Excellent Lecture Notes on Understanding Line Segments 1 1. Textbooks
1. Orientation of teaching materials
Understanding line segments is the first lesson of Unit 6 "Centimeters and Meters" in the first volume of Grade Two Mathematics of Jiangsu Education Press. The teaching content includes 48 pages and 49 pages. The teaching length of this unit "centimeter and meter", including line segments, measurement units and other related knowledge. The content of "knowing the line segment" is the basis of long teaching amount, and it is also an important knowledge preparation for studying the area and volume in the future. The textbook pays attention to students' actual experience, perceives knowledge in the experience, and obtains an intuitive understanding of the line segment through specific activities, and initially understands the characteristics of the line segment.
2. Teaching objectives
According to the new curriculum standards, combined with the characteristics of this class and the age characteristics of students, I set the teaching objectives.
(1) enables students to know some characteristics of line segments through actual observation and operation, know that line segments are straight and have length, and learn to regard the edges of some objects as line segments.
(2) Enable students to identify the line segments in some simple plane graphics according to their preliminary understanding of line segments, count the number of line segments in simple graphics, and choose appropriate tools to draw line segments.
(3) Make students further enhance their curiosity about mathematics and feel the close relationship between mathematics and life in learning activities.
3. Teaching emphases and difficulties
Teaching emphasis: preliminary understanding of line segment characteristics.
Teaching difficulty: the establishment of line segment representation.
Second, talk about teaching methods and learning methods.
Mathematics teaching is the teaching of mathematics activities and the process of interactive development between teachers and students. Teachers play the role of coaches in the teaching process, guiding students to find problems, analyze problems, solve problems and acquire knowledge, so as to achieve the purpose of training thinking and cultivating students' ability. Based on these, I adopted teaching methods such as participation, discussion, interaction and experience. Advocate independent cooperation and independent exploration and other learning methods.
Third, talk about the teaching process
The "New Curriculum Standard" points out that "Mathematics originates from life, is higher than life, and develops life", and I put this concept throughout the classroom.
1. image import
I used the introduction of a few pictures to initially perceive the problems in life, which also reflected the idea that mathematics comes from life and mobilized students' enthusiasm.
2. Newly awarded
I divide the whole process into four steps: pulling, watching, folding and drawing.
(1) pull.
Ask the students to randomly observe the wool on the table and see what it looks like. After the students say it is bent, think about how to straighten the wool. The students began to operate and pulled it to straighten the wool. Let two people at the same table touch each other alternately. The straight line between hands is mathematically called a line segment. (blackboard writing: line segment, straight) The place where two hands pinch is called the endpoint. (blackboard writing: endpoint) In mathematics, we use small vertical lines to represent endpoints. Ask the students to point and count, and know that a line segment has two endpoints. I let the students intuitively perceive the line segment by pulling, touching, pointing and counting, from which they can abstract the concept of the line segment and know what the line segment looks like. In order to consolidate students' understanding of line segments, show the topic 1 "What to think about". Is the line segment drawn below? Judge by name and tell the reason. After the students judged that it was a line segment, I expanded it on this basis, one elongated and the other rotated. The purpose is to make students understand that no matter whether it is long or short, in which direction, as long as it is straight, it is a line segment with two endpoints.
(2) look for it
I asked the group to discuss and find out the line segments, touches and points in life. Students find that the edges of rulers, blackboards and textbooks can all be regarded as line segments. There are line segments in life, and there are hidden line segments in plane graphics. Find out how many line segments these figures are surrounded by. Students have known polygons before, and can quickly tell the number of line segments, which is the expansion of old knowledge and the consolidation of new knowledge. At the same time, let the students understand that the intersection of two line segments is the endpoint of the line segment in the plane figure. Discovery is to let students look for line segments from the things around them, find line segments in life, and apply mathematical knowledge to life, which embodies the close relationship between mathematics and life.
(3) 10% discount
With the help of the rectangle in the last link, let the students create a new line segment by folding, touch it and point out the end point. Compare with your deskmate, who is longer or shorter, and try to fold a line segment longer or shorter than the crease just now. In compromise, let students feel the joy of learning, stimulate students' creative desire and train divergent thinking.
(4) Draw a picture
Discuss with students the tools for drawing line segments before drawing. Some choose rulers, some choose pencil boxes, and some choose books. After comparison, the students found the best tool for drawing line segments-ruler. Please try to draw the line segments yourself. In the process of drawing, talk about how to draw a good line segment. In this link, I let the students choose their own tools and draw their own pictures, instead of the teacher giving them tools and demonstrating painting, turning giving and imitation into self-exploration, and handing over the classroom to the students, which shows that the students are the main body of learning and the teacher is the guide of teaching activities.
After the students draw a line segment, two points appear. How many line segments can you draw by connecting two points? Students begin to draw and understand that only one line segment can be drawn when connecting two points. Then there are three points that are not in a straight line. You can draw several lines connecting every two points. The key point is to understand the meaning of every two points, and then draw them. When there are four points, how many lines can be drawn to connect every two points? Try to draw it yourself. Some students draw 4 pictures and some students draw 6 pictures. Let the students who draw six pictures talk about how you draw them. How can we draw line segments in an orderly way and further understand the meaning of each two points? How many lines can be drawn from five points? Please guess and draw a picture after class. This is a series of orderly but different levels of math exercises, which strive to make students' classroom learning interesting, active and life-oriented, so that students can boldly express their opinions, listen to others' ideas and deepen their understanding of line segments in the process of mutual communication and cooperation.
summary
Finally, review what you learned today with your classmates, introduce the next line segment, and consolidate your understanding of the line segment.
In the whole teaching process, based on the new curriculum standard, I have grasped the characteristics of junior two students who are young and inattentive, but love to do things, have strong curiosity and strong desire to express themselves. Every link allows students to operate and explore, and every student can participate in the teaching activities, give the classroom to students, let students become the masters of learning, and change the traditional teaching mode. This is my idea of this class, please guide, thank you!
Excellent lecture notes on "Understanding Line Segments" 2 I. teaching material analysis and his study.
"Understanding Line Segment" is the first lesson of Unit 6 in the first volume of Grade Two Mathematics of Jiangsu Education Publishing House. Students have learned to compare the length of objects before, and they often come into contact with such content in their lives, which has rich life experience and laid a good foundation for the study of this class. The second-year students are too young to express the essential characteristics of things in complete language. Their understanding is often superficial and fragmentary. It is difficult for them to raise the concept of line segment to a general and abstract understanding. At the same time, they like doing things and have a strong curiosity and thirst for knowledge, which are all favorable factors for learning.
Second, teaching objectives and teaching difficulties
According to the new curriculum standards, combined with the content of teaching materials and the age characteristics of students, the following teaching objectives are formulated:
1. Ask students to know line segments, describe the characteristics of line segments in their own language, count line segments, and draw indefinite line segments with a ruler.
2. Make students experience the process of observation and operation, cultivate students' preliminary observation ability and practical operation ability, and develop students' spatial concept.
3, through observation, operation, discussion and other learning activities, stimulate students' interest in learning and cultivate students' sense of cooperation.
Teaching emphasis: know the characteristics of line segments and learn to draw line segments.
Teaching difficulties: draw line segments and count line segments.
Third, teaching AIDS and learning tools.
Preparation of teaching AIDS: courseware, cotton thread, rectangular paper and ruler.
Prepare learning tools: cotton thread, rectangular paper, ruler.
Fourth, teaching methods and learning methods.
Classroom teaching mainly adopts intuitive demonstration and operation practice, combined with other teaching methods such as guiding discovery and combining teaching with practice. In teaching, we should pay attention to guiding students how to observe operation and cooperate and communicate on the basis of independent inquiry.
Five, the design of teaching program
Based on the above analysis and the characteristics of this class, the teaching process I designed is divided into six parts:
Process 1: comparison of advantages and disadvantages, scenario introduction: (2 minutes)
The courseware shows the situation map: there are many roads between Xiaoming's home and school, only the middle road is straight and represented by a red line segment; Other routes are curves.
Inspire students to think: Which is the shortest way for Xiao Ming to go home from school? Why?
This link makes full use of students' existing life experience and guides students to find that this road is short because it is straight. Make students have a clearer understanding of the concept of straightness. At the same time, the knowledge of the shortest line segment between two points is infiltrated in the situation, which lays the foundation for subsequent study.
Process 2: Repeat the experience and know the line segment (8 minutes)
This process is divided into three teaching levels.
The first is intuitive perception: please straighten the cotton thread on the table and observe its shape.
At the second level, through explanation and variant exercises, students' understanding of line segments is changed from intuitive image to abstract generalization.
Let me explain first: a straight line between the road just now and our hands is a line segment. Holding the two ends of the cotton thread is mathematically called the endpoint of the line segment.
On the basis of explanation, guide students to observe and find out: How many endpoints does a line segment have? What do you think are the main characteristics of line segments? How are the endpoints of line segments represented?
Change the direction and shape of cotton thread: is this a line segment? Why?
Through variant training, students' understanding of line segments is strengthened and the essential characteristics of line segments are further grasped.
The third level: return to the concrete and find the line segment.
Ask the students to look around for line segments. Touch the characteristics of the line segment and tell your deskmate where the line segment is and where the endpoint is.
In the teaching of this link, students can experience the process from intuition to abstraction, and then from abstraction to concreteness through perception, experience, practice and reflection, thus forming a clear and rational understanding of line segments.
At the end of this session, I designed an exercise to identify line segments to test students' learning effect. Courseware demonstration exercise: Which of the following are line segments? Why?
Excellent Lecture Notes of "Understanding Line Segments" 3 I. teaching material analysis
"The length of quantity" is the content of Unit 6 in the first volume of the second grade of Jiangsu Education Publishing House. This unit is divided into four parts: understanding line segments, understanding centimeters, understanding meters and practicing "quantity".
Knowing the content of line segment is the basis of teaching length, because measuring the length of an object with a scale is actually measuring the length of a line segment. The line segment is the first contact for sophomore students, and it is abstract and difficult to understand. In the textbook, students draw line segments first, so that they can intuitively understand the characteristics of line segments. Learning this part well will help students learn measurement units better.
Second, the goal setting:
According to the new curriculum standards, combined with the characteristics of this class, I preset the following three-dimensional goals for this class:
Knowledge and skills: Get to know line segments initially, draw indefinite line segments with a ruler, and cultivate students' observation ability, imagination ability and operation ability.
Process and method: Let students experience the process of operating activities and observing line segments, and describe the characteristics of line segments in their own language.
Emotion, attitude and values: in the situation, make students have a psychological tendency to actively participate in learning activities and feel the mathematical facts in life.
Teaching emphases and difficulties:
Key point: understand the characteristics of line segments and line segments. Difficulty: mastering the characteristics of line segments.
Teaching preparation: Each student prepares a wool, a ruler, a rectangular piece of paper and several game sticks of different lengths.
Thirdly, the analysis of learning situation.
Line segment is an abstract concept in the basic knowledge of geometry. This lesson is the first time that students are exposed to this concept. It can be said that students' original knowledge base is zero, and some are hazy life experiences, but what their parents said when they were young was straight, and what they touched in life plays was curved. In their incomplete concept, there are bends and straight lines, but there is no difference between line segments, rays and straight lines.
The second-year students are young, and their abstract thinking ability is still poor. They can't express the essential characteristics of things in complete language, and their attention is not enough. But like hands-on, have a strong curiosity, a strong desire to express, these are the highlights that need to be used and captured in class.
Fourth, teaching methods, learning methods preset
Cognitive line segment belongs to concept teaching. According to the students' understanding of the concept, the general law is obtained: perception-representation-abstract generalization-forming the concept. We should give full play to the role of teachers, emphasize students' initiative, and guide students to find, analyze and solve problems and acquire knowledge, so as to train their thinking and cultivate their ability. To this end, I preset the following teaching methods:
The preset teaching methods are: intuitive demonstration, dialogue heuristic, trial and error, guided discovery, and combination of teaching and practice.
The preset methods are observation, hands-on operation and independent inquiry.
Fifth, the teaching process;
The New Curriculum Standard points out that the concept of "Mathematics originates from life, surpasses life and develops life" must be embodied and implemented through the important link of teaching. Combined with the characteristics of this lesson, I preset seven sections: first, compare the advantages and disadvantages, and introduce the situation into the new lesson; Second, change the curve to "straight line" to have a preliminary understanding of the line segment; Third, physical perception, strengthen the characteristics of line segments; Fourthly, according to the characteristics, self-built line segment model; Fifth, experience activities to deepen the understanding of line segments; Sixth, the whole class summarizes and abstracts the characteristics of line segments; Seven, in-class test, apply knowledge to solve problems.
The first part: compare the advantages and disadvantages, and introduce the situation into the new lesson.
People's emotions always arise under certain circumstances. The situation of mathematics teaching is different from other subjects such as Chinese. This situation is a gradual process, and it is also a dynamic development process of students' active understanding. In this lesson, I created the following scenario:
1, show two sticks, one is straight and the other is curved.
2. Guide the students to observe the difference between the two sticks.
3. Let the students divide into two categories according to the characteristics of these lines. The design of this link (curve and straight line) grasps the age characteristics of students, creates life situations, guides students' strong excitement and desire to explore, creates a positive, active and upward learning atmosphere, and lays a good foundation for learning new knowledge.
In the second section, the curve is changed to "straight line" to get a preliminary understanding of the line segment.
Suhomlinski said: "You should try your best to let your students see, feel and get in touch with what they don't understand, so that they will have questions. If you can do this, you will be half successful. " So: After students divide lines into curves and straight lines,
1. First of all, can you find a way to straighten these curves? Ask the students to try on the prepared wool, and then report the demonstration: How did you do it? Students may have two situations: one is to grasp the two ends of the wool and tighten it; The other is to hold only one end of the wool and let it hang naturally at the other end. At this time, let the students discuss: which method makes the wool straighter?
2. Then tell the students: Straighten the line, and the part between hands is the line segment. Ask the students to observe the wool in their deskmate's hands and point to the line segment in their hands.
3. The teacher demonstrated and explained that the two ends of the wool held by the students are mathematically called the endpoints of the line segment. Question: How many endpoints does a line segment have?
4. Ask the students to recall the operation just now, and then describe the characteristics of the line segment in their own language.
5. Mathematically, a line segment can also be represented by (). Ask the students to point out the starting point and ending point of the line segment and how the two endpoints are represented.
The design intention of this section is that for students, because of their young age and poor abstract thinking ability, line segments are abstract and difficult to understand. So I guide students to find ways to straighten the curve and highlight the characteristics of the line segment, and then further observe the two ends of the line, making it clear that the two ends of the hand are the two endpoints of the line segment. Through this activity, students can have a direct and real experience of the abstract concept of "line segment".
The third section, physical perception, strengthening the characteristics of line segments
1 First, let the students find out which edges of the objects around us can be regarded as line segments. Let them touch and point respectively. (Touch is to let students feel the straightness of the line segment; Pointing means that the sensory line segment has two endpoints. )
Then ask the students to imagine the line segments in life and give examples. Learn more about the characteristics of line segments.
3. The dotted line is relatively long.
Let the students take out the round paper and fold it in half, then unfold it and observe the crease. What did you find? (Students find that a crease is a line segment) Then ask students to fold a line segment that is longer or shorter than it, and compare the differences between the lines you fold (through comparative observation, you can get different lines. )
4. Compare the length of the line segment around you and reveal whether the line segment is long or short.
Mathematics comes from life and is applied to life. In this link, there is a segment from finding the edge to imagining the line segment in life, from touching, pointing and speaking the line segment in life abstractly, to help students establish the connection between mathematics and life experience and things.
Block four, according to the characteristics of the line segment, self-built line segment model.
At this point, students have gone through the process of recognizing line segments and will describe the characteristics of line segments. On this basis, I made the following design:
1 group discussion: what tools are you going to use to draw line segments and how to draw them?
Students try to draw line segments with different tools and methods?
Report and exchange the lines drawn by the students.
The teacher demonstrated the drawing method and explained that among many tools, it is more convenient and beautiful for us to draw line segments with a ruler.
Constructivism theory holds that the acquisition of knowledge depends on learners' active construction through exploration, operation and trial according to their own experience, rather than on learners' mechanical imitation and memory. This part of teaching requires students to abstract the line segment from the representation of the line segment that has been formed. On the basis of touching, pointing and looking, I asked the students to try to draw a line segment with the tools around them. First, I built the model of the line segment myself, and then I improved the construction process through discussion and communication.
The fifth section, activity experience, deepen the understanding of line segments.
In order to let students better internalize the knowledge of this lesson, I designed basic exercises, expanding exercises and open exercises.
Basic exercises
At the end of the book, "think about it and do it" 1 title. Ask the students to talk about which of the following are line segments. Students can deepen their understanding of line segments through judgment and explanation.
Number of line segments "Think and do" Question 2, let the students count how many line segments are around the following figure first. Then ask the students to point to the end of a line segment and feel the common ground. Finally, ask a question: a triangle is surrounded by three line segments, a quadrilateral is surrounded by four line segments, and a Pentagon is surrounded by five line segments. What did you find? Students observe that the figure surrounded by several line segments is a polygon.
outdoor training
Connecting segment
Think about doing the third question, first show two points and ask: can you draw a line segment with these two points as the endpoint? How many lines can you draw?
Think about doing the fourth question, show three points and understand what "draw a line between every two points" means. Let's guess what this painting will be. Then practice independently and show things, so that students can realize that a triangle is a figure surrounded by three lines.
Think about doing the fifth question and explain four points. Let's guess how many line segments you can draw at most. Let the students draw another picture. Let the students understand the law that a line segment can be drawn between two points in the process of drawing and discussing.
Section VI, class summary, abstract line segment features.
By summing up, let the students answer two questions: what do we know? What are the characteristics of line segments? Let the students know from perceptual knowledge to rational knowledge, and from intuitive knowledge to abstract knowledge. Three characteristics of a line segment are clear: the line segment is straight, the line segment has two endpoints, and the line segment is long and short.
Section 7, classroom test, feedback learning effect
The purpose of this is that teachers can master students' knowledge well, so as to teach students in accordance with their aptitude, give individual counseling to individual students, improve the quality of education and teaching in an all-round way, and realize "reducing burdens and increasing efficiency" in the true sense.
Six, blackboard design:
Summarize the characteristics of line segments into three-point blackboard writing, which is convenient for students to remember and master and can leave a deep impression on students.
Cognitive line segment
1, straight line
2. There are two endpoints.
3, there are long and short.
The overall design intention of this course is to let students walk into mathematics from life, from obscurity to clarity, from perception to abstraction. The above design stems from the following understanding: (1) Educational psychology shows that when learning is linked with existing experience, students' interest in learning can be better stimulated, and mathematics at this time is alive and full of vitality. Therefore, let students feel that there is mathematics in life from familiar life scenes, and then touch, touch and see, so that students can realize that mathematics has a strong life atmosphere, thus abstracting line segments. (2) Dutch mathematicians believe that mathematics learning is an activity that requires students' personal experience. Therefore, in teaching design, I first ask students to find ways to "straighten" curves and highlight the characteristics of line segments, and then let students touch, point and draw a picture. Finally, through a series of activities such as counting line segments and folding line segments, students' understanding of line segments is consolidated.