Double reflection on teaching

Part 1: Reflection on teaching

“Let students learn mathematics in vivid and specific situations” is an important concept of the new curriculum standard. One of the biggest features and advantages of the new textbook is that the introduction of many knowledge and the presentation and solution of the problem are all carried out in a certain situation. Therefore, creating a situation carefully is an important teaching strategy to improve the effectiveness of teaching. However, some teachers only pursue fashion and rack their brains in order to design a “fascinating” “problem situation”, but the result is counterproductive. If this phenomenon is allowed to develop naturally, it will not only affect the quality of mathematics teaching, but also lead teachers to form new and wrong mathematical teaching concepts. So what is the need for effective mathematics teaching?
How is the environment created?
First, the situation should be clearly defined.
A class always has certain teaching tasks, including cognitive skills, mathematical thinking, emotional attitudes, and values. This requires the questions raised by the teachers to be closely related to the teaching objectives, and to be specific and clear, can not blindly ask "What did you find?" On the one hand, we must use mathematical language to refine mathematics problems from the context of life. On the other hand, to fully play the role of the situation, the situation can not be created as a "placement" of classroom teaching.
When I introduced this concept, I first created a situation like this. Today, our students from the second class went to the spring tour. There are many playing projects. We went to rowing, but there were very few boats. We only had three people sitting. Boat, 18 people take a few boats? The students quickly followed your thoughts into the state, and then I said: "There are three people on a ship, that is, one, the multiplication formula is 13, 2 ships, that is, there are two 3, 2 * 3 = 6 or 3 * 2 = 6. The students found the law in the interesting situation and got a preliminary concept.
Second, the context should be proposed from the student's life and realistic background.
Linking the problem situation to the student's life is not only conducive to students' understanding of mathematics problems in the problem situation, but also helps students to experience that mathematics in life is ubiquitous, cultivate students' observation ability and initially solve practical problems. ability.
I designed this in the teaching. Please observe carefully. There are several yellow ships. How many people are there on the boat? The number of green boats is doubled by the number of yellow ships. The number of yellow ships is regarded as one. The number of people on the green ship has two such, and the two 3s also represent twice the number of three. Therefore, the number of people on the green boat is twice that of the yellow ship. The mind here is not coming out of thin air, but from our side, so that students understand that mathematics comes from life and serves life. Moreover, students use different thinking of the same scene map to determine different quantities and obtain different multiplication formulas, which not only cultivates divergent thinking, but also deepens the preliminary understanding of multiplication meaning and multiplication exchange rate.
Third, the form of the situation must be changed.
The form of situation should be diverse, such as problem situation, activity situation, story situation, competition situation and so on. The creation of the situation should be consistent with the psychological characteristics and cognitive rules of children of different ages, and should be changed according to different teaching contents. For children in the lower and middle grades, situations can be created by telling stories, playing games, simulating performances, and visual demonstrations. For upper-class students, it is necessary to focus on creating problem situations that help students to learn independently and communicate with each other. The charm of mathematics itself to attract students.
When I was teaching, I considered that the second-year children were young. I couldn’t sit still after sitting for 20 minutes. So in the end, I used the form of playing games to let the students put out the prepared soybeans and put them on the left. One is a few, the right student must be several times the number of students on the left. Students are able to consolidate and develop new knowledge in a relaxed and enjoyable game.
This will foster the flexibility and divergence of students' thinking and their ability to reason and communicate. Encourage mutual learning between students and share learning outcomes.
These are just some of the strategies I believe in the effective teaching of small and medium-sized teaching. The process of teachers applying effective teaching strategies is actually a creative process, a research process, and the best basic channel for teachers' own development. Let us combine the research materials and teaching practice under the concept of "effective teaching" in the new curriculum, and continuously accumulate and master the effective teaching strategies to make greater contributions to the overall improvement of students' mathematical quality and the development of students.

Part 2: Double reflection on teaching

This is an abstract conceptual lesson - "double understanding". The whole process of the teacher does not take much time, but the students learn to be full and happy. Perhaps it is to follow the cognitive rules of students and meet the psychological characteristics of students.
First, to provide students with a wealth of learning materials "Mathematics Curriculum Standards" pointed out that the way to provide learning materials in classroom teaching should be diverse, can be provided by teachers, but also provided by students, learning materials should be rich, easy for students to carry out Exploration and research. Teachers must first understand the textbooks and dig deeper into the inner meaning of the textbooks. Teachers should make reasonable design improvements based on the concept of “from the textbook is higher than the textbook” and based on the textbook. Therefore, with the beautiful big forest as the background, I designed a situation that is more vivid and more in line with the psychological characteristics of the second-grade children. Introduce two kinds of animals on the green and green grassland, and introduce a new concept--"fold" understanding based on the original knowledge. In the process of student experience, the teacher went with the flow and showed four frogs, eight small fishes, and 12 small birds... to guide students to explore in the scene and perceive in the operation. It can be said that students understand the “double”. It has been quite thorough.
Second, pay attention to the equal dialogue between teachers and students. Teachers are not only organizers and guides, but also older friends and sincere friends. A good math teacher should be good at creating a vivid mathematical scenario, an equal dialogue scenario. Classroom teaching is a “dialogue” in such a situation. Teachers and students not only discuss or communicate through language, but also conduct equal spiritual communication. In the process of dialogue, the students are presented to the teacher as individuals who are independent and complete. The classroom teaching process in this state is a kind of "sharing" for both teachers and students.
The teachers in this lesson sometimes act as “listeners” and sometimes act as “elders” to guide students to listen, communicate and explore. Use "Who can understand, please use the tools to put a pendulum and tell me what I mean." "Don't say the answer, use the tools to set aside, and tell me the idea quietly." Set obstacles for students. To deepen the understanding of knowledge and give students the most effective evaluation... At the same time, teachers always pay attention to the students' thinking trends, generate them in the presets, and change in the generation. The new curriculum standard requires the classroom to give students a modest openness, but it also puts more demands on the teachers. Students are the main body of the teaching activities, play the active role of the teachers, respect the individual's value orientation, and follow the teaching rules. These will always be Classroom teaching enters the preconditions of the mind.
Of course, there are still many shortcomings in this lesson. For example, teachers' classroom control ability should be strengthened, and they need to continuously improve their efforts. The new curriculum reform gives teachers a new stage and puts higher demands on us. Constantly exploring and practicing, we can go further

Part 3: Times of Teaching Reflection

Times, for a new concept for students, students are more familiar with the understanding of the times, and it is difficult to establish a comprehensive representation. Therefore, when teaching, I divided the understanding and problem solving of the times and layered. teaching. The teaching of "The Understanding of Times" can be divided into two parts: one is to recognize times and understand the meaning of times; the other is to solve the problem of "seeking a number is several times of another number".
Students rarely touch "double" in their lives, they are unfamiliar with the times, and they are almost the beginning of a zero. Therefore, my first concern is the student's mathematical reality, based on the students' original knowledge and experience. At the beginning of class, the game was launched. Please ask 2 girls and 6 boys. What do you want to say when you see this situation? After the students tap the quantitative relationship between the two, they go straight to the subject, and the boys have three 2s. In this case, we say that the second row of boys is three times as many as the girls. One of the important ways for students to learn mathematics is to practice it. First of all, with the aid of a tool, there are three rounds, the triangle is twice the circle, and the students may have two triangles; it is possible to put two 3s; It is possible to put two 2s... Make full use of these resources generated by the students, make use of the situation, scientific evaluation, and timely dialing, to determine how much it is. There are several such copies, which are several times, and the use of drawing methods to consolidate the understanding. Use explicit actions to drive the inner thinking activities, abstract the explicit operation process into mathematical expressions, understand and understand the formation and development of new knowledge, and experience the process and methods of learning mathematics so that students can learn Effective development. In the operation, we experience the cognitive process of multiple times, and gradually accumulate and deepen the representation of the multiple. At this time, from the intuitive operation to the abstract line segment diagram, a rational leap in the classroom was implemented, which truly showed the process of knowledge learning that students never learned.
Here, the line graph is the first time in the teaching. The line graph has a very important role in the future study, especially in the middle and upper grades. In the cognitive, it is more abstract from the visual "specific" The transition of the "line segment", which is an effective means to help understand the quantitative relationship and solve the problem. Therefore, when designing the teaching, I will focus on how to look at the line segment diagram and understand the method of the line segment diagram: A line segment represents a quantity, and the two line segments are related, and this connection can be obtained from the information. What is the question mark?
The teaching of this lesson also left me thinking: Mathematics is a rigorous subject, so in the teaching of mathematics, the language of the teacher should be rigorous. Only the accurate and refined language demonstration of the teacher enables the student to accurately describe the problem. In this lesson, some of my language descriptions are inaccurate and not in place. This is not conducive to the formation of accurate mathematical thinking, and it is difficult to achieve the preset goals in the future. Therefore, in the future mathematics teaching, I must pay attention to standardizing my own mathematical language.

Part 4: Double Reflection on Teaching

"Double recognition" is the focus of teaching in the lower grade mathematics class, and it is difficult. The concept of "double" is more abstract, and there is no definition of the concept of "double" in the teaching. Therefore, the concept of "double" should be established in the lower grades. It should be manipulated and compared through a large amount of perceptual materials and observation through self. , thus resulting in a quantitative relationship between the two numbers. This lesson has the following characteristics:
First, the level and slope of the design of the teaching process is reflected.
Beginning with the example, the courseware shows the change of the two butterfly numbers, which causes the change of the multiple relationship, allowing the students to look at the picture and make the students initially perceive the meaning of “double”; then let the students do it themselves and put on the stick. The mathematics is the first level of practice; the second level of drawing, the teacher only draws the first line of graphics, the second line of graphics allows the students to set their own, is several times the first line, by drawing a picture Students deepen their understanding of the meaning of “double”; finally, they designed a context for browsing the zoo, allowing students to solve new problems that are constantly emerging, making students feel fresh and intimate and interested. Throughout the teaching process, the teacher always grasps what to treat as one copy. There are several such ones, which is several times like this, to help students establish the concept of “double”.
This design conforms to the age characteristics and cognitive rules of the students, and reflects the student-centered learning process and cultivates students' learning ability.
Second, attach importance to operational activities and play a major role
Teachers can create opportunities for students to participate in learning with a variety of senses, push students to the main position, let students gain rich perceptual knowledge, and make abstract knowledge concrete and visual. The whole process is well-organized. By speaking, putting a pendulum, drawing a picture, etc., students are allowed to do their hands, brains, and mouths. From participating in the learning process, they are not operating for operation, but operating, understanding concepts, and expressing mathematical principles. Organically combined. Let students look at the graphs they put on the mathematics, reduce the difficulty of mathematical expression, and implement the requirements for burden reduction. Through the operation, the students can learn and understand the knowledge fully, and intuitively establish the concept of “double” to cultivate students' ability to acquire knowledge, observation ability and operation ability.
Third, create a situation, let students experience the fun and practicality of mathematics.
The teacher started from the children's favorite small animals, and the colorful butterfly appeared in the example, which aroused the students' interest. Finally, the storyline with the children's zoo was created. The students were attracted by the colorful and vivid animal shapes, and the students were allowed to use the animal map. "Bei" said a word, mobilized the interest of learning, embodies the fun of mathematics, so that they can feel the mathematics problem from the familiar life experience, appreciate the application of mathematics knowledge, feel that life is inseparable from mathematics and is by my side. Feel the fun and role of learning mathematics.
There are many opportunities to reflect the practicality of mathematics. As long as the teacher grasps the opportunity, the students can fully reflect the practicality of mathematics and cultivate students' practical ability.
4. While studying knowledge, pay attention to the penetration of mathematical thought methods.
Mathematical thinking method is an important part of the implementation of quality education in mathematics. It plays an extremely important role in cultivating students' mathematical thinking ability and improving students' mathematics quality. In teaching, mathematics knowledge is a bright line, which is valued by mathematics teachers. The mathematics thought method is a dark line and is easily ignored by teachers. But the penetration of mathematical thought methods is more important than the knowledge of knowledge, because this is the essence and soul of mathematics. Teach students how to think about methods, learning methods and problem-solving methods, to serve students' future development, and let students leave mathematics consciousness in their minds. In the long run, students will be used for life.
In this lesson, the teacher pays attention to the infiltration of the combination of numbers and shapes while teaching. The perception and understanding of the concept of "double" is started from the graph, so that the extracted concept is visualized, visualized and simplified. To pendulum and painting, it reflects the infiltration of the combination of numbers and shapes, and allows students to be influenced by mathematical ideas in the subtle.

Part V: Times of Teaching Reflection

"The Understanding of Times" is the content of the second volume of the second grade mathematics of the Soviet Union. Double, for students is a new concept, students are relatively unfamiliar with the understanding of times, and it is difficult to establish a representation of multiple times.
The teaching of this lesson can be divided into two parts: one is to recognize the times and understand the meaning of times; the second is to solve the problem of "seeking a number is several times of another number". In the teaching, the first part I pay attention to the students' perceptions, and through the circle painting, let the students learn the multiple relationship based on the difference in the first grade. The second part of the process is through a certain situation, let the students perceive that the number of times is several times the other number can be calculated by division.
Therefore, I paid attention to the operation and observation of students during the design and fully established the visual image. By comparing the quantitative relationship between the number of yellow flowers and the number of blue flowers, the students are guided to put a pendulum, circle, and talk, so that students initially perceive the meaning of "double". The number of safflower is several times that of the blue flower and is given to the students to solve independently. The students can think positively and solve it smoothly. In the teaching, I guided the students to make a second comparison. The first comparison is that the number is the same, so that the students will have several copies of the number, which emphasizes the importance of the number; the second comparison, the number is different, the comparison is the same, the multiple relationship Different, further emphasize the importance of a number.
Students can see from the figure that a number is several times the other, but why it is difficult to understand using division. Here I will guide the students to observe the real thing, to help students explore the algorithm by using "one with two" and "eight can be divided into such a few". This is because this understanding is convenient and in the sense of division. The average score for each of the several requests is linked. Then there are a few in the number, because this expression can more clearly express the relationship between the two numbers compared with "double", so that students can deepen the understanding of the meaning of "fold". After the students have mastered certain methods, practice the consolidation and further understand the meaning of the times. Through practice, consolidate the problem of finding a number that is several times the other number is solved by division. Finally, the game of the flower arrangement allows the students to further understand the “double” in the operation and experience the fun of learning mathematics.
Of course, there are still many shortcomings in this lesson:
1. Students are not thorough enough to understand why they are used to solve such problems.
2. The language of instruction still needs constant tempering.
3. For students, the classroom should give students more time and space for independent exploration.