Changing thinking is an important strategy to solve mathematical problems, and it is a way of thinking from one form to another. When the problem is transformed, both the known conditions and the conclusion of the problem can be transformed. Solving mathematical problems with the idea of transformation is only the first step, the second step is to solve the problem of transformation, and the third step is to reverse the solution of the problem of transformation into the solution of the problem.

Equivalent transformation is one of the four major mathematical ideas. When studying and solving mathematical problems, the idea of equivalent transformation is adopted, and through equivalence, complex problems are transformed into simple problems, difficult problems are transformed into easy-to-solve problems, and unsolved problems are transformed into solved problems.

Transforming ideas-transforming ideas is the fundamental idea of solving mathematical problems, and the process of solving problems is actually the process of transformation. There are many transformations in mathematics, such as from unknown to known, from number to shape, from space to plane, from high dimension to low dimension, from pluralism to monism, from high order to low order, which all reflect the idea of transformation.

Through continuous transformation, unfamiliar, irregular and complex problems are transformed into familiar, standardized and even simple problems. Over the years, the idea of equivalent conversion has been everywhere in the college entrance examination. We should constantly cultivate and train our consciousness of transformation, which will help to strengthen our adaptability in solving mathematical problems and improve our thinking ability and skills. Transformation includes equivalent transformation and non-equivalent transformation. Equivalence transformation requires that causality in the transformation process is sufficient and necessary to ensure that the result after transformation is still the result of the original problem. The process of non-equivalent transformation is sufficient or necessary, so the conclusion needs to be revised (for example, the unreasonable equivalent rational equation needs root test), which can bring people a bright spot of thinking and find a breakthrough to solve the problem. In application, we must pay attention to the different requirements of equivalence and non-equivalence, and ensure its equivalence and logical correctness when realizing equivalence transformation. C.A. Yatekaya, a famous mathematician and professor at Moscow University, once said in a speech entitled "What is problem solving" to the participants of the Mathematical Olympiad: "Solving a problem means turning it into a solved problem". The problem-solving process of mathematics is the transformation process from unknown to known, from complex to simple. The equivalent transformation method is flexible and diverse. There is no unified model for solving mathematical problems by using the thinking method of equivalent transformation. Can be converted between number, shape and shape, number and shape; Equivalent conversion can be carried out at the macro level, such as the translation from ordinary language to mathematical language in the process of analyzing and solving practical problems; It can realize transformation within the symbol system, which is called identity deformation. The elimination method, method of substitution, the combination of numbers and shapes, and the problem of evaluation domain all embody the idea of equivalent transformation. We often carry out equivalent transformation among functions, equations and inequalities. It can be said that the equivalent transformation is to raise the algebraic deformation of identity deformation to keep the truth of the proposition unchanged. Because of its diversity and flexibility, we should reasonably design the ways and methods of transformation and avoid copying the questions mechanically. When implementing equivalent transformation in mathematical operations, we should follow the principles of familiarity, simplification, intuition and standardization, that is, we should turn the encountered problems into familiar ones to deal with; Or turn more complicated and tedious problems into simpler ones, such as from transcendence to algebra, from unreasonable to rational, from fractions to algebraic expressions and so on. Or more difficult and abstract problems are transformed into more intuitive problems to accurately grasp the problem-solving process, such as the combination of numbers and shapes; Or from non-standard to standard. According to these principles, mathematical operations can save time and effort in the process of transformation, just like pushing the boat with the current, often infiltrating the idea of equivalent transformation, which can improve the level and ability of solving problems.