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What kind of teaching situation does mathematics classroom need?
(A) the creation of teaching situations with the help of objects and images

Physical objects in teaching mainly refer to physical objects, models, specimens, experiments and visits. For example, a teacher is teaching coral.

At that time, three kinds of corals, antlers, chrysanthemums and branches, were displayed, which gave students a real understanding of corals.

This is to create a situation through physical objects. The famous Soviet educator Suhomlinski attached great importance to the educational role of field trips. male

Often lead children to nature, carefully observe and experience the beauty of nature, so that students are relaxed and happy.

Learning knowledge in atmosphere can stimulate students' interest in learning and develop their imagination and aesthetic ability. He said, "I'm trying to do it.

Throughout childhood, the surrounding world and nature always give students vivid images, pictures, concepts and impressions.

Ideology provides nutrition. "

The experimental process can present rich and vivid visual images. Taking chemical experiments as an example, from instruments and equipment to drug preparation,

From the complex physical and chemical changes in the experimental process to the production of new substances, including changes in shape, color, state and taste, as well as gases.

Formation and precipitation of precipitation, or phenomena of light, electricity and heat. Students study chemistry based on their perceptions and views on these phenomena.

Check. For example, when it comes to chlorine, teachers usually demonstrate experiments (or students' experiments) first, and students observe the experimental phenomena before learning.

The intuitive images students see summarize the important chemical properties of chlorine, that is, chlorine is a relatively active nonmetallic element.

In teaching, image is an intuitive tool, which includes blackboard writing, pictures, wall charts, slides, videos, movies and electricity.

Audio-visual teaching method such as brain.

Images can present the scenery described in the text to children concretely and intuitively, so that they can get vivid images.

For example, in the teaching of the article Swallow, in order to let students feel the scenery of nature, some teachers use enlarged color wall charts at the beginning of the lecture.

Ask the students to observe the scenery in the picture carefully. What about their colors and dynamics? The rolling mountains, like mirrors on the lake, are green.

Green weeping willows, flying swallows and clear springs let students perceive beautiful pictures visually and lay a foundation for learning the text.

Foundation.

Pictures also have their special value in mathematics teaching: a third-grade elementary school student asked a math expert to explain the following.

Tao arithmetic problem: in a subtraction formula, the sum of subtraction, minuend and difference is equal to 90, and the difference is twice that of subtraction, so bad.

What is equal to? There are too many concepts in the problem. The expert made the children read it twice, but the students still couldn't catch it. Experts use pictures to show.

Stretching and painting gives children a sense of intuition and wholeness, which is easy to master (see figure 1).

Experts and children discuss: since the difference is twice the reduction, can we change the number 1 into the number 2? The child said happily, Yes.

Subtraction formula, simply change Figure 2 to Figure 3! According to "the sum of subtraction, minuend and difference equals 90", there are

Delta+delta+delta = 90, we can know that delta = 15, so the difference is equal to 30. It can be considered that these three numbers are special.

Language gives people a sense of intuition and wholeness, which is much easier to master than ordinary language. Therefore, the American mathematician Stith

Said: "If a specific problem can be transformed into a graph, then the mind will grasp the problem as a whole, and"

Be able to think creatively about solutions to problems. "

(B) with the help of actions (activities) to create a teaching situation

Teachers use gestures to assist language in teaching, such as "this child is so tall" and "this stick is so tall"

"Long" is also vivid for people to be "tall" and "long" and to use their hands. However, the emphasis here is dynamic.

The visualization of writing mainly refers to the operation from the perspective of science, mainly refers to the performance from the perspective of liberal arts.

1. operation

In teaching, a lot of abstract knowledge can be visualized by letting students operate learning tools. If the teacher is teaching Ping

When solving the problem, let the students divide the four piles of matchsticks into "as many" in each pile.

Let students understand the "average idea" of "more activities and less compensation" through intuitive operation, and then pile up the four together (total).

It is required to quickly divide into four piles (total number of copies) and how many blocks (number of copies) each pile has, and the general method of finding the average value is obtained. behaviour

The characteristic of writing is that it is intuitive through action, thus organically combining action thinking with image thinking.

Piaget once described such a "story": four or five-year-old children put some stones away in order to count clearly.

One line, and then count from 1 to 10. After counting, start counting from the other end and find that it is also 10. Then he put the stone away.

Form a circle and count down in turn, and come to the same conclusion. What did he find? He didn't find the sex of the stone.

Quality, but discovered the nature of the order of action. Because these stones are out of order, it is his behavior that makes them become.

Linear order or cyclic order or any order. So the experience gained here has nothing to do with the physical properties of stones.

To be exact, it has nothing to do with stones and can be completely replaced by mathematical symbols. This is the acquisition of logical mathematics experience,

An abstract process that depends on external things and transcends their concrete forms. Understanding this process will help us to give pure

Mathematics "puts on" the appropriate life coat and presents it to children instead of "surgically" transforming mathematics.

Suitable for life. (Yu Huijuan: Education for Discipline Transformation, People's Education, 2006.3-4, P46)

carry out

Performance is a higher level of visualization, because it is not only the external image of the teaching content, but also shows the inner world of the characters.

Boundary. A teacher taught Waiting for the Rabbit, which was soon finished, but the students didn't understand its meaning. At this moment, the teacher had a brainwave.

Dress up as a waiting person, lean against the blackboard, close your eyes and meditate, and let the students "convince" themselves. Students' interest is doubled, and they are advised to be old.

Teacher: "Teacher, you can't wait for the rabbit" ... "Teacher, you will starve to death if you wait any longer!" The teacher also imitated waiting for him.

The rabbit argued with the students in a tone. The more students persuade, the higher their interest and the deeper their understanding of the meaning of this fable. In teaching

In addition to teachers' performances, students can also perform, and students' performances have unique teaching significance. As Suhomlinski said: "From

In essence, all children are born artists. "In fact, children not only have potential acting talent, but also

Personality characteristics of loving performance. Performance can effectively mobilize and give play to children's enthusiasm and creativity. Some China textbooks.

The length of the drama is very strong, and the language is very strong in action. Teachers should be good at adapting them into sketches or textbook plays, so that students can walk in.

Text, play the characters in the text, grasp the connotation of the text in "movement" and "music", and understand the character, language and action of the characters.

Work, behavior, inner world.

3. Activities

The intuitive situation generated by student activities also has its teaching significance. When a math teacher is teaching travel problems, he thinks that students

It is difficult to understand the concepts of "at the same time", "in different places", "meeting" and "meeting time", so he organizes student activities.

Help students understand through activities. He organized two teams of students to race on both sides of the playground. When the teacher blew the whistle, they all came out of the playground.

Go in the opposite direction At this time, the teacher let the students understand the meaning of "simultaneous" and "opposite". Please stop and tell two people when they meet.

Students, this is a "meeting". Then let the students see who walked more when they met, and let the students understand that there are two people at the same time.

How far do students go? After the activity, when the teacher teaches this part of knowledge, the students think of the scene of the activity and learn from it.

Based on the obtained perceptual materials, we can master the knowledge of meeting problems through further analysis and thinking.

demonstrate

Demonstrations can also create intuitive situations. When a math teacher was teaching "mathematical induction", he demonstrated it through a mold ball.

Induction. As soon as class begins, the first thing the teacher touches out of his schoolbag is a red glass ball. Second, third, fourth and fifth.

It is a red glass ball. Q: "Is this bag full of red glass balls?" Student: "Yes". Keep touching and find a white one.

Glass balls, ask: "Are they all glass balls?" The students argued with each other and were highly excited: "Yes". Touch it again,

The teacher touched out a ping-pong ball (laughs) and asked, "Are they all balls?" Student: "Not necessarily". Summary: "This guess.

That's right: if you know that the contents of the bag are limited, you will touch it sooner or later. When you touch everything in the bag, of course.

You can get a positive conclusion. But what if something is infinite? "(Static)" If I agree,

If you touch a red glass ball this time, you will definitely touch a red glass ball next time. Is the bag full?

Is it a red glass ball? "Student:" Yes ". ..... This intuition helps students really understand the essence of mathematical induction.

(C) the teaching situation created by language

The vividness of language expression can make the listener's mind present a vivid and concise picture, rather than some abstract pictures.

Semantic code of image. If the harvest is good, it is not only how much the yield per mu has increased, but also how much sorghum has turned red and the ears of wheat have bent with laughter.

This kind of language, which visualizes and concretes abstraction, must sound full of interest to students, such as A Midsummer and Jude.

It's like enjoying a painting, a play. From the perspective of teaching art, the requirements of visual language expression:

1. Read aloud-full of sound and emotion

Reading aloud with sound and affection can bring students into the artistic realm of works, so that students can be there, hear and see.

The scene described by the teacher came to his mind vividly. The scenery described in many texts in Chinese textbooks is kind and pleasant, expressing.

Our feelings are delicate and warm, which can be described as both affectionate and beautiful. It is not enough for children to appreciate these texts only through the teacher's explanation.

The miracle. Only by reading aloud with rich voices and emotions can we arouse the image of beauty in the text and thus arouse students.

The strings of the heart produce a feeling of * * * in the depths of the heart. In addition to expressive reading, the sound simulation is also vivid and layered.

The second highest image. For example, read Mr. Dong Guo and the Wolf, The Knowledgeable Pig, The Reason of Fisherman and Goldfish.

Like other fables and fairy tales, the expression and sound simulation of reading aloud is an art.

2. Description-vivid

Teachers' vivid descriptions can also make abstract concepts vivid. For example, a math teacher talks about "points"

The trajectory of ",holding up a blue chalk in his hand, said to the students:" I have a new one here.

The' bug' that crawled out of the ink bottle kept crawling and crawling 30 cm away from the fixed point, and stayed.

Drop a little ink. You see, this is the trajectory of the' worm' movement. "Students listen to the teacher's vivid description, people

People will smile. In science teaching, the more abstract concepts are established, the more image description and imagination are often needed.

3. Metaphor-appropriate and wonderful

Metaphor is to compare what you want to say with similar things in order to express it more vividly.

Making good use of metaphors will not only make abstract things concrete, but also make things difficult to understand simple.

Very easy to understand. A chemistry teacher is particularly good at using metaphors, and has achieved strange results in teaching. For example, a catalyst pair

For junior high school students, this is a difficult concept to understand. In teaching, he used the following metaphor: a person wants to cross the river.

There are two ways to get from a to b: one is to cross the bridge along the river bank to a far place, which takes a long time.

Go on but slowly); Another way is to take a boat from A to B, which is faster by road.

The way makes the speed faster), the chemical reaction uses a catalyst, just like a person takes a boat from place A to place B, and the road is very fast. here

The ship is equivalent to the catalyst of the reaction, which accelerates the speed from place A to place B and participates in this process (metaphor for the catalyst itself

Participated in the reaction), but after people get on and off the ship, the quality and nature of the ship itself remain unchanged. For negative catalysts, the opposite may be true.

And use it. There is a piece of knowledge about blood pressure in the textbook of Senior Two: "Normal adult systolic blood pressure 12- 18.7 kPa, diastolic blood pressure 18.7 kPa.

It is 8- 12 kPa. If a person's diastolic blood pressure often exceeds 12 kPa, it is considered as hypertension. If a person's income

When the contraction pressure is often lower than 12 kPa, it is considered as hypotension. "This passage, even if students read it five times, students may not.

Can master. In teaching, the fist (scene) can be used as an analogy: the fist is like the heart, which is very powerful when contracting and produces great pressure.

Relaxation (fist release) produces less pressure. The dividing line is 12. Systolic blood pressure should be high. If it is high, it means low. If it's low,

12, which is hypotension. Diastolic pressure should be low, and low or not is high. If it is greater than 12, it is hypertension. How do you remember this?

12? We usually say that we are very happy, and some people will say that we are extremely happy. So, this is the best number. Draw like this

Describe the situation, students can easily master the knowledge of blood pressure. [2] In this way, by using the familiar concrete image metaphor, the original

Abstract and difficult knowledge becomes easy to understand, students can easily accept and understand, and mechanical memory is transformed into

Understanding memory is not easy to forget.

(D) The teaching situation created by the relationship and contradiction between old and new knowledge and concepts.

What students learn in school is not fragmentary and one-sided knowledge, but a "refined and refined" and "digestible" department.

Unified and holistic knowledge. Any knowledge is a point or a knot on the whole network. Without the internet, you will get lost.

The foundation of survival. Knowledge can only be truly understood and mastered in the overall connection, thus reflecting its meaningful value.

In other words, students' learning of new knowledge is based on old knowledge, and new knowledge is either based on old knowledge and extended.

Develop, or add new content on the basis of old knowledge, or reorganize or transform from old knowledge, so

Old knowledge is the most direct and commonly used cognitive stopping point for learning new knowledge.

The research of American educational psychologist Ausubel further puts forward that the basis of old knowledge is its availability, identifiability,

Stability (clarity) three characteristics (collectively known as cognitive structural variables) to specifically affect the course and effect of meaningful learning.

The so-called availability means that students have old knowledge to fix new knowledge in their original cognitive structure, but there is no such knowledge.

The interaction (assimilation) between old and new knowledge has lost its foothold, and learning can only be done mechanically. For example,

Students don't have the old knowledge of "the invariance of quotient" and "the division rule of divisor is integer", so it is right to say that divisor is decimal.

The new knowledge of division can only be learned mechanically. The so-called identifiability refers to: between old knowledge and new knowledge.

Only when the old and new knowledge can be clearly distinguished can students learn meaningfully.

For example, only when students clearly understand the difference between "divisor is the division of decimals" and "divisor is the division of integers"

When they are different, it is meaningful for them to learn "divisor is the division of decimals", otherwise it will lead to negative transfer in learning.

Thereby generating mechanical learning. The so-called stability and clarity refers to the firmness and clarity of old knowledge itself, which plays a fixed role.

Degree and stability provide a fixed assimilation point for learning new knowledge, and clarity provides an assimilation orientation point for learning new knowledge. Obviously,

If students' grasp of the old knowledge that "divisor is the division of integer" is vague and unstable, then "divisor is decimal"

Learning this new knowledge can't be meaningful and smooth.

Specifically, when explaining the division in which the divisor is a decimal, we should first review the property that the quotient is constant and the dividend is a decimal but a divisor.

Is the fractional division of integers. Show me 37.5÷ 15=2.5 and tell me how you worked it out. Let the students fully explain the reasons, and then

Question 3.75÷ 1.5=? 375÷ 150=? What happened to multiplication, division and division? What is quotient? The quotient of students remains the same.

The nature of (the multiplicand and divisor expand or shrink by the same factor at the same time, and the quotient remains unchanged) determines that the answer is still 2.5. Students are like this.

Thinking is the method we want to teach, revealing that divisor is the operation method of fractional division. At this time, the teacher will guide the correct vertical position.

Calculation method and format, further deepen the calculation, students will master the calculation method. According to the internal connection of knowledge, teachers can benefit

With the transfer of knowledge, create situations and let yourself explore calculation methods, students will be happy to learn, willing to learn, and truly become the main body of learning.

(E) Creating teaching situations with the help of "background"

The so-called background knowledge refers to the general term of knowledge related to the text content of teaching materials. The relationship between background knowledge and new knowledge is not as good as before.

The relationship between knowledge and new knowledge is so close and direct that there is no logical connection between them, but the background knowledge is also learned by students.

An important cognitive station for learning and understanding texts. Without necessary background knowledge, reading and thinking are often impossible.

The richer the background knowledge, the higher the reading comprehension level.

The background knowledge of classroom teaching mainly includes:

1. "Introduction to the author"

As the saying goes, the introduction of people (authors) is of course helpful to promote the understanding of people (works) as they are. because

Because the author wants to "write a magnificent style, he must have a magnificent personality" (Goth). Therefore, "author introduction" is the most.

It is important to let students know the author's personality, so as to better observe and appreciate the style of the work. This will not only have

It is helpful to promote students' meaningful learning and moral education.

2. "background of the times"

The background of the times helps students to deeply understand the inner meaning of the text. Teaching model cards can be analyzed at the end of the article.

Students talk about what happened to Fanka. Why do you suffer so much at such a young age? Teacher guidance-explaining articles

The background of the times enables students to understand Van Gogh's miserable apprenticeship and see the life of the devastated old Russian people in miniature.

3. "Historical allusions"

Appropriate introduction of interesting literary allusions, interesting stories about the history of mathematics, anecdotes about scientists, etc.

For students, meaningful study is very beneficial. When a primary school Chinese teacher was teaching the ancient poem Weeds, it was through a passage.

Learning stories leads to new lessons. As soon as class began, the teacher said to the students, "Today we are going to learn an ancient poem. The teacher will give it to the students first. "

Tell the story of Bai Juyi, the author of this poem. "The teacher explained the poem Bai Juyi on the blackboard. Here's the story.

Bai Juyi was a native of Tang Dynasty in China. He was born in poverty, but he loved learning since he was a child, especially writing poems. White 16 years old

After Juyi left his hometown for Chang 'an, Kyoto, he continued to write poems. In order to improve the level of writing poetry, he turned to famous teachers for advice everywhere. Once,

He visited Gu Kuang, an old poet at that time. Gu Kuang is a joker. When he learned that the young man in front of him was named Bai Juyi,

Want to joke again. He said, "Alas! You have a bad reputation. " Gu Kuang touched his beard and said, "What's your name?

His name is Juyi. Now Chang 'an rice is expensive, and renting a house is difficult. It is not easy to live here. "Bai Juyi

After listening to this sentence, I thought that I often worried about food and clothing after I went to Chang' an, and I borrowed money everywhere. I couldn't help but say with deep feelings: "You

Well said, living in Kyoto is really not easy! "Gu Kuang saw that the young people in front of him were modest and eager to learn, so he said," Ok, let you go.

Read me the poem you wrote. "Bai Juyi began to read poetry. (Reciting the recording "Grass") Bai Juyi has just finished reading it, and Gu Kuang Lian

The voice praised, "A good poem is a good poem. You can write such a good poem, and the future is boundless. It would be nice to get the name of Juyi! " Bai Juyi

He asked inexplicably, "Old man, just now you said my name was not easy to choose, and now you say my name is easy to choose. This is not self-denial. "

Is it contradictory? Gu Kuang said with a smile; "I didn't know you could write poetry just now, so I said it's not easy for you to live in Chang 'an, so I took this name.

Not so good. Now I see you can write such a good poem. So it's easy for you to live in Chang 'an. What a nice name. "Say that finish.

Enthusiastic advice. From then on, Bai Juyi became more diligent and finally became one of the three great poets in the Tang Dynasty (others).

Two are Li Bai and Du Fu). After the story was finished, the teacher went on to say, "Let's learn this poem and see if it can be written well."

What's good about this poem? "The teacher began to explain the new lesson, and the students were very interested in learning the new lesson. This story is ingenious.

This paper introduces the background of the poet and the time when he wrote poems, which not only naturally reveals the teaching content of this course, but also gives students a preliminary understanding of the new curriculum.

The perception of step shortens the time difference and solves the big obstacle that learning ancient poetry can't produce a sense of singing because of the long time interval.

Let students enter the artistic conception created by the poet easily and happily.

(6) Creating teaching situations by asking questions.

There are many types and forms of teaching situations, among which special emphasis should be placed on problem situations and problem consciousness. The problem is scientific research.

The starting point of research is the key to any science. If there is no problem, there will be no way to explain and solve it.

Method and knowledge Therefore, the problem is the logical driving force for the accumulation and development of thinking methods and knowledge, and the growth of new ideas and methods.

Seeds of law and new knowledge. Students must also attach importance to the role of problems in learning. Modern teaching theory research points out that, in essence,

Perception is not the fundamental reason for learning (although students need to perceive learning), but the fundamental reason for learning is the problem.

If there is no problem, it is difficult to induce and arouse curiosity. If there is no problem, students will not go deep and feel the existence of the problem.

Thinking, then learning can only be superficial and formal. Therefore, the new curriculum learning method emphasizes the problems in learning activities.

The importance of. On the one hand, it emphasizes learning through questions, and regards questions as the driving force, starting point and penetration of learning.

The main line in the process; On the other hand, problems are generated through learning, and the process of learning is to find problems, put forward problems and divide problems.

The process of analyzing and solving problems. What needs special emphasis here is the formation and cultivation of problem consciousness. Question consciousness refers to asking.

The problem becomes the object of students' perception and thinking, thus producing an unsolved knowledge in students' minds that must be solved.

State. Question consciousness will stimulate students' strong desire to learn, so that they can pay close attention to and actively participate in learning; ask

Topic awareness can also stimulate students' scientific spirit of exploring, creating and pursuing truth. Without a strong sense of problems, it is not.

It may stimulate students' impulsive cognition and active thinking, and it is even more impossible to stimulate students' innovative thinking and creative thinking. total

In a word, problem consciousness is an important psychological factor for students to learn.