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How to Cultivate Middle School Students' Sense of Mathematical Problems
Students' thinking often begins with the problem of learning materials. The problem is the core of mathematics. Mathematics curriculum standard points out that students have to go through the process of abstracting practical problems into mathematical models and explaining and applying them. This concept is closely related to the cultivation of innovative consciousness and practical ability. The content of mathematics curriculum includes not only some ready-made mathematical results, but also the formation process of these results. This process should be a thinking process of constantly discovering, asking questions, exploring and solving problems in order to acquire new knowledge. To solve this problem, we must find out how to find this is the heart of mathematics in teaching, how to stimulate students' interest in questions, enhance students' awareness of questions, improve students' ability to question, and fully develop students' problem-based learning.

First, create a democratic and harmonious classroom atmosphere so that students dare to ask questions.

Brubeck, an American educator, believes that the most exquisite teaching art is to let students ask questions. Students are curious and eager to learn, and they always want to ask "why", "what to do" and "how to do it" about things they are interested in. Teachers should not suppress or block students' thinking when dealing with their problems. Even if the students' questions are naive, unreasonable and have no thinking value, teachers should give spiritual encouragement. Especially for those students who are unconventional, creative and creative, teachers should fully affirm and appreciate them and encourage other students to think positively. Therefore, in classroom teaching, teachers' kind attitude, encouraging eyes, kind smiles, affirmative gestures and expressions will bring great spiritual encouragement to students and make them dare to ask questions. For example, when teaching three-dimensional graphics in life, you can walk into the classroom with a big black box, put it on the podium, briefly introduce the mysterious legend of Pandora's Box, and then say, "Today I also brought a mysterious Pandora's Box. If you want to know what's mysterious in it, you have to go through me first. " This question aroused the students' interest, and I couldn't hide my inner joy when I saw these eyes shining with longing for light. For another example, in the teaching of "merging similar items", multimedia animation is used to show a green grass, and three puppies and two kittens are playing. Q: "Can the dog and kitten on the screen be added together?" The students answered "No", which caused a series of problems. In this scene, I feel the students' problem-based learning and their enthusiasm for solving problems.

Second, optimize the classroom structure, so that students often ask questions

At present, some students are not aware of problems. One of the important reasons is that in the past classroom teaching, teachers always take themselves as the center and are used to "cramming" and "all in one", or the problem is that teachers designed the teaching plan in advance. When teaching, the teacher asks one by one, and the students wait for the teacher to ask and answer with standard answers. There is no room for students to ask questions at all, which requires us to change the traditional teaching concept, establish the teaching concept of taking students as the teaching center (subject) and optimize the classroom teaching structure. According to the size of the classroom capacity, the difficulty of the content, students' knowledge level and class type, teachers should try their best to talk less and concentrate, leaving students with enough time and space for activities (finding problems and asking questions) so that students can think, discuss and be diligent. On the other hand, teachers should adhere to the principle of "leaving room" in classroom teaching, leaving some "blanks" for students to stimulate students' strong desire to ask questions, find problems and ask questions.

In order to make students form the habit of being diligent in thinking, teachers can use "question cards" to encourage students to think, thus forming the habit of being diligent in asking questions and making asking questions their own conscious behavior. The question card can be designed with name, class, time, question type, questions and requirements, teachers' answers and students' additional questions. Students can take a card to fill in the form, teachers can answer questions alone, and they can also be integrated into classroom teaching through discussions and other forms. At the same time, teachers give different grades to students at different levels, such as whether they can ask questions, whether they can ask scientific and exploratory questions, whether they can ask questions and have solutions, thus stimulating students' enthusiasm for asking questions. In this way, students are often placed in "problem situations", which not only makes them realize that there is mathematics everywhere in their lives, but also makes them develop the habit of thinking.

Third, teach students how to ask questions and make them good at asking questions.

Whether you are good at asking questions and thinking about problems is, to a great extent, an important measure to test whether a person has problem consciousness. Students can't or won't find problems and ask questions. The key is that they don't know where the "doubt" is and where the "confusion" is. Therefore, to cultivate students' problem consciousness, we should not only cultivate students' spirit of actively asking questions, but also guide students to ask questions and put forward difficult problems in class, so as to achieve the purpose of "teaching people to fish". Only in this way can students develop from "dare to ask questions" to "be good at asking questions". In the teaching of concepts and theorems, students should be specially trained to be good at asking questions.

The new curriculum standard points out that mathematics teaching should start from students' life experience and existing knowledge background, and provide them with sufficient opportunities to engage in mathematics activities and exchanges. The cultivation of students' problem consciousness depends on teachers' teaching design. Therefore, teachers should be good at connecting with students' real life and identify students' "nearest development areas". Through various means to present the problem situation, create students' cognitive conflicts, induce students' problem consciousness, and let students really feel that they have questions to ask. Put forward the following questions: a triangular glass is broken into two pieces. To make a triangular glass of the same size, do you want to take both pieces away? If you only bring one, which one should you bring? Why?

Analysis: This is a living example in life. Once the question was asked, the students were very excited. Some people are gesturing with a ruler, while others are measuring with a compass. Students' thinking is instantly activated. When there is a contradiction between cognition and need to know, it can stimulate students' strong desire for knowledge and motivation to explore problems, so that students can find problems through a series of processing of their own thinking.

Fourth, stimulate students' interest in asking questions and make them happy to ask questions.

Interest is the best teacher, and it is also the cornerstone to induce students to find and ask questions. In math class, we should arouse students' cognitive conflicts, arouse students' awareness of questions, and let students really feel that they have questions to ask, dare to ask, and are willing to ask.

Set up problem situations through multimedia teaching methods. Multimedia teaching method stimulates students' senses and active thinking through rich and vivid situations such as pictures, words, sounds and animations, which leads to problems.