What is abstract thinking? How to cultivate students' abstract thinking ability in primary school mathematics? In the method of solving mathematics problems in primary schools, the thinking process of reflecting reality with concepts, judgments and reasoning is called abstract thinking, also known as logical thinking. Abstract thinking is divided into formal thinking and dialectical thinking.

Primary school mathematics should cultivate students' preliminary abstract thinking ability, focusing on:

(1) The thinking quality should be agile, flexible, connected and creative.

(2) In the way of thinking, we should learn to think methodically and systematically.

(3) in terms of thinking requirements, the thinking is clear, the cause and effect are clear, the words must be reasonable, and the reasoning is strict.

(4) In thinking training, we should require correct application of concepts, proper judgment and logical reasoning.

1, control mode

How to correctly understand and apply mathematical concepts? The common method of primary school mathematics is comparison. According to the meaning of mathematical problems, the method of solving problems through understanding, memorizing, identifying, reproducing and transferring mathematical knowledge is called contrast method.

The thinking significance of this method lies in training students to correctly understand, firmly remember and accurately identify mathematical knowledge.

Example 1: The sum of three consecutive natural numbers is 18, so what are the three natural numbers from small to large?

By comparing the concept of natural numbers with the properties of continuous natural numbers, we can know that the average sum of three continuous natural numbers is the middle number of these three continuous natural numbers.

Example 2: True or False: The number divisible by 2 must be even.

Let's compare the two mathematical concepts of "division" and "even number". Only by fully understanding these two concepts can we make a correct judgment.

2. Formula method

Methods to solve problems by using laws, formulas, rules and rules. It embodies the deductive thinking from general to special. Formula method is simple and effective, and it is also a method that primary school students must learn and master when learning mathematics. But students must have a correct and profound understanding of formulas, laws, rules and regulations, and can use them accurately.

Example 3: Calculate 59×37+ 12×59+59.

59×37+ 12×59+59

= 59× (37+ 12+ 1) ............................................................................................................................................

= 59× 50 .........................................................................................................................................................................

= (60- 1) × 50 ........................................................................................................................................................

= 60× 50- 1× 50 .........................................................................................................................................................

= 3000-50 ......................................................................................................................................................................

= 2,950 ..........................................................................................................................................................................

3. Comparative method

By comparing the similarities and differences between mathematical conditions and problems, we study the reasons for the similarities and differences, so as to find a solution to the problem, which is the comparative method.

Comparative law should pay attention to:

(1) Finding similarities means finding differences, and finding differences means finding similarities, and being indispensable means being complete.

(2) Find the connection and difference, which is the essence of comparison.

(3) Comparison must be conducted under the same relationship (same standard), which is the basic condition of "comparison".

(4) To compare the main contents, try to use the "exhaustion method" as little as possible, which will make the key points less prominent.

(5) Because of the rigor of mathematics, comparison must be meticulous, and often a word or a symbol determines the right or wrong conclusion of comparison.

Example 4: Fill in the blanks: the highest digit of 0.75 is (), and the highest digit of the decimal part of this number is (); Compared with the tenth digit 4, the tenth digit 4 has the same (), but the tenth digit 4 is different, the former is smaller than the latter ().

The purpose of this question is to distinguish between "the difference between the highest digit of a number and the highest digit of a decimal part" and "the difference between digits and values".

Example 5: The sixth grade students planted a batch of trees. If everyone plants 5 trees, there are 75 trees left. If each person plants 7 trees, there will be a shortage of 15 seedlings. How many students are there in the sixth grade?

This is a comparison between the two schemes. The similarities are: the number of sixth grade students remains unchanged; The difference is that the conditions in the two schemes are different.

Find a connection: the number of trees planted by each person has changed, and the total number of trees planted has also changed.

Solution (method): each person is 7-5=2 (tree), then the whole class is 75+ 15=90 (tree), and the class size is 90÷2=45 (person).