Curriculum design should meet the needs of students' future life, work and study, enable students to master the necessary basic knowledge and skills of mathematics, develop students' abstract thinking and reasoning ability, cultivate students' awareness of application and innovation, and develop students' emotions, attitudes and values.
It should conform to the characteristics of mathematical science itself and embody the spiritual essence of mathematical science; It should conform to students' cognitive laws and psychological characteristics, which is conducive to stimulating students' interest in learning;
While presenting mathematical results as knowledge and skills, we should attach importance to students' existing experience and let students experience the process of abstracting mathematical problems from the actual background, establishing mathematical models, getting results and solving problems.
Different people have different development in mathematics: according to the modern children's point of view, every child has great educational potential, and our education must fully respect the inherent quality of children, that is, natural nature, and carefully care for and develop them. We should face every different individual, meet every student's different development needs and provide every student with different development opportunities and possibilities. Mathematics curriculum must be based on the general development of students, and it should be a course for every child to grow up healthily, not a "sieve" specially used for elimination.
Teaching practice:
Understand and master the learning situation of children from different families at home and at school, and fully understand the starting point of students' learning.
(2) Create a multi-intelligence environment, grasp the principles of "teaching students in accordance with their aptitude" and "teaching students in accordance with their aptitude", innovate learning methods, develop and apply teaching resources of "multi-dimensional" learning activities, create a "smart environment" suitable for children's life and study, integrate educational resources, and form a new synergy, so that each child's creative potential can be developed in learning and each child's multi-intelligence can be cultivated to the maximum extent.
③ "The art of teaching lies not in imparting skills, but in inspiring, awakening and encouraging." Proper evaluation will bring the feelings between teachers and students closer, make teachers become encouragement and supporters of students from a judge, make students respected, and make every child feel happy and successful from learning. Establishing a comprehensive, pluralistic and scientific evaluation system is a powerful guarantee for developing and implementing multidimensional learning.
Interpretation of the new curriculum standard (2) Second, the curriculum content should not only reflect the needs of society and the characteristics of mathematics, but also conform to the cognitive laws of students.
(1) It includes not only mathematical conclusions, but also the formation process of mathematical conclusions and mathematical thinking methods. ⑵ The course content should be close to students' life, which is conducive to students' experience, thinking and exploration.
⑶ The organization of content should deal with the relationship between process and result, intuition and abstraction, life, situation and knowledge systematization.
⑷ The presentation of course content should be hierarchical and diversified to meet students' different learning needs.
1, which includes not only the conclusion of mathematics, but also the formation process of mathematical conclusion and mathematical thinking method. Mathematics is a science that studies quantitative relations and spatial forms. The essential difference between students learning mathematics and not learning mathematics lies in cultivating people's intuitive ability, deductive ability and logical thinking! In fact, it is to promote the development of students' thinking with mathematical knowledge as the carrier. This is the essence of mathematics learning.
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Mathematical knowledge and mathematical thinking methods are the core of mathematics. In recent years, the tendency of "de-theming" is to ignore the origin of mathematical knowledge and mathematical thinking methods. The reason is that it pays too much attention to form and downplays essence. Grasp the origin of mathematical knowledge and mathematical thinking methods, organically integrate with the ideas advocated by the new curriculum concept, correct the tendency of "de-theming" and restore the true colors of mathematics teaching!
(a) Root-tracing the origin of mathematics;
The origin of mathematical knowledge and mathematical thinking methods in primary school mathematics: reduction thought, optimization thought, symbolization thought, set thought, function thought, limit thought, classification thought, probability and statistics thought, etc. Induction and deduction, analysis and synthesis, abstraction and generalization, association and conjecture.
2. Master the origin of mathematical knowledge and the significance and value of mathematical thinking methods.
(B) show the true colors-return to the true colors of mathematics teaching
1. For specific mathematical knowledge, we should know the source of knowledge and the mathematical thinking method behind it.
(1) By studying the history of mathematics, we can understand the background and development process of mathematical knowledge, and know the ins and outs, so as to master the origin of knowledge and mathematical thinking methods. (For example, introduce students to the origin of decimal notation)
(2) Dig into teaching materials. The arrangement of teaching materials includes the source of knowledge and thinking methods. (For example, the infiltration of the idea of infinite division limit in the derivation of circular area. )
2. In practice, how to develop teaching design with the origin of mathematical knowledge and mathematical thinking methods as the main line. (1) In the process of knowledge generation, we should grasp the origin of knowledge and highlight the process of knowledge generation and formation. Let students be in the state of new knowledge-the problem situation created should include the origin of mathematical knowledge and let students be in the state of solving problems-and there should be the task of thinking about the origin of knowledge in the process of exploration (taking the lesson "Understanding within 1000" as an example, this paper expounds how to grasp the origin of mathematical knowledge for teaching design. The essence of this part of knowledge is position system, carry method and symbolic thinking. )
(2) In the process of rule induction, formula derivation and conclusion discovery, the thinking method is the main line and the thinking process is highlighted.
① Teaching around a mathematical thinking method (derivation and transformation of parallelogram area)
(2) Teaching around a variety of mathematical thinking methods (derivation of triangle angle sum-guess, verification, transformation, etc. )
③ Infiltrate mathematical thinking method with a certain point.
In a word, knowledge is the foundation, method is the intermediary and thought is the source. With thoughts, knowledge and methods can rise to wisdom. Mathematics is a subject that can increase students' wisdom. Only by grasping the essence of mathematics and effectively combining it with the new curriculum concept can we give full play to the maximum value of mathematics education and show the true colors of mathematics! Doing this in itself is to make mathematics class return to mathematics taste and find the soul of mathematics teaching!
2. The course content should be close to students' life, which is conducive to students' experience, thinking and exploration.
① Mathematics learning should be based on students' development, and students' personal knowledge, direct experience and real world should be regarded as important resources for mathematics teaching. Our students are resource developers. Students' own knowledge, experience, intelligence, emotion and other factors constitute the internal "resources" of students, and a student is a unique "resource point". "There are students in the heart and resources in the eyes".
② Mathematics comes from life and ultimately serves life, especially primary school mathematics, and its prototype can almost be found in life. Resources close to students' life can make students' common sense and experience knowledge come in handy and open up a space for them to think, explore and develop in the mathematical world.
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③ Teachers should master students' practical experience and analyze, clarify, guide and respond to it, so as to realize the process of students' creative transformation, exchange and blending of knowledge. This process can be regarded as the development or transformation of children's original knowledge, rather than the accumulation of new information.
3. The organization of content should handle the relationship between process and result, between intuition and abstraction, and between life, situation and knowledge system.
The relationship between process and result:
This process generally includes: discovering the mathematical components in practical problems, symbolizing these components, and transforming a practical problem into a mathematical problem; The problem of symbolization is further abstracted, and different mathematical models are tried to be established and used to develop a more perfect and reasonable conceptual framework.
The process is as important as the result. It should be emphasized that the results should be obtained by students through a certain inquiry process, rather than directly taught by teachers. We should pay attention to the discovery, feeling and experience in the process, and also consider the "result" after the process.
Pay attention to children's attitudes, emotions and behaviors in the process of activities, pay attention to the degree of efforts made by children in activities, and explore, think and create in the process. Even if the final result of the activity does not reach the expected goal, we should cherish it from the perspective of children's precious life experiences.
The two goals have their own connotations and complement each other. In the process of implementation, we should handle the relationship between them dialectically. It is not advisable to talk about the acquisition of knowledge and skills without paying attention to the learning process. At the same time, the formation of emotion, attitude and values should not be separated from knowledge and skills, but closely combined with the mastery of knowledge and skills.
The relationship between intuition and abstraction: (1) Attach importance to intuitive demonstration and inductive abstraction: In teaching activities, teachers should start with intuition, reveal the characteristics and quantitative relations of things, and guide students to make abstract generalizations through analysis, classification and synthesis, so as to draw correct conclusions. For example, when teaching the concept of "addition", the teacher can make an intuitive demonstration first: there are 5 ducks on the shore and 3 ducks in the water. The ducks in the water slowly swam to the shore. How many ducks are there on the shore? Through simple and vivid demonstration, guide students to abstract the concept of "how much is a * * * when two numbers are added".
⑵ Handle the relationship between intuition and abstraction: intuition is the means and abstraction is the development of intuition. It is difficult for students to understand the teaching content from abstraction to abstraction, and it is also not intuitive and intuitive. We just stay in the intuitive demonstration, but on the basis of strengthening the intuitive demonstration, help students sum up the essential characteristics and quantitative relations of things. With the improvement of students' grade and the enhancement of abstract thinking ability, students' dependence on intuitive demonstration can be gradually reduced and their abstract thinking ability can be improved.
The relationship between life, situation and knowledge systematization;
Life-oriented means presenting abstract mathematical knowledge and methods in the form of life prototype and realistic situation, so that students can build their own cognitive system on the basis of interest and existing life experience. Mathematics teaching requires starting from life and students' existing realistic background, capturing materials close to students' life, selecting mathematical examples such as people, things and things familiar with students' life, and excavating mathematical prototypes, so that students can realize the vividness and interest of mathematics, thus stimulating their interest in learning.
Contextualization: From the cognitive essence of mathematics learning, mathematics learning can not be separated from the situation. In fact, the process of students learning knowledge is a process of construction. No matter the understanding of knowledge or the application of knowledge, it is inseparable from the environment in which knowledge is produced and the scope of application. In other words, the construction process in learning is always related to the background and environment in which knowledge produces meaning, that is, knowledge and learning are always situational.
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Paying attention to situational design and strengthening the connection between mathematics and students' life have become an important starting point for mathematics curriculum reform and classroom teaching.
Systematic knowledge: Mathematical knowledge itself is rigorous and systematic. As far as primary school students' mathematics learning is concerned, mathematization can also be said to be a process of guiding students to experience the abstraction of practical problems into mathematical models. The ultimate goal of living and contextualization is to transcend life (life mathematics) and rise to "mathematical model" (book mathematics).
Teaching practice:
Teaching mode of "problem situation-modeling-explanation, application and expansion"
We should pay attention to three points: from the perspective of "life experience" rather than "life situation", the latter is generally the real life material of mathematical problems, while the former can come from mathematics itself and the new situation triggered by inquiry, that is, mathematical situation is not limited to real life material; It is necessary to put an end to the mathematical situation design that pays more attention to form than essence, ignores the "taste of life" and ignores the "mathematization" process of essence; Not all mathematical knowledge should pursue "life", but all should pursue "life".
4. The presentation of course content should be hierarchical and diversified to meet the different learning needs of students (the principle of teaching students in accordance with their aptitude).
Facing up to students' differences is an eternal topic. We should face up to children's differences, acknowledge and develop their personalities, and provide them with opportunities to show their unique personalities. It is of great significance to design different courses, implement different teaching and get different evaluations.
② Construct an elastic curriculum system. It is necessary to establish a diversified, hierarchical and optional curriculum system according to children's different development needs and learning needs, so that each student can have a personalized learning process through the way of "catering" by teachers and "ordering" by students themselves. When creating an open learning environment that respects children's personality, students should follow the operating idea of "different students-different personalities-different choices-different teaching". By respecting students' choices, we can create a harmonious atmosphere in the classroom and give students greater autonomy in learning.