In this lesson, I set my knowledge goal as: let students deeply experience and understand the derivation process of triangle area calculation formula in inquiry activities. The goal of ability is to gradually cultivate students' ability of induction, reasoning and language expression in hands-on activities. The goal of emotion and will is to stimulate students' interest in learning mathematics, learn the methods of learning mathematics, and cultivate students' team spirit through group cooperation.
In the whole class, I pay attention to caring and caring for every child from every detail. For example, after revealing the topic, I will investigate the students: which students know the calculation formula of triangle area; Which student doesn't know the calculation formula of triangle area; In addition, students should not only know the formula of triangle area, but also know how the formula is derived, so as to understand the student's knowledge base and help him complete the learning process better. If he is the first to answer, I will praise him. He can learn knowledge not only at school, but also by surfing the Internet and reading books. If he is the second answer, I will tell him, it doesn't matter, this is new knowledge, you can learn it as long as you work hard; If he is the third answer, I will encourage him to continue to strive for higher goals. In short, let different children learn different mathematics as much as possible.
When deducing the calculation formula of triangle area, two operations are arranged. First, let the students spell out two identical triangles to see what figures they can spell out, and then guide the students to think and discuss: What is the connection between triangles and your parallelogram? Guide the students to find that the area of each triangle is half that of the parallelogram, and then let the students try to convert a triangle into a learned figure and deduce the area formula of the triangle. Through two practical activities, students personally participated in the derivation process of the area formula, and truly achieved "knowing why, knowing why", and their thinking ability, spatial feeling ability and hands-on operation ability were exercised and improved.
In this class, students are independent and open in the exploration of triangle area calculation formula, which makes them experience "re-creation" However, there are some shortcomings in the teaching of this course. For example, the participation in the second operation is not wide enough. Some students have a triangle in their hands, and they don't know how to start, and they just passively accept it in the process of derivation and verification. If they are allowed to fully operate and experience, time is not allowed. How to solve this contradiction is also a problem that we need to reflect on.
Reflections on the second part of the teaching of triangle area calculation mathematics In this section, I want to talk about the teaching ideas and some thoughts of this class in combination with the design and research of exploratory problems.
I think there are two aspects in the design and research of inquiry questions. One is the teacher's careful design of questions, and the other is to cultivate students' ability to ask questions. Teachers explore with students as collaborators and guides, and experience the process of acquiring knowledge, so as to achieve the purpose of inquiry. In view of this understanding, this class has made such a design under the collective preparation of the members of our research group. This lesson is mainly to let students feel the fun of learning, carefully design questions, and let students actively explore knowledge and develop their thinking.
The content of this lesson is based on the calculation of parallelogram area, mainly through the derivation of triangle area formula, to guide students to understand and master the triangle area calculation formula. Therefore, in teaching, I pay attention to students' hands-on operation, master methods from operation, find problems and solve problems.
First, hands-on operation, using the pendulum method to understand the triangle area calculation formula.
In teaching, I let students operate, put three groups of two identical triangles into a parallelogram respectively, and compare the relationship between each triangle and each part of the parallelogram. At the same time, the method of rotation and translation is infiltrated into students in the operation, so that students can experience and perceive the derivation process of triangle area formula. In this process, students showed great interest, and they were all very active and devoted to the operation, which greatly mobilized students' thinking activities. Students really become the main body of learning.
Second, guide students to find and think about problems and cultivate the spirit of cooperation.
In this lesson, we discuss the difference between the parallelogram area formula and the triangle area formula, and how did the "divide by 2" in the triangle area formula come from? When discussing this problem, I adopt the way of group discussion, and find and solve problems in the discussion, which can not only cultivate students' cooperative spirit, but also enliven the classroom atmosphere.
Third, cultivate students' creative thinking through cutting and folding.
Students have experienced the derivation of parallelogram area formula, and the formula of learning triangle area will be transferred to learning triangle area with the experience gained in the derivation of parallelogram area. When discussing how to transform a triangle into a learned figure, some students use the cut-and-fill method learned in parallelogram to transform a triangle into a rectangle, some into a parallelogram, and some fold out two rectangles. Students' thinking has been activated, and every student is actively participating and thinking seriously. The students' enthusiasm for learning is unprecedented, and I fully feel the students' strong enthusiasm for inquiry.
I feel that when exploring the calculation of triangle area, let students explore with several pairs of identical triangles cut out at the back of the book, and then communicate with each other in class. Students spell out a parallelogram with two identical triangles, and easily deduce the area formula of the triangle from the area formula of the parallelogram: S=ah÷2. On the surface, the students started to operate, but in fact, the students were just led by the teacher. Students do not actively think, guess and create. Why do you spell with two identical triangles? Are there any other derivation methods? "Without thinking. The materials provided in this way have low thinking content, which is not conducive to showing the process of knowledge generation, missing the process of students actively looking for materials, and affecting the cultivation of students' awareness of problem-solving strategies. This kind of operation is superficial and does not play a role in promoting students to construct knowledge.
Reflections on the third part of the teaching of triangle area calculation mathematics; the area of triangle is taught on the basis of students' learning parallelogram area. This lesson allows students to explore and experience the process of deriving the triangle area formula independently in actual situations. The area formula of triangle can be used to calculate the area of related figures and solve practical problems.
Before teaching, I asked students to preview 25 pages of textbooks, find out what they don't understand, and get a preliminary understanding of the relationship between triangles and parallelograms. And cut out two identical triangles for further study.
In the teaching process, I arranged for students to spell out two identical triangles first to see what figures they could spell out. It is easy for students to know that they can spell a parallelogram with figures. Some students can spell a rectangle with two right triangles and then spell a parallelogram with another spelling. Through hands-on operation, students learned that triangles can be spelled into rectangles and parallelograms.
The most important thing is to let students think about the relationship between the base of parallelogram and the base of triangle, and the relationship between the height of parallelogram and the height of triangle. In this important link, I organize students to look at the spelled graphics, think first, and then express their ideas. The students had a heated discussion, talked with triangles while gesticulating, and finally came to the conclusion that two identical triangles can be combined into a parallelogram. The base of this parallelogram is equal to the base of the triangle, which is higher than the height of the triangle. The area of the triangle is half that of the combined parallelogram.
Seeing the students' hands-on operation, brainstorming and enthusiastic communication, I know that the students really participated in the process of exploring knowledge, their thinking was opened, their desire to explore was activated, and their interest in learning was improved.
Besides two identical triangles forming a parallelogram, is there any other way to turn a triangle into a parallelogram?
This time, many students were puzzled. When they started cutting, they also found that they couldn't spell parallelogram. Finally, they found that they could spell out a parallelogram by cutting along the middle line.
Through students' independent exploration, this paper explores the formula for calculating the triangle area by using the methods of transformation and shearing;
Triangle area = base × height ÷ 2
Expressed in letters: S = a h ÷ 2
In this lesson, students learned how to transform a triangle into a parallelogram by using transformation method and cut-and-fill method, and deduced the calculation method of triangle area, which cultivated students' ability of independent exploration, cooperative communication and solving problems by using various methods.
Reflection on Mathematics Teaching of Triangle Area Calculation Part IV "Triangle Area Calculation" This course is based on parallelogram area calculation, mainly through the derivation of triangle area formula, to guide students to understand and master the triangle area calculation formula, and to use the triangle area formula to calculate the area of related graphics and solve practical problems. According to the requirements of new curriculum and new concept, teaching should be changed from simple teacher teaching to guiding students to learn to learn. Therefore, in teaching, I pay attention to guiding students to operate by themselves, mastering methods from operation, finding problems and solving problems.
The first teaching goal of this lesson is to let students express the derivation process of triangle area formula in their own language in the activity of deducing triangle area formula. In addition to setting knowledge goals, it is more important to cultivate students' ability, so this lesson not only allows students to calculate the area of triangle, but also pays more attention to cultivating students' ability to communicate, cooperate and learn with others. Let students learn new knowledge and skills through cooperation and communication with others. Finally, in terms of emotional goals, let students feel that mathematics is closely related to our lives.
I will let students explore the calculation formula of triangle area independently, prepare several pairs of triangles in advance, and explore the calculation formula of triangle area. According to their own understanding, students quickly explore the calculation formula of triangle area. Every student in the group is the protagonist and can express his own opinions, so that the students' personality can be developed.
Next, I ask students to communicate and report according to the three categories of triangles. Students quickly come to the conclusion that no matter what kind of triangle it is, the formula for calculating the area is the base multiplied by the height divided by 2. So far, has the learning task been completed? It is easy for students to learn this part of the content on the basis of the previous class. If they get here, won't they stand still? At this time, I threw out a new question: Can triangles be cut into parallelograms or rectangles? Students experience the happiness of success in the first half of the class and devote themselves to the study of new problems with strong interest.
Later, students found through operation that the base of the newly cut parallelogram is half of the original triangle and the height is the original height, so the area of the new parallelogram is half of the triangle base multiplied by the height, that is, S triangle = base ÷2× height. Experiments show that it can also be S triangle = height ÷2× bottom. The students are very happy. They know how to use the characteristics of numbers flexibly to calculate the area of triangles. For poor students, mastering these three numbers, as for the positions of these three numbers, can be flexibly discharged and calculated more easily.
Reflections on Mathematics Teaching of Triangle Area Calculation Chapter 5 "Triangle Area" is a regular course. There are many teaching plans about this course, and I have also listened to many classes. How to embody "renewing ideas, laying a solid foundation and living in thinking", I think the teacher's grasp and handling of teaching materials in the past is very good for the design and handling of the classroom, and this lesson makes me feel deeply.
1, in line with the concept of new curriculum reform, highlighting the development of students and rationally designing the teaching process.
Previous teaching only focused on students' double-base training, ignoring the process of knowledge generation. However, all the designs of this class focus on students' thinking and ability to analyze problems. The whole class reflects students' active participation, willingness to explore and hard work, and cultivates students' ability to acquire new knowledge, analyze and solve problems, as well as their ability to communicate and cooperate. The teacher put the whole learning process on the students, let the students cooperate in groups and the whole class participate.
2. Try to cultivate students' divergent thinking.
Open inquiry learning should not be bound by anyone, but should be guided by teachers at all levels. In the design of this class, teachers pay attention to the openness and thinking of teaching materials, and constantly encourage students to think and explore different methods, so that students have the right to choose independently and broad thinking space, and combine independent thinking with group cooperation. In the process of mutual communication, they sum up the triangle area formula themselves, and students show themselves in the operation activities. The methods are diverse and unique, which are not found in previous teaching, and the effect is very good. Create a teaching environment, guide students to actively participate, stimulate students' enthusiasm for learning, cultivate students' attitude and ability to master and use knowledge, and make every student develop in an all-round way.
3. Building a harmonious new teacher-student relationship
In this course, the teacher gives students many opportunities to think, practice and communicate. Teachers play the roles of organizers, guides and collaborators, and give full play to students' main role, which better reflects that teachers are the guides of students' learning and guide students to explore and collide with each other around the core of the problem. It fundamentally changed the traditional teaching mode, made students have a deep understanding of knowledge, and also cultivated their spirit of exploration and innovation. Expanding students' space in mathematics teaching activities.
To some extent, this case reflects the need to change traditional teaching methods and implement new curriculum reform. The most fundamental thing is the change of teachers' role, the change of teachers' teaching and students' learning in the traditional sense, and the continuous formation of mutual teaching and learning between teachers and students, forming a "learning body" with each other. In order to further stimulate students' potential and make their discussion and thinking more valuable, each of our teachers should keep learning and improve their personal quality, so as to design better teaching links and let teachers and students grow together!
Reflections on Mathematics Teaching of Triangle Area Calculation Part VI "Triangle Area Calculation" This course is based on parallelogram area calculation, mainly through the derivation of triangle area formula, to guide students to understand and master the triangle area calculation formula. According to the requirements of new curriculum and new concept, teaching should be changed from simple teacher teaching to guiding students to learn to learn. Therefore, in teaching, teachers should attach importance to students' hands-on operation, master methods from operation, find problems and solve them.
First, hands-on operation, spell a spell.
Creative use of teaching materials in teaching, I let students operate separately, three groups of two identical triangles are spliced into a parallelogram, and the relationship between each triangle and the parts of the spliced parallelogram is compared. At the same time, the method of rotation and translation is infiltrated into students in the operation, so that students can experience and perceive the derivation process of triangle area formula. In this process, students showed great interest, and they were all very active and devoted to the operation, which greatly mobilized students' thinking activities. Students really become the main body of learning. This is the place where this class is more successful.
Second, guide students to find and think about problems and cultivate the spirit of cooperation.
In this lesson, we discuss the difference between the parallelogram area formula and the triangle area formula, and how did the "divide by 2" in the triangle area formula come from? When discussing this problem, we can use group discussion in the future, and find and solve problems in the discussion, so the teacher should not interfere. Group discussion can not only cultivate students' cooperative spirit, but also enliven the classroom atmosphere.
Third, applying formulas to solve problems in life The new curriculum attaches great importance to students' experience in activities and emphasizes students' immersive experience.
Let the students use the triangle area formula to solve practical problems. This is not enough in this course. When time permits, add some examples from life, so that students can taste the joy of applying knowledge and push the classroom atmosphere to a climax. In addition, in the teaching process of this course, I found my own shortcomings in the usual teaching methods. For example, when students answer questions, it is easy for junior students to fish in troubled waters, which is not conducive to showing students' personality characteristics. We should pay attention to avoid using this method in teaching in the future.