Teaching difficulties generally refer to key knowledge points that are difficult for most students to understand and master, or problems that are easy to be confused and make mistakes. \x0d teaching pays attention to knowledge itself, which exists objectively because of the inherent logical structure of mathematical knowledge; Teaching difficulties depend on students' own understanding and acceptance, both of which are determined by the teaching objectives of the same teaching content.
Second, the significance of studying teaching difficulties \x0d can be summarized in this sentence: implementing teaching priorities is the premise for students to master knowledge, and breaking through difficulties is the key to teaching success. Teachers' methods of breaking through difficulties in the teaching process are often the catalysts for students' active thinking and stimulating interest.
Three, several main strategies to break through the key and difficult points
1. Mastering textbooks is the prerequisite. \x0d To guide students to learn to walk, we must first know the way. In order to highlight the key points and break through the difficulties in teaching, first of all, we should dig deep into the teaching materials and grasp the key points and difficulties of each lesson from the knowledge structure. Secondly, according to the students' actual cognitive level and considering the differences of different students' cognitive structures, prepare enough students to grasp the key and difficult points of teaching. Prepare carefully before class.
The key content grasps the main characteristics: first, it is widely used; Second, it has the most direct and close relationship with future study. This is usually called the growth point of new knowledge or the connection point of old and new knowledge.
When determining the difficulties, we should pay attention to two points: first, put ourselves in the students' shoes and carefully analyze the difficulties in the process of students' understanding and mastering knowledge; Secondly, we should fully consider all kinds of obstacles that may appear in students' cognitive and psychological processes. Therefore, I have determined that the teaching focus of this lesson is to understand acute triangle, right triangle, obtuse triangle, isosceles triangle and equilateral triangle, and to understand the characteristics of each type of triangle; The difficulty in teaching is to understand and master the characteristics of various triangles.
Finding the growing point of knowledge is a condition.
Primary school mathematics is a highly systematic subject. Mathematics teaching is to guide students from the old to the new, organize active migration, promote reasoning from the known to the unknown, understand the relationship between simple problems and complex problems, and constantly improve the cognitive structure with the help of mathematical logical structure. Therefore, the formation of new knowledge has its fixed knowledge growth point. Only by finding the growth point of knowledge can we highlight the key points and break through the difficulties.
We can identify the growing point of knowledge according to the following three points: (1) Some new knowledge is similar or similar to some old knowledge, so we should highlight "* * * similarities". For example, the divisor divided by two or three digits is based on the divisor divided by one digit, and the latter is the divisor changed from one digit to two or three digits, and the dividend should be divided from which digit. (2) Some new knowledge is composed of two or more old knowledge, so it is necessary to highlight the "connection point". For example, "addition and subtraction of fractions with different denominators" is composed of addition and subtraction with the same denominator and general division of two old knowledge. Its key problem is that the fractional units are different, so the general division becomes the connection point of two old knowledge. (3) Some new knowledge is developed from some old knowledge, so it is necessary to break through the "evolution point", such as the "check calculation of division with remainder", which is based on the previous check calculation of division by division. Both types of check calculations have to be multiplied by quotient and divisor, while the latter has evolved into "addition of remainder".
This lesson is a further study on the basis of students' preliminary understanding of triangles, so teachers always grasp the characteristics of angles and sides to deeply understand the "evolution points" of various triangles, carry out teaching activities, and then constantly break through. \x0d3, adopting appropriate teaching methods is the key \x0d 《 Curriculum Standard 》 points out that teachers' teaching should be based on students' cognitive development level and existing experience, and be open to all students. Pay attention to heuristics and teach 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, explore actively and study cooperatively 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. \x0d Therefore, according to students' reality, appropriate teaching methods are the key to highlight key points and break through difficulties. Commonly used teaching methods include: reviewing the past, learning new methods (transfer method), hands-on practice method, intuitive demonstration method, inspiration and guidance method, contact life method, trial and error method, comparison method, discovery method, transformation method, verification method, game method and so on.
This lesson mainly adopts hands-on practice, intuitive demonstration, inspiration and guidance, comparison, discovery, verification and games. For example, when looking for classification standards, "We just classified these people in the room according to different standards. What criteria are you going to classify these triangles according to? " Heuristic guidance method is adopted; In triangle classification activities, through independent exploration and group cooperation, the methods of hands-on practice, comparison and discovery are used. When we know all kinds of triangles, we use intuitive demonstration method, discovery method, comparison method, verification method and game method, especially when we break through the difficulty of "knowing and mastering all kinds of triangle characteristics" In the students' visual presentation report, the teacher found that students knew the names and concepts of various triangles on the basis of preview, but the classification was not accurate, which showed that students did not understand their characteristics at all. It changed the previous design thinking, conformed to the students' thinking, first asked students to say various concepts of triangles, then guided them to use comparison method, verification method and other methods to verify, and finally summed up their memories. In this process, students actively participate in activities by watching, watching, dividing, discussing, comparing, testing and speaking. Because of their rich experience, teachers have broken through the key and difficult points in teaching. However, due to the late organization of intuitive demonstration, students' thinking and expression skills are poor, and the teaching link of "activity experience and exploration of new knowledge" takes a long time.
Reasonable design of blackboard writing is the way \x0d blackboard writing is the epitome of classroom teaching, the schematic diagram to reveal the key points and difficulties of teaching, and the radiation source to grasp the key points and difficulties. The blackboard writing plays the role of outlining, which is designed according to the teaching requirements, characteristics and students' actual situation on the basis of thoroughly understanding the teaching materials. It integrates the outline, artistry and intuition, which not only improves the outline, but also stimulates interest.
Well-designed exercises are the guarantee.
Carefully designed classroom exercises are an important guarantee to improve teaching quality. Students can further understand and consolidate knowledge through practice and turn knowledge into skills, thus improving their comprehensive ability to use knowledge. The key to well-designed exercises lies in "precision", that is, highlighting key points-new knowledge points and strengthening difficult points-confusing and difficult parts. Therefore, when preparing lessons, we should carefully study the exercises in the textbook, understand the arrangement intention, and clarify the purpose and function of the exercises.
This class has corresponding real-time exercises and game activities in the process of inquiry, so I designed three levels of exercises in the whole class, namely, the basic exercises of filling in the blanks, the variant exercises of judgment and the extended exercises of solving problems. However, due to time, I only completed the real-time exercise, which failed to better reflect the teaching purpose of this link.
In addition, it is not enough to deal with difficult content only by teaching methods, methods and means. We should also pay attention to the following points: First, teachers should not inform or hint at difficulties in advance, which may easily cause psychological pressure on students. For example, students should concentrate on "the content of this class is very difficult, so don't be nervous". Second, the teaching rhythm. Adjust the speech speed, intonation and tone appropriately. Pay close attention to students' expressions, especially when explaining difficult content. If you find that most students are frowning blankly, or when there are few people raising their hands, the teacher should slow down the speed of speaking, give students enough time to think, set up steps in time, and make good preparations. On the other hand, we should encourage them in time with the tone of encouragement and trust to help them overcome difficulties. After making things easy, they should resume their pace and move on.