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(一) 教学中易于发生困难的问题一、对于概念性质、定理等理解不透,因而掌握不够巩固,运用不够确切。 1.不习惯使用“确定平面的条件”就直接引用平面几何中有关的性质与定理,造成逻辑推理中的缺陷或错误。 2.易于发生概念间相互混淆。例如把异面直线的距离误认为是“两异面直线的公垂线”或“同垂直于两异面直线的线段”等。 3.叙述不确切,例如将二面角的平面角说为:“从二面角的棱上任意一点向两个面作垂线……”或“从二面角的棱上一点向棱作垂线……”等。 4.不善于从概念出发来确定元素间的位置关系,有时造成束手无策。例如习题二第12(5)题常有一部
(1) Difficulty in teaching problems First, the understanding of the nature of the concept, theorem, etc. is not fully understood. Therefore, the mastery is not consolidating and the application is not precise enough. 1. Not being accustomed to using “determining plane conditions” directly refers to the properties and theorems in plane geometry, causing defects or errors in logical reasoning. 2. Prone to confusion between concepts. For example, the distance from a straight line on a different surface may be mistakenly considered to be a “public line perpendicular to two different straight lines” or “a line segment perpendicular to two straight lines different from each other”. 3. The narrative is inaccurate. For example, the plane angle of a dihedral angle is: “From a point on a dihedral edge to a perpendicular on both sides ...” or “From a point on a dihedral angle to an edge. Vertical line ...” and so on. 4. Not good at deciding from the concept to determine the positional relationship between elements, sometimes causing no help. For example, there is often a question in Question 12(5) of Exercise Two