Transformational thinking is a mathematical thought that transforms an unknown solution or problem into a solved or easily solved problem method within the known knowledge through observation, analysis, association, analogy and other thinking processes.

The idea of transformation 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.

The mathematical method from special to general is a part of transforming ideas, that is, the process of summing up half the laws from special situations, which is called the mathematical method from special to general.

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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, and the conclusion should be revised to 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.

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