How to create junior high school mathematics teaching situation. Creating teaching situation means that in mathematics class, teachers take certain interests and images as the main body, and purposefully introduce or create positive and specific situations to arouse students' attitudes and experiences, thus helping students understand the teaching materials. Today, Park Shin-bian Xiao has brought a blow to mathematics teaching methods.

Extend old problems and create problem situations discovered by analogy.

There is a lot of knowledge with similar attributes in middle school teaching. For these knowledge, teachers should first guide students to learn the existing knowledge, and create a problem situation discovered by analogy through the mathematical thought from special to general, so that students can assimilate and construct in the original structure.

Example 3. When talking about the "parallel line segment proportion theorem", first review the content and graphics of the "parallel line segment equality theorem" (as shown in figure 1). At this time, ab ∶ BC =1∶1= de ∶ ef; Then the straight line CF is translated downwards, and it is obtained that if AB∶BC= 1∶2 and other conditions remain unchanged, DE∶EF=? Encourage students to further explore the conclusion; Then continue to translate BE and CF, so that when AB∶BC=m∶n (m, n is a real number), other conditions remain unchanged, then DE∶EF=? Inspire students to take the form of cooperative discussion and draw conclusions.

Using Mathematical Stories to Create Problem Situations

Mathematical stories sometimes reflect the formation process of mathematical knowledge and sometimes reflect the essence of knowledge points. Using such stories to create problem situations can not only deepen students' understanding of knowledge, but also deepen students' interest in mathematics and improve their aesthetic ability. Example 4: When talking about "plane rectangular coordinate system", the author first talks about the process of mathematician Euler inventing coordinate system. Euler lay in bed quietly thinking about how to determine the position of things. At this time, a fly stuck to a spider web, and the spider quickly climbed over and caught it. Euler suddenly realized, "Ah, you can use a web to locate things like a spider." So, I introduce the topic of this section.

Use multimedia courseware to reflect problems in real life, create problem situations and stimulate thinking. 5. When talking about the calculation of "fan area", the author first designs an interesting animated plot "Dog and Sparrow" with Flash to introduce the topic. There is a post on the open lawn, and a 3-meter-long rope is tied to the post. At the other end of the rope, there is a dog tied. What is the maximum active area of a dog? Suddenly, a sparrow came to tease the dog, so the dog turned N degrees around the post. So, how big is its maximum activity area? After watching this short film, the thirst for knowledge was strongly stimulated, and the mathematical model of practical problems in this life was immediately established, so the calculation of fan area was introduced. Using modern teaching methods in teaching, students can experience life while enjoying animation freely, and have a desire to explore in the situation, so that autonomous learning is stimulated.

2. How to create a situation

Stimulate interest and create story situations

In the history of human development, there have been many well-known mathematical stories and anecdotes of mathematicians. These mathematical allusions sometimes reflect the process of knowledge formation and sometimes the essence of knowledge points. Using such stories to create problem situations can not only deepen students' understanding of knowledge, but also deepen students' interest in mathematics and improve their aesthetic ability. When designing mathematics teaching situations, we should fully tap the historical materials of mathematics and create mathematics situations by using these rich cultural resources, which can not only stimulate students' desire for knowledge, but also learn mathematics knowledge, appreciate mathematicians' personality charm and receive ideological education.

Such as Gauss, Descartes, Newton and China mathematicians Zu Chongzhi, Hua and Chen Jingrun, have many stories that can be used to design mathematical situations. For example, when we talk about Pythagorean Theorem, we can tell students a story: If there are other civilizations besides human beings in the universe, how should human beings communicate with them? Hua, a famous mathematician in China, pointed out that Pythagorean theorem can best represent human civilization. If there are other civilizations in the universe, if they receive this information, they will respond to human beings. After listening to this story, students will be eager to know, what is the content of Pythagorean theorem? Thus paving the way for learning new lessons.

Develop thinking and create problem situations.

Students' thinking activities of seeking knowledge always start from problems and develop in the process of solving problems. Carefully design the question situation and ask questions skillfully. Students should feel that "there is no way to regain their doubts" and be encouraged and induced. Then through their own efforts, to explore the artistic conception of "bright future, bright countryside". Creating problem situations in this way can stimulate students' thirst for knowledge and open the floodgates of thinking. For example, in the teaching design of "making an isosceles triangle", I created such an attractive problem situation: in △ABC, AB=AC, I was accidentally smeared with ink, leaving only a bottom BC and a bottom angle ∠ C. Is there any way to redraw the original isosceles triangle? First, students draw the residual figure and think about how to draw the part smeared with ink.

Various painting methods have emerged. Some students first measure the degree of ∠C, and then take BC edge and point B as vertices to make ∠B=∠C, and the edges of B and C intersect to get vertex A; In addition, take the midpoint D of BC, take the point D as the vertical line of BC, and intersect with one side of ∠C to get the vertex A. The correctness of these drawings needs to be formulated through the "formulation theorem", which is exactly the subject to be studied. So I grabbed "Is the triangle drawn necessarily an isosceles triangle?" Lead out the topic, and then guide the students to analyze the essence of painting, and summarize this essence in geometric language, that is, "in △ABC, if ∠B=∠C, then AB=AC". This judgment theorem is obtained by the students themselves from the problem.

3. Create problem situations

Using mathematical allusions to create problem situations

The allusions in mathematics class can include the history of mathematics and some anecdotes of celebrities, or some interesting folk stories to be solved with mathematical knowledge. Historical mathematical allusions sometimes reflect the process of knowledge formation and sometimes the nature of knowledge points. Using such allusions to create problem situations can not only deepen students' understanding of knowledge, but also deepen students' interest in mathematics, understand the history of mathematics and improve their mathematical literacy. Telling students a story according to the teaching content in math class will get unexpected results.

For example, when studying "The Application of similar triangles", the teacher told the students a story about Thales, an ancient Greek philosopher, measuring the height of the pyramid, and showed the scene pictures with multimedia. The students are very confused. The teacher conveniently introduced similar triangles's knowledge application study. After learning the new lesson, they came back to think about how Thales measured the height of the pyramid. Such a persistent problem situation runs through the whole classroom teaching, which not only stimulates students' thinking, but also cultivates students' awareness of applying mathematical knowledge to solve problems.

Create problem situations by analogy.

Analogy is a way of thinking that compares two different things, finds some similarities or similarities, and speculates that there may be similarities or similarities in other aspects. Because the knowledge of mathematics has a strong outward expansion, and the newly expanded knowledge always has many similarities with the pre-expanded knowledge, it is a clever and efficient teaching strategy to compare the new knowledge with the pre-expanded knowledge. Examples of making great discoveries and inventions by analogy are common in the field of mathematics. It is necessary to guide students to carry out various colorful exploration activities such as induction/analogy, encourage students to carry out analogy between general and special, high and low dimensions, infinite and limited, and cultivate and develop students' creative thinking.

For example, the hybrid algorithm of learning rational numbers can be compared with the hybrid algorithm of primary school mathematics; The mixed algorithm of real numbers can also be compared with the mixed algorithm of rational numbers; Power meaning can be analogized to multiplication meaning; The meaning of bivariate quadratic equation can be compared with that of univariate quadratic equation. The basic properties and algorithms of fractions can be compared with fractions. It can be said that where there is learning, there will be migration, because there is no isolated learning that does not affect each other. In the teaching process, actively creating positive transfer situations is an effective means to cultivate students' thinking ability.

4. Create a teaching situation

Create discussion and operational situations to deepen understanding.

In math class, understanding math knowledge is an important way for students to master math knowledge and skills. As a mathematics teacher, we should create a harmonious situation for students' understanding of mathematics, touch students' life accumulation, make students feel something, and make since the enlightenment adapt to it, so as to deepen their understanding in practice.

Creating discussion and operation situations can create a relaxed and harmonious teaching atmosphere. For inquiry questions, students need to explore in practice, try in operation and dispel doubts in discussion. Through oral discussion, brain thinking, eye observation and hands-on operation, let their senses participate in teaching activities, such as drawing, measuring, collecting information, cutting, folding, moving, rotating, making models, etc., which not only enable students to actively acquire knowledge, but also enrich their experience in mathematics activities, cultivate their ability to observe, analyze, apply and solve problems, and activate their creative potential.

Create argumentative situations to inspire students to divergent thinking.

In mathematics class, in order to satisfy students' competitive psychology, teachers can consciously create "argumentative writing" situations according to students' existing knowledge structure, set up knowledge arena for students, trigger cognitive conflicts, enlighten students' thinking, cultivate students' ability to analyze and solve new problems with existing knowledge and experience, and cultivate students' profound thinking. Teachers can create an argumentative problem situation in the following ways: (1) only give the conditions (or conclusions) of the problem, so that students can debate different results (or conditions); (2) Add or delete given conditions (or conclusions), so that students can summarize the changes of given conclusions (or conditions) in the exchange debate; (3) For questions with complete conditions and conclusions, first give the conditions, so that students can guess the conclusions in communication and argumentation and prove them.

Creating Trial and Error Situations and Optimizing Students' Thinking Quality

In math class, in view of students' incomplete understanding of some concepts, laws, theorems and properties, teachers can purposefully create some chaotic problem situations. Or connect the mistakes and puzzles in the senior high school entrance examination, so as to let students walk into the maze, constantly hit a wall, guide them out of the misunderstanding of thinking, guide them out of the maze, let them learn from a pit, gradually abandon the wrong thinking and optimize the correct thinking.