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在论证某些数学命题时,往往需要用数学符号、图形等将该命题的已知条件、求证的结论进行新的表述,我们不妨把这一过程称之为命题“具体化”。这种“具体化”过程既是数学论证的特殊要求,又有利于解题者根据“具体化”后的命题的某些直观性(特别是几何命题),寻找解题途径,用简洁的数学语言进行论证表述。在数学命题“具体化”的过程中,学生容易不自觉地加进某些新的条件,犯数学命题“特殊化”的逻辑错误。甚至现行中学教科书与教参书也有这类失误。下面举几个命题“具体化”与“特殊化”的例子,用以展示它们的区别。一、命题“具体化”的例子。高中《立体几何》(甲种本)第59页例2。
In the demonstration of certain mathematical propositions, it is often necessary to use mathematical symbols, figures, etc. to make a new formulation of the known conditions and the conclusions of the propositions. We may call this process a “concretion” of propositions. This “concretization” process is not only a special requirement of the mathematical argumentation, but also helps the solver to find the solution to the problem based on some intuitions (especially geometric propositions) of the “concretized” proposition, using a concise mathematical language. Argumentation statement. In the process of “concretization” of mathematical propositions, students are apt to unconsciously add certain new conditions and make logical mistakes in the “specialization” of mathematical propositions. Even the current high school textbooks and textbooks have such errors. Here are a few examples of “substantiation” and “specialization” propositions to show their differences. First, the example of the “concrete” proposition. High School “Three-Dimensional Geometry” (Type A) Page 59, Example 2.