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在中学的立体几何里,是在学生已有的平面图形知识的基础上来研究空间图形的。因此,它具有两个突出的特点:第一,它要依据和采用许多平面图形的性质和结论;第二,由于空间图形与平面图形构成一个发展的系列,这又决定了它们有着极多的相似之处。相应地,也就为我们的教学提出了两个问题:第一个问题,怎样更好地将一些空间图形的问题转换成平面图形的问题去解决;第二个问题,怎样利用相似的关系,类比地由平面图形的性质去探求空间图形的有关性质和寻找更好的解题途径。教师引导学生逐步地掌握和运用这两条,可以说有如交给他们一把学习立体几何的钥匙。对于系统知识和形成整体结构,特别是对于智力品质的提高,是有积极的意义的。
In the three-dimensional geometry of middle school, spatial graphs are studied based on students’ existing knowledge of plane graphics. Therefore, it has two outstanding features: first, it has to rely on and adopt the nature and conclusions of many plane graphics; second, because spatial and planar graphics constitute a series of development, this in turn determines that they have a lot of Similarities. Correspondingly, we also raised two questions for our teaching: the first question is how to better solve the problem of converting some spatial graphics problems into planar graphics; the second question, how to use similar relationships, Analogically, the nature of planar graphics seeks out the nature of spatial graphics and finds better ways to solve problems. The teacher guides the students to gradually grasp and use these two items. It can be said that they are given a key to study solid geometry. It is of positive significance for system knowledge and overall structure, especially for the improvement of intellectual quality.