First, the use of life examples to introduce concepts
Concept belongs to rational knowledge, and its formation depends on perceptual knowledge. The psychological characteristics of students are easy to understand and accept specific perceptual knowledge. In the teaching process, various forms of intuitive teaching are the main ways to provide rich and correct perceptual knowledge. Therefore, when telling a new concept, it is easier to reveal the essence and characteristics of the concept by guiding students to observe and analyze specific physical personnel. For example, when explaining the concept of "trapezoid", teachers can introduce typical examples of trapezoid (such as ladders, cross sections of dams, etc.). ) Combine with students' real life, and then draw the standard figure of trapezoid, so that students can have a perceptual understanding of trapezoid. For another example, when the teacher talks about the concept of "number axis", he can imitate the points on the scale to represent the weight of the object. The balance beam has three elements: ① the starting point of measurement; ② unit of measurement; (3) A clear direction of increase and decrease inspires people to express numbers with points on a straight line in real objects, thus leading to the concept of number axis. This kind of image description conforms to the cognitive law, and students are easy to understand and impressed.
Second, pay attention to the formation process of the concept.
Many mathematical concepts are abstracted from real life. Explaining their sources will not only make students feel abstract, but also help to form a lively learning atmosphere. Generally speaking, the formation process of concepts includes: the necessity of introducing concepts, the understanding, analysis, abstraction and generalization of some perceptual materials, and the emphasis on the formation process of concepts, which conforms to students' cognitive laws. In the teaching process, if we ignore the process of concept formation and turn the vivid process of concept formation into a simple "article with examples", it will not be conducive to students' understanding of concepts. Therefore, paying attention to the formation process of concepts can reveal the essential attributes of concepts completely, essentially and internally, so that students can have an ideological basis for understanding concepts and cultivate students' thinking methods from concrete to abstract. For example, the establishment of the concept of negative numbers shows that the formation process of knowledge is as follows: ① Ask students to summarize the numbers they learned in primary school, indicating that the number of objects is represented by natural numbers 1, 2,3 ...; If there is no object, it is represented by a natural number of 0: sometimes the result of measurement and calculation can't be an integer, so it is represented by a fraction. ② Observe two thermometers, 3 degrees above zero. Write it down as +3, subtract 3, and write it down as -3, and a new number-negative number appears here. (3) Let the students say the meaning of the given question and observe the characteristics of the given question. ④ Guide students to abstract the concepts of positive numbers and negative numbers.
Third, in-depth analysis. Reveal the essence of the concept
Mathematical concepts are the basis of mathematical thinking. In order for students to have a thorough and clear understanding of mathematical concepts, teachers should first analyze the essence of concepts and help students understand the connotation and extension of a concept. That is, the object reflected by the concept is clearly defined from both qualitative and quantitative aspects. For example, mastering the concept of vertical lines includes three aspects: ① understanding the background of introducing vertical lines: when one of the four angles formed by the intersection of two straight lines is a right angle, the other three are also right angles, which embodies the connotation of the concept. ② Knowing that two straight lines are perpendicular to each other is an important special case of the intersection of two straight lines, which embodies the extension of the concept. (3) I will use the definition of two perpendicular lines for reasoning, knowing that the definition has the function of judgment and nature. In addition, students should learn to solve problems with concepts and deepen their understanding of the nature of concepts. For example. "Formula (a≥0) is generally called quadratic radical", which is a descriptive concept. Formula (a≥0) is a whole concept, in which a≥0 is a necessary condition. For another example, in teaching the concept of function, in order for students to better understand and master the concept of function, it is necessary to reveal its essential characteristics and analyze it layer by layer: ① "there is a certain process of change"-explaining the existence of variables; ② "There are two variables X and V in a certain change process"-the representation function is to study the dependence between the two variables; (3) "For every certain value of X within a certain range"-means that the value of the variable X is limited, that is, the value range is allowed; (4) "V has a unique definite value corresponding to it"-it means that there is a unique definite corresponding law. From the above analysis, we can see that the essence of function concept is correspondence.
Fourth, through variants. Highlight contrast. Consolidate the understanding of concepts
Consolidation is an important link in concept teaching. According to the principle of psychology, once a concept is acquired, it will be forgotten if it is not consolidated in time. To consolidate the concept, students should be guided to repeat it correctly after the concept is initially formed. Here, students are not simply required to memorize, but to grasp the key points, main points and essential characteristics of concepts in the process of retelling, and at the same time pay attention to the variant practice of applying concepts. Proper use of variants can make thinking not bound by negative stereotypes, realize flexible transformation of thinking direction and make thinking divergent. Such as "π and 3. 14 159" in the concept teaching of "rational number" and "irrational number". Through such training, we can effectively eliminate external interference and have a deeper understanding of "rational numbers" and "irrational numbers". Finally, when consolidating, we should compare the concepts taught with similar and related concepts through appropriate positive and negative examples, distinguish their similarities and differences, pay attention to the scope of application, and carefully hide the "trap" to help students reflect, thus arousing deeper positive thinking about knowledge and making the acquired concepts more accurate, stable and easy to migrate.
Fifth, pay attention to application. Deepening Concept Understanding and Cultivating Students' Mathematical Ability
A deep understanding of mathematical concepts is the basis of improving students' ability to solve problems; On the other hand, only by solving problems can students deepen their understanding of the concept, and understand and master the connotation and extension of the concept more completely and profoundly. There are many examples of solving problems directly with concepts in textbooks, so we should make full use of them in teaching. At the same time, in view of the concept that students are prone to make mistakes in understanding, some targeted topics are designed, so that students can understand the concept more thoroughly through practice and comments.
In a word, mathematics concept teaching plays a vital role in the whole mathematics teaching. Teachers should try to cultivate students' dialectical materialism concept by revealing the process of concept formation, development, consolidation and application. Improve students' cognitive structure and develop students' thinking ability, thus improving the quality of mathematics teaching.