Number sense mainly refers to the perception of logarithm and quantity, the relationship between numbers, 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.
Symbol consciousness mainly refers to the ability to understand and use symbols to express numbers, quantitative relations 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.
The concept of space mainly refers to abstracting geometric figures according to the characteristics of objects, and imagining 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.
Geometrical intuition mainly refers to describing and analyzing problems with graphics. With the help of geometric intuition, complex mathematical problems can be made concise and vivid, which is helpful to explore the solution ideas and predict the results. Geometric intuition can help students understand mathematics intuitively, and it plays an important role in the whole process of mathematics learning.
The concept of data analysis includes: to understand that there are many problems in real life, we must first do investigation and research, collect data, make judgments through analysis, and realize that the data contains information; Understand that there are many analysis methods for the same data, and choose the appropriate method according to the background of the problem; Experiencing randomness through data analysis, on the one hand, the data collected for the same thing may be different every time, on the other hand, as long as there is enough data, it is possible to find patterns from it.
Computing ability mainly refers to the ability to perform operations correctly according to laws and algorithms. Cultivating students' computing ability is helpful for students to understand computing theory and seek reasonable and concise computing methods to solve problems.
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 people often use in their study and life. Reasoning generally includes perceptual reasoning and deductive reasoning. Perceptual reasoning is to infer some results from existing facts through induction and analogy with experience and intuition. Deductive reasoning is based on existing facts (including definitions, axioms, theorems, etc. ) and some rules (including definitions, laws, operation sequences, etc.). ), and it is proved and calculated according to the law of logical reasoning. In the process of solving problems, use perceptual reasoning to explore ideas and find conclusions; Deductive reasoning is used to prove the conclusion.
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: abstracting mathematical problems from real life or specific situations, and establishing equations, inequalities and functions with mathematical symbols. Express the quantitative relationship and changing law in mathematical problems, find the results and discuss the significance of the results. The study of these contents is helpful for students to initially form model ideas and improve their interest in learning mathematics and their awareness of application.
In order to meet the needs of the development of the times for personnel training, mathematics education in compulsory education stage should pay special attention to cultivating students' awareness of application and innovation.
Applied consciousness has two meanings: on the one hand, it consciously uses mathematical concepts, principles and methods to explain phenomena in the real world and solve problems in the real world; On the other hand, it is recognized that there are a lot of problems related to quantity and graphics in real life, which can be abstracted into mathematical problems and solved by mathematical methods. The cultivation of students' application consciousness should run through the whole process of mathematics education, and comprehensive practical activities are a good carrier for cultivating application consciousness.
The cultivation of innovative consciousness is the basic task of modern mathematics education, which should be reflected in the process of mathematics teaching and learning. Students' finding and asking questions themselves is the basis of innovation; Independent thinking and learning to think are the core of innovation; It is an important method of innovation to get conjectures and laws through induction and verification. The cultivation of innovative consciousness should start from the compulsory education stage and run through the whole process of mathematics education.