Numbers and shapes are two main objects of mathematical research. Numbers are inseparable from shapes, and shapes are inseparable from numbers. On the one hand, abstract mathematical concepts and complex quantitative relations are visualized, visualized and simplified through graphics.

Step 2 change your mind

Changing ideas is a way of thinking from one form to another, and its own size is unchanged. Such as geometric equal product transformation, homotopy transformation for solving equations, formula deformation, etc. A-B = A × 1/ B is also commonly used in calculation.

3. Algebraic thought

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

4. Corresponding thinking methods

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

5. Hypothetical thinking method

Hypothesis is a way of thinking that first makes some assumptions about the known conditions or problems in the topic, then calculates according to the known conditions in the topic, makes appropriate adjustments according to the contradiction in 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.

6、? 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 of teaching scores, teachers are good at guiding students to compare the situation before and after the change of known quantity and unknown quantity, which can help students find solutions quickly.

7. Symbolic thinking method

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

8. Extreme thinking methods

From quantitative change to qualitative change, the essence of limit 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 line" is to imagine their limit states on the basis of observing the limit division, which not only enables students to master the formula, but also germinates the limit idea of infinite approximation from the contradictory transformation of curves and straight lines.