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数学归納法是数学中一种重要証題工具。但是,高中学生往往难以理解它的实貭,对它的証題步驟,也往往是死記硬套,因此数学归納法是中学数学课中較大难点之一。下面对这一段教学及学生常出現的問題提出几点意見。 (一)怎样提出数学归納法人們进行邏輯推理时有归納和演繹二种方法。演繹法是由一般命題推出特殊命題的方法。例如:任何平行四边形其对角綫互相平分。菱形是平行四边形, 所以菱形的对角綫互相平分。与此相反,归納法是由特殊命題概括出一般命題的方法。
Mathematical induction is an important test tool in mathematics. However, it is often difficult for high school students to understand its practicality, and the procedure for the testimony of it is also often recorded in a rote manner. Therefore, mathematics induction is one of the major difficulties in middle school mathematics classes. Here are some suggestions for this section of teaching and students often appear problems. (I) How to Present Mathematical Induction There are two methods for induction and deduction when people make logical reasoning. The deductive method is a method of introducing special propositions from general propositions. For example: any parallelogram has its diagonals bisect each other. The rhombuses are parallelograms, so the diagonals of the rhombuses bisect each other. In contrast, induction is a method of generalizing propositions by special propositions.