1. The requirements of the order of students' cognitive process for primary school teaching methods
Modern cognitive psychology research points out that students' learning process is fundamentally a cognitive process, that is, the process of transforming the knowledge structure of textbooks into their cognitive structure, and this transformation process can only be realized through the development stage of "action-perception-representation-concept-symbol". Among them, "action" or "perception" is the starting point of cognition and the first step for students to acquire knowledge; "Representation" is the initial image of things formed in the mind on the basis of operation or observation, and it is the intermediary for the transformation from knowledge structure to cognitive structure. Finally, the obtained representation is "deeply processed" in the mind, and perceptual knowledge is upgraded to rational knowledge, forming "concepts" (even some concepts are further symbolized). Obviously, there is a strict logical order between the stages of this cognitive process, which is a common phenomenon in children's cognitive process. This cognitive law of students directly restricts teachers' teaching methods, which requires teachers to strengthen intuitive teaching and teaching tool operation activities in teaching, enrich students' representation of what they have learned and promote students' understanding through intuitive teaching and operation activities. In the arrangement and design of teaching materials, children's cognitive laws are fully considered. For example, the establishment of the concept of numbers within 100 (especially the concept of numbers within 10), the learning of the meaning of addition and subtraction operations, the mastery of calculation methods, the understanding of the relationship between the number of applied questions and the understanding of geometric figures all begin with students' understanding of the operation of learning tools or the observation of teaching AIDS. In teaching, we should follow the students' cognitive rules, according to different teaching contents. Practical operation activities with learning tool operation as the basic form and intuitive teaching with teaching aid demonstration as the main content are important means to help students acquire mathematical knowledge, and guide students to master abstract mathematical knowledge in the specific operation process of spelling, swinging, testing or related observation activities. For example, in the teaching of "Preliminary Understanding of Addition", we should put two balloons together, bind two (or several) sticks into a bundle, and stack two piles of books together to enrich students' representation of the addition of two numbers and promote their understanding of the essence of addition.
According to the objective requirements of children's cognitive law for primary school teaching, we should pay special attention to the following problems in the activities of strengthening practical operation and intuitive teaching.
1. 1 The essence of learning tool operation is to externalize the activity mode of mastering mathematical intelligence into a hands-on program, and then internalize the learned mathematical knowledge into students' mathematical cognitive structure through this externalized program. Therefore, in teaching, the operation of learning tools should not be simply changed into simple calculation tools, but should be regarded as the basic way and necessary means for students to acquire mathematical knowledge and develop their thinking ability.
1.2 Visual teaching does not exclude teachers' necessary explanations, so the demonstration of teaching AIDS must be closely combined with teachers' vivid language explanations.
1.3 Hands-on operation and intuitive teaching can only be teaching methods to help students better acquire mathematical knowledge, not teaching purposes. Therefore, on the basis of operation and intuition, we must pay attention to abstract generalization in time to promote students' understanding of the essential attributes of mathematical concepts and the development of abstract logical thinking ability.
2. The influence of the gradual development of students' cognition on the mathematics teaching process in primary schools.
From the perspective of cognitive psychology, the essence of students' systematic mastery of a certain knowledge is the gradual enrichment and perfection of their cognitive structure in the corresponding fields, and this process of enrichment and perfection is always realized in a gradual way, that is, the cognitive development process of students generally presents an inevitable trend from simple to complex, from phenomenon to essence, and from dispersion to system. This cognitive development trend with common laws is called the gradual development of students' cognitive development. This cognitive law of students directly restricts the process of primary school mathematics teaching, which objectively requires teachers to teach step by step.
Step by step is the unity of opposites between the systematization of knowledge in teaching activities and the gradual mastery of knowledge by students. Its core is "step by step", which is the basic premise of step by step. As a teaching strategy, it should be applied to the teaching practice of primary school mathematics, and special attention should be paid to the following aspects in the implementation process.
2. 1 deeply analyze the structure of teaching materials and grasp the internal logical order of primary school mathematics knowledge. The knowledge structure in primary school mathematics textbooks is the product of the combination of scientific mathematical knowledge structure and children's psychological structure at a specific age, and it is itself a structural system with a gradual order. For example, "understanding of numbers within 10" is arranged in the logical order of "counting-recognition-order of numbers-comparison of numbers-composition of numbers-ordinal meaning of numbers-writing of numbers". Therefore, in teaching, we should try our best to show the internal logical order of textbook knowledge from macro to micro according to the ideas of textbook writers, and establish the starting point of teaching and the gradual teaching process on this basis.
2.2 Mastering the basic sequence of students' mathematical cognitive development is a necessary condition for step-by-step teaching. Therefore, teachers should know what the students' mathematical cognitive structure is based on and what kind of development track it will continue to enrich and improve (such as the cognitive structure of adding and subtracting fractions, students taking the meaning of fractions as the cognitive starting point, adding and subtracting fractions with the same denominator, adding and subtracting fractions with different denominators and adding and subtracting fractions according to the meaning of fractions, and taking this as the psychological basis for arranging the teaching process and taking teaching measures).
2.3 Optimize the "order" in the teaching process. On the basis of fully prompting the "order" of mathematics knowledge and students' psychology, teachers should unify the "order" in the structure of mathematics knowledge and the "order" in the process of students' psychological development into the "order" in teaching activities, take effective measures to help students solve various obstacles that may occur in the cognitive process, and promote the active adaptation of students' psychological structure and textbook knowledge structure.
3. The repetition of students' cognitive formation restricts their process of mastering knowledge.
According to the research of modern cognitive psychology on the formation process of children's cognitive structure, students' cognitive process of a specific thing is not completed at one time, but needs to be repeated many times. Because this repetition process is an objective phenomenon with universality in students' learning activities, we call it the repetition of students' cognitive formation. What influence and restriction does this cognitive law have on primary school mathematics teaching, especially on students' mastery of mathematics knowledge?
3. 1 Students can only gradually master the level of mathematics knowledge. According to the repetition of cognitive formation, it is normal for students to have difficulty in mastering certain knowledge for a while or to appear repeatedly in a later period of time, which is a concrete reflection of students' cognitive laws in a specific learning environment. Therefore, teachers must correctly treat students' repetition in the learning process, allow students to gradually master the mathematics knowledge they have learned in their studies, and do not force students to master all the contents they have learned in one class.
3.2 Strengthen the connection between old and new knowledge and handle the relationship between consolidation and development. In view of the phenomenon that students are prone to repeat in the process of mastering knowledge, special attention should be paid to the connection between old and new knowledge in teaching, so that students can consolidate their original knowledge and strengthen the formed mathematical cognitive structure in the study of new knowledge. For example, in the mathematics of "dividing by divisor is decimal", it is necessary to highlight the consolidation and application of "quotient invariance" and "integer division law" of division, on the one hand, to promote students to master the calculation method of fractional division smoothly, on the other hand, to prevent students from mastering quotient invariance and integer division law.
3.3 Strengthen practice and review. Practice and review itself is a process of repeatedly recognizing the knowledge learned, which has a strengthening and stabilizing effect on the mathematical cognitive structure initially formed by students. Therefore, in teaching, we should study the process and methods of students' practice and review, grasp the "quantity" and "degree" of practice, overcome the ineffective labor phenomenon such as mechanical repetition in the process of practice and review, improve the efficiency of practice and review, and promote the profound understanding and skilled application of the learned mathematical knowledge.