Transformation And Reduction Method In Mathematical Problem Solving In High School

The problem is the heart of mathematics, so it is important for mathematics to solve the problem.Although the mathematical questions are endless, they share some common principles and ideas.Transformation thought is one of the important ideas of solving mathematic problems, which is reflected onmany modules in high-school math, such as number shape union thought, function thought, equivalentlytransformed thought and classified discussion thought and so on. The number shape union thoughtemphasizes the mutual transformation between number and graph, and the function thought reflects themutual transformation between dynamic and static, and the classified discussion thought embodies themutual transformation between overall and local. So the transformation thought is the essence ofhigh-school math thought.Firstly, based on previous studies and the important knowledge modules of high-school math, thispaper summarized meaning and essence, and principles and strategies of the transformation thought, whichprinciples included the familiar principle, simplification principle, harmonious principle, intuitionalprinciple, extreme principles and standardization principle, which strategies contained thecomplex-to-simple strategy, strange-to-familiar strategy, number shape union strategy, abstract-to-concretestrategy, general-to-particular strategy, root transformation strategy, dynamic static transformation strategyand push-back strategy. Secondly, this paper discussed the application of transformation thought on themodules in high-school math. Finally, according to the author’s teaching experience, this paper explainedhow to develop and improve the students’ ability of transformation thought from four aspects.