First, the concept of customs clearance.
Junior high school geometry combines logic with intuition, abstracting geometric concepts from practical geometric models in production and life, which is a major feature of nine-year compulsory education textbooks. Therefore, in teaching, students should observe the geometric model as much as possible, form perceptual knowledge, give mathematical names, draw mathematical figures, define figures and study properties. For example, when introducing the undefined concept of "straight line", it can be divided into four steps: (1) show a tight thin line, let students think about the tracks on the railway, and let them have a perceptual understanding of the actual model. (2) Give a mathematical name. The line with the above picture is called a straight line. (3) Give a definition: A straight line is a straight line extending infinitely in two directions. A straight line is a descriptive definition. As long as we understand "straight" and "extending infinitely in two directions", it has no length and thickness and is an ideal straight line. (4) Graphic: "axiom of straight line: there is only one straight line after two points." You can give an example. After the above four steps, students will deeply remember a concept and apply what they have learned in place.
Second, language barriers.
There are three forms of geometric language: one is graphic language, which is the geometric figure we study. Such as angle, triangle, trapezoid, etc. The second is written language, that is, a language that uses words to express concepts, theorems, axioms or a geometric problem. The third is symbolic language, such as "//"⊥ "△" and so on. These three languages usually coexist in geometry, and sometimes they infiltrate and transform each other. Strengthening the basic training of these three geometric languages in teaching requires each student not only to express each language skillfully, but also to accurately "translate" one of them into other language forms according to the needs of solving or proving problems. For the study of geometric languages, it is the key to learn geometry well to be rigorous and accurate, especially to master the "mutual translation" of three geometric languages and comprehensively use graphics, characters and symbols.
Third, pull away
Geometric figures are the main object of study and research, and drawing accurate figures is the basis of solving (proving) problems. Drawing the correct figure that conforms to the meaning of the question will often leave a deep and intuitive impression on students, and also bring clear ideas to solving problems (proofs). On the contrary, inaccurate graphics will bring illusion to thinking and solving problems, and even lead thinking astray, making it impossible to start with obvious problems. Therefore, students are required to be strict with themselves in their study and carefully draw standardized and accurate geometric figures. Never be afraid of trouble or trouble, and draw by hand without learning tools.
Fourth, the reasoning proves that:
The reasoning of geometry proves that compared with algebra, the way of thinking is obviously different, and geometry thinks with the help of graphics, and its words must be well-founded. Therefore, we should pay attention to the following points when learning geometric reasoning proof:
(1) Learning the basic knowledge of geometry is the premise of learning the proof of geometric reasoning, and definition, axiom, theorem and inference are the theoretical basis of geometric deduction. Therefore, we should deeply understand its meaning and thoroughly understand its topic and conclusion. Only in this way can we use them flexibly and correctly to deduce, prove and solve problems.
(2) We should practice three basic skills: reading pictures correctly; Can use three geometric languages to "translate" each other, and have accurate and skilled oral and written language expression.
(3) Strengthen the training of the basic structure and format of proof derivation in learning.
(4) Under the guidance of teachers, pay attention to the training of proof methods. There are generally two methods to prove geometry: analytical method and synthesis method. The combination of these two methods is called "reverse deduction of proof", that is, the process of finding proof by analytical method and writing proof by comprehensive method.
In junior high school geometry teaching or learning, if every student passes these four levels well, geometry learning will become easy and interesting, and geometry can really get twice the result with half the effort.
If you don't understand anything, you must ask your teachers and classmates in time. Don't hide it, you will become more and more confused.