1 How to carry out in-depth teaching of junior high school mathematics
Clarify the purpose and update the educational concept.
Metabolism is the universal law of the universe, and all major reforms are guided by the renewal of ideas. This is the case in education reform, especially in mathematics education. Only with a clear purpose can we do a good job in educational reform. The main purposes of junior high school mathematics teaching are: (1) grasping double basics; (2) Cultivating ability; (3) Cultivate good personality and dialectical materialism. It is necessary to abolish the practice of taking mathematics education as an exam-oriented teaching, engaging in sea tactics and betting on mathematics, focusing only on the teaching of methods and ignoring the cultivation of abilities. The purpose of mathematics teaching is to cultivate talents and improve the quality of citizens. With the rapid development of high technology, people gradually realize that people's quality is the core of comprehensive national strength. In order to improve the quality of the whole people, compulsory education and mathematics education must be strengthened.
Part of compulsory education. Mathematics itself has high cultural value and great charm. It can not only broaden the brain, make the thinking rigorous and agile, but also cultivate people's ideological quality and improve the quality of citizens. Mathematics teaching is an art, and only by mastering this art can we give full play to the educational function of cultivating, perfecting, harmonious and modern personality of mathematics. The traditional exam-oriented education is mainly manifested in: imparting knowledge as the main body, taking exams as the driving force, emphasizing written culture, emphasizing top-notch education, setting high and low scores, while ignoring the education of mathematical thoughts and the cultivation of ability, resulting in high and low scores. Quality education is mainly aimed at most people, aiming at improving the quality of all students, giving full play to the charm and educational function of mathematics itself, and paying attention to cultivating people's development creativity. Of course, quality-oriented teaching does not exclude the imparting of knowledge or the top of the college entrance examination, but pays more attention to the cultivation of knowledge, teaching ideas and consciousness and students' psychological quality. Quality education is the necessity of reform and the only way to cultivate modern talents. Quality education will certainly replace exam-oriented education.
Teaching through fun, teaching through fun.
Mathematics teaching should not only impart the basic knowledge of mathematics and cultivate students' basic skills, but more importantly, consciously cultivate the above abilities. Modern mathematical theory holds that the first condition to stimulate students' enthusiasm for learning is not examination, but real interest in courses; Mathematics teaching is the teaching of mathematical thinking activities. The learning process of mathematics is not only a process of accepting, storing and applying knowledge, but also a process of training and developing thinking. Mathematics teaching is an active process. During the whole activity, students should be in a state of active creation. Students should first participate in this activity and feel the need of creation. It is possible for him to re-create, and the teacher's task is to provide a free and broad world for students' development and creation, guide the way to acquire knowledge and skills, and cultivate students' creativity.
The success of students' learning depends on their motivation, and the successful psychological experience of mathematics learning can stimulate their strong thirst for knowledge. Therefore, teaching must be geared to all, give full play to students' dominant position, and put all students in the position of "learning masters". In the teaching process, with the gradual increase of knowledge, the design of problem exercises should be deep, and the purpose, hierarchy and pertinence should be studied for inspiration and guidance, so as to create some pleasant situations for students and fully display their potential abilities, so that everyone can have a chance to succeed and enjoy learning, thus stimulating their strong thirst for knowledge and urging students to love learning mathematics.
2 Cultivation of interest in mathematics teaching
Achieve mastery through a comprehensive study and stabilize interest in learning.
Mathematics is a subject with close memory and strong logic, which easily causes certain difficulties for primary school students. If students encounter difficulties that cannot be overcome, their interest in learning will decline, which will seriously lead to the loss of confidence and interest in mathematics learning. Therefore, measures must be taken in teaching to highlight key points, disperse difficulties, grasp key points, and strive to help students overcome difficulties in learning, so as to stabilize students' interest in learning. However, combining new knowledge with old knowledge, closely connecting with students' reality, starting from students' existing mathematical knowledge, creating situations and guiding students to observe, operate, guess, reason and communicate can play a prominent role, and thus stabilize students' interest in learning.
For example, when teaching the arithmetic of fractional division, we should first import it from integer division. ① For example, 12? Tell the meaning of the formula by the students and divide 12 into three parts. How much is each part? (2) It can be expressed by a line graph (omitted). For another example, when teaching the meaning of reciprocal, show the following formula: 1/4? 4,3/5? 5/3,6? 1/6,4/9? 9/4, let the students do oral calculation, and guide them to find the same features (both are the multiplication of two numbers, and the product is 1), so that the two numbers whose product is 1 are reciprocal. Using this teaching method, students have a deep understanding of new knowledge, cultivate the spirit of inquiry, highlight the key points and disperse the difficulties. Students learn easily and happily, which naturally stabilizes their interest in learning.
Set suspense and stimulate interest in learning
Curiosity is the most prominent psychological feature of primary school students. Therefore, in primary school mathematics teaching, teachers are good at setting suspense and stimulating students' curiosity, which is one of the effective methods to stimulate students' interest in learning. For example, when teaching multiplication and estimation, we can introduce a new lesson through such a story: Uncle Goat has opened a bicycle shop, and his business is very good, and he is going to recruit a buyer. Both the bear and the monkey came to sign up. Uncle goat asked each of them to buy seven bicycles, each of which cost 298 yuan, to see who was the fastest. Bear quickly picked up a pen and calculated how much * * needed from Uncle Goat to buy it. The little monkey had a brainwave and immediately advanced 2 100 yuan to Uncle Goat. After a while, the little monkey's car has been bought, and the invoice and 14 yuan's change have also been paid. Bear is busy collecting the 2086 yuan he needs to buy a bike from Uncle Goat. Finally, Uncle Goat hired a quick and accurate little monkey. How did the little monkey finish it quickly and well?
For another example, when teaching a number divisible by 2, 3, and 5, students can say a number casually, and the teacher can immediately judge whether it can be divisible by several numbers. In this way, students' curiosity arises spontaneously, which arouses students' psychological desire to find out, stimulates students' interest in learning, urges them to actively learn new knowledge, and makes the learning effect twice the result with half the effort.
3 infiltration of mathematical thought
The gradual transformation of mathematical problems must be guided by theorems, properties, laws, formulas and laws. Therefore, students should be guided to actively participate in the process of exploration, discovery and deduction of these conclusions in teaching, and under the guidance of mathematical thinking methods, the causal relationship of each conclusion should be continuously found out, and then conclusions can be drawn. Solve the ever-changing mathematical propositions with unchanging mathematical ideas and methods, speed up and optimize the problem-solving process, and achieve the effect of knowing one problem at a time.
Attach importance to the formation process of concepts. Concept is the cell of thinking and the result of the leap from perceptual knowledge to rational knowledge. The realization of leap should go through the logical processing of thinking such as analysis, synthesis, comparison, abstraction and generalization, and should be guided by mathematical thinking methods. Therefore, concept teaching should fully reflect this process and guide students to reveal the thinking core hidden in concepts. For example, the knowledge about monotonicity of function in the second chapter of the first volume of Mathematics, a new textbook for senior one, is the best material to infiltrate the idea of combining numbers with shapes into teaching, so we should fully seize this favorable opportunity in teaching. The function f(x) is the increasing function in the interval a, or the subtraction function can be visually represented by an image. Through the visualization of images, students can deeply understand the monotonicity of functions and have a clearer understanding of the definitions of increasing function and subtraction functions.
In the process of summarizing and reviewing the teaching, reveal, refine and summarize the mathematical thinking methods. In the exam-oriented education, the mathematics summary and review class often falls into an endless sea of questions, which makes teachers and students carry out excessive and mechanical exercises training in the boring sea of questions. As a result, teachers and students are exhausted, at a loss, and have little gain. How to improve the effect of summarizing and reviewing lessons? Because the same content can contain several different mathematical thinking methods, and the same mathematical thinking method is often distributed in many different basic knowledge, we should consciously and purposefully combine the basic knowledge of mathematics to reveal, refine and summarize the mathematical thinking methods in the process of summing up and reviewing, so as to strengthen the stimulation and leave a deep impression on students, which can not only avoid the problem of simply pursuing the teaching of mathematical thinking methods, but also promote students to realize the leap from perceptual to rational.
4. Optimize the teaching of mathematical thinking
Cultivate creative personality and individuality and develop intuitive thinking.
Intuitive thinking is a positive expression of creative thinking, which is not only the forerunner of invention and creation, but also the fruit suddenly born after being confused about everything. The discovery of Archimedes principle and the reappearance of the periodic table of elements are free association or thinking activities. Keep moving on the edge of consciousness related to the problem, the brain function reaches the best state, and the old nerve connections suddenly communicate to form new connections. In order to cultivate students' creative thinking, teachers should consciously help students develop intuitive thinking. First of all, let students master the basic knowledge, concepts, principles and systems of various disciplines seriously, which is the basis for developing intuitive thinking. Secondly, we should guide students to practice and explore boldly, so that they can gain more experience in applying knowledge and solving problems. In addition, students should be encouraged to speculate or guess about problems and cultivate good intuition. Try to guide the students to guess and prove.
For example, after learning the area calculation of plane graphics, students are required to summarize the area formulas that can be used for all plane graphics learned in primary schools, so students put forward various conjectures and I asked them to test in groups. After verification, students can use the trapezoidal area formula. In this way, students can consolidate their proficiency in what they have learned and use what they have learned to prove their guesses, thus improving their intuitive thinking ability. When students guess wrong or are not completely right, it may be meaningful for teachers to guide them to rethink, improve and perfect these immature ideas. But satire and sarcasm must not dampen the enthusiasm of students' intuitive thinking. It is necessary to give full play to the spirit of students' newborn calves who are not afraid of tigers, dare to ask questions in the end and dare to challenge authority. For example, I put forward my own suggestions and ideas on the arrangement of the mathematics textbooks I have learned. When creating problem situations, teachers often use intuitive thinking methods to put forward various inconclusive views, which will play a role in demonstrating or imperceptibly influencing students.
Stimulate motivation and develop creative imagination
Creative imagination is a process of creating new images independently without referring to ready-made descriptions. Is based on a predetermined purpose, by selecting an existing representation. Processing and reorganization produce a new image, which can be used as a "blueprint" for creative activities. Creative imagination needs raw materials, and students should be allowed to expand their knowledge and scope and increase their representation reserves. Teachers constantly improve the requirements of creating new things and solving new problems, stimulate students' motivation and curiosity in creative activities, cultivate students' curiosity, mobilize students' enthusiasm and initiative in learning, create certain situations, and make students think positively and keep them for a long time. Only through long-term efforts will inspiration appear. Lie Bin said: "Inspiration is the reward for hard work." Teaching activity is a complex mental work, which requires creating imagination, making full use of heuristic teaching, teachers teaching creatively and students learning creatively.
If "A number divided by 6, 8 and 9 equals 1" is displayed, what is the smallest number? Students can get 73 soon, so they show it again: "What is the minimum number that is greater than 10, divided by 6 equals 4, divided by 8 equals 2, and divided by 9 equals 1?" Students don't know how to start at the moment. The teacher guided the comparison and thinking of two problems in time. If the remainder of the second question is the same, you can get it. So some students found that the quotient was 1 and the remainder was 10, so it was 82. In this way, students can associate and compare raw materials and greatly improve their creative imagination.
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