Reflections on the Teaching of Pythagorean Theorem 1 This lesson focuses on introduction and arouses students' interest. Now let's talk about reflection in this lesson:
1. Life-based teaching makes students feel the joy of learning.
In the course of Pythagorean Theorem, we first introduce the scene:
Pingping Lake is clear, and the lotus is half a foot above the water.
Suddenly, there was a strong wind and lotus water.
The lake is no longer visible, and it was discovered by fishermen in autumn.
The flower is two feet away from the root. How deep is it?
Knowledge aftertaste: review Pythagorean theorem and its formula deformation, and then several simple calculations.
2. Walking into life: Taking decorating the house as the main line, designing whether the wooden board can pass through the door frame, how much the bottom of the ladder slides out, and finding the shortest distance for ants to climb are typical examples of the application of Pythagorean theorem.
3. When using Pythagorean theorem in teaching, students always use formulas to calculate, which makes them feel bored. In order to attract students' attention, enliven the classroom atmosphere and broaden students' thinking, a thinking problem put forward by "Grandpa Wisdom" is displayed with multimedia: the problem of bamboo breaking and falling to the ground. And the problem is displayed in the form of animation, which not only visualizes the problem, but also improves students' interest in learning. At the same time, the process of transforming practical problems into mathematical problems is represented by intuitive graphics, which reduces the difficulty and encourages students to see the mathematics around them, so as to apply what they have learned. Finally, let students discuss with each other, let students solve problems in an open and free way, and cultivate cooperation among students.
4. Finally, the history of Pythagorean Theorem is introduced, and some websites are recommended for students to consult after class. This is to facilitate students to search for knowledge treasures in a broader ocean of knowledge, use the Internet to retrieve relevant information, enrich and expand classroom learning resources, and provide various learning methods so that students can learn to select, organize, reorganize and reuse these broader resources. This reorganization of network resources makes students' demand for knowledge from narrow to wide, which effectively promotes autonomous learning. In this way, students can not only learn knowledge in class, but also give them ways to learn knowledge. This has achieved the predetermined goal of the new concept of the new curriculum standard.
Through the teaching of this course, students can feel the mathematical ideas of "combination of numbers and shapes" and "transformation" in Pythagorean theorem learning, and realize the application value of mathematics and the convenience brought by infiltrating mathematical ideas to solve problems; Feel the power of human civilization and understand the importance of Pythagorean theorem. Really achieved the self-study of stimulating interest first, then cooperating and communicating, and finally showing the results. This course integrates information technology into the classroom, which is conducive to creating a teaching environment. The teaching mode will be changed from teacher-centered teaching to students' brainstorming, group learning and discussion, and the mathematics classroom will be changed to? "Math Lab", students draw conclusions through their own activities and cultivate innovative spirit and practical ability. Disadvantages: students' sense of cooperation is not strong and the discussion atmosphere is not active enough; Unskilled in calculation and irregular in writing.
Teaching reflection on Pythagorean Theorem 2 Through review, students can fully recall what they have learned about triangles and deepen their understanding of knowledge, thus laying a good foundation for the study of this lesson. At the same time, the process of students' memory is also the process of thinking, especially the area method to verify Pythagorean theorem is the difficulty of this chapter. Students should form impressions and concepts in order to learn and master them well.
It is known that two right angles in a right triangle find the hypotenuse, which was the content of last class. In the last class, the students had already practiced. But why do some students still make mistakes in this course? The reason is that there are too many contents and methods in the last class, so students still have perceptual knowledge of every content and method, but they still have not reached the level of understanding and mastering. Therefore, when students are allowed to complete problems independently, their thinking is often insufficient, which leads to various mistakes. On the other hand, in teaching, we often take the form of "one question and one answer", so it is easy to cover up students' real thoughts. In fact, when answering this question, it is easy for the teacher to walk into such a question-and-answer way, because we think such a question is too simple, and students seem to have learned it in the last class, which leads to a neglected teaching. But the reality is often not the case. We believe that simple knowledge is often not simple for students (especially those with weak foundation). Therefore, the question-and-answer method of deceiving teachers should be used as little as possible in teaching, so that students can fully express their opinions, and at the same time guide students to analyze their mistakes and cultivate a sense of reflection. Only in this way can students really learn something.
Different variants of the same question can make students check whether they can really understand, master and use knowledge and methods, thus improving their self-confidence in learning. The solution to this problem is actually the area method, which is used to verify Pythagorean theorem. At the beginning of classroom teaching, students have a preliminary impression of the memory method of the last class, so if they mention it here again, students will not feel sudden and strange, which plays a connecting role. On the other hand, when explaining the answers to questions, teachers don't tell all the methods and processes of answering questions at once, but guide students to think step by step, so that students can get the answers to questions in their own thinking and perception, which can cultivate students' thinking methods and improve their thinking ability. It will be better if we can praise the students who have finished answering and let them guide them to answer the remaining questions.
Life mathematics problems, using mathematics knowledge to solve practical problems in life, are the contents that must be implemented in mathematics classroom teaching after the curriculum reform. When answering questions in real life, the key is to turn life problems into mathematical problems and make life problems mathematical. In this process, teachers often need to help students understand and transform, and more often, students need to explore and try themselves to find successful methods in failure. In the teaching of this topic, it will be better if students can reflect on the rationality of their answers and methods. Pre-class presupposition and classroom generation,
This is one of the most common problems since the curriculum reform. Complete the task of classroom teaching, return the classroom to students, and let students give full play to their autonomy. So how to deal with this problem? In the last part of this class, if we can guide students to sum up their methods, especially the area method, and then make a simple question to consolidate it, then the effect will definitely be better than the class in such a hurry. But when will this knowledge be solved? Can we not solve it? This is a problem that bothers me after class. "Classroom teaching should be based on the specific conditions of students in their own classes. Whether it is pre-class preparation (preparing lessons) or classroom teaching process, it should be based on the premise that most students can really learn and master. " After the teaching of this class, I have such an understanding of effective classroom. On the question of "knowledge-centered" or "students' learning-centered", I think we should take students as the center and give consideration to the completion of teaching content. If there are contradictions, then I think we should still take students as the center. What if I can't finish the teaching task like this? What should I do to affect the teaching progress? What about the exam? ..... In fact, after all, what should I do after the exam? Curriculum reform has reached its seventh year. Examination is always a tangible and intangible baton, which affects our teaching in every class, our teaching ideas and methods, and even our teaching ideals. In fact, we all know very well that although such a hasty classroom teaching seems to have completed the teaching content, in fact, students have not mastered it well, and when the exam really appears, students still can't answer it. So, isn't this teaching also invalid? Is ineffective teaching a waste of students' energy and time? Isn't this a little self-deception? The more I think about it, the more I feel uneasy.
Therefore, if I have the opportunity to take this class again, even if I can improve efficiency and save some time, I will leave out the latter part, add some interesting life problems, and summarize the methods of reflecting on this class, so that students can better master this class and have more confidence in their math learning.
Teaching Reflection on Pythagorean Theorem 3 In the first lesson of Pythagorean Theorem, the standard experimental textbook for compulsory education, the focus of the textbook is to let students experience the exploration and proof process of Pythagorean Theorem, understand the background knowledge of Pythagorean Theorem, feel the rich cultural connotation of Pythagorean Theorem while learning knowledge, stimulate students' interest in learning, and carry out ideological and moral education for students.
In the lecture, students are not allowed to prepare learning tools because they are not carefully prepared, so in the classroom, students are only allowed to use the graphics in the book to explore. The proof of Pythagorean theorem is only spelled out by four congruent right triangles, and the conclusion is drawn by different representations of the same figure. In one class, the memory and application of the conclusion of Pythagorean theorem were emphasized, but the exploration and proof process of Pythagorean theorem in textbooks were ignored. Results Only a few students in the class learned the method of exploring and proving Pythagorean theorem, and the teaching effect was not good.
It wasn't long after the lecture, because I had to take part in the quality class competition, so I prepared my lessons carefully. According to the task requirements of the textbook, I designed the teaching process of this lesson like this:
1, enjoy pictures and stimulate interest.
By appreciating the emblem pattern of the International Congress of Mathematicians held in Beijing, China in 2002, this paper introduces "Zhao Shuangxian's Picture", so that students can understand China's brilliant mathematical achievements in ancient times and introduce the subject.
Next, let the students enjoy this legend: It is said that Pythagoras, when visiting a friend's house 2500 years ago, found that the brick floor of his friend's house reflected a certain quantitative relationship between the three sides of a right triangle. Let the students understand through stories that most of the great achievements of scientists are discovered and studied in seemingly insignificant phenomena; There is mathematics everywhere in life, so we should learn to observe and think, and combine study and life closely.
On the one hand, it stimulates students' curiosity, on the other hand, it also cultivates students' learning methods and problem-solving ability.
2. Analyze and explore, and get a guess.
By exploring the relationship between isosceles right triangle and general right triangle in floor graphics, students can experience the exploration process from special to general and learn this research method.
In this process, students make full use of learning tools to try to solve problems, try to let students explore by themselves, communicate in groups first, then communicate with the whole class, and try to learn more methods.
3. Prove the puzzle and get the theorem.
Understand Zhao Shuang's proof thinking first, and then let students cut and paste and spell with learning tools, and prove with graphics.
Because it is difficult, students are organized to study in groups. Teachers should make itinerant tutoring and give students the necessary help.
4, reflection and induction, summary and sublimation
First, let the students review and summarize the gains of this section. (Of course, most of them are specific knowledge and methods). Second, teachers should guide students to learn from scientists' keen observation and diligent way of thinking, constantly improve their mathematics literacy and educate everyone in time.
5, practice consolidation
Mainly practice other proof methods of Pythagorean theorem.
6, homework design
Please use the proof method of Pythagorean theorem of network resource collection to learn. Write a small paper about Pythagorean Theorem, which can be used to participate in the "Little Scientist" innovation competition in the city. A month has passed, and I have forgotten this special assignment, but some students have written unexpected compositions.
In the quality class, not only multimedia courseware is made for the inquiry content in the textbook, but also inquiry graphics and jigsaw puzzles are prepared for each student. In the classroom, students participate in classroom activities through their own attempts, group exchanges and cooperation, and concentrated results display. Although the knowledge has been talked about, in the trial lecture (students in our class) and the competition (students from other schools attend classes), because this time students are allowed to explore and acquire knowledge, students generally participate, have a strong interest in learning, have a high enthusiasm for participating in activities, have a clear task of group division of labor and cooperation, and have a good classroom effect. While mastering knowledge, students really experienced the whole process of inquiry, gained a deep understanding of scientists' keen observation and diligent way of thinking, learned some new inquiry methods, and were also educated and enlightened ideologically. The classroom teaching goal has been successfully completed, and there is no trace of "familiar class" students who don't want to go to school.
Through the two different teaching methods of this course, as well as the different performances and gains of students, I have a deeper understanding:
(1) Only by fully infiltrating the concept of new curriculum reform into education and teaching work and closely combining it with normal work can students' all-round development be promoted;
(2) Teachers should make full use of the classroom content to serve the overall curriculum objectives, not just the knowledge objectives and requirements of this class, and "teach" knowledge in knowledge, but acquire the methods of learning these knowledge through knowledge learning, and at the same time make full use of the classroom to educate students' emotional attitudes and values, so as to truly make the teaching materials become the materials for educating students, rather than the whole subject teaching;
(3) Believe in students' ability and create opportunities for students to learn and create themselves (such as arranging open learning tasks: mathematical practice, research study, writing small papers, etc.). I believe that as long as we insist on doing this, we can not only implement the new curriculum reform well and realize the original goal of education, but also let students "get good grades"; However, teachers will not be so relaxed.
Reflections on the Teaching of Pythagorean Theorem On Thursday afternoon, I talked about the first class of the inverse theorem of Pythagorean Theorem, and now I reflect on this class as follows:
(1) The design idea of this lesson is reasonable: around the theme of "exploration", from a series of activities such as "How did the ancient Egyptians get right-angled triangles" to students imitating operations with wooden sticks, and then drawing their own proofs, they get the "Pythagorean Theorem Inverse Theorem", while the explanations of concepts such as reciprocal propositions, original propositions and inverse propositions are just a little like those introduced in the new lesson. Through classroom exercises and classroom tests, students' understanding of the inverse theorem of Pythagorean theorem is strengthened, and students are guided from the sides and angles of the triangle respectively.
(2) PPT is used in this course to highlight the teaching ideas of "characteristics for students to observe, ideas for students to explore, methods for students to think, significance for students to summarize, conclusions for students to verify, difficulties for students to break through, and students as the main body", and all links are closely linked.
(3) I am very satisfied with the teaching process and teaching effect. The students are very active in answering questions. In the process of breaking through the difficulties, students summarize the inverse theorem of Pythagorean theorem through group cooperation experiments. I give students enough time to think and let them finish it themselves. The whole process embodies the role of students and teachers, and the classroom atmosphere is active and the effect is quite good.
Shortcomings and improvement methods of this lesson;
1, I didn't find the students' mistakes in time in this class. The mistakes made by students when doing problems on the blackboard were not found and corrected in time.
2. Students should be allowed to explain themselves after the classroom test, but the lack of time led to students not completing this link, but projecting the correct answer.
In the future teaching, I will constantly update the educational concept, re-create the mathematics textbooks in combination with the students' cognitive laws and life experiences, and choose lively and interesting mathematics textbooks closely related to the students' real life, so as to provide students with sufficient space for mathematics activities and communication, truly return the creativity to the students, make the students move, and make the classroom glow with new vitality.