Common mathematical thinking methods in primary school mathematics are:
Transformation thinking, * * * * thinking, combination of number and shape thinking, functional thinking, symbolic thinking, corresponding thinking, classified thinking, inductive thinking, model thinking, statistical thinking, etc.
What are the basic mathematical thinking methods in primary school mathematics?
1, corresponding thinking method
Correspondence is a way of thinking about the relationship between two * * * factors, while primary school mathematics is generally an intuitive chart with one-to-one correspondence, which breeds the idea of function. For example, there is a one-to-one correspondence between points (number axes) on a straight line and specific numbers.
2. 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.
3. 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.
4. 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.
5. Analogical thinking method
Analogy means that based on the similarity between two types of mathematical objects, the known attributes of one type of mathematical object can be transferred to another type of mathematical object. Such as additive commutative law's sum-multiplication commutative law, rectangular area formula, parallelogram area formula, triangle area formula, etc. The idea of analogy not only makes mathematical knowledge easy to understand, but also makes the memory of formulas natural and concise.
Step 6 change your way of thinking
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.
7. Classified thinking method
The thinking method of classification is not unique to mathematics, but embodies the classification of mathematical objects and its classification standards. For example, the classification of natural numbers can be divided into odd and even numbers according to whether they can be divisible by 2; Divide prime numbers and composite numbers according to the number of divisors. Another example is a triangle that can be divided by edges or angles. Different classification standards will have different classification results and produce new concepts. The correct and reasonable classification of mathematical objects depends on the correct and reasonable classification standards, and the classification of mathematical knowledge is helpful for students to sort out and construct their knowledge.
8, * * * way of thinking
The idea of * * * is a way of thinking that uses the concepts of * * *, logical language, operation and graphics to solve mathematical problems or impure mathematical problems. Primary schools use intuitive means, graphics and objects to infiltrate the idea of * * *. When talking about common divisor and common multiple, we adopt the thinking method of intersection.
9. The thinking method of combining numbers and shapes
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. On the other hand, complex shapes can be expressed by simple quantitative relations. When solving application problems, we often use the intuitive help of line segment diagram to analyze the quantitative relationship.
10, statistical thinking method:
Statistical charts in primary school mathematics are some basic statistical methods, and finding the average application problem is the thinking method of data processing.
1 1, extreme thinking method:
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.
12, alternative thinking method:
He is an important principle of solving equations, and one condition can be replaced by other conditions when solving problems. If the school buys four tables and nine chairs, it will cost 504 yuan. The price of a table and three chairs is exactly the same. What is the unit price of each desk and chair?
13, reversible thinking method:
It is the basic idea in logical thinking. When the positive thinking is difficult to solve, we can seek the way to solve the problem from the condition or problem thinking, and sometimes we can use the line segment diagram to push back. For example, a car travels from A to B in the first hour. ......
What are the common mathematical thinking methods in primary school mathematics?
What are the thinking methods of primary school mathematics?
1, corresponding thinking method
Correspondence is a way of thinking about the connection between two elements. Primary school mathematics is generally a one-to-one intuitive chart, and the idea of latent function is conceived by it. Such as the one-to-one correspondence between points on a straight line (number axis) and numbers representing specific sizes, and the correspondence between specific quantities and abstract fractions (fractions) in fractional application problems. Corresponding thought is also a common method to solve general application problems. Example 1, how many points is greater than or less than? Example 2: Employee's annual salary 12 rubles plus a robe. When he worked for seven months, he got five rubles and a robe. How much is a robe worth?
In primary school mathematics teaching, dashed lines, solid lines, arrows, counters and other graphics are mainly used to connect elements, objects, numbers and formulas, and quantities, thus infiltrating corresponding ideas.
For example, in the first volume of the first grade textbook, rabbits and deer, monkeys and bears, rabbits and birds are in one-to-one correspondence, so as to penetrate the corresponding relationship between things into students and provide them with thinking methods to solve problems.
2, change the way of thinking:
This is an important strategy to solve mathematical problems. This is a way of thinking that changes from one form to another. And its own size is constant. Such as the equal product transformation of geometry, the same solution transformation of solving equations, the deformation of formulas, etc. Conversion is often used in calculation, such as A-B (divide by zero) = A ×, and division with decimal divisor can be converted into division with integer divisor to calculate. When solving application problems, conditions or problems are often transformed. Through transformation, we can simplify the complex, change the new into the old, simplify the complex, break the whole into parts, and turn the song into a straight one.
Example 3: Both teams can complete a project within 120 days. Now Team A has worked alone for 30 days, while Team B has continued to work for 20 days, and * * * has completed 20% of the projects. How many days will it take Team A to do it alone?
Example 4. The picture below is a square made up of three rectangles. It is known that the width of a large rectangle is equal to the sum of the widths of two small rectangles. A, b and c respectively represent the areas of the three shaded parts, with a being 6cm2 and c being 3cm2. Find b ..
3. Symbolic thinking method
Symbolic thinking method uses symbolic language (including letters, numbers, graphics and various specific symbols) to describe mathematical content, which is symbolic thinking. 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 law, ab=ba formula, s=vt, etc. They all represent the general laws of numbers and quantities with letters, and the operation itself is a symbolic language, so the symbolic thinking method is the carrier of mathematical information and also the carrier of quantitative analysis and systematic analysis.
The current primary school mathematics textbooks attach great importance to the infiltration of symbolic ideas.
Example 5: A car travels 50 kilometers per hour from A to B and 40 kilometers per hour when it returns. Find the average speed of the car.
From the first grade, the variable X is replaced by "□" or "()", so students can fill in the numbers. For example: 1+2 = □, 6 +( )=8, 7 = □+□+□; Another example: the school originally had seven balls and bought four more. How many balls are there in the school now? Please fill in □□□□□□□ =□ (pieces). In the content of primary school mathematics, symbolic thought can be seen everywhere, and teachers should consciously infiltrate it.
4. Classified thinking method
The thinking method of classification is not unique to mathematics, but embodies the classification and standard of mathematical objects. For example, the classification of natural numbers can be divided into odd and even numbers according to whether they are divisible by 2, and into prime numbers, composite numbers and 1 according to divisor. For example, a triangle can be divided into angles and sides. Different classification standards will have different classification results and produce new concepts. Correct and reasonable classification of mathematical objects depends on the correctness and rationality of classification standards. The classification of mathematical knowledge helps students to organize and construct knowledge.
Example 6: Classify 20 natural numbers 1, 2, 3 ...
5. 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.
6. Analogical thinking method
The idea of analogy means that it is possible to transfer the properties of one kind of known mathematical objects to another kind of numbers according to the similarity between the two kinds of mathematical objects. ......
What are the primary school mathematics thoughts and corresponding examples?
Mathematical thinking in primary school mainly includes food symbol thinking, transformation thinking, analogy thinking, equation thinking, * * * thinking, function thinking, one-to-one correspondence thinking, model thinking, combination of numbers and shapes thinking, deduction and popularization thinking, transformation thinking and so on. The case is listed as "year, month and day" in the third grade. By observing the characteristics of some calendars, it is found that there are 12 months in a year: 12 months in a year, 3 1 day in March, May, July and August, 10 months and 12 months. In April, June, September,165438+1October, there were 30 days of abortion; In some years, February has 29 days, which is neither a big moon nor a small moon. What permeates here is the idea of incomplete induction.
What are the common mathematical ideas in primary school mathematics?
Mathematical thinking method is the soul and essence of mathematics. Mastering the scientific mathematical thinking method is of great significance for improving students' thinking quality, for subsequent mathematics learning, for other studies and even for students' lifelong development. It is the key to strengthen students' mathematical concepts and form good thinking quality to consciously infiltrate some basic mathematical thinking methods in primary school mathematics teaching. Not only can students understand the true meaning and value of mathematics, learn to think and solve problems with mathematics, but also can organically unify the learning of knowledge with the cultivation of ability and the development of intelligence.
What are the ideas in primary school mathematics teaching?
For example, the process of understanding distance = speed × time is the process of infiltrating mathematical ideas when students study distance-related problems, and the process of establishing equations is also the process of infiltrating model ideas.