Cases On The Application Of Geometry Sketchpad In Number-shape Combination

Number-shape combination is one of the most significant ways of thinking in senior high school. There are a number of questions occurring in the College Entrance Examination every year, which require students to apply this method in solving them,thus bringing unbelievable convenience. Geometry sketchpad is the practical software which enjoys great popularity among teachers and students. Thanks to its dynamic,visualization, operability, students are provided with a platform to explore independently.However,sometimes it may be difficult to reveal the "shape" when the teacher is merely using simple drawing on the blackboard. It can not be displayed dynamically, and the effect is not as good as we expect. Therefore, it is of vital importance to effectively combine the geometry sketchpad,an extremely powerful mathematical tool,with number-shape combination. It is suggested that we should integrate the application of tools into thinking, but not merely in single case. If number-shape combination is fully taken advantage of, we can surely embark on a new journey of mathematics teaching in senior high school.This thesis will be illustrated from the following five aspects.The first part is the introduction, which mainly includes the questions put forward,the research background and its significance, the present research situation analysis, the research method, the research content and the innovation and so on.The second part depicts the learning theory and teaching theory that support the application of geometry sketchpad to the number-shape combination.The third part explains the significance of geometry sketchpad applied to the number-shape combination and the principles to be followed. Additionally, it is suggested that we should apply Geometry sketchpad in some chapters involving number-shape combination in senior high textbooks, such as exponential function, logarithmic function,function and conic curve after reading. The thesis also emphasizes the effective combination of the two, but not about which one is a substitute, and adherence to the principle. Moreover, the application of geometry sketchpad to the mathematical teaching of number-shape combination is to enable students to better understand the nature of mathematics. It would be inappropriate to simply demonstrate and put the cart before the horse. Bear in mind that the traditional calculation and derivation is essential.The fourth part introduces the typical topics using the number-shape combination ideas in the high school mathematics teaching, such as the function of intersection point,image and its transformation, the fixed point in the plane analytic geometry trajectory, a constant fixed point and fixed value, the inequality of the optimal solution to linear programming and nonlinear problems in turn; and restudy the application of these typical topics via using geometry sketchpad in the number-shape combination.The fifth part reveals some thinking and prospect of applying the geometric sketchpad to the number-shape combination.