1 how to expand the depth of students' mathematical thinking
Change ideas and roles to create a democratic, harmonious and relaxed learning atmosphere for students.
If students really want to get rid of the shackles and take the initiative to explore, then teachers should first put down their airs, approach students, and strive to create a harmonious and relaxed teaching environment, so that students can feel that teachers are their close partners-teachers and students can communicate smoothly, so that teachers can become veritable "organizers, collaborators and participants." Therefore, teachers should regard students as the masters of learning in teaching, communicate with students in an equal and friendly tone, and try to eliminate the natural psychological barriers between teachers and students.
For example, I once saw a teacher in the fifth book "Understanding Rectangles and Squares". When he talked about the process of changing a rectangle into a square by folding and cutting, he took out a rectangular piece of paper and said to the students, "Students, now the teacher is going to perform a little magic trick for you. Do you want to see it? " "think!" The students are looking forward to it, so the voice is very strong. The teacher turned around and immediately cut the rectangular paper into square paper. The teacher then deliberately asked the students, "Is this magic fun?" "It's not fun, so will we!" The students said with a smile. "Are you? I don't believe it, just show it to me. " The students were really fooled, and everyone finished the task quickly. Seeing this result, the teacher deliberately said in dismay, "It's over, all my secrets have been discovered by you." "Ha ha ha ha ha ha" students smiled, laughing very proudly. In fact, the most gratifying thing at this time is the teacher himself, because at this moment, not only the problem of "knowing rectangles and squares" has been solved, but also the psychological distance between teachers and students has been greatly shortened, the classroom atmosphere has become more harmonious, and the later learning activities have become more relaxed and happy.
Teachers should pay attention to evaluating students' art and strive to promote students' deep thinking from the emotional point of view.
In an open teaching environment, students' thinking is always in a positive state, and in the process of solving problems, such thoughts will inevitably appear. In order to avoid weakening students' enthusiasm, the art of teacher evaluation is particularly important. Because it is an effective catalyst to promote the all-round development of students' thinking. Teachers must adhere to the principle of giving priority to motivation when evaluating students. Especially when students' ideas are reasonable and creative, teachers should not pity their own praise, so that students can truly feel the value of success;
When students are not clear enough in expressing a certain point of view, teachers should never completely deny it. They must listen to the students patiently and sincerely, and try to find the "central idea" of the students. Even if there is no concrete gain, the teacher can encourage them to say, "Your idea is very reasonable. If you can speak more clearly, that would be great, you can try "; When students' ideas or ideas are obviously wrong, teachers should also respect students' speeches and let them finish. Finally, they should say in a euphemistic tone, "I can see that you are actively thinking, think again." Of course, when teachers motivate students, the language must be just right. They shouldn't exaggerate and give people a false feeling. They shouldn't always mechanically repeat boring and monotonous language. They should make an objective evaluation according to the actual situation.
2 the cultivation of mathematical thinking
Encourage questioning and seeking differences, and expand the depth of thinking.
In teaching, I regard solving students' difficult problems as an essential teaching link, so that students can gradually develop the habit of asking questions, learn to turn "question marks" into "periods" and generate new "question marks" from "periods". Persist in it for a long time, and the classroom is often colorful. For example, after teaching the drawing method of parallel lines, some students put forward different views: it is enough to draw parallel lines with a ruler, and a group of parallel lines can be drawn with a group of opposite sides of the ruler. As soon as this was said, the whole class immediately exploded. After some arguments, a student finally pointed out that it is good to do so, but the parallel lines drawn should not be arbitrary, and two rulers should be used to draw them.
The student who asked the question showed an unconvinced expression on his face and muttered to the classmate next to him: It's so troublesome to use two rulers. You must use one ruler. I smiled and said, "Since this classmate is so determined, he wholeheartedly wants to solve the trouble of drawing with two rulers for everyone. What a good wish! Why don't we study together? Maybe we can really realize this wish! " Through the efforts of the students, we really found a way: draw two equal and vertical vertical lines on the same side of the determined straight line, that is, find two points on the same side of the straight line with the same distance, and then draw parallel lines of the known straight line through these two points. At this time, all the students showed smiles on their faces, especially the students who raised this question, and their smiles were even brighter.
Guide students to actively participate in learning, teach students to learn to learn, and get pleasure from learning.
In classroom teaching, guide students to participate in learning, teach them to learn to learn, and get pleasure from learning, which requires teachers not to sing solo on the podium just according to the teaching plan. The biggest feature of classroom teaching is the alternation of teaching and learning, which is the communication between teachers and students. Teachers play a leading role in the communication process, while students play a major role. A classroom is a place where teachers and students discuss problems together. Teachers should not only impart knowledge, but also teach students the methods, procedures and thinking strategies to acquire this knowledge in combination with their own teaching, so that students can not only acquire knowledge through teaching, but also acquire methods to understand problems, so that students can learn to learn and experience the fun of learning.
In the usual teaching, we should choose different teaching methods according to different teaching contents, different teaching objectives and students' characteristics, strive to create a harmonious and pleasant teaching atmosphere and diverse teaching situations, and carefully design teaching processes and exercises. Give students the right of independent exploration, cooperation and communication and hands-on operation in class, so that students can fully express their opinions. Over time, when students realize the joy of success, they will arouse their curiosity, thirst for knowledge and interest in learning mathematics, and feel that mathematics is no longer those boring formulas, calculations and numbers, but has changed from "passive acceptance" to "autonomous learning" in thought.
3 the cultivation of mathematical thinking
1. Show students the process of thinking in the teaching process. "It is better to teach people to fish than to teach people to fish." When explaining examples, teachers should not simply introduce the steps of solving problems to students, but should show their own thinking process. When explaining examples, teachers should show students how to analyze problems and how to adopt problem-solving strategies, so that students can feel the actual process of teachers' thinking, so that students can not only master knowledge, but also learn the way of thinking to solve problems.
2. Cultivate the agility and flexibility of students' thinking. Many secondary vocational school students are rigid in thinking and stylized in doing problems, which is caused by a lot of repeated exercises and lack of their own thinking and exploration. Teachers should guide students to master the essence of mathematical concepts and principles and improve the generalization and abstraction of mathematical knowledge in their minds. The more abstract the mathematical knowledge in students' minds, the faster it is extracted and the more flexible it is applied. In addition, teachers can teach students some quick calculation skills, so that students can remember some commonly used data. The training of these mathematical skills can also develop students' mathematical thinking ability.
3. Cultivate the profundity of students' thinking. Guide students to understand the essence of concepts, think about problems comprehensively, and understand the differences and connections between concepts, so as to understand concepts in depth. Students can understand the essence of mathematical concepts and theorems through variant exercises. In the process of solving problems, guide students to grasp the key words in the problem stem and dig out the hidden information in the problem.
4. Cultivate students' generalization ability in mathematics teaching. Generalization is the basis of thinking, allowing students to experience the process of obtaining teaching conclusions and cultivating students' generalization ability at different levels. Provide students with appropriate steps, pave the way and guide them to draw conclusions.
4 the cultivation of mathematical thinking
Organize debates and competitions to broaden your thinking.
Debate is a fierce battle, a collision of ideas, and a contest between wisdom and profound thinking. It is like a powerful engine, prompting students to think deeply. Organizing debates in class can encourage students to explore questions boldly in class and stimulate their interest in inquiry. When I was teaching "Preliminary Understanding of Fractions", I asked the students to fold out half of the rectangular paper and talk about what half means. A student said, "Divide a rectangle into two parts, and each part is half of it." Before I could speak, the quick-talking Amy shouted, "Wrong! Wrong! " Other students are fidgeting, and students with different views form two camps. At this time, I simply threw the question to the students: "Please be quiet. Since there are two different opinions, let's have a debate today to see who is right and who is wrong."
What Party A thinks is right and what Party B thinks is wrong. Debate begins! "Party A picked up a rectangular piece of paper, folded it in half and divided it into two parts, saying," Divide a rectangle into two parts, and each part is half of it. Look, isn't this half of a rectangle? "A student of Party B immediately said," Divide a rectangle into two parts, and each part is not necessarily half of it. "He picked up a rectangular piece of paper and folded it at will, and the rectangular piece of paper became two different sizes." Which is the half of a rectangle here? "Party A does not show weakness:" You don't get the average score, as long as you get the average score. "This statement actually provides a reason for Party B:" Party A said it was divided into two parts, but did not say it was divided into two parts equally, so this statement is wrong. "Party A still insists:" We didn't say average score, nor did we say uneven score. "Party B:" Yes, you said that dividing a rectangle into two parts includes two situations: average score and uneven score. Only if the average score is equal, each share is half, otherwise it is not half. Therefore, this statement is not rigorous and wrong. "After several rounds of debate, the two students reached an agreement: they must be expressed by scores on the basis of average scores.
Cultivate the habit of using mind mapping
To some extent, the improvement of junior high school math scores is influenced by study habits, and good study habits can achieve twice the result with half the effort. As we all know, the knowledge points of junior high school mathematics are closely related. Using mind map can help students master the relationship between knowledge points, let students see the clouds and grasp the key points of learning. Therefore, in junior high school mathematics teaching practice, teachers should pay attention to cultivating students' habit of using mind maps, so as to better guide students to complete the study of mathematics knowledge.
On the one hand, teachers should encourage students to learn to apply mind maps, not just teach them to draw mind maps, that is, teachers can encourage students to compile related math problems and try to solve them according to mind maps, so as to have a deeper understanding and understanding of math exercises. On the other hand, when teachers explain mathematics knowledge, they can extend it from mind map and list typical exercises for different knowledge, so that students can understand the knowledge points involved in the exercises and find solutions as soon as possible.