The first is "mathematicization", and the activities you engage in should have clear mathematical goals. Activities without mathematical goals are not "mathematical activities". The most basic quantitative relationship, graphic relationship and random relationship (mainly statistical relationship) in primary school mathematics learning.

The second is "demonstration". Experience is a kind of perceptual knowledge, which contains double meanings, one is the thing to experience, and the other is the process of experience. Mathematical experience is the perceptual knowledge of mathematics, which is accumulated in mathematical activities.

Once again, it is "active". Stolyar, a famous mathematics educator in the Soviet Union, believes that mathematics teaching is the teaching of mathematics activities and thinking activities. Then the whole mathematics teaching activities, including abstract thinking, mathematical proof and mathematical problem solving, are all "mathematical activities", which is too general. The specific meaning of "activity" that I understand by "mathematical activity experience" is mainly the concrete operation of mathematical materials and the exploration of image operation.

With regard to "foundation", the mathematics curriculum standard names mathematics knowledge, skills, thoughts and activities as "foundation", which is called "four foundations".

As an educational goal, "gaining the experience of basic mathematics activities" is based on "dynamic mathematics view", which regards mathematics as an activity of human beings and an activity full of emotion and thinking. This view of mathematics will inevitably affect the view of mathematics education.

First of all, the goal of mathematics teaching is not simply reflected in the mathematical facts accepted by students, but more to organize "empirical materials" and "logical mathematical materials" through the understanding of mathematical thinking methods and the accumulation of mathematical activities experience. Mathematical knowledge includes not only "objective knowledge" of mathematical facts such as definitions, formulas, rules and theorems, but also "subjective knowledge" belonging to students themselves, that is, personal knowledge and mathematical activity experience with individual cognitive characteristics, which is experiential, perceptual and not strict "tacit knowledge".

Secondly, mathematics teaching is not only the result teaching, but also the process teaching. Mathematics classroom teaching must be combined with specific content to let students "experience the process" in mathematics learning activities.

Third, mathematics classroom teaching should be open. Mathematical activity experience is not "tangible" like factual knowledge, and its expression is unique. Students' understanding of a mathematical object in mathematical activities has individual characteristics, and the experience gained in the process of understanding is diverse, so students' development is different. This determines that mathematics classroom teaching should not be indoctrinated in a closed way, but should organize activities in an open way. Every student has a certain degree of autonomy in the learning process. Teachers should give all kinds of different opinions a full opportunity to express and actively expand students' learning space.

Second, the characteristics of the basic activities of mathematical experience:

1 subjectivity. Experience is a kind of psychological representation or structure, which exists in the individual's mind and cannot be directly observed. As the main body, students participate in actual social life or situations created by teachers and experience their own personal experiences. Therefore, the basic activity experience of mathematics is based on the learning subject, belongs to the concrete learners themselves, and has obvious subjective characteristics. For example, students can learn the proposition that the sum of the internal angles of a triangle is equal to 1800 by drawing, cutting, jigsaw, piecing together and measuring, which is a kind of discovery learning in which students actively acquire knowledge. Students fully mobilize a variety of sensory collaborative activities, use their brains, hands and holes to effectively gain experience in mathematics activities through multiple channels. For example, in teaching, teachers use operational teaching AIDS and learning tools reasonably, and through physical operation, observation and experience, establish a sense of mathematics and form a mathematical experience for the learning object. Because experience is the subjective product when the subject reflects the object on the basis of the interaction between subject and object, the acceptance and possession of experience can not be carried out in the state of neither changing the nature nor changing the existing form, just like accepting the real thing. The process of accepting experience is the process of reconstructing the experience structure of the subject, which is also the process of constructing the psychological structure of the subject. The subject must be in a very active state and actively carry out a series of complex psychological operations in order to complete the construction process and truly "accept" the corresponding experience. Therefore, students' learning is to "accept" the existing experience from the results, while the process is an active experience construction process.

2 practicality. Experience is inseparable from activities, and mathematical activities are the source of experience. Therefore, without mathematical activities, meaningful experience in mathematical activities will not be formed at all, and experience can only be formed by personal experience, which is obviously practical. Primary and secondary school students learn formal mathematics, which is basically combined with their own life reality. For example, when primary school students learn decimals, they will naturally be linked to the price of goods when shopping; If you learn the percentage, you will associate it with the qualified rate of students in this class who have reached the standard in physical exercise. Junior students have little life experience and weak hands-on ability. Only by actually experiencing effective practical activities can we master the steps and methods of activities, gradually accumulate experience and form positive emotional experience. For example, in the corner of understanding, the teacher deliberately created such a situation, giving each student a pocket with some items in it, so that students can find a corner from it. After the students lifted the corner they found, the teacher said, "Look how well you touched it. I want to touch them, too Can you tell me how you found it? " The children said, "There is a sharp one in the corner, which is tied in a panic." The teacher reached for the thumbtack; The children said, "A horn has two sides." The teacher reached out and touched a really sharpened pencil; The children quickly added: "The angle is flat." The teacher pulled out a leaf. "Sharp and flat. How come there are no horns? " The children replied, "Keep the sides straight." This time, the teacher drew a triangle. The teacher sincerely said to the students, "Thank you for helping me find the feeling of touching the corner." Obviously, the teacher is consciously guiding students to experience and let them understand and grasp the key features of the corner.

3 Tacit (tacit knowledge). As individuals, people form a large number of individual experiences through daily life, communication with people or other activities, expand the nearest development zone, and turn the nearest development zone into a real development zone through the construction of meaning. Experience is gained through construction, and construction is also gained through experience. Experience belongs to individuals and depends on specific activities. No activity, no experience. All knowledge is constructed in the dialogue between the individual and the experience world, and it must be based on the individual's cognitive process. Experience cannot be passed on. For example, "60 water heat" has been handed down as knowledge. If "60 water heat", it is a matter of experience. If you haven't experienced it, you won't have a thermal experience. Constructivism holds that knowledge is not passively accepted by individuals through feeling or communication, but actively constructed by cognitive subjects, and the construction is realized through the interaction of old and new experiences. The cognitive skill is to adapt to one's own experience world and help organize one's own experience world, rather than discovering the reality in the ontological sense. As a psychological phenomenon, experience belongs to individuals and is hidden in their own hearts. The experience of mathematical activities reflects the learners' empirical understanding of the learning object in a specific learning environment or a certain learning stage, which is more implicit. It is this hidden experience that makes it difficult for us to grasp and ponder.

4 diversity. For the same mathematical activity, even if the external conditions are the same, for the same object, each student may still have a different understanding and form a different experience. Students fully mobilize a variety of sensory collaborative activities, use their brains, hands and holes to effectively gain experience in mathematics activities through multiple channels. For example, in teaching, teachers use operational teaching AIDS and learning tools reasonably, and establish their own feelings about mathematics through physical operation, observation and experience, thus forming their own experience of learning objects in mathematics activities. It is precisely because of the diversity of experience that the differences in mathematics learning arise. As students, learning is based on experience, but also beyond experience, that is to say, they have vision, ability and accomplishment beyond experience and practice, they have higher pursuit and ideal, higher taste and realm, and become the real masters of education and teaching through continuous reading, understanding and surpassing themselves. Real experience can't be taught. Experience is an emotional experience. Only through more experience can we tell the truth from the false. Water is hot, water is scalding, scalding is experience, and heat is knowledge, which can only be known by personal experience. As a practical activity, mathematics education must attach great importance to the role of "experience". Educational research points to practice, and to some extent, it studies "experience", or it is a kind of research with "experience" as the object. Studying "experience" itself really needs "experience", without which it is impossible to study "experience", which requires researchers to go deep into the front line of education and teaching to form personal experience and experience, which is also one of the basic experiences for successful educational researchers to obtain successful research.

5 guidance. Where there is learning, there is experience. The experience gained by students through basic mathematics activities should be reflected and refined to form a guiding role for similar situations and activities in the future. Guidance can be understood as "the influence of the existing cognitive structure in students' minds on new mathematics learning activities." "Experience can predict the future situation on the basis of reality and make appropriate arrangements and plans. If a Weiqi master can see five or more moves at the same time, he needs his first four moves to appear exactly as he expected, relying on experience. Experience becomes a bridge between students' existing cognitive structure and new mathematics learning activities. Another example is the results sometimes guessed from experience in number theory, such as Goldbach conjecture, Fermat's last theorem and so on. Faced with new situations and problems, students need to mobilize existing and appropriate experience to absorb new situations and problems and form a reasonable and essential connection with the original knowledge. Situational cognitive theory holds that knowledge is contextualized through experience. The latest experience gained by students in activity A does not directly interact with the stimulus-response component of activity B now, just because it affects the relevant characteristics of the original cognitive structure, thus indirectly guiding the solution of activity B, and learning the operation rules of "number" can effectively guide the learning of the operation rules of "formula"; Learning how to find the trajectory on the plane can effectively guide the space to find the trajectory.

6 process. From the perspective of knowledge, experience is a kind of process knowledge and an "activity schema" formed in practical activities. It mainly consists of three parts. One is the knowledge component, which refers to the personal meaning of the subject and object of the activity, including the intuitive perception of the operation, the relationship between old and new knowledge and the perception of the activity process. It is the truth that people realize in the process of activities, and it is an intuitive grasp of the process of activities. Its rationality is mainly guaranteed by the effectiveness of activities, such as "an old horse knows the way"; The second is the experience component, which refers to the emotional experience produced in the process of activities, including the sense of accomplishment and failure, the experience of self-adjusting mentality and so on. , such as "competition experience"; The third is the concept component, which refers to the consciousness and belief formed in the process of activities, such as application consciousness, innovation consciousness, confidence and belief in doing things and so on. [6] Experience the process of attention and inspire thinking. The process of making students explore, think, abstract, predict, reason and reflect may all be part of the experience. In fact, when a student participates in a certain mathematical activity, he will form a schema registered in his cognitive structure, and then he will begin to consider its logical basis and relate it to the previous related content, so that he will be in harmony with his own mathematical cognitive structure. When he reaches a certain stage, the experience will gradually get feedback when facing different specific situations, thus deepening the experience of the experience.

I hope I can help you!