A lecture with axis symmetry in life
I said that the content of the class is the standard experimental textbook of compulsory education curriculum published by East China Normal University, and the seventh grade mathematics (II) chapter 1 section1"Axisymmetry in life". Next, I will elaborate the teaching design of this lesson from six aspects.
I. Background analysis
1, learning task analysis
The textbooks of the new curriculum strive to embody the spirit of mathematics curriculum standards, pay attention to the connection between learning content and real life, reflect the process of students' active learning, take students' development as the foundation, and let students find conclusions and sum up themselves through observation, operation and imagination. This lesson just embodies this point. Axisymmetry in life is an important part of this chapter. From concrete to abstract, from perceptual knowledge to rational knowledge, and then from practice to test theory, the teaching materials gradually guide students to know things with axisymmetric nature in nature and daily life, which makes students have a further understanding of the plane graphics they have learned before, and also lays a good foundation for learning the nature of isosceles triangle and learning "translation and rotation" in the eighth grade later in this chapter. Therefore, the teaching focus of this course is to understand axisymmetric figures and axisymmetric figures through the observation and analysis of real life examples and typical patterns, and to find out the symmetry axis of simple axisymmetric figures.
2. Analysis of students' situation
When students learn the basic knowledge of geometry in the sixth grade of primary school, they have briefly learned the concept of axisymmetric graphics and can know some simple axisymmetric graphics. In the first volume of the seventh grade, they have already learned a chapter on the preliminary understanding of graphics. In the previous chapter, they learned polygons, and their understanding of graphics is gradually enriched. The lines, angles, isosceles triangles and regular polygons that students have seen are all axisymmetric. It can be said that the previous textbooks have been well infiltrated and paved. On the other hand, students are exposed to a large number of axisymmetric graphics in their daily life and have a certain perceptual knowledge of axisymmetric graphics. Therefore, it is not too difficult for students to understand axisymmetric graphics and axisymmetric graphics. What is difficult is to understand the differences and connections between them. Another difficulty is to accurately and completely find the symmetry axis of the axisymmetric figure.
Second, the design of teaching objectives
1. Knowledge objective: By observing and analyzing real life examples and typical patterns, and by understanding axisymmetric figures and axisymmetric figures, find out the symmetry axis of simple axisymmetric figures.
2. Ability goal: cultivate students' observation ability, hands-on operation ability and ability to explore knowledge, and gradually develop the habit of analyzing and thinking about problems.
3. Emotional goal: Feel and appreciate the axisymmetric graphics in real life, realize the wide application of axisymmetric in real life and its rich cultural value, and cultivate students' interest in learning and love for life through the combination of teaching materials and practice.
Third, the classroom structure design
Design of teaching methods.
The new curriculum concept emphasizes that "the experience process is as important as the conclusion". For students, the process is sometimes more meaningful than the conclusion. I use inquiry teaching method. The whole process of inquiry learning is full of communication and interaction between teachers and students, which shows that teachers are organizers, guides and collaborators of teaching activities and students are the main body of learning.
According to the content and arrangement characteristics of the textbook in this section, in order to highlight the key points and break through the difficulties more effectively, according to the students' cognitive law and the process of knowledge discovery development, the experimental discovery method is adopted as the main method, supplemented by intuitive demonstration method and question induction method. In teaching, we should carefully design enlightening and thinking questions, create problem scenarios, induce students to observe, think and operate, teachers demonstrate in time, and use multimedia teaching to stimulate students' desire to explore knowledge and gradually draw conclusions, so that students are always in a state of actively exploring problems, thus cultivating their thinking ability.
2. Mathematics curriculum standards emphasize that hands-on practice, independent exploration and cooperative communication are important ways for students to carry out effective mathematics learning activities. Therefore, in the guidance of learning methods, this course aims at students' cognitive laws and guides students to operate, communicate and cooperate according to the principles of autonomy and difference of learning methods, and experience the learning process of discovering, exploring and solving problems. Participate in the occurrence, development and formation of knowledge, so that students can master knowledge.
Fourthly, the design of teaching media.
1, in order to deepen students' perceptual knowledge of axisymmetric graphics and show some common axisymmetric graphic objects in life.
2. In order to stimulate students' interest in learning and desire to explore knowledge, students can experience the process of observing axisymmetric graphic examples and typical patterns in real life. Using multimedia courseware, they can intuitively demonstrate examples and typical patterns of axisymmetric graphics in real life, so that students can fully experience the close relationship between mathematics and life, further enrich their perceptual knowledge, and thus effectively improve the effect of classroom teaching.
3. In order to cultivate students' practical ability and deepen their understanding of knowledge, practical activities such as paper cutting and origami are designed, and rectangular, square, isosceles triangle and circular pieces of paper are prepared.
Five, the teaching process design
Follow the principle: introduce pictures to stimulate interest, the learning process reflects autonomy, the knowledge construction is gradual, and the thinking method is organically infiltrated.
1, introduction of interesting doubtful points
First of all, play multimedia and enjoy the axisymmetric graphics in reality. Ask the students to think about these questions while enjoying them: Are there similarities in each figure? What kind of feeling do these figures give you? Which pictures look better?
The teacher said: Since ancient times, symmetrical forms have been regarded as harmonious, beautiful and true. Symmetry is everywhere in nature, architecture, art, science and daily life. Why is symmetry so closely related to us? ..... Today, let's learn about "axis symmetry in life".
Design purpose: The new curriculum pays more attention to let students start with practical problems, arouses students' strong interest in learning, realizes the connection between mathematics and life, endows mathematics with life breath, enables students to use mathematical knowledge to solve practical problems in life, ignites the sparks of students' thinking, and also cultivates students' mathematical modeling thoughts.
2. Explore new knowledge through cooperation and exchange.
First of all, divide into groups and ask students to name some objects with "symmetrical" shapes in their lives. Students can explore independently and express their opinions freely. Then inspire students to think: What are the characteristics of these figures we just saw? First discuss in groups, cooperate and communicate, and then several students report their learning results. (Play multimedia pictures repeatedly at the same time)
Design purpose: Let students think boldly, express their views actively, and cultivate students' observation ability, analysis ability, language expression ability and ability to appreciate and feel beauty. Group communication can cultivate students' cooperative ability and team spirit.
3. Form the concept of manual eye movement
Fold a piece of paper in half and cut a figure from the fold. Think about what kind of graphics it will be after expansion. First, the teacher demonstrated cutting out a figure, and then everyone was free to use their imagination and cut out the pattern. Then the teacher guides the students to observe the numbers in the picture 10. 1. 1 and think: What do they have in common? At the same time, the teacher demonstrated the process of graphics folding in half in time. Through observation, students can answer that the two parts of these figures are equal and can overlap.
Summarize the observation and thinking of the displayed pictures and the patterns cut by the students. Students will summarize the concepts of axisymmetric figures and axes of symmetry, guide students to read the narratives in the textbooks and deepen their understanding.
Design purpose: Don't let students' hands-on activities just stay at the level of manual operation, but have a spirit of self-exploration. Students can discover conclusions by hands, eyes and brains, so that students can devote themselves to the process of acquiring knowledge. This reflects the change of students' learning style and the role of teachers' organizers. In this process, the training of cutting and spelling ability is of great benefit to students in further learning graphics.
4, deepen the understanding of the actual operation
In order to help students accurately judge axisymmetric figures and find out the symmetry axis, let students take out prepared pieces of paper, fold them as required to see which are axisymmetric figures, and then fold them from different directions to see how many symmetry axes there are. After the discount, let the students report their grades and the teacher will summarize them.
Then find the symmetry axis of each figure in the figure 10. 1. 1 Do the first "do" in the textbook 8 1, and fully understand that some axisymmetric figures have more than one axis of symmetry.
Design purpose: Through hands-on practice, cultivate students' hands-on operation ability, deepen their understanding of concepts, and initially learn the method of finding symmetry axis by folding.
5. Guide students to observe, think and summarize in the same way, and summarize the concepts of axis symmetry, axis symmetry and symmetry point. Ask the students to do the second "doing" on page 8 1 in the textbook, so as to deepen the understanding of "symmetry point".
Try it, let students break the ink paper, and let students experience the formation process of axial symmetry through practice, so as to deepen their understanding of axial symmetry.
Let students reflect on the differences and connections between axisymmetric graphics and axisymmetric graphics, and make students have a clearer understanding of axisymmetric graphics and axisymmetric graphics through comparison, induction and discrimination. Finally, summarize the learning content of this lesson.
Design purpose: To check whether students can use the methods they have learned to understand the axisymmetry, that is, to realize knowledge transfer. In the operation, students move their eyes, brains, mouths and hands, which fully mobilizes students' various senses to participate in learning, which not only exerts students' initiative in learning, but also cultivates students' divergent thinking.
6, variant practice to develop thinking
(1) The more axisymmetric figures in life, the better. Take the form of group competition.
(2) Which of the 26 letters in English is an axisymmetric figure? See who speaks quickly and accurately. Do numbers in mathematics have axisymmetric figures?
(3) Read the material "Cut the Five-pointed Star" on page 83 of the textbook and ask students to cut the Five-pointed Star and think about the answer: What is the mathematical truth implied in this method?
What did you get from this lesson? Write a report within 100 words after class. Students who like to design design some axisymmetric graphics and bring them to school for everyone to enjoy.
Design purpose: design some topics related to life, design some topics that can exercise students' practical ability and develop students' thinking, and stimulate students' learning enthusiasm. At the same time, we should also pay attention to strengthening the connection and integration between disciplines.
Evaluation and analysis of intransitive verbs
1, teaching effect evaluation
Through classroom activities such as students' understanding of what they have learned, exchanging views on a certain question, performing and trying to answer various questions, teachers can understand students' knowledge from the aspects of students' thinking activities, understanding and mastering relevant contents, and students' enthusiasm for participating in activities, so as to make an appropriate evaluation of the teaching effect of this class.
2. Teaching feedback and adjustment
In the whole teaching process, students' participation in mathematics activities, self-confidence, awareness of cooperation and communication, and habits of independent thinking are evaluated, and problems exposed by students in the operation process are corrected in time to encourage students to have unique ideas or conclusions.