"A Preliminary Understanding of Axisymmetric Graphics" is the content of the first lesson of Unit 2 in the second volume of the third grade primary school mathematics published by Beijing Normal University. Through trial teaching, attending lectures and attending classes, I have a very deep understanding of the content of this lesson.
First, the interpretation of teaching materials
The content of this lesson belongs to the broad category of "space and graphics", and the existing knowledge of students is based on the orientation and simple plane graphics of grade one; It lays a foundation for learning how to rotate a simple figure 90 in the future. The textbook of this lesson provides pictures of folk paper-cutting, Facebook, Tiananmen Gate, etc. As well as many pictures that the teacher collected after class, they created a strong aesthetic atmosphere for this class, allowing students to appreciate beauty and ask questions: What are their similarities? Then ask students to find the characteristics of axisymmetric graphics by observing pictures and operations. The textbook attaches great importance to practical activities and fully embodies the concept of "thought begins with action". In order to deeply understand the teaching of "Preliminary Understanding of Axisymmetric Graphics", I decided to explore in practice. After reading the teaching materials and preliminary teaching ideas, I began to try teaching.
Second, the first teaching and reflection
[Teaching Summary]
First, appreciate and feel symmetry.
Teacher: Appreciate the symmetrical pictures collected in life. How do you feel? Please observe carefully and find that they have the same characteristics.
Health: symmetry.
Teacher: You are really something. You know the word. How do you understand symmetry?
Health: Both sides are the same.
The teacher summed up: an object with the same shape and size on both sides like this is said to be symmetrical.
Second, understand symmetrical graphics
Teacher: Are all the figures symmetrical? How are they symmetrical? How can we prove whether they are symmetrical figures? This is what we are going to learn in this class. In order to study these problems, the teacher also brought some plane graphics.
Teachers show the plane figures, and students discuss the classification in groups.
Teacher: Judge the classification by yourself and guide the students to prove the symmetry of the figure by "folding".
Guide students to fold all symmetrical figures in the same way and talk about your findings.
Health 1: I found nothing more or less neatly stacked.
Health 2: Both sides are together.
……
Teacher: That is to say, after being folded in half, the left and right sides are completely coincident.
Third, understand the symmetry axis.
Teacher: Now, let's look at our folded symmetrical figures. What did you find?
Health: There are creases.
Teacher: The left and right sides of the crease are "completely coincident".
A symmetrical figure, which can completely overlap after being folded in half, is called the symmetry axis. Students, these symmetrical figures can completely overlap when folded in half, so we call them "axisymmetric figures"
Fourth, practice consolidation.
1, students judge the axisymmetric figure.
Teacher: Mathematically, the axis of symmetry can also be drawn, and we usually use dotted lines to indicate it.
2. Is there an axisymmetric figure among the geometric figures we know today? Display: square, rectangle, triangle, circle, parallelogram.
Student: Take out the parallelogram, fold it by hand, and judge whether it is axisymmetric?
3. Game: The teacher shows half of the symmetrical letter figure, and the students guess what letter it is. (He Xiao)
Please spell it together-why laugh? This is the place where students live and study, the beautiful Hecun Primary School.
4. The teacher gives you half a figure and draws its axisymmetric figure.
Fifth, the teacher summarizes the lesson.
[reflection]
There are three main forms of human learning activities, one is experiential learning, the other is discovery learning, and the third is receptive learning. Students sit in the classroom and listen to the teacher talk about how disabled people live. This is-learning; And let students blindfold and do simple housework like blind people, which is experiential learning. Compared with the two learning effects, the latter is obviously better than the former, because the latter is a personal experience. Experiential learning not only activates students' cognitive needs, but also activates students' body and mind. It is a comprehensive study of knowledge, which can leave a deep impression on students.
After the first teaching, it is a pity that students can't master the characteristics of axisymmetric and axisymmetric graphics well; "Complete coincidence" is like a mirage built on the beach. Both beginners and Protestants always feel too rough and lack some taste of mathematics. So, I asked myself:
What is the essence of (1) axial symmetry?
Like translation and rotation, axial symmetry is also one of the methods to transform graphics. After class, I looked up some information and had two ideas:
1, the symmetry phenomenon of an object is a symmetrical figure after it is abstracted into a plane figure. In this lesson, we learn the axisymmetric phenomenon of plane graphics. So there is a big loophole between the first link and the second link. How to transition from the symmetry of objects to the symmetry of "plane graphics" is an urgent problem for me to solve.
2. Axisymmetric graphics are graphics that can be completely overlapped after being folded in half. What is "integrity"? What is the axis of symmetry? What are the characteristics of symmetry axis? In the above teaching design and process implementation, students are forced to "never tire of products" and never fully understand what "coincidence" and "complete coincidence" are. In the process of hands-on operation, students can't summarize the characteristics of axisymmetric graphics in their own language, so there is great doubt about how to judge whether plane graphics are axisymmetric.
(2) What is the carrier of essence?
Mathematics teaching should be carried out at the key points that affect the whole body, and the teaching of axisymmetric graphics is to grasp the two key points of "folding in half" and "completely overlapping", otherwise it will be scratches on the boots and waste time. But if the key points are chosen correctly, there must be no scenes and no carriers, otherwise students will not understand. Such teaching has become our teacher's wishful thinking. "All our teaching should be based on students' development", and we should find activities and forms that are suitable for knowledge itself and can be understood and accepted by students. Many schemes have been comprehensively considered. I think we should make a fuss about the activity of "folding in half". The understanding of "coincidence" and "complete coincidence" and the concept of axisymmetric graphics will also leave a deep impression on students' minds.
With the above understanding and thinking, I conducted the second teaching.
Third, the second teaching and reflection
[Teaching process]
First, appreciate and feel symmetry.
Teacher: Appreciate the symmetrical pictures collected in life. How do you feel? Please observe carefully and find that they have the same characteristics.
Health: symmetry.
Teacher: You are really something. You know the word. How do you understand symmetry?
Health: Both sides are the same.
The teacher concluded: As we have just seen, objects with exactly the same shape and size on both sides are said to be symmetrical. (blackboard writing: symmetry)
What other symmetrical objects have you seen in your life?
Second, understand symmetrical graphics
Teacher: What we just saw were photos of these symmetrical objects. We drew them on paper and got these plane figures. Are these figures still symmetrical? (Figure omitted)
Health: It is symmetrical.
Teacher: The children are very clever. They can see at a glance that these figures are all symmetrical. A graph like this is called a symmetric graph. (After "symmetry" on the blackboard: graphics)
Teacher: Are all the figures symmetrical? How are they symmetrical? How can we prove whether they are symmetrical figures? This is what we are going to learn in this class. In order to study these problems, the teacher also brought some plane graphics. The teacher showed the plane figure.
Ask the team leader to take out the envelope. The teacher sent you 1 before class. Take out the plane graphics inside. Students discuss the classification in groups.
Teacher: Do you all agree with his division? How do you know these figures are symmetrical? Is there any way to prove it?
An important way to guide students to get "folding in half" Students show it to their classmates.
Guide students to fold all symmetrical figures in the same way and talk about your findings.
Health 1: I found nothing more or less neatly stacked.
Health 2: Both sides are together.
……
Teacher: That is to say, after being folded in half, the left and right sides overlap. (blackboard writing: coincidence)
Students, just now we folded these symmetrical figures in half and found that they overlapped. Now the students in our group will fold the asymmetrical figure again and see what they find this time.
Do they overlap?
Really not? No coincidence at all?
This picture is overlapped after being folded in half, and so is this one. What's the difference between these two overlaps?
These symmetrical figures completely overlap after being folded in half, that is, completely overlap! (blackboard writing: finished)
Teacher: By clapping your hands, you can experience the complete coincidence of the two palms.
Third, understand the symmetry axis.
Teacher: Now, let's look at our folded symmetrical figures. What did you find?
Health: there are creases (blackboard writing: creases)
Teacher: The teacher also got some different creases by folding. Are these two creases different from yours?
Health: Our creases are the same on the left and right.
Teacher: It can also be said that the left and right sides of the crease are "completely coincident", but the left and right sides of the crease folded by the teacher will not be the same.
The teacher summed up the symmetrical figure, which can completely overlap after being folded in half. We call it the symmetry axis. (blackboard writing: symmetry axis)
Students, these symmetrical figures can completely overlap when folded in half, so we call them "axisymmetric figures" (supplementary blackboard writing: axis)
axial symmetric figure
Fold in half and completely overlap.
Folding symmetry axis
Fourth, the judge.
1, Teacher: Axisymmetric graphics can be seen everywhere in our lives. Determine which of the following figures is axisymmetric. Where is the axis of symmetry of these axisymmetric figures? Please think about it in your mind.
Mathematically, the symmetry axis can also be drawn, which is generally represented by a dotted line. (demonstration)
Health: independently judge whether the graph is axisymmetric.
2. Is there an axisymmetric figure among the geometric figures we know today? Show: square, rectangle, triangle, circle, parallelogram (and simply judge how many symmetry axes they have respectively. )
Student: Take out the parallelogram from the No.2 envelope and judge whether it is axisymmetric.
Through the activity just now, what do you think is the most important when judging whether a figure is axisymmetric? (folded in half, completely coincident)
3. Game: What the teacher wants to show you are several letter figures, all of which are axisymmetric figures. The teacher can only show you half of the picture. You have to guess what letter it is. (He Xiao)
Please put it together and see what it is. (It's He Xiao) Yes, this is the place where students live and study, the beautiful Hecun Primary School.
4. The teacher gives you half a figure and draws its axisymmetric figure.
Fifth, teachers sum up new lessons.
In fact, symmetry not only gives people a sense of beauty, but also has a certain scientific nature. The symmetry of the eyes makes us see objects more accurately. The symmetry of the ear makes us hear the sound clearer and more stereoscopic. The symmetry of dragonflies is for the need of balance. Inspired by people, the designed plane can fly smoothly in the blue sky.
Today, we have entered an axisymmetric world, a beautiful world. I hope students can keep their eyes open and find more beauty in their future math study.
[Second reflection]
My classroom
1, just one step away-draw the object in the photo and it will become a plane figure. It makes the study of axisymmetric graphics meaningful.
2. There are only two more comparisons: first, fold the "symmetrical figure" and then fold the "asymmetrical figure" so that students can have a profound comparison process of "partial coincidence" and "complete coincidence". The concept of "integrity" is clearly and accurately established. Students have mastered an important method to judge whether a graph is axisymmetric. Secondly, the comparison between the crease of the symmetry axis of an axisymmetric figure and the crease folded by the teacher makes students understand that only the crease that can completely overlap after the symmetrical figure is folded in half is called the symmetry axis of the figure.
My student
My students are at the junction of lower and higher stages, and their mathematical thinking is constantly developing, but experience is always one of the best forms of education. Only when we bend down, walk into the child's heart, walk into the child's spiritual world, capture cases from the student's life, and create situations in a way that students like, can students get real feelings and profound experiences, and finally precipitate into his heart and become a quality, an ability and a companion.