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近年来,中考题型中“动点问题”非常炙热,该类问题融几何与代数知识于一体,数形结合,有较强的综合性,动静结合,能够在运动变化中有力地发展学生逻辑思维能力、空间想象能力、综合分析能力、创新能力及辩证唯物主义观点。而“几何画板”可以帮助学生在动态中去观察、探索和发现对象之间的数量变化关系与结构关系,因而能充当数学实验中的有效工具,使学生通过计算机从“听数学”转变为“做数学”。本人纵观近年全国各地中考试题,通过研究动点型问题的特点,对动点问题、动线问题、动圆问题三大类型进行研究,解析蕴含在该类题型中的重要的数学思想和相关的解题策略,以期抛砖引玉,为所有几何问题中动点问题的教学提供些许帮助。
In recent years, senior high school entrance examination questions type “moving point problem ” is very hot, such problems melt geometry and algebra knowledge in one, the combination of number, there is a strong comprehensive, static and dynamic combination, can forcefully develop in the movement change Students' logic thinking ability, space imagination ability, comprehensive analysis ability, innovation ability and dialectical materialism point of view. The “geometric drawing board” can help students to observe, explore and discover the relationship between the quantity and the changes of the objects in the dynamic state, and thus can be used as an effective tool in mathematical experiments to enable students to learn mathematics from “Change to” do math ". Through examining the characteristics of the moving point type questions in recent years, I study the three types of moving point, moving line and moving circle problems, and analyze the important mathematical ideas contained in such kinds of questions and questions. Relevant problem-solving strategy, with a view to start a discussion, provide a little help for the teaching of the problem of moving point in all geometric problems.