"Mathematics Curriculum Standards" clearly stated in the overall goal: "Students can acquire important mathematical knowledge, basic mathematical thinking methods and necessary application skills necessary to adapt to future social life and further development." This overall goal runs through primary school and junior high school, which fully illustrates the importance of mathematical thinking methods. Consciously infiltrating some basic mathematical thinking methods into students in primary school can deepen students' understanding of mathematical concepts, formulas, rules and laws, improve students' problem-solving ability and thinking ability, and is also the real connotation of primary school mathematics quality education. At the same time, it can also lay a good foundation for the study of mathematical thinking methods in junior high school. The mathematical thinking methods in primary school mainly include symbolic thinking, reduced thinking, analogical thinking, inductive thinking, classified thinking, equation thinking, set thinking, functional thinking, one-to-one correspondence thinking, model thinking, mathematical combination thinking, deductive reasoning thinking, transformation thinking, statistics and probability thinking and so on.
In order to enable the majority of primary school mathematics teachers to infiltrate these mathematical thinking methods in their teaching, the author systematically summarizes and sorts out these thinking methods, clarifies the concepts of these thinking methods, combs their applications in various knowledge points of primary school mathematics, and puts forward some suggestions on how to teach.
First, symbolic thought.
1, the concept of symbolic thinking.
Mathematical symbols are the language of mathematics, and the mathematical world is the symbol world. As a tool for people to express, calculate, reason and solve problems, mathematical symbols play a very important role: because mathematics has symbols, it makes mathematics concise, abstract, clear and accurate, and promotes the popularization and development of mathematics; The use of international mathematical symbols makes mathematics an international language. Symbol is a universal way of thinking and has universal significance.
2. How to understand symbolic thought?
Mathematics curriculum standards pay more attention to cultivating students' symbolic consciousness, which is interpreted as one of the contents of mathematics and algebra. So, how to understand this important idea in primary school? The following is a brief analysis of the case.
First, the relationship and changing law of abstract mathematical quantities, the process of exploration and induction from special to general in specific situations. For example, add several specific groups of two numbers, exchange the sum of the positions of addends, and get the additive commutative law, which is expressed by symbols: A+B = B+A. Another example is to spell a small square with unit area on a rectangle, explore and summarize the area formula of the rectangle, and mark it as: S=ab. This is a symbolic process, but also a modeling process.
Second, understand and use symbols to express quantitative relations and changing laws. This is a process from general to special, from theory to practice. Including the use of relational expressions, tables and images to represent the relationship between quantities in the situation. If the side length of a square is assumed to be a, then 4a represents the perimeter of the square and a2 represents the area of the square. This is also a symbolic process, and it is also a process of explaining and applying the model.
Third, there will be conversion between symbols. Once the relationship between quantities is determined, it can be expressed by mathematical symbols, but mathematical symbols are not unique and can be colorful. If the car travels at a constant speed of 80 kilometers per hour, the distance traveled by the car is proportional to the time. The quantitative relationship between them can be expressed in the form of table, formula s=80t or image. In other words, these symbols are interchangeable.
Fourthly, we can choose appropriate procedures and methods to solve the problems represented by symbols. This is the next step after symbolization, that is, mathematical operation and reasoning. Being able to perform correct operations and reasoning is a very important basic mathematical skill and a very important mathematical ability.
3. Specific application of symbolic thinking.
The development of mathematics has gone through thousands of years, and the standardization and unification of mathematical symbols has also gone through a long process. For example, the decimal counting symbol numbers 0~9 in our common arithmetic were produced in India in the 8th century, and it took hundreds of years to be used worldwide, and it has only been used for hundreds of years now. Early algebra was mainly based on the calculation of words. It was not until 16 and 17 centuries that mathematicians such as Veda, Descartes and Leibniz gradually introduced and perfected the symbol system of algebra.