From the teaching content of high school mathematics, algebra, trigonometric function, analytic geometry, solid geometry and plane vector can all make full use of geometry sketchpad software. The use of geometry sketchpad software provides a good learning environment for mathematics teaching, so that students' dominant position can be truly established, autonomous learning, inquiry learning and cooperative learning can be truly realized, students' interest in learning can be stimulated, and their innovative spirit and practical ability can be cultivated. With the support of information technology, learning new mathematical knowledge, exploring mathematical problems and applying mathematics to solve practical problems have gained new development momentum, which can be internalized into students' mathematical literacy more efficiently and deeply. From the teaching form of high school mathematics, compulsory courses, extracurricular activities, elective courses and research-based learning can all be infiltrated. 1. Use the Geometer's Sketchpad in function teaching 1 to show the functional relationship between two variables. 6 4 2 -2 -4 -5 5 Geometry Sketchpad 4.03 can directly input the resolution function to get an image with a specific function. Through the flexible use of parameters, a large number of similar images can be drawn, which is convenient for the study and research of some functions. For example, to discuss the image and essence of the function y=ax+b/x(ab is not equal to zero), we must first follow the principle of from special to general and from general to special; Secondly, when studying a multivariable problem, we should pay attention to the research strategies of reasonable classification and analogy; Finally, pay attention to the application of classified discussion and the combination of numbers and shapes in solving problems. By studying the simplest function f(x)= x+ 1/x, it is extended to the functions f(x)= x+2/x, f(x)= x+3/x, f(x)= x+4/x, and then f(x)= x+ is abstracted. 0), using the properties of this function to study the maximum value of the function. In the process of research, we should know the laws from the special to the general, and then from the general to the special, and realize the concrete application of this dialectical thought that develops from the individual special to the general and exists in the individual. In the research process, students use their hands and brains, learn independently, use computers to solve problems, improve research efficiency, stimulate students' willingness to guess boldly and innovate, and experience mathematical ideas such as combination of numbers and shapes and analogy in the process of solving problems. -22 1- 1-222. Represents the transformation of plane graphics. The transformation of plane graphics is the basic knowledge of graphic drawing. The study of various function images and the discussion of curve equations in middle school mathematics textbooks involve image transformation, and we should see that the transformation laws of various curves are consistent in theory and method. The general law of the transformation of arbitrary function y=f(x) is studied by using the geometric sketchpad. 3. Using the image "Properties" menu of the new version of the Geometer's Sketchpad, the range of independent variables of the function can be directly limited, so as to achieve the purpose of making segmented function images. Let's take the function as an example to explain how to make full use of the new function added by the new version of the Geometer's Sketchpad-you can limit the range of function images and make images of various parts in sections. The specific operation is as follows: (1) Click the "Define Coordinate System" command in the "Chart" menu to establish a rectangular coordinate system; 4 2 -2 -4 -5 5 (2) Click "Draw New Function" in the chart menu, enter the function formula: 3x+ 12, and click OK. Draw a straight line (3) Select a straight line, right-click, select the Properties command in the pop-up menu, then select the Image command, change the upper limit to -3 in the Range, and click OK. (4) Repeat (2) and (3), but change it to x2+2x when inputting functions; (5) Repeat (2) and (3) again, but change the input function to -2x+6 to get the drawing. As shown in the figure, this method is fast, simple and accurate for the image of piecewise function. At the same time, it embodies the mathematical method of subsection processing of subsection function. 4. Making method of function image with variable interval: (1) constructing interval; [a, b] a is controlled by the parameter or the abscissa of the moving point on the X axis; B is represented by a or obtained through translation. On the connected line segment ab; (2) On the line segment AB, take any point C and measure the abscissa of this point C; (3) calculation: calculation by function expression; (4) The two measurement results are selected in turn to construct a point p (,); (5) Select point P and point C to construct the trajectory. (6) Make the function image directly according to the original analytical formula, and select the image to make the line shape a dotted line. 2. Use the Geometry Sketchpad 1 to show different viewing angles of space graphics in the teaching of plane geometry and solid geometry. The "Geometry Sketchpad" can make three-dimensional geometric figures with various visual angles controlled by the operator, so that students can observe them and the line segments and sections on these geometric figures from any direction. On the basis of observing physical objects, students can call these courseware again, so that they can see these dynamically changing geometric figures, which are not only clear, but also can be seen from many angles, making up for the shortcomings in physical observation, and also establishing an intermediate connection between physical objects and figures, which is more conducive to spatial graphics. 2. Express the universal significance of geometric figure properties. Geometric properties are of universal significance, but they can only be learned from specific examples. Using "Geometry Sketchpad" to make courseware solves this contradiction well. Courseware made with "Geometric Sketchpad" can make every specific figure move, and in the process of moving, the given geometric relationship can be maintained. For example, when exploring "three midlines of a triangle intersect at a point", in this property, we make two midlines in a triangle, and then let the third midline pass through the intersection of these two midlines, which is the center of gravity of the triangle. When measuring the two line segments formed by the intersection, we will find that their ratio is 2: 1. In order to illustrate the universal significance of this property, you can make an "animation" button, or drag the vertices of the triangle to make the triangle move, but in the process of change, the three midlines always intersect at one point. In this way, students have a deep impression that any triangle has this property. Thirdly, in the teaching of analytic geometry, the geometric sketchpad is used to express the movement process of various mathematical phenomena. It is difficult to express the movement process of an object clearly with words and characters, but a new artistic conception can be achieved with graphics. For example, an ellipse is defined by a trajectory, and a trajectory is represented by motion. We use the "Geometer's Sketchpad" to make a moving point whose sum of distances to two fixed points is constant, measure the distance from the moving point to two fixed points, and then calculate the sum of the two distances. In this courseware, students can clearly see the trajectory of moving points and leave a clear impression on the elliptical trajectory. Motion point ABB F 1F2m Method 1: Draw according to the first definition of ellipse: (1) Make a line segment AB with a length of 2a; P is any point on the line segment; Get line segments PA and Pb; (2) establishing a coordinate system; Draw two focal points; Construct circles with, as the center and PA and PB as the radius, respectively; Then two circle are selected to construct that intersection point of the two circle; (3) selecting point P and one of the intersections to construct a trajectory; Then choose point p and another intersection point to construct trajectory; Note: To build a point trajectory, you need to select related points at the same time. Moving point method 2: Drawing according to the first definition of ellipse: (1) Draw a circle with a center and a radius of 2a; Inside the circle; (2) take any point p on the circle; Connection; The vertical line of the structure; Construct a line segment (or straight line) through point p and point; Construct the intersection of vertical line and line segment (straight line); (3) Select point P and intersection point to construct trajectory. Method 3: Drawing according to the second definition of ellipse (1), first defining eccentricity e; Methods: Take a point C on the AB line and measure and calculate it. And mark the proportion; (2) Make a line segment DE with adjustable length, and take any point m on the line segment DE; Mark center d; Select point m, transform/scale/select. . . . , get the point m'; (2) Make a straight line and a fixed point f; (3) making the vertical line of the straight line pass through f to obtain the vertical foot h; Mark vector DM; Select point H, menu: transform/translate/mark to get H '；; (4) constructing a circle with f as the center and the length of DM' as the radius; Parallel lines forming a straight line through h' intersect with a circle; Structural intersection; (5) Select point m and intersection point to construct trajectory. Method 4: Draw (1) into two concentric circles according to the parametric equation of ellipse, with radii of A and B respectively and center of O; (2) take any point p on the great circle; Connect the OP intersection circle to point a; (3) Passing P is the vertical line of X axis, and Passing A is the vertical line of Y axis; Construct their intersection point m; (4) Select point P and intersection point to construct trajectory. Of course, there are several elliptical practices, so I won't introduce them here. In the process of learning and discovering ellipses, students will have a new understanding of ellipses. In the process of analyzing and solving problems, they will naturally improve their ability, master knowledge and cultivate the spirit of exploration. Fourthly, carry out the activities of learning "Geometry Sketchpad" among students to improve their computer application ability and practical innovation ability. 1. "Geometry Sketchpad" is an important tool for students to carry out mathematical experiments. Nowadays, mathematics teaching should not only cultivate students' strict reasoning ability with fundamental significance such as calculation and expression, but also cultivate students' informal or specious reasoning ability such as premonition experiment, trying to induce, "hypothesis-test", simplification and complication, and finding similarity. Only in this way can we improve the creative temperament of mathematics curriculum. The role of experimental methods in mathematical science has been paid more and more attention, and the use of "Geometry Sketchpad" gives students a useful tool to carry out mathematical experiments, which makes it possible for each student to carry out mathematical experiments in class. This kind of mathematical experiment will play a role in the formation of students' subjective consciousness, the improvement of their ability to actively participate in mathematical practice and the cultivation of their ability to acquire mathematical knowledge independently. 2. Using "Geometry Sketchpad" to carry out inquiry learning activities has improved students' innovative ability and practical ability. Using "Geometer's Sketchpad" to carry out inquiry learning activities has greatly changed teachers' teaching methods and students' learning methods, promoted students' innovative ability and practical ability, and produced a vivid educational situation of teacher-student interaction. Although the topics of this kind of problems are different, the inquiry process in the "Geometry Sketchpad" is almost the same, and too much has been done. Some students use the "Geometer's Sketchpad" to summarize and model this kind of function problems with parameters: (1) Establish parameters; ⑵ Establish a function with parameters; ⑶ Make function diagram, ⑶ Change parameters, observe the changes of function diagram and explore the nature; 5] Verify or prove the nature obtained from the inquiry, or give an example to deny it. Using the "Geometry Sketchpad" to carry out inquiry learning activities, through students' own operation and active participation, students can find and solve problems, and their innovation and practical ability can be improved rapidly, which I didn't expect. 3. The activity of learning "Geometer's Sketchpad" improves students' awareness and ability to use computers. Learning Geometry Sketchpad is not only beneficial to mathematics teaching, but also beneficial to the learning of information technology. Because "Geometer's Sketchpad" is closely related to students' study and life, students will learn "Geometer's Sketchpad" and make computers a tool that students often use, which will improve students' awareness of using computers in their study and life and effectively improve their computer application ability. In order to effectively let students actively participate in mathematics practice and cultivate their ability to acquire mathematics knowledge independently in mathematics teaching, I teach geometry sketchpad knowledge through elective courses, extracurricular activities and research-based learning. In the teaching process, students not only master the use of "Geometer's Sketchpad", but also improve their understanding of some important mathematical concepts, such as the understanding of functions, and improve their abilities in many aspects, such as the ability to explore and solve problems. Appendix: The training content of Geometer's Sketchpad is 1, and the point is free point; Fixed point; A point on a line segment; A point on a straight line; Points on the coordinate axis; A point on a circle; A point on a curve; Coordinates of measuring points; Mark (rotate) center; Structure of intersection; 2. Line segment: construct a line segment through two points; Free line segment; Line segments that can slide on the X axis (identification vector, parameter method, circle truncation, translation, etc.). ); Use a linear function to define the line segment of the domain; A line segment determined by a moving point on a circle; Measuring line segment; Identification vector; 3. Straight line: a free straight line; A fixed straight line; Equation x = a；; Function y = kx+b; A straight line passing through a fixed point (equation y=k(x-x0)+y0 or a straight line formed by a fixed point and a moving point passing through a circle); Parallel straight line system (equation y=kx+b, k is a constant and b is a parameter, or parallel lines are constructed geometrically through moving points); 4. Circle: a free circle; A fixed circle; A circle with a constant center and a variable radius; A circle with a fixed heart radius; The geometric structure of a semicircle; Function construction of semicircle; A circle that can intersect a straight line; Cannot build a circle with intersection points; The interior of a circle; Unit circle;