| Problem solving is an important reason for the student learning math badly or even giving upmathematics. Many mathematicians and math educators emphasize that the thinking method oftransformation and conclusion plays an important role on mathematical problems solving. At present, theresearch on the thinking method of transformation and conclusion mainly includes the research on themethod of problem solving and the research on the method of teaching transforming ideas.Applying the thinking method of transformation and conclusion to solve problems follows theprinciple as listed below: the transformation from non-standard type to standard type, the transformationfrom abstract to concrete, the transformation from complex to simple, the transformation from unfamiliar tofamiliar, the transformation from clutter to harmony, the transformation from the high level to low level.But, it is not an easy thing to comprehend the thinking method of transformation and apply these ideas tothe problem solving, because the method of transforming ideas includes many mathematical methods, andthis method has the characteristic of diversity, repetitiveness and hierarchy. So it is necessary to do somein-depth and detailed digging researches on the transforming ideas which are contained in the currentteaching materials, analyze factors that affect high school students to comprehend the method ontransforming ideas, and put forward some effective teaching strategies according to the characteristics ofthe teaching materials and students’ own factors.Digging in the present textbook material, can not only provide some richer material on the method ofthe transforming ideas, but also can help students break through difficulties on their studies, and helpteachers break through teaching difficulties. From the analysis of the materials about the methods of thetransforming ideas from the current obligatory textbook version of the People’s Education Press, thetransforming ideas is embodied by the using of language, the knowledge formatting process (including thegeneration of the concepts, the found of theorems, the derivation of the formulas), and the way of thesample problem solution.In general, the major factors which affect the formation of transforming ideas include students’ ownfactors and external conditions factors, the former include the degree of mastery of basic knowledge, thinking activity, and cognition of the transforming ideas. In order to promote the cultivation of thetransforming ideas, first of all, it is necessary to help students understand the basic knowledge and basicskills well, which needs teachers to research diligently on the teaching material, weave a knowledgenetwork diagram composed of basic knowledge, and understand thoroughly about the mutualtransformation relationship between the scattered points. Second, insist on the principle of heuristicteaching, and stimulate students’ interest in learning; Third, emphasize on the process of problem solvingvariations, and cultivate the extensity of students’ thinking. Fourth, encourage students to associate, analyze,and cultivate the activity of students’ thinking; Fifth, insist on infiltrating during teaching: giving tips by theteaching language, learning through the knowledge getting process, extracting in the process of problemsolving, analyzing the conclusive method.It is necessary to fully affirm that the transforming methods play an important role during themathematics learning and research, however, at the same time, it is also necessary to notice the negativefactors and limitations of these ideas. Paying too much attention to the original problem solving experience,to a certain extent, can restrict the students’ innovation consciousness in math. So, it is essential to cultivatethe thought of the transforming learning, at the same time, it is also essential to strengthen the cultivation ofthe thought of other methods, and try to solve problems by using different thought of methods reasonableand flexible. |
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