Basic steps of inquiry teaching in primary school mathematics

Basic teaching mode of primary school mathematics

First, the teaching mode of computing problems

1. Establish the migration direction and lay the foundation for migration.

Teachers should start from the content of this section and guide students to establish corresponding knowledge preparation and psychological preparation. There are two kinds of knowledge preparation in the teaching of calculation problems in primary schools: ① Oral calculation: Teachers can prepare various forms of oral calculation training according to the subject content, such as rushing to answer, answering by themselves, answering each other, etc., which can be carried out by the whole class or by groups or individuals, but we should pay attention to all aspects and let all students actively participate. 2 Ask questions about definitions, laws and calculation rules related to this section. Psychological preparation is to clearly tell students to use prepared knowledge to solve new problems, encourage students and arouse their enthusiasm. Lay the foundation for the smooth transfer of knowledge.

2. Summarize the calculation rules by using the migration law.

(1) Guide the discovery of the internal relationship between old and new knowledge and form a positive migration. First of all, it depends on the same factors between knowledge. Therefore, in this process, teachers should fully inspire students to grasp the similarities between old and new knowledge and lead their thinking to the connection point of old and new knowledge. ② Grasp the essence of old and new knowledge and compare and distinguish. When students find out the internal relationship between old and new knowledge, teachers should put them together, guide students to analyze, grasp the essence, distinguish them and prevent negative transfer. ③ Generalization of calculation rules This is a process of analysis, synthesis, abstraction and generalization. Under the guidance of teachers, stimulate students to speak the calculation rules enthusiastically. One person can't say it all, and other students can add it. On this basis, the teacher summed up the correct calculation rules.

3. Try to calculate rules to deepen knowledge understanding.

After the teaching, teachers carefully design various forms of exercises around the teaching objectives, so that students can try to use the calculation rules, find mistakes through practice, and teachers can promptly guide and correct vacancies. 4. Consolidate the calculation rules and summarize the teachers' evaluation.

Closely related to the teaching content, teachers let students independently complete exercises with moderate difficulty, and at the same time prepare difficult thinking questions for students who can master them quickly. Through collective correction, it is required to correct and comment on common mistakes in time.

Second, the application of problem-based teaching mode

Generally, the procedure of the classroom teaching mode of mathematics application problems in primary schools is "review and lead-in, understanding new knowledge, practicing and consolidating, testing feedback, correcting and summarizing" (1), which is the initial link of teaching. Teachers can organize students' learning according to the key old knowledge and key skills needed to learn new knowledge, clear obstacles for learning new knowledge, create situations and push students to the contact point of old and new knowledge. Promote the positive transfer of knowledge. (2) Understanding new knowledge is divided into four steps: understanding the meaning of the question, analyzing the quantitative relationship, table calculation, checking and answering. A. To understand the meaning of the question, we should teach students to read the question: read and reason. Let the students know what is said in the topic, and guide them to find out what is known and what they want in the topic. Read and repeat the meaning of the question for the second time, and ask the students to tell the general idea of the topic, focusing on the quantitative relationship, so as to prepare for the analysis of the quantitative relationship. B. Analysis of quantitative relations When analyzing quantitative relations, due to different thinking processes, it can be divided into comprehensive method and analytical method. The former is from condition to problem, that is, "from cause to effect", while the latter is from problem to condition, that is, "from effect to cause". For application problems with simple content and direct quantitative relationship, the comprehensive method is usually used for analysis. The application problems with complex quantitative relations are usually analyzed by analytical method. Of course, in many cases, the analysis of compound application problems adopts the method of "analysis and synthesis". In teaching, we should find the dependence between known numbers and unknowns through analysis and determine the order of operation. C. Formulaic calculation On the basis of clarifying the quantitative relationship, judge the calculation method of each step according to the concept of four operations, and list the formulas. Choosing algorithm and establishing formula are the most important and critical steps to solve application problems. Therefore, teachers should pay special attention to the basic training of problem-solving ideas and methods, flexibly use a variety of methods to analyze and solve, and find a simple and easy-to-use method. D. checking calculation and answer checking calculation methods, one is to comprehensively review the meaning and calculation process of the formula according to the meaning of the question. Another method is to adapt the calculated number as a condition and a condition as a problem into a new application problem. After solving, see if the calculation result is consistent with the original number, and write a reasonable answer under the condition that the whole formula and calculation process are all correct. (3) After consolidating teaching, design multi-level, multi-angle and multi-form exercises for students to practice, and the designed exercises should be inspiring and interesting. (4) The drafting of the test feedback questions should closely follow the requirements of the teaching materials in this section, with appropriate difficulty, not exceeding the teaching materials, and pay attention to the coverage. At the same time, it is necessary to prepare difficult thinking questions for students who study well, reflecting the teaching of students in accordance with their aptitude. ⑤ Various methods are adopted for rectification, summary and correction. First, organize students to evaluate in groups, teach and learn from each other, and cultivate students' self-evaluation ability; The second is the teacher's evaluation, which uses * * * for key issues and problems; The third is to give face-to-face guidance to individual students with problems. In short, we should correct the vacancies in time and "clean the classroom".

Third, the "concept" teaching model

Basic procedures: introduction of concepts-formation of concepts-consolidation of concepts-development of concepts 1. The introduction of concepts mainly adopts the following methods: ① Introducing concepts from reality, that is, starting with things familiar to primary school students. ② Introduce new concepts on the basis of old concepts. When the old and new concepts are closely related, it is not necessary to start with the original meaning of the new concept, but only to extend from the concepts that students have learned and guide them to acquire new concepts. ③ Introducing new concepts through calculation.

2. The form of concept should be based on the introduction of concept and sufficient perceptual materials, and guide students to grasp the essence and laws of things through logical thinking activities such as comparison, analysis, synthesis and abstract generalization, thus forming concepts. ① Provide necessary perceptual materials as the material basis for the formation of concepts; ② Guide students to abstract and summarize, and find out the essential attributes of all materials; ③ Prompt the connotation and extension of the concept.

3. Consolidation of concepts Once the concept of teaching is formed, we should pay attention to its application in practice, that is, consolidation and concept application, which is a process from abstract to concrete. ① Consolidate concepts in application Teachers should carefully design exercises to guide students to consolidate concepts. The types of exercises are as follows: A. Exercises for applying new concepts B. Exercises for key problems C. Exercises for this D. Discriminating exercises E. Error correction exercises ② Bringing the old with the new, reflecting the comprehensive attention of exercises, which can not only cultivate students' ability to analyze and solve problems with the help of comprehensive exercises, but also guide students to learn, review and consolidate old concepts.

4. The development of concepts After students master a certain concept, it does not mean the end of concept teaching. They should teach concepts from the perspective of development. (1) loses no time in expanding the meaning of denotative concepts. A concept is always embedded in some concept groups, and there are criss-crossing internal relations between them, which must be clearly expressed. (2) to form a certain stage of understanding, abstract concepts can not exceed the requirements of teaching materials, otherwise it will exceed the students' tolerance.

Fourth, the teaching mode of law (nature)

1. All the perceptions of guiding observation are selective, and the selectivity of students' observation is restricted by the observation tasks put forward by teachers. Students should make clear the task of observation before observation, so that students will be highly focused when observing and get a relatively complete and clear representation when observing things. It is convenient to grasp the essential characteristics of things.

2. Through the comparative analysis of practice and observation, students get a clearer representation, and then further improve their own requirements. They first say the formula according to the specific numbers, and then say the law (nature) in concise words. This is not only a process of understanding the teaching relationship, but also a process of training and generalization, and the two processes promote each other. 3. Summary Through the above comparative analysis, and on the basis of the previous observation and sentiment, students can sum up the law (nature) and receive the effect of turning the stone into gold as long as they make a little comparative analysis of the examples.

4. Consolidate exercises ① Basic exercises Students master the law (nature) by observing and comparing examples, then strike while the iron is hot, and then design some basic exercises and comprehensive exercises for the law (nature) to further consolidate, so that students can form skills and skills to solve practical problems. (2) Variant exercises Students have mastered the law (nature) through the training of basic exercises and comprehensive exercises. On this basis, some variant exercises are appropriately added, so that students can master the law (nature) flexibly and tell the basis of operation, so as to achieve the teaching effect of drawing inferences from one instance to another.

5. Testing and marking ① Closely follow the teaching materials, draw up testing questions with moderate difficulty and highlight key and difficult points, and mark papers in groups. (2) teachers should correct problems in the classroom and make a summary.

Fifth, the teaching mode of geometric quadrature calculation

First explain the goal, cultivate the mood, check the learning tools and blackboard writing topics, and then teach in six steps. 1. Intuitive understanding, forming a representation. Intuitive understanding generally refers to three kinds: intuitive objects, intuitive images and models, and intuitive visual language. In teaching, we should pay attention to let students operate, touch, teach, pose, stack, spell, cut, draw and do. Let students have a variety of senses in their eyes, brain, hands and ears, actively participate in them, and let students form a certain perceptual knowledge with curiosity and interest.

2. Knowing the diagram and mastering the essential diagram is an important part of intuitive teaching, and it is also a bridge between concrete and abstract, which requires the basic premise of product calculation. Therefore, students are required to learn to read drawings, or master the essential attributes of different shapes according to the corresponding meanings of drawings, and can meet the requirements of checking the number of drawings and objects, laying a good foundation for drawing calculation.

3. Derive formulas and answer examples. In order to enable students to master the formula, remember the formula firmly and use the formula accurately, students should use their brains, move their mouths and hands, actively participate in the derivation of the formula and describe the origin of the formula widely. Teachers should give proper guidance and emphasize key points, so that students can truly understand the internal relations and differences among various forms. On this basis, they can use formulas to answer examples and then further consolidate or ask questions.

4. Practice consolidation, respectively, to guide the content of classroom exercises to closely follow the knowledge points of examples, pay attention to various forms, gradient, ideological and interesting.

5. Examining and testing, independently completing the in-class test, can timely feedback students' achievements in mastering new knowledge, thus tracking vacancies in a targeted manner. The content of the exam should not exceed the textbook, and the amount of questions should be completed by middle school students. Excellent students should add thinking questions, and poor students can only list them. Teachers can tour to know the situation, and students can do it independently.

6. Feedback correction, evaluation and summary. The teacher announced the answer, asked the students to exchange test papers, and guided and corrected individual students who made mistakes. Or extra tutoring in self-study classes. Then make a summary and generalization of the knowledge in this section, give encouragement and put forward hopes and requirements.

VI. Teaching mode of law

1. Directional thinking ① Knowledge-based teachers grasp the relationship between the laws according to the laws they have learned, make use of students' existing knowledge, prepare review questions, and pave the way for learning new knowledge. (2) Thinking orientation is closely related to the essence of new knowledge, giving students a clear thinking range. Thinking orientation can be started from three aspects: a. Grasp the orientation of the connection between old and new knowledge. B. Create problem orientation C. Use rules to transfer orientation ③ Goal orientation: Show the teaching objectives of this lesson.

2. Explore new knowledge ① Prompt topic: Stimulate students' desire to explore new knowledge ② Research and calculation A. Provide students with enough materials to guide them to analyze and study one by one. B. In the process of analysis and research, teachers mainly grasp the contact point of old and new knowledge and the turning point of thinking, and guide students to calculate their own theories. C. Generalization law After analyzing and studying all the materials and completing the calculation, students should contact the actual calculation and summarize the generalization law. A. Strengthening memory After the students' language summary, the teacher will show the rules and regulations to strengthen the students' memory.

3. The skills and skills of forming skill mastery calculation must be realized through practice, and the following forms of practice can be adopted. A. single exercise, focusing on breaking through the key points of the law. B. imitation exercise: the topic is similar to the example. C. Counterexample exercise: Show the wrong questions and let students judge, correct and reason. D. Compare some related laws and find out the similarities and differences. E. Regular practice: complete a certain amount of practice within the specified time.

4. Summarize the learning content of this section, evaluate students' learning situation, and put forward hopes and requirements for students.