1 How to achieve a breakthrough in mathematics teaching
First, turn abstraction into intuition.
Strengthen practical operation, let students establish knowledge representation in puzzles, strengthen intuitive teaching, let students enrich perceptual knowledge in perception, so as to ensure the smooth progress of their abstract logical thinking. For example, when teaching the formula for calculating the surface area of a cuboid, let students touch each face of the cuboid, see what shape each face is, think about how to calculate the area of each face, and let students establish the representation of knowledge by touching, looking and thinking. Then guide the students to sum up a formula for calculating the surface of a cuboid.
Second, the bridge pavement is difficult to assimilate.
Teachers should contact students' real life and use familiar examples to help students better understand mathematics knowledge.
Third, comparative analysis, analogy difficulties
Teachers strengthen comparative analysis in teaching. Through comparative analysis, guide students to analogize and discriminate easily confused knowledge from similar knowledge difficulties, so as to prevent old knowledge from interfering with new knowledge learning. For example, when teaching "simplification and comparison", we should compare it with "comparison": "comparison" means seeking "quotient", and what we get is a number, which can be written as fractions, decimals and sometimes integers; "Simplified ratio" is to get the simplest integer ratio, which can be written in the form of true fraction or false fraction, but not in the form of fraction, decimal or integer.
Fourth, innovate with the old and pull skillfully.
Before teaching new knowledge, students can acquire the basic knowledge necessary to master new knowledge through review and other means. Make full use of old knowledge in the teaching of new knowledge and promote the mastery of new knowledge by clever traction.
2 to stimulate students' interest in learning
1. Discussion at the growing point of new knowledge is helpful for students to internalize knowledge.
In teaching, teachers should grasp the problem of setting new points and the key to knowledge generation, organize students to discuss and promote students' understanding and understanding of new knowledge. After observing, guessing, experimenting, calculating and applying the concepts, definitions, theorems, formulas and laws in mathematics, students can initially perceive the laws, but they are not very clear. At this time, organizing students' discussion can not only stimulate students' enthusiasm and interest in understanding problems, but also "grow" new knowledge and experience on the basis of original knowledge through students' independent exploration.
2. Discussing the difficulty of the problem is helpful to the development of thinking.
In the process of learning, students will have difficulties in understanding abstract mathematical knowledge, and obstacles will easily appear in the processing and transformation of knowledge. Teachers should give timely inspiration and guidance to help students adjust their thinking activities, remove obstacles and continue to think, thus solving difficult problems.
3. Discussing the application of problem-solving strategies helps students learn to learn.
The application of problem-solving strategies can reflect students' understanding of knowledge and their ability to solve problems by using knowledge. If we discuss strategies and put forward different methods to solve problems, we can not only provide feedback information for teachers, but also help students inspire each other in the process of using strategies, broaden the thinking of solving problems and learn to learn.
Homework can also be interesting, enlightening and flexible, with diverse contents, forms and angles, which should be corrected in time. As long as students make a little progress every time, they should be encouraged to evaluate, so that students can have the courage and determination to continue to tackle key problems when they taste the sweetness of wisdom.
3. Guide students to actively study mathematics.
The main line of teaching design should focus on the occurrence process of mathematical knowledge, and reasonably arrange teaching content and teaching progress. Mathematics teaching is based on students' initiative to explore, discover and solve problems, so that students can repeat and reproduce the process of knowledge generation, master mathematical thinking methods, develop thinking and form abilities. Teaching design should fully consider students' actual situation, integrate textbook knowledge into students' real life and objective environment, and conform to the law of students' thinking development.
Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. We should understand students' practical ability and experience through various channels, strengthen the connection between teaching process and real life, and let students use their own mathematical knowledge and methods to deduce new mathematical conclusions through their own thinking and exploration. This can not only develop their thinking ability, but also cultivate their innovative spirit. Teaching design should be good at borrowing familiar problem-solving methods from students in life, creating situations, paying attention to inspiration, allowing students to think and seek actively, and mastering mathematical methods in comparison and migration.
Teaching design should create problem situations suitable for mathematics learning, hide new mathematics problems in students' existing knowledge structure, and let students discover new problems by themselves through their own activities in the problem situations set by teachers, so as to actively explore the process of new ideas. Setting teaching situation is the premise of this model, which plays a role in guiding thinking and stimulating motivation, prompting students to find new problems in the situation, which can not only consolidate students' original knowledge, but also develop students' new knowledge. The creation of situations should be related to students' existing knowledge and experience, and students can think and explore conditionally, so that students can't simply use existing knowledge and experience to solve problems.
For example, solve the following exercise, the famous mathematician Stephen? Barnah died on August 3 1, 1945. When he was alive, his age was exactly the arithmetic square root of that year (that year was the square of his age), so what year was his birth? Shake it? Shake it? Shake it? Shake it. How old was he when he died? Shake it? Shake it? Shake it? Shake it. I instruct students to analyze. First, I find out the complete square number less than 1945 and greater than 1845, including 1936=442, 1849=432. Obviously only 1936 is realistic, so Stephen? 1936 Barnah is 44 years old. Then the year of his birth is 1936-44= 1892. He died at the age of 1945- 1892=53. In this way, students can find their own problems and get cognitive conflicts, so that students have a familiar feeling and can solve problems with existing knowledge. This is conducive to improving students' enthusiasm and active participation consciousness, and to cultivating students' desire to explore and study problems. Students' learning is an understanding of the process and reasons, and a reflection and prospect of the past, present and even future development.
4. Create a math classroom atmosphere
Attach importance to experimental teaching and extend harmony
When the mathematics laboratory enters the mathematics course, it is necessary to make full use of experimental means to stimulate students' interest to the maximum extent. Mathematics experiment provides students with rich perceptual information with its intuition and visualization. Mathematics experiment has many teaching functions, among which mathematics experiment helps students to understand mathematics knowledge correctly. It is particularly important to improve the ability to analyze and solve problems.
In teaching, we often encounter such a problem: a mistake in an assignment has been corrected, and it won't be long before some students commit it again. For example, (2a)n=2an is a common mistake made by students, which is influenced by the thinking of multiplication and division method 2(a+6)=2a+26. (1) Fold a piece of A4 printing paper in half for 5 times and observe. (2) After folding two A4 printing papers in half for five times, observe their thickness. This experiment can help them deepen their understanding of the formula (ab)n=anbn, correct their mistakes independently, and make students step by step through the design of mathematical experiments. Step by step, it not only cultivates students' keen observation, systematic analysis and comprehensive induction, but also enhances their persistent exploration spirit.
Guided by infiltration method, sublimate harmony
The mathematics curriculum standard issued by the Ministry of Education clearly points out that "students' mathematics learning activities should not be limited to memorizing, imitating and accepting concepts, conclusions and skills. Independent thinking, independent exploration, hands-on practice, cooperation and communication, and reading self-study should all be important ways to learn mathematics. Therefore, mastering scientific methods is tantamount to getting the golden key to opening knowledge. "It is better to teach people to fish than to teach them to fish", and the guidance of learning methods is very important in mathematics teaching. Therefore, in classroom teaching, students should not only be guided to learn by themselves, but also be trained in learning methods. The author thinks that we can start from three aspects: cultivating students to read, question and reflect.
The first is to learn to read textbooks. Every chapter in a math textbook is a logical exposition. Teachers can ask questions first, so that students can read and answer questions with questions. Besides textbooks, there are actually many math books for students to read. Secondly, learning to reflect and guiding students to learn to reflect actively in teaching are very important for cultivating students to learn to learn.