1 how to improve the performance of mathematical application problems
Encourage positive thinking and analyze quantitative relations.
Analysis of the relationship between the number of questions is the focus of "solving problems" teaching. The intuitive teaching of topic map pays attention to students' complete expression of problems, which can effectively improve students' ability to solve problems. For example, this question in the exercise book: "Xiaolan walked 540 meters from home to the library for 9 minutes. It took her six minutes to walk from the library to school at the same speed. How many meters is it from the library to the school? " Use the topic map to let students intuitively feel the mathematical phenomena and problems described in the topic, so as to better understand the requirements of the topic. However, some students still have difficulty in solving problems, because students ignore the understanding of the implicit conditions in the topic in the process of understanding the meaning of the topic.
Students must understand the meaning of "same speed" in this application problem. Then, using the known conditions in the topic "Xiaolan walks 540 meters from home to the library in 9 minutes", we first find out the "speed of Xiaohong", and then use this "same speed" as a "bridge" to answer the questions in the topic. The whole topic revolves around three quantitative relationships: speed, time and distance. Some students have difficulty in solving problems because they don't grasp the condition of "the same speed" implied in the topic.
Create a harmonious atmosphere and give full play to internal potential.
In the process of training, teachers should pay attention to creating more opportunities for students to think and debate, give full play to their inherent potential, and urge them to constantly create desires. In the process of continuous exploration and discovery, students not only have the joy of success, but also have some wrong or imperfect ideas. Teachers try their best to keep them in active thinking, the sparks of wisdom are constantly flashing, the enthusiasm for learning is constantly rising, and the mathematical ability is gradually improved.
Appearing in the form of a combination of pictures and texts that students can easily understand, its essence is to visualize the incomprehensible quantitative relationship, and to combine image thinking with abstract thinking, so that students can realize a new power together with their left and right brains, thus making the incomprehensible things easier to understand and achieving the purpose of revealing the essence through phenomena, not only knowing why, but also knowing why. Students have a deep understanding and understanding of the concept of "harmony", which will lay a good foundation for future consideration from multiple angles and directions, so as to draw inferences from one another.
2 Mathematics teaching methods
Mobilize emotional factors and stimulate learning passion
Lenin said: "Only when a person's thoughts are infiltrated by strong emotions can he gain strength and arouse positive attention, memory and thinking." Classroom is the main place for students to learn. Besides cognitive factors, emotional factors play a particularly important role in learning itself. Therefore, in classroom teaching, every kind smile, every encouraging look, every gentle word and every clear gesture of the teacher will touch students' learning emotions, encourage students to open their voices boldly, and induce students' positive emotional input. All these can promote the harmony, democracy and harmony between teachers and students, make everyone unrestrained, give full play to their initiative and mobilize their learning enthusiasm.
Leave room for thinking and enhance self-confidence.
At present, in classroom teaching, we often see such a scene: due to some teachers' one-sided understanding of the new curriculum concept, as long as students ask questions or teachers show their thinking problems, they immediately organize students to discuss, or discuss at the same table, or discuss in groups, and the atmosphere is extremely warm. Some students with quick thinking will soon raise their hands to answer, while most students with slow thinking will be filled with other people's opinions before they can think. Over time, when they encounter problems again, they will just listen to others' analysis and explanation, or simply don't leave room for students to think independently, and then organize their discussions in front of the camera. In this way, students can get the answer through their own thinking or reach the edge of the answer, which will bring them great happiness and enhance their confidence in learning.
Strengthen the guidance of learning methods and master learning methods.
Cultivating modern students' mathematics quality requires them not only to learn knowledge, but also to cultivate their learning ability. In the mathematics textbook of junior middle school New People's Education Edition, there are basically corresponding examples for the teaching of every new knowledge, so we should give full play to this advantage in teaching and guide students to master the methods of self-learning examples. For example, the teaching of many examples in the textbook is not in place in one step, but presents the problem-solving process step by step, and there are many blanks that students need to fill in, so students should think and fill in according to their own problem-solving ideas; Some examples are accompanied by colorful wireframes with virtual and real colors, so that students can understand the intention of wireframes. Some examples have thinking content, so that students can know that this is a thinking process, and some words such as laws, concepts and conclusions are expressed in color, so that students can understand that this is the key content. In some cases, schematic diagrams and operating procedures are arranged to break through difficulties. Students should know how to analyze and infer according to the order of charts, so as to master the thinking process of mathematics teaching and learning.
3 Cultivation of interest in mathematics learning
Reasonable supplement of teaching materials according to local conditions.
Mathematical knowledge is widely used in daily life. However, due to the lag of the teaching materials, it is difficult for students' colorful life to be reflected in the teaching materials in time. Therefore, in teaching, it is necessary to contact the reality of life, use local materials and choose topics close to students' lives to enrich the teaching materials, so that the teaching materials can better serve the teaching and improve students' interest in learning mathematics.
For example, in the teaching of "the meaning and writing of percentage", I assigned such an investigation task before class: tomorrow we will study "percentage", who will understand "percentage", find out which items have "percentage" on them and think about what it means? Through this arrangement, on the one hand, students understand the expression and significance of percentage through preview, on the other hand, they also know that percentage is used in many places in life. Because students investigated various percentages before class, they reported them in class and explained their meaning. For example, on the composition label of clothes, the composition is 90% wool and the composition is 10% polyester; China's arable land accounts for 7% of the world's arable land. Through the pre-class investigation report, the distance between teaching materials and life has been narrowed, and the original cognitive structure has been greatly enriched.
According to the actual situation, the textbook should be adapted appropriately to make it easy for students to accept.
General mathematics textbooks have the same characteristics, but in the process of practical application, there is a certain gap with students' life experience. At this time, teachers need to contact the students' reality and make appropriate additions and deletions according to the teaching objectives and the key and difficult points of teaching.
For example, there is such an example: (Example 2) The school canteen has issued coal 1 ton and plans to burn it for 40 days. Due to the improvement of the stove, 5 kilograms are saved every day. How many days can this batch of coal burn? The situation described in Example 2 is different from the real life in rural areas, and it is more difficult to analyze and understand the quantitative relationship between plan and reality on this basis. In teaching, I adapted the example as follows: Jiang Bin, a classmate of our class (who spends a lot of money in his life), has 10.5 yuan in his pocket. He planned to spend this week (7 days), but the teacher talked to him and hoped that he could save some money. He decided to save 1 yuan every day to buy extra-curricular books. So how many days can Jiang Bin spend the money in his pocket now? This adaptation allows students to face their familiar classmates, and the familiar life situation reduces the psychological difficulty of students' learning and is easy to understand. Students quickly and easily mastered the knowledge points.
4. Students' divergent thinking ability
Cultivating students' divergent thinking ability by using multiple solutions to one question
It is an effective way to cultivate students' thinking agility, help them overcome their narrow thinking, and thus cultivate their divergent thinking ability. Many questions are divided into non-sexual and fixed patterns. Through vertical and horizontal divergence, knowledge series and comprehensive communication, the purpose of comprehensive communication is achieved. In teaching, we can inspire students' thinking through discussion, open up ways to solve problems, and ask students not to be satisfied with one solution. Starting from a problem, according to the given conditions, we can break through the inherent ways to solve problems and find a variety of solutions. When teaching examples, teachers can change the conditions or conclusions of problems from many angles and aspects to improve students' analytical ability. The design of exercise questions should be hierarchical, gradient and diverse, so that students can constantly master the shortcut of solving problems through variant training and improve their divergent thinking ability.
Strengthen basic knowledge and lay a solid foundation for divergent thinking.
Mastering the basic knowledge of mathematics affects the ability of primary school students to understand and solve new problems. For students with poor basic knowledge, innovative consciousness and innovative thinking in mathematics are like castles in the air without foundation. Therefore, innovative teaching should start with strengthening the basic knowledge, so that students can learn the basic knowledge of mathematics in a down-to-earth manner, strengthen the basic skills of mathematics, infiltrate mathematical ideas and accumulate experience in solving mathematical problems. Primary school mathematics should start from the most natural and simple realm, work hard in the place that is most conducive to the development of students' basic mathematical literacy, and work hard to consolidate students' mathematical foundation. Only by studying in constant practice can students' mathematical quality be stimulated and leap forward, and new problems can be solved. Teachers can accurately understand students' mastery of basic knowledge according to students' practice, so as to find the most suitable guidance and learning methods for each student and effectively improve the teaching efficiency of mathematics classroom.
Create an environment conducive to the establishment and cultivation of divergent thinking
The harmonious, relaxed and free atmosphere in the teaching process can arouse students' innovative consciousness to the maximum extent. In order to promote students' creativity, it is necessary to have a harmonious environment and leave a platform for students to fully express and display their individuality. This democratic and harmonious atmosphere is a fertile ground for cultivating students' innovative consciousness. Teachers should overcome the deviation of innovative knowledge. Every reasonable new discovery is different from other people's ideas, and the unique observation angle is innovation. How to tap and improve this potential depends on the degree of students' main role. In order to enable students to actively explore knowledge and give full play to their creativity, we must overcome the old teaching mode that teachers are the leading role, a few students are supporting roles and most students are the audience, give students sufficient thinking space, treat students with an equal, tolerant and encouraging attitude and adopt more ways of discussion and inquiry. Give students the opportunity to fully demonstrate, let students actively participate in the teaching process from beginning to end, and truly become the main body of exploration and research. This relaxed and free classroom atmosphere is more conducive to cultivating students' divergent thinking.