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1.“特殊化”与“一般化”的策略和方法 “特殊”和“一般”这对普遍存在于自然界中的对立而又统一的矛盾,在数学中同样有着十分广泛的应用基础。具体反映在解答数学问题的解题策略中,就是将一般问题化归特殊情形进行研究的策略和将特殊问题一般化的策略,前者即第四讲中已讨论的“枚举归纳的策略,”在此不再赘述。至于化归一般的策略,在数学中也有着广泛的应用,究其实质是演绎推理原理在解题中的具体应用,是小学生学习数学、解答数学问题时经常使用的必备的思维模式。例如当学生解答“求长5厘米,宽3厘米的长方形面积”这一问题时,首先反映在学生脑海中的是“长方形面积=长×宽”这个一般性的结论,进而把这一结论运用到问题的具体环境中去求出该长方形的面积。即先把问题一般化,然后根据(或求出)一般性的结论解决所需解决的具体问题。我们称这类解题的思维模式为化归一般的解题策略。运用这一解题策略,可以加深学生对数学基础知识的理解,提高学生对学习数学概念、法则、定义、定律的重要性的认识,从而加强学习数学基础知识的自觉性。除此之外,还可提高学生运用所学知识解决实际问题的能力,提高学生的演绎推理能力。因此在数学基础知识的教学中应注意加强演绎推理原理的渗透,而在解题教学中更应加强学
1. “Specialization” and “Generalization” Strategies and Methods “Special” and “General” The contradictory and unified contradictions that prevail in nature are equally widely used in mathematics. Specifically reflected in the solution to the mathematical problem solving strategy is to general problems into special cases to study the strategy and the special problems of a general strategy, the former is already discussed in the fourth lecture “enum induction strategy,” “ Not repeat them here. As for the return to normal strategy, it also has a wide range of applications in mathematics. The essence of deductive reasoning is the concrete application of deductive reasoning in solving problems. It is an essential thinking mode frequently used by pupils when learning mathematics and solving mathematical problems. For example, when students answered the question of ”finding a rectangular area 5 cm long and 3 cm wide,“ the first thing reflected in the mind of the student was the general conclusion that ”rectangular area = length × width" To the specific circumstances of the problem to find the rectangular area. That is, to generalize the problem first, and then solve (or find out) the general conclusion of the specific problem to be solved. We call this type of problem-solving mode of thinking a normalized problem-solving strategy. Using this problem-solving strategy, students can deepen their understanding of the basic knowledge of mathematics and enhance students' understanding of the importance of learning mathematical concepts, laws, definitions and laws so as to enhance their awareness of the basic knowledge of mathematics. In addition, students can improve their ability to use practical knowledge to solve practical problems and enhance students' ability of deductive reasoning. Therefore, in the teaching of basic mathematics knowledge, we should pay attention to strengthening the infiltration of the principle of deductive reasoning, but should strengthen the learning in problem-solving teaching