Lecture Notes on Observing Objects 1 I. teaching material analysis:
"View and projection" is the content of "space and graphics" in the Curriculum Standard, which has clear requirements in different classes. The first issue is the first volume of Senior Two, which allows students to understand that the same object sees different shapes from different positions and gradually cultivate students' concept of space. Just let students observe specific objects, so as to prepare for learning to observe more abstract geometric figures in the future. The second phase is the first volume of grade five, which allows students to experience the process of observation and realize that when observing objects from different positions, they see different shapes. Through the observation of real objects, we can correctly identify the position relationship and shape of two objects or a group of three-dimensional graphics observed from the front, side and above. Cultivate students' spatial imagination and reasoning ability through splicing activities. In the first and second stages, it is required to "know the shape of simple objects observed from the front, side and above" and "know the shape and relative position of objects seen from different directions". It was not until the third stage that the knowledge of projection and three views was formally learned.
Students have accumulated rich perceptual experience in observing objects in daily life. The first textbook shows three students observing a dinosaur toy from the front, side and back respectively. The shapes observed from these three directions are given below, so that students can judge who saw these three shapes respectively. Make students realize that the shape of the same object is different when viewed from different angles, and initially understand the relationship between the part and the whole. No matter which observation point students choose, they only observe a part of the object, and different observation points see different shapes. Only by synthesizing the shapes observed in different positions can a complete representation of this object be formed. Through the study of the first period, we have been able to identify the shapes of simple objects observed from different positions. On this basis, by observing more abstract geometric shapes, students can further realize that the shapes they see are different in different positions. Enable students to correctly identify the position relationship and shape of simple objects observed from the front, side and above.
Based on the above understanding of the textbook, the goal of this lesson is to locate it like this.
1, let students see different faces in different positions, and only three faces of a cuboid can be observed at a time.
2. Through observation, imagination, operation and other mathematical activities, we can learn to recognize the shape and relative position of one or two objects observed from different directions, and cultivate students' spatial imagination.
Grade five students have accumulated rich perceptual experience in observing objects in daily life, but their generalization ability is weak and their reasoning ability needs to be continuously developed. Therefore, the focus of this course is to be able to identify the shape and relative position of one or two objects observed from different directions. The difficulty lies in cultivating students' spatial imagination and observing from three different directions.
Second, the preparation and delivery of teaching AIDS and learning tools.
(a) Preparation of teaching aids and learning tools
In order to attract students' attention and arouse their initiative in learning, the preparation of teaching AIDS and learning tools must be sufficient. In this lesson, I prepared cuboids, cubes, cylinders and spheres, and students also prepared corresponding learning tools for students to observe. Provide specific teaching methods for students, enrich teaching situations, improve students' interest in learning, and let students acquire new knowledge on their own initiative, so as to feel the happiness brought by mathematics activities.
(B) Teaching process
The process of observation, imagination, guessing, analysis and reasoning runs through the whole classroom, so that all students can really observe and operate. Instead of letting the teacher's demonstration or the activities and answers of several students replace each student's hands-on, personal experience and personal thinking. And encourage students to dare to express their views, exchange ideas with their peers, sort out ideas and inspire each other in communication. It can train students' spatial imagination and thinking ability and develop the concept of space.
1, teaching example 1.
By observing the movement of rectangular objects, students realize that the shape of three-dimensional graphics is different in different directions, and they can't see all the faces at any position at the same time. Enable students to identify the shapes of simple objects observed from the front, left and above.
Teaching is divided into the following two steps.
(1) Provide rectangular objects, and let students stand in different positions to observe and tell which faces they see. Make students really experience that the same object looks different from different directions and sees different shapes; And it is found that standing in any position, it is impossible to see all the faces of the cuboid at the same time, and only three faces at most.
(2) Instruct students to observe from the front, left and top respectively, so that students can know the plane graphics obtained by looking at three-dimensional graphics from different directions. During the observation, through the demonstration of students, students with incorrect observation posture can understand why it is difficult for them to see only one side, and emphasize that the line of sight should be perpendicular to the surface of the observed object. Let the students make it clear that the front, left and up mentioned here are all relative to the observer. Let the students stand in different positions and say what figures they see from these directions.
2. Teaching example 2.
Example 1 is to observe an object from different directions, and example 2 is to observe the combination of two simple three-dimensional figures. Further learn to observe the positional relationship and shape of two objects from different directions. First, let the students observe the sphere and cylinder respectively and tell what shape they see. Put two objects together and ask the students to imagine what they are from different angles. Finally, according to the student's description, show the shape to verify.
Third, the focus of teaching research
The focus of this semester's teaching research is the effectiveness of space and graphics teaching activities. This class not only designs observation activities, but also designs activities that require students to imagine, guess and reason, so as to cultivate students' spatial imagination and thinking ability. For example, in teaching example 2, when the teacher presents a combination of a sphere and a cylinder, so that students can learn to recognize the position and relationship of two objects from different directions, students can combine and adjust these representations in their minds according to the existing representations of shapes obtained by observing these three-dimensional figures from different directions, and finally verify them through the given shapes, so that students' spatial imagination and thinking ability can be fully exercised.
Lecture Notes on Observing Objects 21. Talking about Teaching Materials
The lecture content is the observation object in the fifth unit of the first volume of the second grade of the compulsory education curriculum standard experimental textbook "Mathematics". These contents are the necessary basis for learning the knowledge of space and graphics, and play an important role in helping students to establish the concept of space and cultivate their spatial imagination. Teaching materials are based on students' life experiences and positions, and are taught with the help of real objects in life and students' operational activities.
Based on the above understanding, I have determined the teaching objectives of this course as follows:
1, knowledge goal: Through practical operation, we can initially understand that the shapes of objects seen from different angles are different, and learn to correctly judge the position of observers according to the shapes seen.
2. Ability goal: cultivate students' ability of observation, comparison and practice, develop students' initial concept of space, and infiltrate mathematics from life.
3. Emotional goal: to stimulate students' enthusiasm for learning through inquiry activities and cultivate students' ability to explore actively;
Key points and difficulties:
The key point of this lesson is: learn to judge the position of the observer correctly according to the shape you see.
Second, oral teaching methods
1. Curriculum Standard of Situational Teaching Method points out that mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Therefore, the creation of scenes should be based on students' life experience and knowledge background. At the beginning of the new class, by observing photos, guess activities with games, stimulate students' interest in learning and introduce the names of posts.
2. With the help of visual image, the discovery method promotes students to rise from perceptual knowledge to rational knowledge.
When teaching symmetrical figures, teachers guide students to observe toys carefully. Through the independent exploration of standard observation and transposition observation, on the basis of observation and discovery, I feel that the shape of the same object in different positions is different. The role of teachers is to organize discovery activities, pay attention to students in the activities, make students learn new knowledge in exploration, experience the exploration process, and infiltrate students with the idea that mathematics comes from life and is applied to life.
Third, theoretical study.
Curriculum standards point out that effective mathematics learning activities can not only rely on imitation and memory, but also practical, independent exploration and cooperative communication are important ways for students to learn mathematics. Practical operation and independent inquiry are also the main ways for students to learn new knowledge in this course, and at the same time, they attach importance to the guidance of observation methods.
1. In the teaching of independent inquiry method, students' dominant position and participation in the process of knowledge formation are emphasized. We always provide students with sufficient learning materials, create sufficient learning space and time, let students explore independently, experience the process of knowledge formation, and cultivate the ability to explore actively.
2. Observation law 1 Observation is a good learning method in the teaching of observed objects. For example, when teaching example 1, the observation purpose is clear. The teacher asked the students to observe the different positions of the teddy bear and correspond to different photos. Why do the same bear have so many different photos? This arrangement not only gives students the opportunity to think independently, but also teaches students the thinking method of observation.
Fourth, talk about teaching procedures.
This lesson is mainly completed by four links.
(A) observation and exploration to cultivate students' concept of space
1. Let the students guess who the child is in the photo.
2. Make clear the position and let the students in the group talk to each other and guess where they are sitting. Photography is familiar to every student, but it is impossible to tell who the object of this class is from the photos at once, which gives the students a suspense. Let students feel novel and interesting, fully arouse their enthusiasm, let students enter the learning state immediately, and let students participate in the process of perception initially.
3. Standard observation.
Observe the real thing and experience the same object from different positions.
Let the students sit in their seats, choose the photos of the bears they see and say them.
4. Questioning understanding
Guide students to observe and compare the same bear. Why are their photos different in shape? Organize each group of students to discuss.
Then report the results. Finally, the guide concluded that because the three students observed different positions, they saw different shapes of bears.
5, comprehensive observation, experience new knowledge.
On this basis, further guide the overall observation. At this time, let the students observe the bear comprehensively in their favorite way, and guide and sum up that if you want to know an object, you must observe it comprehensively.
(2) Connecting with the reality of life
1, let's see who can react quickly (start work)
Look at the math textbook made by the teacher, think about where you should see this side, and run to the corresponding position immediately. Imagine: encouraging students to leave their seats provides students with more space to explore, which is a transition from intuition to abstraction.
2. Example 6 in the book is completed and connected.
3. Guess the game.
Show the picture of the classroom taken from the front, the bucket seen from above, the cups that are the same from the left, right and front positions, and the paper on the side. Guide the students to say: observe an object, not just one side, but from different positions. When students guess in many ways, they show rich imagination. Through guessing, they also realize that to truly understand an object, we must observe it comprehensively, which is helpful to cultivate students' good way of thinking.
(3) Application expansion.
Look at three-dimensional figures and cultivate students' spatial concept.
(4) Summary
This class will be over soon. Who can tell us what you have learned from this class? What do you think is the most successful?
Lecture Notes on Observing Objects 4 I. Talking about Teaching Materials
The content of the lecture is the observation object in the eighth unit of the first volume of the third grade of the compulsory education curriculum standard experimental textbook "Mathematics" of Jiangsu Edition. When learning "observing objects", students in the first volume of Grade Two mainly observe from the front, back, left and right of simple daily necessities (toys, cars, teapots, etc.). ), and choose the appropriate graphics to represent the shape of the objects they see. This part of the content is to observe the daily necessities in the shape of a cuboid or cube and the objects composed of two cubes with the same size from the front, side and top of the object. Through this part of the study, students can further master the specific methods and skills of observing objects and feeling objects and plane graphics.
Based on the above understanding, I have determined the teaching objectives of this course as follows:
Knowledge goal:
Let the students know that the shapes they see are different when standing in different positions. You can see up to three faces in one position. Can identify the front, side and top of an object; Learn to recognize the shapes of objects observed from different positions.
Ability goal:
Initially develop students' concept of space and cultivate their ability of observation, operation and cooperation.
Emotional attitude goal:
Fully mobilize the enthusiasm of students to participate in mathematics activities and experience the happiness of learning mathematics.
Key points and difficulties:
The focus of this lesson is to recognize the shapes of objects seen from different positions by combining specific things.
The difficulty of this lesson is that you can see different shapes from different angles, and you can only see three faces at most.
Second, oral teaching methods
1, Situational Teaching Method: The curriculum standard points out that mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Therefore, the creation of scenes should be based on students' life experience and knowledge background. At the beginning of the new lesson, by observing the different faces of mobile phones, let students guess the activities of objects, stimulate students' interest in learning, not only review old knowledge, but also prepare for new knowledge learning, thus leading to the topic of this lesson. Then, by observing the scenes of Fuwa toys, let the students initially perceive different positions and see different shapes.
2. Demonstration method: Make full use of visual image to promote students to rise from perceptual knowledge to rational knowledge. Teaching graphics, through computer dynamic demonstration of the composition of different surfaces of objects, enable students to obtain perceptual knowledge. Then use computers to demonstrate different aspects of objects in life, learn to appreciate the beauty of mathematics, and infiltrate the idea that mathematics comes from life and is used in life.
Third, theoretical study.
Curriculum standards point out that effective mathematics learning activities can not only rely on imitation and memory, but also practical, independent exploration and cooperative communication are important ways for students to learn mathematics. Practical operation and independent inquiry are also the main ways for students to learn new knowledge in this course, and at the same time pay attention to the guidance of learning methods.
1, practical operation method. Modern educational psychology believes that the development of children's thinking is the transition from concrete image thinking to abstract thinking. They need to learn knowledge and develop wisdom through various activities.
2. Independent inquiry method. Emphasis is placed on students' dominant position in teaching and students' participation in the process of knowledge formation. We always provide students with sufficient learning materials, create sufficient learning space and time, let students explore independently, experience the process of knowledge formation, and cultivate the ability of active exploration.
3. Observation method. For example, when introducing the course, the teacher shows students the different faces of mobile phones and Fuwa through slides for students to observe. After the observation, they can organize discussions about why students observe different shapes of the same mobile phone. This arrangement not only gives students the opportunity to think independently, but also teaches students the thinking method of observation.
Fourth, talk about the teaching process
(A) create a situation to stimulate interest perception
(Show the front, side and top of the phone)
Students, please guess, what are these objects? Why are all mobile phones with different shapes?
Today we are going to learn to observe an object from different angles.
Writing on the blackboard-observing objects
(B) teacher-student interaction, exploring new knowledge
1, standard observation value
Let the students think, from which angles can we observe an object? Which angle do you like to observe? Why?
Students think independently, then talk at the same table and answer by name.
Show Fuwa and give a brief explanation.
Students observe carefully. The teacher shows the photos of Fuwa taken from the front, side, top and back.
Question: What do you think of Fuwa? Which picture is on the courseware? Students think independently, then communicate in groups and answer by name.
2, transposition observation
Listen to the teacher and ask some students to change their positions clockwise to observe the objects. Are the Fuwa shapes you see now the same as those just now? What side of Fuwa do you see in your own style?
Why is what you see now different from what you just saw? What's going on here?
Discuss in groups and exchange reports.
3. Comprehensive observation
Game: Compare who reacts faster.
Rules of the game: Listen carefully to the teacher who says which group should look at which side of Fuwa, think about where to stand and look at this side, and run to the corresponding position immediately.
(3) Experience that an object can see up to three faces from different positions, and present different color gift boxes on each face.
Guess: How many faces do you think you can see from anywhere in this gift box? Guide students to observe and verify.
Division; Look at the gift box carefully How many faces can you see? What color or quantity are they? (Student answers)
Teacher: In the observation activity just now, we found that there are three different results: we may see 1 face, we may see two faces, and we may see three faces at most. Please look at other objects around you again. You can only see three faces at most?
Answer.
Summary:
What have you learned from the observation and discussion just now? (blackboard writing: you can see up to 3 faces)
(4) Know the front, side and top of a cuboid.
1, know the names of three faces.
Who can come up and choose a position where you can see the three faces of a cuboid and touch them with your hands?
Who can give these three kinds of noodles a proper name?
(Teacher writes on the blackboard)
2. Instruct students to change the position of a cuboid at will and talk about its three sides.
(5) Level exercises and application expansion.
Think about doing 87 pages 1 to 5 questions.
Students practice independently, give feedback and exchange opinions.
Verb (abbreviation of verb) abstract
This class will be over soon. Which student can tell me what you have gained from this class? What do you think is the most successful?
The design of the whole class fully embodies that students are the main body and teachers are the organizers, guides and collaborators of students. In the whole teaching process, students always learn knowledge through hands-on practice and independent inquiry. Students love learning, which makes students change from learning to "I want to learn, I will learn", which stimulates students' enthusiasm for learning and cultivates students' inquiry ability and independent learning consciousness.