How to break through the teaching design of the key and difficult points of the humanistic version of mathematics

Whether a lesson is good or not depends on whether the teacher correctly explains the basic content of the textbook, breaks through the key points of the textbook and solves the difficult points of the textbook, so that the students really understand and master the basic knowledge of the textbook. Whether a teacher can grasp the key points and break through the difficult points in teaching is the basic condition for good teaching, and also the performance of teachers' ability. First, what is the teaching key and teaching difficulties The so-called teaching key, "in the logical structure of the content of the material in a particular level of the relatively important premise of judgment", that is, "in the whole knowledge system or subject system in an important position and prominent role of the content". The following are some examples of the types of knowledge that can be used in the textbook. If a knowledge point is the core of the content of a unit, is the basis for subsequent learning or has a wide range of applications, etc., it can be determined that it is the focus of teaching. That is, students must master the basic knowledge and basic skills, such as meaning, laws, properties, calculation methods also include quantitative relationships, problem-solving strategies. For example, the first grade within 100 number size comparison of this lesson focuses on the method of comparing the size of two numbers; second grade translation and rotation of the teaching focus is the initial perception of the phenomenon of translation and rotation; the average of the third grade teaching focus is to understand the meaning of the average; 24-hour timekeeping method of the teaching focus is to know the meaning of the 24-hour timekeeping method, will be used to indicate the moment of 24-hour timekeeping method; fourth grade subtraction of simple Calculation teaching focus is to master the easy algorithm of continuous subtraction; fifth grade the volume of the rectangular body teaching focus is to use the formula of the volume of the rectangular body to solve real-world problems; sixth grade problem solving with the knowledge of proportions teaching focus is to be able to solve problems with the knowledge of proportions. Difficulties in teaching generally refer to key knowledge points or problems that are easy to be confused or wrong for most students to understand and master. For example, the difficulty of the first grade practical activities of the pendulum, think about the difficulty is to find out through observation the rule of using the circular pieces of different numbers; second grade translation and rotation of the teaching difficulty is to be able to draw a simple figure on the grid paper along the horizontal and vertical direction after the translation of the figure; the teaching difficulty of the third grade of the year, month and day of the year is to remember the number of days in each month and in the year of equal years and leap years, and initially learn to determine whether a particular year is a year of equal years or leap years. The difficulty of the two lessons taught by Ms. Li Zhilan and Ms. Liu Yongxia in Grade 4 is the flexibility in choosing computational methods to solve real-world problems; the difficulty of teaching the volume of a rectangular body in Grade 5 is to understand the process of deriving the formula for the volume of a rectangular body; and the difficulty of teaching the zooming in and out of shapes in Grade 6 is to zoom in and out of shapes in a certain proportion. The difficulty is sometimes the same as the focus. Understanding the significance of multiplying a number by a fraction in grade 6 is both a teaching difficulty and a teaching focus at the same time. Instructional focus and instructional difficulty also have their own characteristics. The focus of instruction comes from the knowledge itself, which exists objectively due to the inherent logical structure of mathematical knowledge and is therefore consistent for every student. The teaching difficulty is different, it depends on the students' own understanding and acceptance ability. Practice has proved that different levels of students for the same knowledge point of the difficulty of the breakthrough speed and level is uneven. Due to the formation of teaching key and difficult points of the two based on different, so some of the teaching content is both the teaching key and teaching difficulties, some of the content is the teaching key but not necessarily teaching difficulties, some of the content is difficult to teach, but not necessarily the teaching key. But teaching key points and difficult points are determined by the teaching objectives of the same teaching content. Second, the significance of the study of teaching key points can be summarized in this sentence - the implementation of teaching key points is to enable students to master the knowledge of the premise, breakthroughs are the key to the success of the teaching of the difficult points. Teachers in the teaching process to break through the difficult points of the method is often to make students active thinking, stimulate interest in the catalyst. Third, how to break through the key and difficult points in mathematics teaching This requires every mathematics teacher in teaching practice, constantly learning, summarizing, groping. Below I will talk about the problem of a little experience and practice. 1. seize the knowledge of the interface, the use of migration methods to break through the key and difficult points We first focus on the characteristics of the subject of mathematics. One of the characteristics of elementary school mathematics is a strong systematic, each new knowledge is often closely linked to the old knowledge, new knowledge is the extension and development of the old knowledge, the old knowledge is the basis of new knowledge and growth points. Sometimes new knowledge can be migrated from the old knowledge, but at the same time it becomes the basis for subsequent knowledge. Therefore, mathematical knowledge points are like a chain linking and interlocking. It can be seen that if the teacher is good at capturing the interface between mathematical knowledge, consciously "migration" as a way to help students learn, to the old lead to the new, the old in the new, the organization of active migration, it is not difficult to achieve the breakthrough of the teaching of important and difficult points. Case 1: the basic nature of fractions The basic nature of fractions is described in this way: the numerator and denominator of the fraction at the same time multiplied or divided by the same number (except 0), the size of the fraction remains unchanged. Teaching, if it is taught as an isolated point of knowledge, by observing 1/2 = 2/4 = 6/12 from left to right, right to left one by one, over and over again to describe the process of change from who to who, the teacher's purpose is to let the students in the constant repetition of the existence of this law, and learn to express the same language, but in the end the students may not be able to combine with their own understanding, with a But at the end of the day, students may not be able to combine their understanding with a more concise and accurate mathematical language to describe the basic properties of fractions. If we analyze the knowledge base of the basic properties of fractions before teaching, we will find a very similar narrative with its "quotient invariant nature" and communication between the two links "the relationship between fractions and division"; at this time, in order to break through the "guide students to generalize and generalize". In order to break through the "guide students to summarize the basic properties of fractions" teaching difficulties, we can arrange in the pre-class review session for the "quotient invariant nature" and "the relationship between fractions and division" exercises. "The following are some examples of the exercises that can be practiced before the lesson. Can be used to transfer the method of teaching a lot of knowledge, such as the divisor is a two-digit divisor, it is in the study of the divisor is a single-digit divisor on the basis of the transfer of learning, only to increase the test quotient and the adjustment of the quotient and the difficulty of the method is more flexible. Another example, the multiplication of multi-digit multiplication is in the study of one-digit multiplication on the basis of migration, the same arithmetic method. It can be seen that, in the process of teaching mathematics, we should pay attention to reveal and establish the intrinsic connection between new and old knowledge, from the existing knowledge and experience, the use of migration methods to highlight