I. teaching material analysis
The understanding of trapezium is the content of the second lesson of "Parallelogram and Trapezium" in the eighth volume of the primary school mathematics experiment textbook. It is on the basis of mastering the characteristics of parallelogram that students learn to understand trapezoid. In the whole primary school stage, it belongs to the last linear plane figure, which is closely related to all kinds of figures learned before (can be transformed into each other). Therefore, the new curriculum standard points out that the teaching in this period should focus on making students gradually understand the shape, size, positional relationship and transformation of simple geometric shapes and plane graphics through observation, operation and reasoning; By observing objects, knowing the direction, making models and designing patterns, we pay attention to the development of students' spatial concepts, so that students can gradually rise from perceptual knowledge to rational knowledge.
Second, the analysis of learning situation:
Before this lesson, students have mastered the essential characteristics of rectangular, square, parallelogram, triangle and other plane graphics and the distance between parallel lines, and made some knowledge and skills preparations for this teaching. Although the trapezoid is the first contact figure for students, in real life, students have established a certain representation. However, it is difficult to accurately abstract its essential attributes, and it is also difficult to understand and practice the concept of trapezoidal height.
Third, the teaching objectives:
1, knowledge and skill goal: to know the names of all parts of the trapezoid; Understand and master the essential characteristics of trapezium, and know several special trapeziums and their properties; Cultivate students' abilities of observation, comparison, analogy, induction and operation imagination, develop students' concept of space and form a certain sense of innovation.
2. Process Method Objective: Combining with real life, through observation, classification, comparison and operation, guide students to carry out independent inquiry activities.
3. EQ goal: Through independent inquiry, cooperation and communication, let students experience success, build self-confidence, stimulate interest in learning, cultivate aesthetic taste, and feel the transformation thought and dialectical materialism education in mathematics.
Teaching emphasis: To master the essential attributes of trapezoid and understand the concept of trapezoid height, we can make trapezoid height.
Teaching difficulties: understanding and mastering the essential attributes of trapezoid.
Fourth, teaching methods.
The design concept of this lesson is:
● Classroom teaching is the process of emotional growth first, and then the process of knowledge growth.
● The learning process of students is a process of active construction and dynamic generation. Teachers should activate students' original experience, stimulate students' enthusiasm for learning, and let students truly understand new knowledge through experience, experience and application.
● Mathematics learning should be a process in which students enjoy the service of teachers.
Based on the above ideas, in teaching, I follow the teaching reform idea of "guiding inquiry learning and promoting active development", and strive to embody the principles of active learning, best motivation, step by step and intuition in teaching. Mainly adopt the following teaching methods:
1, guiding students to carry out inquiry learning activities by means of "classification, comparison and operation".
2. Organize students to carry out conscious group cooperation and exchange learning.
3, timely use of CAI courseware and multimedia teaching, give full play to the advantages of modern teaching methods.
Five, the teaching process theory:
According to the new curriculum concept, teaching objectives and the actual situation of learning, the author tries to construct a vertical structure model of inquiry mathematics classroom teaching, which is mainly divided into five teaching links: "initial understanding of trapezoid → operation experience, understanding characteristics → operation inquiry, deepening new knowledge → game activities, expanding new knowledge → exchange and evaluation, summary and sublimation".
Teaching link
Teaching and learning process
Design intent
First, classification and comparison, a preliminary understanding of trapezoid
1, organize teaching, review introduction: Last class, we learned parallelograms, and we know that their essential feature is (revealing that two groups of sides are parallel).
2. Draw a picture (find a quadrilateral that is not a parallelogram): Please find the `plane figure you see and divide it into two categories, and explain the classification basis. Seek common ground while reserving differences: only one set of opposite sides is parallel.
3. Reveal the theme: trapezoid
4. Perception of life: In connection with reality, what objects in life have trapezoidal surfaces? (Photo story demonstration)
Guide observation and comparison, stimulate inquiry motivation and cultivate discovery consciousness.
A good beginning is half the battle. Starting from students' existing experience, this paper introduces a new lesson with life pictures. Through two progressive classification and comparison (seeking common ground in differences and seeking differences in similarities), it is almost the essential attribute of trapezoid: quadrilateral, with only one group of opposite sides parallel. On the basis of trapezoidal feature cognition, combined with students' practical experience in life, students can experience that mathematics comes from life and further stimulate their interest in learning. Connecting with the reality of life, stimulating the vibration of thinking and cultivating the ability of discovery.
Second, the operation experience, understand the characteristics
1. Make a trapezoid: Can you make a trapezoid? Students use origami, painting, nailing boards, etc. Give students time, and then report and show the results. )
2. Features: Did you find any essential features when you made the trapezoid just now? Name three or four people to answer. It is written on the blackboard that only a group of quadrangles with parallel opposite sides are trapezoidal. )
3. Compare similarities and differences: What's the difference between a trapezoid and a parallelogram? Students discuss in groups first, and then call 2-3 students to answer.
4. Name the trapezoid of each part of the trapezoid. On page 47 of the guide self-study textbook, the names of all parts of the teaching ladder indicate: upper bottom, lower bottom, waist and height. )
5. Draw a picture and measure it: draw a trapezoid and point out the names of each part, higher.
In this link, students can learn about trapezoid, find its basic features, know its height and know its isosceles trapezoid through hands-on operation, comparison, communication and discussion.
High means the distance between the two bottoms; It is also clear that there are countless vertical segments (heights) between the two bottoms. It shows the main characteristics of trapezoid more clearly and visualizes abstract knowledge, which not only conforms to the principle of intuition, but also highlights the key points and breaks through the difficulties.
Third, the operation of inquiry, deepen new knowledge
Activity 1: use any one of parallelogram, rectangle and square to cut a knife along a straight line to make a trapezoid.
(Description: Destroy a set of parallel lines)
Blackboard writing: right-angled trapezoid
Activity 2: Cut a knife from a triangle along a straight line and turn it into a trapezoid.
(Description: Create a set of parallel lines)
Activity 3: Use a rectangular piece of paper, cut a knife along a straight line and turn it into a trapezoid.
(Discussion and communication summary: isosceles trapezoid)
Description: Right-angled trapezoid and isosceles trapezoid are two special forms of trapezoid.
Guide the main body to participate, preset the activity flow, and strengthen the ability of discovery.
This session focuses on group cooperation and operational inquiry, and guides students to further deepen their understanding of the essential attributes of trapezoid through comparison and transformation, and at the same time understand the unique attributes of "right-angled trapezoid" and "isosceles trapezoid". The main advantages are:
1, through observation and thinking, cooperation and communication, hands-on practice, enlighten students' thinking and cultivate innovative consciousness, which meets the requirements of the new curriculum.
2. From * * * to the opposite sex, from appearance perception to creating new knowledge, it embodies the principle of step by step and cultivates students' innovative consciousness.
3. Create an open dynamic learning process of teacher-student interaction and student-student interaction, instead of deliberately distinguishing the differences between trapezoid and various graphics, and guide students to explore independently, which fully embodies the comparative inductive mathematical thought.
Fourth, game activities expand new knowledge.
1, found it
Show the puzzle and ask: How many trapezoids can you find in the picture? How high can this ladder reach at most? (See the courseware)
2, spell a spell:
(1) with two identical trapezoid spell out a familiar figure.
(2) use a variety of trapezoidal pictures to pose a favorite pattern.
Create problem situation, deepen thinking level and build knowledge system.
1, through activities, cultivate students' innovative consciousness and aesthetic taste, and fully embody the new curriculum concept of "entertaining through education".
2. Teach students to use new knowledge in activities, expand their thinking, deepen their understanding, and enhance their sense of participation and subjectivity.
3. Infiltrate and transform ideas in the pendulum, pave the way for the derivation of trapezoidal area and build a three-dimensional framework for new knowledge learning.
V. Exchange evaluation, summary and sublimation
1, class summary:
Talk about your own gains and feelings.
2. Collective evaluation:
Evaluate yourself and your partner's performance in this class.
Improve knowledge structure, train thinking quality and sublimate discovery ability.
(1) embodies the people-oriented thought through humanized language.
(2) Introduce interactive evaluation methods to exchange activities feelings and form a self-feedback mechanism.
Sixth, classroom evaluation.
This course is teacher-led, student-centered, comparison-oriented, with teacher-student interaction and independent inquiry as the main methods, supplemented by multimedia teaching, which makes mathematics close to life, reality and original experience, and enables students to actively learn mathematics, explore mathematics and learn mathematics happily, which fully embodies the dynamic structural model generated by interaction in classroom teaching, achieves the preset teaching objectives and realizes the high efficiency of classroom teaching.