As follows:

Algebraic thoughts

This is one of the basic mathematical thoughts. The unknown number X in primary school and a series of letters representing numbers in junior high school are all algebraic thoughts and the most basic roots of algebra!

The combination of numbers and shapes

is one of the most important and basic thinking methods in mathematics, and it is an effective idea to solve many mathematical problems. It is a famous saying of Professor Hua Luogeng, a famous mathematician in China, that "the number is less intuitive when it is missing, and it is difficult to be nuanced when it is countless", which highly summarizes the function of the combination of number and shape. There are many problems in junior high school and senior high school that involve the combination of numbers and shapes. For example, solving problems by marking data with geometric figures and using function images are all manifestations of numbers and shapes.

transformation thought

In the whole junior middle school mathematics, transformation (conversion) thought has been running through it. Transforming thought is to solve an unknown (to be solved) problem into a solved or easy-to-solve problem, such as simplifying the complex, making the difficult easy, turning the unknown into the known, turning the high order into the low order, etc. It is one of the most basic ideas for solving problems, and it is one of the basic thinking methods of mathematics.

Correspondence thinking method

Correspondence is a way of thinking about the relationship between two set factors, and primary school mathematics is generally an intuitive chart with one-to-one correspondence, which breeds the thought of function. For example, there is a one-to-one correspondence between points (number axes) on a straight line and specific numbers.

Hypothesis thinking method

Hypothesis is a kind of thinking method that first makes some assumptions about the known conditions or problems in the topic, then makes calculations according to the known conditions in the topic, makes appropriate adjustments according to the contradictions in the quantity, and finally finds the correct answer. Hypothetical thinking is a meaningful imaginative thinking, which can make the problem to be solved more vivid and concrete after mastering it, thus enriching the thinking of solving problems.

comparative thinking method

comparative thinking is one of the common thinking methods in mathematics, and it is also a means to promote the development of students' thinking. In the application problem of teaching scores, teachers are good at guiding students to compare the situation before and after the change of known and unknown quantities in the problem, which can help students find the way to solve the problem quickly.

Symbolic thinking method

Symbolic language (including letters, numbers, graphics and various specific symbols) is used to describe mathematical content, which is symbolic thinking. For example, in mathematics, all kinds of quantitative relations, quantitative changes and the deduction and calculation between quantities all use small letters to represent numbers and express a large amount of information in the condensed form of symbols. Such as laws, formulas, etc.

extreme thinking method

things change from quantitative change to qualitative change, and the essence of extreme method is to achieve qualitative change through the infinite process of quantitative change. When talking about "the area and perimeter of a circle", the idea of limit division of "turning a circle into a square" and "turning a curve into a straight one" imagines their limit state on the basis of observing the limited division, which not only enables students to master the formula, but also germinates the limit idea of infinite approximation from the contradiction transformation between curve and straight.