary school, we can use "enumeration method", "approximation method" and "hypothesis method", and these methods will still play a role in future study. But more attention should be paid to learning the "equation group method". Because mathematics teaching is not only to solve a specific problem, but also to think about how to solve a class of problems, a larger class of problems. All the problems of chickens and rabbits in the same cage are turned into a mathematical problem, and a general solution method-operation program is given. Not only that, but also lay a foundation for introducing binary linear equations into junior high school to solve a larger class of problems. In high school, we can further interpret it from the perspective of analytic geometry and vector ... In this process, students will constantly feel and understand the role of abstraction, reasoning and intuition, obtain new mathematical models, expand the application scope, enhance key abilities and improve the quality of thinking. 2 theme (unit) teaching
Mathematics teaching based on the core quality of mathematics requires teachers to jump out of teaching section by section and take "theme (unit)" as the basic thinking object of teaching. We can take "chapter" as the unit, such as "trigonometric function" as the teaching design unit; You can also take important topics in mathematics as teaching design units, such as "distance" or "geometric measurement relationship: distance, angle" and so on; It can also be based on general methods in mathematics, such as "model and undetermined coefficient". This is the core of deep learning, the grasp of deep learning and the overall grasp of mathematics curriculum, which can highlight the essence-the core literacy of mathematics, help diversify teaching methods, combine "teaching" with "learning" and promote students' autonomous learning; It is helpful to improve the professional level of mathematics teachers (mathematics, education and teaching theory, practice), which is the basic skill of backbone mathematics teachers, not teaching textbooks, but creatively teaching mathematics with textbooks.
The most important element of theme (unit) teaching is to carry out overall analysis, including mathematical analysis, standard analysis, learning situation analysis, comparative analysis of teaching materials, analysis of key points (essence and core literacy) and analysis of teaching methods, so as to determine the theme teaching objectives and choose design situations and learning activities. According to the students' reality, determine the teaching process, design the teaching of each class, carry out the teaching implementation, and then constantly reflect-cycle-improve.
3 Grasp the essence of mathematics
Hua, a famous mathematician in our country, has repeatedly stressed that reading can accumulate a lot, and thin reading is to grasp the essence and key points. Only by grasping the essence can we better understand and improve the core literacy of mathematics. 4 problem-oriented-find problems, ask questions, analyze problems and solve problems.
In the great discussion about mathematics and mathematics education, when asked what is the most important thing in mathematics and mathematics education, the famous mathematician P. Harmous emphasized in a summary article that "the problem is the key", and mathematical concepts, theorems, models and applications are all summarized and formed in the process of solving problems. In the goal of mathematics curriculum, special emphasis is placed on developing students' ability to find problems, put forward problems and analyze and solve problems, which is also the focus of attention in teaching based on mathematics core literacy. Step 5 create the right situation
Creating suitable situations is another teaching focus based on the core literacy of mathematics. First of all, we should have a comprehensive understanding of "situational needs", including actual situations, scientific situations, mathematical situations and historical situations. The basic principle of situation selection is to gradually understand the learning content and tasks to be completed, and then consider stimulating students' interest and enthusiasm.
6. Grasp the learning situation and strengthen the guidance of "learning to learn"
It is an old saying that it is better to teach people to fish than to teach them to fish, which is consistent with the concept of learning to learn. "Learning" is more important than "learning". "Learning mathematics" should include: reading comprehension, questioning and asking questions, combing and summarizing, and expressing communication. Taking Mathematical Reading Comprehension as an example, we need to understand that mathematical language is composed of mathematical natural language, symbolic language and graphic language, and its characteristics are accurate, clear and concise. Mathematics reading requires reading Mandarin Mathematics, Symbols and Figures (Tables). Mathematical symbols and figures (tables) are a system, which are interrelated. Students can't get used to it quickly, need guidance and can't rush into it. It is a good experience for math teachers to attach importance to "learning and teaching", which needs to be persisted, summarized and improved.
Second, mathematics learning based on the core literacy of mathematics
The following problems should be paid attention to in mathematics learning based on mathematics core literacy. 1 vision-knowledge
Learning mathematics needs to have a broad vision, understand the history of mathematics, understand the development of mathematics and understand the role of mathematics in social development. In its advisory report to the President of the United States, the American Science Council particularly emphasized that "high technology is essentially mathematical technology"; Understanding the role of mathematics in real life, the evaluation report of the British Research Council believes that the contribution of mathematics research to the British economy accounts for about 10% of all jobs in the UK and 16% of the total GDP. For excellent students, teachers should guide them not to be satisfied with learning mathematics knowledge, get good grades and gain good knowledge. Knowledge is more important than knowledge. 2 Question = Math study? Learning autonomy
It is a prominent problem in mathematics education to replace mathematics learning with doing problems. Consolidating learning content by doing problems is an important part of learning mathematics, but just doing problems has great limitations. Learning mathematics also requires understanding mathematical concepts, theorems and applications, and understanding the relationship between different contents.
There is a difference between doing problems and doing math. To do mathematics, we must first choose the problem, then guess the conclusion, determine the conditions and explore the method of solving the problem; Doing problems is completely different, the conditions and conclusions are certain, and the methods have been learned, which has certain limitations in exercising mathematical literacy.
3. Actively participate in mathematical modeling and mathematical inquiry.
Mathematical modeling is a process of abstracting realistic problems mathematically, expressing problems in mathematical language, and establishing models to solve problems with mathematical knowledge and methods. Mathematical inquiry is a process of independent inquiry and cooperative research around a specific mathematical problem, and finally solve the mathematical problem. They are the important content of high school mathematics curriculum. "Mathematical modeling activities" and "mathematical inquiry activities" are mainly carried out in the form of subject research. The research process of the subject includes four links: selecting a topic, opening a topic, doing a topic and concluding a topic, which is an important measure to promote students' autonomous learning and let them experience the problem-solving process.
The topic can be given by the teacher, can also be determined by the students and the teacher through consultation, and can also let the students choose their own practical or mathematical problems. They can work independently or in groups and write opening reports. Teachers should organize "opening the topic" exchange activities. "Doing problems" refers to the process of solving problems, including describing problems, mathematical expression, establishing models, solving models, drawing conclusions, reflecting on perfection and so on. "Conclusion" includes writing research reports and reporting research results. Teachers can organize students to make closed defense, which can take various forms such as special assignments, measurement reports, algorithm programs, making physical objects or research papers. For the evaluation of research reports, teachers can organize evaluation teams and invite experts from outside the school, the public and parents. The research report and its evaluation should be stored in personal study files as documents to provide reference and basis for university enrollment. 4 can communicate
Communication is very important in the mathematics learning stage. Why don't you listen, read and write? That makes sense. The main way for graduate students to teach is to let students report, and it is easy for tutors to judge whether students really understand from the process of reporting. I hope middle school teachers and students can also learn from this method-communication.
Evaluation based on mathematics core literacy is an important measure, especially the evaluation of college entrance examination. This reform will be difficult to implement if the questions and examination forms of the college entrance examination are not changed. Of course, step by step. Based on the evaluation of mathematics core literacy, the proposer should pay attention to the following elements: (1) The proposer should grasp the high school mathematics curriculum as a whole and focus on the main content lines-theme (unit) and key concepts, conclusions, models, thinking methods and applications; (2) Highlighting the essence of mathematics; (3) Create appropriate situations and emphasize the background of finding, putting forward, analyzing and solving problems, including actual situations, scientific situations, mathematical situations and historical situations; (4) Emphasis on openness and inquiry.
How to improve students' mathematics core literacy in mathematics education is a new topic faced by mathematics educators. Front-line math teachers are the key to implement the revision of senior high school curriculum standards. It is hoped that teachers will pay attention to improving their own mathematics literacy, especially the core literacy of mathematics, pay attention to the organic combination of mathematics content, mathematics teaching theory, mathematics teaching practice and mathematics core literacy, face up to problems, keep exploring, and create a good mathematics education environment for students.