1, number sense. Understand the relationship between number and quantity, quantity and the estimation of operation results. Establishing a sense of number helps students understand the meaning of number in real life and understand or express the quantitative relationship in specific situations. ? Space concept, abstract geometric figures according to the characteristics of objects, and imagine the actual objects described according to the geometric figures; Imagine the orientation of objects and the positional relationship between them; Describe the movement and change of graphics; Draw pictures according to the language description, etc.

2. Symbolic consciousness. Able to understand and use symbols to represent numbers, quantitative relationships and changing laws; Knowing that symbols can be used for operation and reasoning, the conclusion is general. Establishing symbol consciousness is helpful for students to understand that the use of symbols is an important form of mathematical expression and mathematical thinking. ?

3. Geometric intuition uses graphics to describe and analyze problems. With the help of geometric intuition, complex mathematical problems can be made simple and vivid, which is helpful to explore problem-solving methods and predict results. Geometric intuition can help students understand mathematics intuitively, and it plays an important role in the whole process of mathematics learning. ?

4. The concept of data analysis. Understand that there are many analysis methods for the same data, and choose the appropriate method according to the background of the problem; Experience randomness through data analysis. Data analysis is the core of statistics. Operational ability, the ability to correctly carry out operations according to laws and operating rules. Cultivating students' computing ability is helpful for students to understand computing theory and seek reasonable and concise computing methods to solve problems. ?

5. Reasoning ability. The development of reasoning ability should run through the whole process of mathematics learning. Reasoning is a basic way of thinking in mathematics, and it is also a way of thinking that is often used in study and life. Model thinking. Establishing model thinking is the basic way for students to experience and understand the relationship between mathematics and the outside world. The process of establishing and solving the model includes: abstract problems, establishing equations, inequalities, functions, etc. Use mathematical symbols to express the quantitative relationship and changing law in mathematical problems, find the results and discuss the significance.