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初学几何証明題的困难究竟在哪里?从学生的反映,作业中发現的問題以及平时观察了解,不外有下列几点: 1.缺乏叙述問題的能力。当学生初接触几何証明,就会感到这种証明的叙述过程不同子在算术或代数里的解題方法,不习慣于层层推理論証,叙述吋詞語不通,例如把“以A点为圓心,4cm为半径作弧交CE于B”。叙述成:“以A点为圆心,半径4cm为弧到B”。往往用冗长的文字叙述代替用数学符号来表达問題。对于常用的詞,如相同与相等、平分与平均、含有与具有等往往区别不清。 2.概念不清,表达錯誤。我們常見学生把△ABC三内角和等于180°写成△ABC=180°;把图1中的∠BDC和∠CEB写成∠D和∠E,或写成∠1和∠2(图中未标∠1,∠2);分不清三角形的高与垂綫;
Where is the difficulty of the beginner geometry proving problem? From the student’s reflection, the problems found in the homework, and the usual observation and understanding, there are the following points: 1. The lack of the ability to describe the problem. When the students first contact with the geometric proof, they will feel that the narrative process of this proof is different from the method of solving problems in arithmetic or algebra. They are not accustomed to theoretical proofs at the layers, and they are unreasonable in terms of narration. For example, taking the A point as the center, 4cm radius for arc CE to B“. Described as: ”A point as the center, radius 4cm arc to B". Long textual narratives are often used instead of mathematical symbols to express problems. For common words, the same and equal, equal and average, contain and have often are not clear. 2. The concept is unclear and it is expressed incorrectly. Our common students write △ABC three interior angle equal to 180° and write △ABC=180°; write ∠BDC and ∠CEB in Figure 1 as ∠D and ∠E, or write ∠1 and ∠2 (not shown in the figure) , ∠ 2); can not tell the height and vertical line of the triangle;