Pay attention to the transfer of mathematical knowledge.
Every mathematical knowledge point does not exist independently, but is objectively related. If it is separated, the mathematics classroom will undoubtedly be inefficient and will also affect students' knowledge mastery. Cognitive activity in primary school is a process from simple to complex, which needs to be based on specific knowledge. To help students break through key and difficult knowledge, we must attach importance to the transfer of mathematical knowledge. The teaching of new knowledge should be based on old knowledge, find the connection between them and promote the transfer of knowledge. With the knowledge learned in the past as the foundation, it is much easier for students to learn.
For example, in the teaching of parallelogram area, the key and difficult point is the derivation of area. When studying, you can first review the solution methods of rectangular and triangular areas, guide students to think, see which figure the parallelogram is similar to before, and turn it into the one you have learned. Through comparative analysis, students can know that there are many similarities between parallelogram and rectangle they have learned before, which is easier to deduce and has a good breakthrough in teaching difficulties and key points.
Using multimedia to break through difficulties and key knowledge
The application of multimedia technology has brought brand-new vitality to mathematics teaching in primary schools. Reasonable application of multimedia teaching can change the traditional teaching mode of chalk+textbook+blackboard, show knowledge points with interesting videos, pictures, sounds and words, let students participate in various senses, visualize abstract mathematical knowledge and vividly show static images to students.
For example, in the teaching of "Rotation of Cuboid", multimedia can be used to play the expansion of cuboid, so that students can realize that a cuboid is composed of six faces, and these six faces are relative. In this way, students will form a comprehensive understanding of this figure, better solve difficult and important knowledge, exercise their spatial thinking ability, and make them no longer afraid of geometry knowledge.
Emphasis and difficulty of mathematics teaching II
Taking old knowledge as the growing point to break through key and difficult points.
One of the characteristics of primary school mathematics is very systematic. Every new knowledge is often closely linked with old knowledge. New knowledge is the extension and development of old knowledge, and old knowledge is the foundation and growing point of new knowledge. Sometimes new knowledge can migrate from old knowledge, but at the same time it becomes the basis of subsequent knowledge. Therefore, the knowledge points of mathematics are like a chain, interlocking. Being good at grasping the connection point between mathematical knowledge, consciously taking "transfer" as a method to help students learn, introducing new from the old, accumulating new from the old, and organizing active transfer, it is not difficult to achieve breakthroughs in teaching key points and difficulties.
For example, when learning the area of a circle, after knowing the area of the circle, encourage students to question boldly. In this way, students naturally think of how to calculate the area of the map. What is the formula? How to find the area formula of a circle and derive it? At this time, students may be at a loss, or they may make amazing discoveries. In any case, students should be encouraged to guess, imagine and tell their preset plans. How are you going to calculate the area of the circle? Randomly handle students' feedback in class. It is estimated that most students will not get to the point. Even if they know, they can let everyone experience the discovery of the formula. At this time, because the students are young, they can't establish contact with the previous plane graphics, and they need the guidance of teachers. What plane graphics have they studied before? Let students recall quickly, mobilize the original knowledge reserve and prepare for the "re-creation" of new knowledge. According to the students' answers, choose parallelogram, triangle and trapezoid. Ask the students to discuss and reproduce the derivation process of area formula. According to the students' answers, the computer cooperates with the demonstration to give students visual stimulation. The parallelogram is derived from a rectangle, the triangle area formula is derived from two identical triangles, and so is the trapezoid. Thinking about a process is not only for memorizing, but also permeates an important mathematical thought through this link, that is, transforming thought, which guides students to abstract and summarize that new problems can be transformed into old knowledge and use old knowledge to solve new problems. So we can infer whether the area of a circle can be transformed into a plane figure I learned before! If I can, I can easily find its calculation method. After such abstraction and generalization, the essence of the problem is summed up, because knowledge itself is not important, what matters is the method of mathematical thinking, which is the essence of mathematics.
Prepare lessons carefully, thoroughly understand the teaching materials, and break through the key and difficult points of teaching.
The key to improve the effectiveness of mathematics classroom teaching lies in the enrichment and solidity of the classroom, so as to highlight the key points, break through the difficulties and implement the "two basics". In order to do this, teachers need to grasp the objectives and requirements of mathematics curriculum standards. Before class, they must study the textbook carefully, be familiar with the content structure, arrangement intention and requirements of the textbook, master the main points, characteristics and knowledge context of the textbook, and strive to truly understand the textbook. Starting from the students' existing knowledge and life experience, the study situation is carefully analyzed, the teaching materials are handled appropriately and flexibly, and the teaching links are carefully preset for preparation.
The formation of teaching focus is related to the inherent logical structure of mathematical knowledge, so teachers should read the teaching materials carefully, read the books used by teachers intensively, grasp the relationship between knowledge and knowledge, and find out the knowledge points with prominent position and function in this lesson, so as to find the teaching focus. Difficulties in teaching On the one hand, teachers should always put themselves in others' shoes according to their own experience; On the other hand, they should look at the content to be taught from the students' point of view and find out the knowledge points that students find difficult to learn according to their cognitive characteristics, which is to find out the difficulties in teaching.
Emphasis and difficulty of mathematics teaching 3
1. Grasping the key points and difficulties is the premise.
From the above analysis, we can draw the following conclusions: teachers should highlight key points and break through difficulties in teaching, first of all, they should dig deep into teaching materials and grasp the key points and difficulties of each chapter and lesson from the knowledge structure; Secondly, we should prepare enough students to grasp the key and difficult points of teaching according to their actual cognitive level and taking into account the differences of different students' cognitive structures. Teachers' careful preparation and accurate positioning before class can provide favorable conditions for highlighting key points and breaking through difficulties in teaching.
2. Finding the growth point of knowledge is a condition.
Primary school mathematics is a highly systematic subject. Teachers should use the logical structure of mathematics to guide students from the old to the new, promote reasoning from the known to the unknown, understand the relationship between simple problems and complex problems, and constantly improve the cognitive structure. The formation of new knowledge has its fixed knowledge growth point. Only when teachers correctly find the growing point of knowledge can they highlight key points and break through difficulties. Teachers can identify the growing point of knowledge according to the following three points: (1) Some new knowledge belongs to the same kind or similar to some old knowledge, so we should highlight "* * * similarity" and then break through the difficulties; (2) Some new knowledge is composed of two or more old knowledge, so it is necessary to highlight the "connection point" and then break through the important and difficult points; (3) If some new knowledge is developed from some old knowledge, it is necessary to highlight the "evolution point" and then break through the key and difficult points. For example, in the teaching of "problem-solving strategies", although each strategy has its own applicable topics, teachers should comprehensively use the existing strategies in the process of forming new strategies, such as learning to replace, drawing and arranging hypothetical strategies, and comprehensive and analytical methods should run through. Therefore, the teaching of this unit is a process of reforming the mathematical cognitive structure. Teachers should highlight the "evolution point" and then break through the important and difficult points.
3. Adopting appropriate teaching methods is the key.
The Mathematics Curriculum Standard for Full-time Compulsory Education (Revised Edition) points out that teachers' teaching should be based on students' cognitive development level and existing experience, oriented to all students, and pay attention to heuristic teaching and teaching students in accordance with their aptitude. Teachers should play a leading role, properly handle the relationship between teaching and autonomous learning, and guide students to think independently, actively explore and cooperate through effective measures, so that students can understand and master basic mathematical knowledge and skills, mathematical ideas and methods, get necessary mathematical thinking training and gain basic mathematical activity experience. According to students' reality, adopting appropriate teaching methods is the key to highlight key points and break through difficulties. For example, when teaching problem-solving strategies, teachers can adopt the following teaching methods: independent thinking-trying to solve problems-cooperation and exchange-comparison and induction-reflection and summary-forming experience. This teaching method can make students know and form problem-solving strategies in the process of solving problems, appreciate the value of strategies, consciously use strategies to solve problems, really highlight key points and break through difficulties.