初谈以进为退的数学解题策略

Discussion on the Strategy of Solving Mathematical Problems with Taking Advance as Retreat

以进为退作为一种解题策略,与以退为进逆向。其策略机制是联想,由局部联想到整体。在《高等数学》解题中以进为退策略归纳为8种递进方式:个别到普遍、静态变动态、局部变整体、离散到连续、特殊到一般、具体到抽象、单一到无限、常量到变量。策略体现了形而上向形而下相互转变的辩证哲学思想。解题从整体出发,高屋建瓴,视野更宽阔,思维起点高,指导性更强。以进为退,小题大做,似难实简,能使问题迎刃而解。

Taking advance as retreat is a kind of problem solving strategy, it’ s the opposite of taking retreat as advance. Its strategic mechanism is association, which means from the local to the whole. In solving problems in Advanced Mathematics, the strategy of advance as retreat can be summarized into eight progressive ways: individual to universal, static to dynamic, local to whole, discrete to continuous, special to general, concrete to abstract and single to infinite, constants to variables. The strategy shows the dialectical philosophy transition from the metaphysical to physical. The strategy starts from the whole, builds high-rise buildings, so the vision of strategy is wider, the starting point of the strategy is high, and the guidance is stronger. Taking advance as retreat, storm in a teacup,making real simple can solve the problems.