Teaching Reflection on Pythagorean Theorem

The exploration and proof of Pythagorean theorem contains rich mathematical ideas and research methods, which is the carrier of cultivating students' thinking quality. It plays an important role in the development of mathematics. The following is the teaching reflection of Pythagorean Theorem that I collected for you. I hope you like it.

Reflection on Pythagorean Theorem Teaching: Fan Wenyi

This lesson is the first section of Chapter 3 of Grade 8 of East China Normal University. At the beginning of this class, the logo of the 2002 International Congress of Mathematicians held in Beijing was introduced by multimedia, and its pattern was "string diagram" to stimulate students' interest. Introducing new courses is an important part of classroom teaching. A good beginning is half the battle. At the beginning of class, it is very important to quickly concentrate students' attention, bring their thoughts into specific learning situations, and stimulate students' strong interest in learning and thirst for knowledge. Using multimedia to display this meaningful pattern can effectively open the floodgate of students' thinking, stimulate association and inquiry, make students' learning state change from passive to active, and make students learn knowledge in a relaxed and happy atmosphere.

When explaining the conclusion of Pythagorean Theorem, in order to let students better understand and master the exploration process of Pythagorean Theorem, let students explore it themselves first, then discuss it, and finally demonstrate it on stage. This can deepen students' participation and make interaction between teachers and students and between students. Then the teacher will demonstrate the exploration process of Pythagorean theorem of right triangle with computer. Repeat the demonstration many times, so that students can feel and finally realize the conclusion of Pythagorean theorem. Through the animation demonstration, I realized that there are various methods to solve problems, which can easily break through the difficulties of this course, greatly improve the teaching efficiency and cultivate students' problem-solving ability and innovation ability. In this process, students show their magical powers and gain satisfaction and pride in solving problems.

Pythagorean theorem is always used in teaching, and students are 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 folding bamboo to the ground. As soon as the students saw it, their interest came. Finally, let students discuss with each other, let students solve problems in an open and free way and cultivate their imagination.

Finally, the history of Pythagorean Theorem is introduced, and some websites are recommended for students to consult after class. It is only for the convenience of 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, sort out, 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.

Pondering over Pythagorean Theorem in Teaching —— Fan

I spent four hours teaching Pythagorean Theorem in the first section of Chapter 18 of the eighth grade Mathematics Education Edition. The first lesson mainly teaches the exploration and verification of Pythagorean theorem, and gives an example to calculate the right triangle with known two sides to find the third side. In the second class, I mainly teach various problems related to the side length or area of a right triangle; The third lesson teaches how to solve practical problems in life with Pythagorean theorem; The fourth lesson mainly teaches how to find the corresponding point of irrational numbers on the number axis. The teaching methods I use in these four classes are: guidance-exploration-discovery method; The learning mode designed for students is: the combination of independent inquiry and cooperative communication.

In the classroom teaching of the first class, I always pay attention to mobilizing students' enthusiasm. Interest is the best teacher, so whether it is introduction, jigsaw puzzle or history review, I pay attention to mobilizing students and let them devote themselves to activities with passion. So the classroom efficiency is high. As an "eternal truth", Pythagorean Theorem's charm lies in its historical value and application value, so I pay attention to fully explore its connotation, especially for students to investigate in advance. Showing Pythagorean Theorem in class greatly mobilized students' enthusiasm, not only deepened their understanding of Pythagorean Theorem culture, but also cultivated their ability to collect and sort out data. The verification of Pythagorean theorem is not only the focus of this class, but also the difficulty of this class. In order to break through this difficulty, I designed a jigsaw puzzle activity, made exquisite courseware for students to feel metaphysically, and then asked questions layer by layer, starting from three aspects: area (number), teachers and students.

In the second class, based on the concept of "students are the main body of learning", in the whole process of exploring Pythagorean theorem, this class always adopts the way of combining students' independent exploration with peer cooperation and communication for active learning. Teachers only guide or organize students to break through difficulties through discussion when they encounter difficulties. In order to let students discover Pythagorean Theorem by themselves in the learning process, this lesson first creates scenes to stimulate their interest, and then through several inquiry activities, guides students to start with the special case of isosceles right triangle and naturally transition to the inquiry of general right triangle. Students find out the relationship among the three sides of a right triangle by observing the figure, calculating the area and analyzing the data, and then get the Pythagorean theorem.

In the third class, we always pay attention to students' independent inquiry and introduce examples to stimulate students' interest in learning. Then, through a series of independent exploration, cooperation and exchange activities, such as hands-on operation, bold guessing and brave verification, a theorem is obtained, which further consolidates and perfects the theorem and effectively embodies the new curriculum concept that students are the masters of mathematics learning. Students have not been exposed to jigsaw puzzle verification, so in teaching, teachers give students appropriate guidance and encouragement, and teachers act as organizers, guides and collaborators of students' mathematics learning. In addition, it teaches students to think and cultivates their abilities. Check the information before class to cultivate students' self-study ability and classification and summary ability; The inquiry in the classroom cultivates the students' ability to use their hands and brains, observe, guess, summarize and cooperate ... but the method of puzzle verification in this course has never been used by students before, so it is a bit difficult. Therefore, in the future teaching, it is necessary to pay more attention to students' experimental operation activities and improve their practical ability.

In the fourth class, I also introduced the proof method of Pythagorean theorem to the students: taking Zhao Shuang's String Diagram as the representative, the identity relationship between algebraic expressions is proved by cutting, cutting, spelling and supplementing geometric figures; Taking Euclid's proof method as the representative, it is proved by using the basic theorem of Euclid geometry; It is represented by Liu Hui's "Qing-Zhu Incoming Map" and "No Word Proof".

Generally speaking, students have a good grasp of the situation and can meet the expected requirements. However, there are many types of Pythagorean Theorem, which cannot be explained to students one by one. However, I still suggest adding the type of "How do ants get to the nearest place" published by Beijing Normal University to this textbook.

Reflection on Pythagorean Theorem Teaching: Fan Wensan

The exploration and proof of Pythagorean theorem contains rich mathematical ideas and research methods, which is the carrier of cultivating students' thinking quality. It plays an important role in the development of mathematics. Pythagorean theorem is an old wine with a fragrant taste and endless aftertaste. It depicts the harmonious and unified relationship of nature in a concise and beautiful form, with rich and profound connotation, and is a beautiful example of the combination of numbers and shapes.

In teaching, I take teachers as the leading factor, students as the main body, knowledge as the carrier, and pay attention to cultivating ability. Create a teaching situation of "doing and playing mathematics" for students, so that students can change from "learning" to "learning" and from "learning" to "learning with pleasure".

1, check the information

I asked the students to consult the information about Pythagorean Theorem before class. Students have a preliminary understanding of the historical background of Pythagorean Theorem and are confident to meet the challenge of learning new knowledge Pythagorean Theorem.

Students find information: Many scientists around the world are looking for "aliens". 1820, the German mathematician Gauss proposed to cut a right-angled triangular clearing in the Siberian forest, plant wheat on the clearing, and plant three square pine forests on three sides of the triangle. If aliens pass by the earth and see this huge mathematical figure, they will know that there is intelligent life on this planet. Hua, a mathematician in China, suggested that to exchange information between two different planets, it is best to take this figure with a spaceship and launch it into space.

Step 2 tell stories

Pythagoras was an ancient Greek mathematician. According to legend, 2500 years ago, Pythagoras visited a friend's house and found that the floor tiles laid by his friend's house reflected the quantitative relationship among the three sides of a right triangle.

I tell Pythagoras stories and ask questions. Students think independently and guess. I cooperate with the demonstration to make the questions vivid and specific. Teaching activities begin with "counting small squares", with a low starting point and strong interest. Students discuss and explore the mathematical problems in the stories of great men. There is a profound truth behind the prosaic phenomenon.

ask questions

Question is the starting point of thinking, a lively and interesting animation, ignites students' thirst for knowledge, inspires them with passion and emotion, introduces them into the learning situation and introduces them into the classroom with questions.

For example, a ladder AB with a length of 10m leans against the wall. If the vertical distance between the top of the ladder and the ground is 8m, does the bottom of the ladder slide 2m?

Although what the students say is not completely correct, it cultivates the students' ability to use mathematical language for abstract generalization, and students experience the thinking process of solving problems by using Pythagorean theorem, which increases their knowledge and wisdom.

For example, Nine Chapters of Arithmetic records an interesting problem: there is a pool with a square side length of 10 foot. In the middle of the pool, there is a new reed, which is 1 ft above the water surface. If you pull this reed to the shore, its top will just reach the surface of the shore. How deep is this pool and how long is this reed?

Through the exploration of "famous questions", I let students know the ancient and magical Pythagorean theorem. The question itself is extremely challenging, which stimulates students' strong thirst for knowledge and desire to explore knowledge. Students discuss and communicate, and find the idea of proving geometric problems with algebraic point of view. I use demonstration to disperse difficulties and cultivate students' divergent thinking and ability to explore mathematical problems.

4, speak card method

I introduced Zhao Shuang's string diagram, and Zhao Shuang proved the algebraic identity relationship by cutting, cutting, spelling and supplementing geometric figures, which was rigorous and intuitive, and was a model of the integration of form and number in ancient China. Zhao Shuang pointed out that four congruent right-angled triangles make up a hollow square, and the area of the big square is equal to the sum of the area of the small square and the area of the four triangles. Zhao Shuang's String Diagram shows the spirit and wisdom of ancient people in China in learning mathematics, which is the pride of China's mathematics. This pattern was chosen as the emblem of the International Congress of Mathematicians held in Beijing in 2002.

Subsequently, it shows the American presidential certificate law. On April 1876 and 1 day, Garfield published the proof of Pythagorean theorem in the New England Journal of Education. 188 1 year, Garfield became the president of the United States. In order to commemorate his intuitive, simple, easy-to-understand and clear proof, this proof method is called "presidential" proof method.

I think that student is Little Inventors. Students appreciate the works and enjoy the joy of success while constructing knowledge.

5. Clever design

Practical design: I base myself on consolidation, pay attention to development, take into account differences and meet students' development aspirations. The exercises include basic training, variant training and mid-term examination questions, which lead to Pythagorean tree and students marvel at the wonderful beauty of mathematics. The extension of in-class knowledge to out-of-class knowledge opens students' thinking and provides them with a broad space. Mathematics teaching has become full of vitality, and students like and love mathematics.

I let the students explain and collect information, which enriches the students' background knowledge and embodies the way of autonomous learning. I have carried out patriotic education for students, which has aroused their national pride and enterprising learning spirit. I let students appreciate the colorful mathematics culture, show the colorful cultural background, and inspire their patriotic enthusiasm.

6. Be good at summing up

Classroom summary is a review of teaching content and a summary of mathematical thinking methods. I emphasize the key content, pay attention to the formation of knowledge system, and cultivate students' habit of reflection. ?

I also want to say to my classmates:

Newton-the law of universal gravitation was finally established from the falling of apples.

We found the Pythagorean theorem from the triangle where we live together day and night.

Although they are not the same.

But exploration and discovery are ultimately valuable.

Maybe it's nearby.

Maybe it's just around the corner

There are endless "laws of gravity" and "Pythagorean theorem" hidden. ...

I hope the students-

Cultivate a mind that thinks about the world with mathematical thinking.

Practice a pair of eyes to observe the world from a mathematical perspective

Open a new exploration-