The reading questions in the math exam mainly examine students' mastery of the language. But when students often answer such questions, some don't know how to answer, some don't know how to explain, and some don't know why. The main reason is that they don't have a good command of mathematical language. Therefore, in mathematics teaching, we should strengthen our understanding of three languages. Let me talk about my teaching methods for your reference.
1. Understanding of written language. Mathematical language is characterized by simplicity and rigor. In teaching, we should follow the idea that teachers are the promoters, guides and collaborators of students' learning, strengthen students' understanding training of written language and help students improve their understanding ability of written language.
1. 1 Understand by comparison. In teaching, it is helpful to compare the confusing places between the new knowledge to be learned and the knowledge already learned. For example, when learning "Decomposition Theorem of Space Vector", we can compare it with "Decomposition Theorem of Plane Vector". The same points are all linear representations of "arbitrary vector" and "unique" ground, but the differences are: ① * * * surface and * * * line; ② Ordered real number pairs and ternary ordered arrays. For example, they are complementary, adjacent to each other, complementary to each other's internal angles, all in different positions, but the number is the same.
The expansion and contraction of the sentence 1.2 is helpful for understanding. In the teaching process, concise words, especially definitions, axioms and theorems, can be understood by students with the help of expanded sentences or contracted sentences. For example, expand "diagonal equality" to "if two corners are diagonal, then the two corners are equal" so that students can understand the conditions and conclusions. Sometimes it can also be understood by abbreviations, such as the definition of number axis, which can be understood as follows: "The straight line that specifies the origin, unit length and positive direction is called number axis." It is not an arbitrary straight line, but three elements, so that students can master the concept of number axis.
1.3 Multi-angle understanding. Multi-angle understanding can make students fully understand and master knowledge. For example, what is the "necessary and sufficient condition for two straight lines to be perpendicular" can be understood from the perspective of composition, the general formula of two straight line equations and the oblique formula of two straight lines. Multi-angle reproduction strengthens understanding, activates thinking and cultivates divergent thinking ability.
1.4 translated into symbolic language and graphic language for understanding. In this way, students can clearly understand the definition of geometric formulas and the conclusion of theorems. At the same time, it is also an inevitable method to solve the problem of proof in written language, such as drawing a graph that conforms to the meaning of the problem, and expressing the conditions and conclusions in symbolic language combined with the graph.
1.5 can be understood by examples and analogy. For example, abstract and profound things can be made concrete and simple. For example, when talking about the concept of collection, we should talk about it first and then give examples, such as: students in one class, all classes in a school, etc.
2. Understanding of graphic language.
2. 1 pattern recognition: it is necessary to be able to identify the patterns from complex patterns, which are relevant and which are irrelevant. For example, in the cube ABCD-A1B1C1D1,what is the positional relationship between A 1C and D 1B? Another example is (as shown in the figure) plane ADC⊥ plane ABC, and ∠ ADC = ∠ ACB = 90, AD=CD=a, AB=2a, and find A-DB-C. On the basis of understanding A-DB-C, find the angle formed by plane ADB and plane CDB, and at the same time, from the plane ADC, Of course, we can also cultivate the ability to understand graphics from the translation, folding and rotation of graphics.
2.2 Drawing: Drawing is the writing of graphic language, from imitation to independent completion.
3. Understanding of symbolic language. Symbolic language has a high degree of generality and abstraction, which should promote students' understanding from its characteristics.
3. 1 Understanding the meaning of symbolic language is the key. You must know the meaning of symbolic language, otherwise you will be helpless when you meet strangers. At the same time, it should be classified to make it easy to master. Real number set, positive real number set, non-zero real number set, positive integer set, etc. , but also to guide students to distinguish between reading, so as to master. Such as -a2 and (-a)2, only by mastering the meaning of symbolic language can students improve their ability to distinguish and use symbolic language.
3.2 Master the characteristics of symbolic language. Grasping the characteristics of symbolic language is the key to eliminate interference, such as the characteristics of CUAUB and CU(AUB). If you don't understand clearly, you will be confused. Such as (a+b)2=a2+b2, sin(A+B)=sinA+sinB, such an error is that the essential features are not clear. Therefore, it is necessary to emphasize both external characteristics and essential characteristics, and organically combine language understanding with ability training.