Reflection on the nature of teaching

Part 1: Reflection on the nature of teaching

The basic nature of learning is that students have mastered the nature of the quotient and the basic nature of the score in the previous study. The sixth grade students have certain reasoning and generalization ability. They can completely based on the relationship between score and division and division. Deriving the basic nature of the ratio, so I fully mobilized the thinking in this lesson, let the students make conjectures - verification, and can use the mathematical language to summarize and summarize the basic nature of the ratio - the previous and the latter Multiply or divide by the same number at the same time, the ratio does not change. This is called the basic nature of the ratio. This lesson has cultivated students' logical reasoning ability and high-level generalization ability of mathematics knowledge in guiding students to sort out mathematics knowledge.
1. After the students reviewed the basic nature of the scores and the nature of the quotients, ask questions in time – what is the nature of the comparison? If so, what do you think of it? When some students are based on the relationship between score and ratio, the relationship between score and division, they naturally guess the basic nature of the ratio—the ratio of the previous and the latter is multiplied or divided by the same number, and the ratio is unchanged. This is called the basic nature of the ratio. In the process of verification, students are guided to analyze, organize, and deduct the specific language expression ability of the verification in the group cooperation exchange. For example, the pre- and post-items of 6:8 are multiplied by 2 to get 12:16. Their ratio is still equal to 3/. 4, so the first part: the ratio of the former and the latter is the same as the same number ratio, and the ratio of the former and the latter of 6:8 is divided by 2 to 3:4 is still the same 3/4 , so the second part: the former and the latter are divided by the same number, the ratio is the same, and if the previous and the latter are multiplied by 0 at the same time, then the ratio formed is meaningless, so Combining the above three conclusions, it is concluded that the former and the latter are multiplied or divided by the same number, and the ratio is unchanged. This is called the basic nature of the ratio. In the students' reporting ideas and processes, the students are very strong! When expressing problems in mathematical language, students consider the issues very thoughtful and logical reasoning is very strict!
Second, when the basic nature of the ratio is simplified, the students' ability to generalize knowledge is cultivated. After finishing the basic nature of the ratio, there are three more representative practices of simplification, so that students can summarize and sort out the simplification method in the process of doing exercises. 15:10 2:0.75,1/6:2/9, after the students finished the communication, they found that there are more than one solution. Through communication and discussion, a set of more practical methods is summarized. 1. When the first and last terms of the simplification ratio are integers, the form of the number of components can be reduced. 2. The decimal is first converted to the integer ratio → the simplest ratio, and 3 is the score can be used to find the ratio. Method simplification. But beware, this result must be a ratio. Most of the students have mastered the above three solutions, saving a lot of trouble in the process of simplifying the ratio, and the efficiency of the exercises is also faster!
It is true that this class has greatly promoted the cultivation of students' thinking, and the effect is also obvious. Many students can also express in a more accurate mathematical language when answering questions, such as 6:8 into a simple ratio. It is 3:4. However, the level of practice in this lesson is not reflected. For example, only the ratio and the reduction ratio are practiced, but there is not enough time to analyze the difference between the ratio and the reduction ratio.

Part 2: Reflection on the nature of teaching

This lesson begins with the students recalling the existing knowledge, and then the analogy and guessing of the basic nature, and then through examples to jointly derive the basic nature of the perfect ratio. In this process, students comprehend the use of old knowledge to learn new knowledge, communicated the connection between knowledge, and cultivated a preliminary analogy reasoning ability. The difficulty in reducing the ratio is the form of the final result, so let the students discuss "what is the simplest integer ratio". The result of making students clear and simplified can only be a ratio, and the items should be mutually qualitative, and then let the students follow this principle, try to simplify the various proportions, so that students can master the initiative of learning, actively explore and complete Learn. Incredibly, when students try to simplify: Some of them divide these two scores into decimals and then simplify them. Some of the former items are simplified except for the latter items. Most students use the method of multiplying 4 before and after. To simplify. Therefore, I asked the students to discuss and compare in time to get the general method of reducing the score ratio.
However, the students are boldly guessing that the basic nature of the ratio is that the former and the latter are both enlarged or reduced by the same multiple. When the ratio is constant, I give the students full affirmation, but they do not compare the students at the same time. Multiplying or dividing by the same number and at the same time expanding or reducing the small difference of the same multiple causes a certain conceptual confusion of the student.

Part 3: Reflection on the nature of teaching

In the basic nature of the lesson, I make full use of the students' existing knowledge, starting with the interaction between old and new knowledge, and analyzing the similarities of them, by letting students associate, guess, observe, analogy, contrast, and analogy. , verification and other methods to explore the law of the "basic nature of the ratio." Since the basic properties of the derivation ratio are used in comparison with the division, the score, the quotient invariant nature of the division, and the basic nature of the score, some lessons are reviewed during the new lesson to guide the students to recall and apply. These two characteristics make the knowledge preparation for the next guess and analogy. Facts have also proved that the success of the paving is conducive to the development of new lessons. Through the analogy with the division, the score, and the analogy, the students quickly introduce the basic nature of the ratio. This saves a lot of time, and secondly, it allows students to initially perceive new knowledge. The whole lesson exemplifies that students are the masters of learning, and the process of students' active exploration is infiltrated from time to time. Whether it is the language description of the basic nature of student comparison or the summary of the method of reduction ratio, students are left behind. Successful footprints. At the same time, it adopts the methods of combining practice, speaking and understanding, comparing and summarizing, questioning and exploring, summarizing and summarizing, mastering knowledge, applying knowledge, deepening knowledge, forming a clear knowledge system, and cultivating students' innovative ability and exploration spirit. The students learn easily and the teachers teach them happily!
Focus on the design of practice questions to enable students to learn actively. The design of exercises should emphasize the ability of students to learn mathematics in mathematics teaching. In teaching, I can grasp the psychological characteristics of students and design some problems that students can easily enter into traps. In these small traps, let students happily master the knowledge and break through the key points and difficulties. For example, when the student draws the law of “the basic nature of the ratio”, I immediately show it: try: the 4:5 item is expanded by 2 times, so that the ratio should be the same, if the latter item should be, if 3:2 The latter term becomes 10. To make the ratio unchanged, the previous item of the ratio should be the two questions. If the student is completed, this basic nature is also understood. Another example: the three examples in the example I showed, all the mistakes that students will appear in the process of simplification are presented, and the mastery of the students' first impressions will help future exercises.
As the saying goes: "Interest is the best teacher." Pupils' fascination with mathematics often starts with interest, from interest to exploration, from exploration to success, generating new interest in successful pleasure, and promoting the success of mathematics learning. . However, the abstractness, rigor and extensiveness of mathematics often make it difficult for students to understand and even discourage. Therefore, the teachers in this lesson start from stimulating students' interest in learning, and guide students to use a series of conjectures to enhance their interest and enhance the fun of mathematics, thus triggering students' desire to explore new knowledge. With the support of interest, the new lessons in the future will be proactive.
In short, in teaching, I focused on the teaching philosophy of “student-based development”, giving full play to the main role of students, making students the masters of learning, and striving to achieve balanced development in terms of innovative spirit, practical ability and emotional attitude, but There are also regrets in the class, in the future teaching to strive to make students more accurate in the knowledge points and concepts.

Part 4: Reflection on the nature of teaching

After teaching the basic nature of the ratio, I kept thinking about a question: students have the most important foundation for learning mathematics: existing knowledge, especially for sixth-graders, in the process of their previous studies, He has accumulated a wealth of mathematical knowledge, although the acquisition of this knowledge comes from the help of others, and some comes from his own perceptions, but no matter what, regardless of its source, since the students have mastered, they have incorporated the existing knowledge of the students. In the structural system, these are indeed objective reality, and as part of the existing knowledge of primary school students constitute a mathematical resource for further learning new knowledge. The New Mathematics Curriculum Standard states: "Mathematical teaching activities must be based on the level of cognitive development and existing knowledge and experience of students." The knowledge that primary school students have is an important resource for students to learn mathematics.
In fact, for primary school students, because they already have a lot of relevant mathematics knowledge, the "new knowledge" in many textbooks is not "new knowledge" for students. Because of this, the essence of mathematics learning that primary school students understand is the process of re-constructing their own knowledge system by interacting with their existing knowledge and new knowledge. The “laws of constant quotient”, “the basic nature of the score”, “the relationship between the score and the division”, and the “basic nature of the ratio” learned by the students are related to each other, so that the students have existing knowledge. On the basis of learning new knowledge, you can achieve twice the result with half the effort.
Therefore, the students' existing knowledge has naturally become an important foundation for their mathematics learning, and thus become a huge resource for us to teach mathematics. The mathematics that these students already have has provided a favorable condition for them to further study mathematics. If the teacher can notice these situations and use the knowledge and science of the students, and combine them with the new knowledge of mathematics, it will have a good effect. Therefore, paying attention to the existing knowledge of students and being close to the actual situation of students is not only determined by the characteristics of mathematics, but also necessary for mathematics learning.
First, guide students to construct concepts through contrast and thinking.
The essence of mathematical constructivism learning is that the subject constructs the meaning of the object psychologically through the construction of the thinking of the object. The so-called "thinking structure" refers to the acquisition of new knowledge in the process of linking the new knowledge with various factors in multiple aspects. By observing specific perceptual materials, students have initially formed the appearance of concepts, and further guided students to compare and think, to link new knowledge with existing appropriate knowledge, and to combine new knowledge with the original cognitive structure. Inclusion, reorganization and transformation constitute a new cognitive structure and construct new concepts. In this lesson, the students are guided to observe the characteristics of the two groups, further inspiring the students to contact the invariant nature and the basic nature of the scores, through thinking, thinking, reorganization and other thinking activities.
Second, apply concepts to solve problems, broaden the way, and develop students' innovative thinking.
The ultimate goal of the learning concept is to apply concepts to solve practical problems. The principle of psychology tells us that once a concept is acquired, it will be forgotten if it is not consolidated in time. Applying concepts to solve problems is actually further consolidating conceptual knowledge. Learning is meaningful only if you apply what you have learned to practice. In this lesson, the basic nature of the ratio is simplified, and there are more than one method. No matter which method is adopted, as long as it conforms to the law, it is fully affirmed. Respecting the students' emotions, attitudes and values, so that students can experience the joy of success, improve their interest in learning, and cultivate students' sense of innovation. Later, comprehensive exercises were arranged. These exercises not only helped to consolidate and deepen the concept, but also cultivate students' ability to analyze and solve problems.

Part V: Reflection on the nature of teaching

The lesson of "Basic Nature of Ratio" is a section of the sixth grade of the National Primary Mathematics. The teaching goal of this lesson is to let students understand the basic nature of the ratio, correctly apply the ratio of simplicity, and cultivate students' abstract generalization ability. The mathematical idea of ​​transformation.
In the previous teaching, I basically made it on the basis of the old knowledge, let the students reasonably guess, self-verify, and finally practice and improve their ability, and achieved good results. Since the practice of the "learning after teaching" model, I feel that such a design does achieve student autonomy to a certain extent, but the essence is that the teacher's thought dominates the student's thinking, and the student is guided by the teacher. Achieve the knowledge of knowledge. Therefore, I made the following attempts.
The first is bold exploration. Let students study the nature of the ratio according to the nature of the ratio and the scores. In the form of fill in the blanks, let the students feel the relationship between the scores and the divisions, and thus the basic nature of the initial perception ratio; then try to simplify. Present three sets of test questions, let the students turn the following ratio into the simplest integer ratio, including a set of integer ratios, a set of decimal ratios, and a set of score ratios. Students independently try and group exchange methods. Then feedback summary. Discussion: What is the basic nature of the ratio? The general method of simplification, and the manifestation of the results. Finally, consolidate the application. The necessary and optional exercises will examine the students' basic knowledge and skills and improve their training.
The design of the four major pieces of content, from the "guide - exploration - total - use" four aspects, allows students to fully participate in the process of knowledge formation, and achieve the "learning after learning."