2. The idea of connection and transformation: Things are interrelated, restricted and transformed. All parts of mathematics are also interrelated and can be transformed into each other. When solving problems, if we can properly handle the mutual transformation between them, we can often turn the difficult into the easy and simplify the complicated. Such as: substitution transformation, known and unknown transformation, special and general transformation, concrete and abstract transformation, partial and whole transformation, dynamic and static transformation and so on.
3. The idea of classified discussion: In mathematics, we often need to investigate under different circumstances according to the different nature of the research object. This classified thinking method is an important mathematical thinking method and an important problem-solving strategy.
4. undetermined coefficient method: When the mathematical formula we are studying has a certain form, we can determine it only by finding the value of the letter to be found in the formula. Therefore, substituting the known conditions into the formula with undetermined form will often produce an equation or equation group with undetermined letters, and then solving this equation or equation group can solve the problem.
5. Matching method: try to construct an algebraic expression into a plane, and then make the necessary changes. Matching method is an important deformation skill in junior high school algebra, which plays an important role in decomposing factors, solving equations and discussing quadratic functions.
6. Substitution method: in the process of solving problems, take one or several letters of the formula as a whole and use a new letter to represent it, thus further solving problems. Method of substitution can simplify a complicated formula and turn the problem into a more basic problem than the original one, so as to achieve the purpose of simplifying the complex and turning the difficult into the easy.
7. Analysis method: When researching or proving a proposition, the conclusion is traced back to the known conditions. From this conclusion, the sufficient conditions for its establishment are derived. If the establishment of this condition is not obvious, then take it as a conclusion and further study the sufficient conditions for its establishment until the known conditions are reached, so that the proposition can be proved. This kind of thinking process is often called "grasping the fruit and finding the cause"