2. The idea of classification. On the basis of comparison, according to the similarities and differences between things, objects with the same nature are classified into one category, and objects with different properties are classified into different categories-this is classification, also called division. The classification idea of mathematics embodies the classification of mathematical objects and its classification standards.
3. Function thought. The concept of function profoundly reflects the relationship between the movement and change of the objective world and the quantity and quantity of actual things. It tells people that things are constantly changing, interrelated and restricted, so as to understand the changing trend and motion law of things. As for the function, the standard puts forward the requirements of students in various learning periods. Combined with experimental teaching materials, the requirements for primary and secondary school students are "to explore the quantitative relationship and changing law in specific problems" and "to understand the meaning of constants and variables through simple examples".
4. Turn to thinking. "Transformation" means transformation and belonging. When solving mathematical problems, people often reduce the problem that needs to be solved to another problem that is relatively easy to solve or has a solution, so as to get the answer to the problem. The thought of conversion is reflected everywhere in primary school mathematics, and it is the most basic and commonly used way of thinking in solving problems.
5. Induce ideas. When studying general problems, we should first study several simple, individual and special situations, and draw general laws and properties from them. This way of thinking from special to general is called inductive thinking. Induction can be divided into incomplete induction and complete induction. Most of students' primary school contacts are incomplete induction. In the fourth grade, the first volume of the algorithm teaching (taking additive commutative law and the law of additive combination as an example), we started the teaching with incomplete induction.
6. Optimize ideas. It is not only a natural law, but also a good way of thinking to "choose the good ones and use their strengths". Diversification of algorithms is an important embodiment of diversification of problem-solving strategies. Calculating the perimeter of a rectangle is a multi-solution problem, seeking common ground while reserving differences. We should choose the best method among the right methods, make clear the right and good ones, and choose the good one. Infiltrate optimization strategies and methods in teaching, guide students to evaluate and reflect on various methods in time, help students understand the characteristics and advantages of different methods through analysis and comparison, achieve the purpose of "eliminating the false and retaining the true, eliminating the rough and retaining the essence", cultivate students' awareness of optimization of "choosing the good and using their strengths", construct mathematical knowledge, and realize the optimization and systematization of knowledge.
7. Combination of numbers and shapes. Mathematics is a science that studies the spatial form and quantitative relationship of the real world. The idea of the combination of numbers and shapes is the idea of combining the quantitative relationship and spatial form of the problem.