20 12 first prize of Shandong quality class competition

Disclaimer: This lecture is prepared for participating in the 20 12 Shandong Junior High School Mathematics Excellent Course Competition, which lasts about 14 minutes, and is accompanied by a courseware demonstration. This lecture is a valuable first-hand resource for teachers to refer to. Please don't imitate mechanically.

Dear judges and teachers, hello, I'm Song Ning from Cangshan Experimental Middle School in Linyi. Today, what I am talking about in class is the first lesson of Pythagorean Theorem, Chapter 18, Volume 1 of Grade 8 Mathematics of People's Education Press. I will explain the understanding and design of this course from five aspects: teaching materials, teaching methods and learning methods, teaching process, teaching evaluation and design instructions.

First, teaching material analysis:

(A) the status and role of teaching materials

Pythagorean theorem reveals the quantitative relationship among three sides of right triangle from the perspective of knowledge structure, which provides an important theoretical basis for subsequent learning to solve right triangle and has a wide range of applications in real life.

From the perspective of students' cognitive structure, the characteristics of shape are transformed into quantitative relations, which builds a bridge between geometry and algebra.

Pythagorean theorem is a good material for patriotism education for students, so it has a very important position and role.

According to the new curriculum standards of mathematics and the cognitive level of eighth grade students, I have determined the following learning goals: knowledge and skills, mathematical thinking, problem solving and emotional attitude. Among them, emotional attitude, with China's mathematical culture as the main line, inspires students to love the long-standing culture of the motherland.

(2) Key points and difficulties

In order to change passive acceptance into active exploration, I have determined that the focus of this lesson is: the exploration process of Pythagorean theorem. Limited to the thinking level of eighth-grade students, I will make Pythagorean theorem discovered by area method (puzzle method) the difficulty of this class, and I will guide students to do experiments to highlight key points and break through difficulties through cooperation and communication.

Second, the analysis of teaching methods

Teaching method Ye Shengtao said, "The teacher's teaching is not the total prize, but the camera induction." Therefore, teachers use geometry to ask questions intuitively, guide students to explore from the shallow to the deep, design experiments for students to verify and understand the thinking methods contained in them.

In order to return the initiative of learning to students, teachers encourage students to adopt hands-on practice, independent exploration and cooperative communication, so that students can personally perceive and experience the formation process of knowledge.

Third, the teaching process

China's mathematical culture has a long history and is profound. In order to let students feel the charm of its inheritance, I design this lesson as the following five links.

First of all, the situation introduces the ancient rhyme and the present style.

Give a set of seven clever eight diagrams, and let the students cooperate with two sets of puzzles. Let the students observe and think about the relationship between the areas of three squares. What triangle do they form? Reflected in three aspects, what mathematical mystery does it contain? Education through fun can stimulate students' curiosity and desire to explore.

The second step is to trace the history and decrypt the truth.

The exploration process of Pythagorean theorem is the focus of this lesson. According to the principle of gradual and spiral increase of mathematical knowledge, I designed the following three activities.

Starting from the above problems, the starting point is low, which is conducive to students' participation in exploration. Students can easily find that the isosceles triangle has the following relations. Ingeniously transforming the relationship between areas into the relationship between side lengths embodies the idea of transformation. It is found that although intuitive, the area calculation is more convincing. The figure is transformed into a figure with edges on the grid line, so as to calculate the figure area, which embodies the idea of combining numbers with shapes. Students will think of the method of "counting grids". Although this method is simple and feasible, it is not suitable for the next step to explore the general right triangle and has limitations. Therefore, teachers should guide students to find the area of square C by "cutting" and "filling", so as to pave the way for exploring the area of complex graphics in the next step.

Break through the shackles of isosceles right-angled triangles and explore whether this conclusion also exists in right-angled triangles. It embodies the cognitive law of "from special to general". The teacher gave right-angled triangles with side lengths of 3, 4 and 5 respectively, which avoided the mistakes made by students due to inaccurate drawing and laid the foundation for the following proposal of "hook three strands, four strings and five". With the foreshadowing of the previous link, the difficulties are effectively dispersed. When calculating the area of square C, students will show the methods of "cutting" and "filling", and some students may find the methods of translation and rotation. Teachers should praise these two new methods, affirm students' research results, and cultivate students' analogy ability, transfer ability and problem exploration ability.

Using the dynamic demonstration of geometry sketchpad, the relationship between geometry and algebra is visualized. When it is a right triangle, the relationship among the three sides remains unchanged by changing the length of the three sides, and when ∠ α is an acute angle or an obtuse angle, the relationship among the three sides changes, further emphasizing that the premise of the proposition must be a right triangle. It deepens students' understanding of Pythagorean theorem and broadens their horizons.

The above three steps are step by step, and students get the proposition 1, thus cultivating students' reasonable reasoning ability and language expression ability.

Perceptual knowledge is not necessarily correct, and reasoning verification confirms our conjecture.

The third step is to bring forth the new and borrow the old to innovate.

The proof method of "Zhao Shuang's String Diagram" given directly in the textbook is a kind of imprisonment for students' thinking. Teachers creatively use teaching materials, use jigsaw puzzles to liberate students' brains, and let students use their intelligence to prove Pythagorean theorem. This is the difficulty and focus of teaching. Teachers should give students enough time and space to explore independently, so that students' thinking can collide in mutual discussion and improve in mutual learning. Teachers go deep into students, observe students' inquiry methods, accept students' questions and affirm different solutions to puzzles. Thus, it embodies the teaching concept of "students are the main body of learning, and teachers are organizers, guides and collaborators". Students will find two proof schemes.

Scheme 1 is Zhao Shuang's string diagram. Students explain the demonstration process and reproduce the exploration methods of ancient mathematicians. Scheme 2 is the result of students' own exploration, and the skillful demonstration is similar to scheme 1. The whole exploration process allows students to experience the excavation process from surface to essence, from perceptual reasoning to deductive reasoning, and to appreciate the rigor of mathematics. Through the comparison of ancient and modern proofs, students can feel the joy of "blowing away yellow sand begins with gold" and the pride of "shine on you is better than blue". Write Pythagorean Theorem on the blackboard, and then express it in letters to cultivate students' symbol consciousness.

The teacher introduced the meaning of "Gou, Gu and Xian" and the research on Pythagorean Theorem at all times and at home and abroad, so that students can feel the mathematical culture and cultivate national pride and patriotism. Use Pythagoras tree to demonstrate dynamically, so that students can realize the exquisiteness and beauty of mathematics.

The fourth step is to take its essence and make the past serve the present.

I designed the following three groups of exercises according to the gradient of "understanding-mastering-using".

(1) correspond to the difficulties and consolidate the learned knowledge; (2) Examining key points and deepening new knowledge; (3) Solve problems and feel the application.

The fifth step is to review and reflect on the task extension.

At the end of the class, I encourage students to summarize this class from the requirements of "Four Basics". Then summed up a theorem, two schemes, three ideas and four experiences.

Then assign homework. Hierarchical homework embodies the idea of education for all students.

Fourthly, teaching evaluation.

In the inquiry activities, teachers' evaluation, students' self-evaluation and mutual evaluation are combined, which embodies the diversification of evaluation subjects and evaluation methods.

Verb (abbreviation of verb) design description

This course runs through exploration and experience, exhibition and communication, habit formation, emotional education and cultural education.

"Tangram" is used to replace "Pythagoras Floor Tile" in the textbook, and China traditional culture is used to introduce the subject. Zhao Shuang's illustration proves the theorem, which conforms to the design concept of this course with China's mathematical culture as the main line, shows the glorious history of ancient mathematics in China, and stimulates students' desire to create brilliant mathematics again.

The above is my design description of Pythagorean theorem. Please correct me if there are any shortcomings. Thank you.

blackboard-writing design