So how to cultivate students' geometric intuition ability and how to better play the teaching value of geometric intuition? Today, we mainly talk about how to cultivate students' geometric intuitive ability through the lesson of "line segment ray straight line".
First, cultivate students' spatial imagination
1. Let students gain graphic knowledge through active participation. In teaching, I pay attention to students' basic life experience and life experience, and pay attention to guiding students to connect their feelings about graphics with related knowledge. In students' active participation in learning, I give students an intuitive understanding through a set of pictures, which leads to a straight line, so that students can easily find the characteristics of the straight line, especially the straight line is an idealized concept, and the geometric intuition is more important. Learning intuitive geometry, as the book says, makes use of students' favorite specific practical activities, such as "looking, stacking, cutting, spelling, putting, measuring and drawing", and guides students to coordinate their vision, hearing, touch and kinesthetic sense through personal touch, observation, measurement, production and experiment, which effectively promotes the internalization of psychological activities.
2. Pay attention to the cultivation of students' ability to read and draw pictures. Graphics is the soul of geometry, and knowing and drawing are the most basic qualities in learning geometry. In the teaching of line segment ray straight line representation, it is a personal demonstration, which emphasizes the name, details and precautions of graphics, so that students can draw them in practical problems and correct them at the same table. Comparing who draws better, students will be more serious and standardized when drawing, and consolidate the basic drawing method again in the process of correcting each other, killing two birds with one stone.
3. Do more translation between three languages: written language, symbolic language and graphic language. In geometry teaching, train students to express their theorems, axioms and definitions in three languages; After such training, students' spatial imagination ability and theorem understanding and memory ability have been greatly improved. When introducing the definition of ray and line segment, I converted written language into graphic language, and then converted graphic language into written language in three representations. The important axiom of straight line and "I say you draw" are actually simple graphic language transformed into written language, which consciously guides students to further improve their spatial imagination.
4. Use multimedia information technology.
Multimedia technology not only shows students a colorful graphic world, but also provides a way to solve problems. When students begin to explore how many straight lines there are in a point, although they find that there are countless straight lines, multimedia shows students its unimaginable graphics, expands students' spatial vision, and truly experiences that there are countless straight lines in a point.
Second, cultivate students' intuitive insight
1. Solid basic knowledge. A solid foundation is the source of intuition. Without a deep foundation, it is impossible to think intuitively and improve students' intuitive insight. In teaching, students are strictly required to understand the definition and master the properties and theorems of graphics. For example, after exploring linear axioms, students should standardize their own language, remember the contents of linear axioms, fix a thin board on the wall, at least need a few nails and how to plant trees more neatly, and strengthen important knowledge points again.
2. Create the artistic conception of cultivating students' intuitive insight. In students' geometric figures, let students "follow their feelings", speak their intuition boldly, find out the relationship they need in complex figures and identify it accurately. For example, in two intersecting straight lines, let students express the straight lines in different ways, explore the positional relationship between points and straight lines, and judge whether the graphic expression is right or wrong.
3. Combine observation with thinking. To overcome the shortcomings of carelessness, cursoriness and ignorance, we must observe carefully, think hard, find problems and solve them. If you take a point C on a straight line, * * * has several line segments; if you take a point N, there will be several line segments; For example, finding the difference between line segments, rays and straight lines requires both the accuracy of knowledge points and the rigor of language description.
4. Important application of mathematical thought. There are many mathematical thinking methods in geometry, the most important of which is the transformation thinking method, which runs through geometry teaching and occupies a very important position in geometry teaching. We often turn the unknown into the known, the complex problem into the simple, the abstract into the concrete, such as the fare problem, into the number of line segments, and once again strengthen the single and double cycle problem. We can convey mathematical methods to students, but we can't convey mathematical vision. Therefore, we should pay attention to the teaching of mathematical ideas, which will help students actively explore ways to solve problems, experience strategies to solve problems, and improve their awareness of mathematical application.
Third, cultivate students' ability to think with graphics.
1. Memorize basic knowledge with graphics. Many theorems, axioms, properties and definitions of plane geometry are difficult for students to remember clearly. It is easier to solve problems by guiding students to use graphic memory, and at the same time cultivate students' awareness of using graphics. For example, the definition of ray and line segment can visually and vividly reproduce the trajectory formed by graphics under the demonstration of graphics, which is conducive to the generation and memory of concepts.
2. Use graphics to strengthen the understanding of concepts, axioms and conclusions. When thinking about mathematical problems, we can draw pictures as much as possible in order to express abstract things intuitively and show essential things. When learning mathematics, we should guide students to form the habit of describing and thinking about problems with intuitive graphic language. Strengthen the understanding of concepts, theorems, etc. by using graphics. In fact, it is the advantage of geometric intuition and the idea of combining numbers with shapes.
Our teaching should be based on textbooks and guide students out of them. Textbooks have little effect on improving students' spatial concept. Little by little, they can have a great impact. Textbooks contain abundant opportunities to cultivate students' concept of space. Teachers should consciously and deeply understand every design intention of textbooks and make good use of these materials. As teachers, we should use materials more wisely and creatively, create good conditions for students' spatial concept and even the accumulation of mathematical ability in all aspects, truly make mathematics teaching serve the accumulation of students' mathematical literacy, pay attention to teacher-student interaction and student-student interaction in teaching, and let students establish the corresponding relationship between their own experience and foreign experience.