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传统的平面几何推理论证新课入门伊始,就教给学生严格的演绎推理,辅助线几乎都是教师想好了,要么直接地画到具体的图形中去,要么通过指导学生操作图形,得到辅助线的痕迹,学生就可以通过观察法获得辅助线;这些都是下乘的教学设计。平面几何的教育价值主要体现于逻辑思维与理性思维,它需要避开物质性材料的干扰,促进学生深入到空间点线面体的结构性本质。因此,探究辅助线方法的过程就是理性思维展开的过程,这正是发挥平面几何理性思维教育价值的核心任务,我们从这方面有所突破。
The traditional plane geometric reasoning demonstration of the new course at the beginning of the entry, to teach students a strict deductive reasoning, the auxiliary line almost all the teachers think well, or directly drawn to the specific graphic, or by guiding students to manipulate graphics, get auxiliary line Traces of the students can get auxiliary lines through observation; these are inferior teaching design. The educational value of plane geometry is mainly embodied in logical thinking and rational thinking. It needs to avoid the interference of material materials and promote students’ deep understanding to the structural essence of point-line surface. Therefore, the process of exploring the auxiliary line method is the process of developing rational thinking. This is exactly the core task of exerting the educational value of plane geometry and rational thinking. We have made some breakthroughs in this respect.