2 1 century, social progress, the development of science and technology and mathematics are extremely rapid, even beyond imagination, which will inevitably affect education, basic education and mathematics education. Are the basic abilities that students should have in the 20th century consistent with the core qualities that students should have in the 20th century? What are the inconsistencies? This is a cross-century challenge and the background of establishing a curriculum system based on core literacy.
First, correctly understand and understand the core literacy of mathematics
In the 265438+20th century, China established the guiding ideology of education reform, which is "moral education" and "people-oriented", emphasizing the implementation of the guiding ideology with curriculum as the carrier, and then taking the revision of senior high school curriculum standards as a breakthrough, we explored, accumulated experience and gradually popularized it. "Literacy-oriented curriculum system" mainly aims at cultivating and improving students' core literacy (general education) and subject core literacy. According to the characteristics of each subject, the three-dimensional goal is implemented through the core literacy of each subject, and the overall goal of the course is organically combined with the subject education.
Chinese mathematics educators have been thinking: what should mathematics education leave for students? Mathematics core literacy is the key ability and thinking quality of people who have the basic characteristics of mathematics and meet the needs of personal lifelong development and social development. Broadly speaking, the core literacy of mathematics includes not only explicit ability, but also internal thinking quality. The revision group of mathematics curriculum standards put forward six core qualities: mathematical abstraction, mathematical reasoning, mathematical modeling, intuitive imagination, mathematical operation and data analysis, which are the continuation and deepening of the five basic abilities.
Mathematics core literacy is an important basic component of mathematics curriculum objectives. Each mathematics core literacy is expressed through four aspects: situations and problems, knowledge and skills, thinking and expression, communication and reflection, which are also four dimensions to describe the level of core literacy.
Every core accomplishment of mathematics has its own independence. In the process of learning mathematics, it plays different roles in discovering, putting forward, analyzing and solving different links of mathematical problems and practical problems, but we need to emphasize integrity more. The six core qualities are an organic whole. They are not independent literacy, but "cross" and "penetrate" each other. In intuitive imagination, they contain. In abstract generalization, intuition, reasoning and model are also indispensable; In the process of mathematical modeling, intuition, reasoning and model interaction are more needed. ...
Mathematics core literacy is not a mysterious concept independent of knowledge, skills, thoughts and experiences, but a comprehensive reflection of the understanding of mathematics knowledge, the mastery of mathematics skills and methods, the perception of mathematics thoughts and the accumulation of experience in mathematics activities.
Second, based on the core quality of mathematics mathematics curriculum system
The mathematics curriculum based on the core quality of mathematics should highlight three points: first, it conforms to the laws of mathematics and has a clear structure; The second is to highlight the essence of mathematics; Third, it is easy to transform into the core literacy of mathematics.
1. Selective high school mathematics curriculum structure
Different students have different specialties, will choose different development directions and need different levels of mathematics core literacy, while the mathematics curriculum standards design different courses for students with different development directions.
Compulsory courses provide the same foundation for students' development and are the content requirements of high school graduation exams. Elective I is a course for students to choose, and compulsory courses and elective I are the content requirements of the college entrance examination. Elective two courses are divided into five categories: ABCDE. These courses provide guidance for students to determine the development direction, provide a platform for students to show their mathematical talents, provide choices for students to develop their interests in mathematics, and provide reference for independent enrollment in colleges and universities. Students can choose to study some of these courses according to their own aspirations and the requirements of university majors.
A course is a course for some science and engineering students (mathematics, physics, computer, precision instruments, etc.). ) you can choose. Course B is an elective course for students majoring in economics and society (mathematical economics, etc.). ) and some science and engineering (chemistry, biology, machinery, etc. C course is a course for students to learn humanities (history, language, etc.). ) you can choose. D course is an elective course for students majoring in physical education, music and fine arts. E-course (school-based course) is a course provided by the school for students to choose independently, especially CAP.
2. High school mathematics content structure reflecting the development of mathematics core literacy.
Mathematics is rich in research fields, problems and methods, and has formed many branches of mathematics with distinctive characteristics and different functions, but mathematics is an organic whole with clear structure, especially from the perspective of learning. Only in this way can we better improve and develop students' mathematics core literacy. According to the characteristics and needs of senior high school learning, senior high school mathematics content will highlight three main lines: function and application, geometry and algebra, statistics and probability. Mathematical modeling and mathematical inquiry are another main thread running through it. In addition, mathematics culture should be infiltrated into the curriculum content of senior high school. Only by grasping these main lines, can we repeatedly feel the role of abstraction, reasoning (operation), model and intuition, and effectively promote the promotion and development of students' mathematics core literacy.
3. Key problems and main concepts, theorems, models, thinking methods and applications that embody the essence of mathematics.
On the basis of understanding the content structure and main line of senior high school mathematics as a whole, we need to think deeply about the key issues, main concepts, theorems, models, thinking methods and applications that support the main line. Taking the main line of function as an example, we must first grasp the following key issues: understanding the concept of function as a whole and comprehensively; Deeply understand the properties of functions-global properties and local properties; Master some basic function classes; Master function application; Understand the thinking method of research function; Deeply understand the main concepts, theorems, models, thinking methods and applications. Step by step, gradually improve the core literacy of mathematics.
Third, 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 cannot rely on imitation and memory, but also need to understand and feel. 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. In this process, students will constantly feel and understand the role of abstraction, reasoning, operation and intuition, gain new mathematical models, improve the quality of thinking, expand the scope of application, 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 teaching thinking object. 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 starting point of deep learning, and the starting point of grasping mathematics curriculum as a whole. It can highlight the essence-the core literacy of mathematics, which is conducive to the diversification of teaching methods, combining "teaching" with "learning" and promoting students' independent 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.
3. Grasp the essence of mathematics
Hua is a famous mathematician in China. He has repeatedly stressed that reading can be thick or thin. Reading thin books is to grasp the essence, the key points and the essence, so as to better understand and enhance 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.
5. Create a suitable environment
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"
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). Moreover, mathematical symbols and graphics are a system, which is 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.
Fourthly, mathematics learning based on the core quality 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 broaden our horizons, understand the history of mathematics, understand the development of mathematics and understand the role of mathematics in social development. In the consultation report written by the American Science Council to the President of the United States, it is 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, to get good grades and to need good knowledge. Knowledge is more important than knowledge.
2. Problem solving = math learning? 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.
exchange; 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. Under the revision group of mathematics curriculum standards, there is a topic research group based on the core literacy test of mathematics to study the elements and forms that need to be improved in the proposition.
Therefore, the proposition based on the evaluation of mathematics core literacy 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 line of content-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 good mathematics education for students.