Set is an important concept in modern mathematics. Set thought is an important symbol of the infiltration of modern mathematical thought into primary school mathematics. When solving some mathematical problems, if we use the set idea, the problems can be solved more simply and clearly. The founder of set theory is German mathematician Cantor (1845-1918), and his main thinking methods can be summarized into three principles, namely, generalization principle, extension principle and one-to-one correspondence principle. Since the establishment of set theory, its concepts, ideas and methods have penetrated into all branches of modern mathematics and become the basis of modern mathematics. Euler (1707— 1787), a Swiss mathematician, first used a graph to express the relationship between two nonempty sets, which is now called Euler graph. Wayne, a British mathematician, first used another kind of graph, which can be used to represent any set (regardless of their relationship, they can be drawn in the same style), also known as "venn diagram". venn diagram used it to represent sets, which is helpful to explore the solutions to some mathematical problems.

Bruner once said that mastering the basic mathematical thinking method can make mathematics easier to understand and remember, and understanding the basic mathematical thinking method is the "bright road" to the migration avenue. Mathematical thinking method not only has universal guiding significance for students' learning, but also helps students to form scientific thinking modes and habits.

Set thinking includes concept, subset thinking, intersection thinking, union thinking, difference thinking, empty set thinking, one-to-one correspondence thinking and so on. As one of mathematical thinking methods, it has important guiding significance in teaching. Then, how to apply the set idea to teaching activities in primary school mathematics teaching?

First, the application of set concept in primary school mathematics teaching

There is no need to explain the concept of set thought to students in teaching. Teachers mainly guide students to understand the meaning of set diagram, and will solve problems or help them according to set diagram. The graph itself intuitively uses the representation method of set-graph, so it is very helpful to use this method for teaching in the lower grades of primary schools.

In the teaching of digital recognition, teachers should combine various set diagrams, which can be selected from books or drawn by themselves with some common things in life. At the same time, students can be given a number in turn and asked to draw a set diagram, which can not only let students use their brains and exert their imagination, but also let them know more about the relationship between the elements in the set and the cardinality concept.

In daily teaching, teachers should also let students understand some common terms used to describe sets, such as "some", "a bunch", "a group" and "a group". For example, there is such a picture for students to observe in the fourth unit classification of the first grade (Volume I) of the primary school mathematics textbook Beijing Normal University Edition. Require a pile of toys, stationery, clothing, shoes and hats, so that things with the same attributes are put together. This is the whole concept of collection.

Among the eleven numbers that know 0- 10, each number has a corresponding set diagram, which tells students how many elements there are in a set, so it is represented by "several". For example, "1" in the activity of looking for it on page 4 of Grade One of Beijing Normal University Edition (Volume I) can represent a house in the picture; "2" can represent two people in the picture. This vividly associates the elements in the set with the concept of cardinality.

Secondly, the application of subset, intersection, union, difference and empty set in primary school mathematics teaching.

The application of 1 and subset thought in primary school mathematics teaching

When the problem of the number of teachers is solved, the subset idea can be applied. For example, on page 36 of the Second Middle School Attached to Beijing Normal University (Volume II), some numbers are given to form a set of numbers, with elements of 387, 99, 809, 345, 1725, 4300, etc. At the same time, it is required to classify the given numbers first and then compare the sizes. This classification of numbers is equivalent to putting the elements in the whole set of numbers into three subsets as required. (as shown below) For this kind of problem, students can understand it intuitively and easily by using the fixed thinking.

2. The application of intersection thought in primary school mathematics teaching.

If there is such an application problem: there are 48 people in a class. The head teacher asked at the class meeting, "Who finished the math homework?" At this time, 42 people raised their hands. Ask again: "Who finished the Chinese homework?" At this time, 37 people raised their hands. Finally, I asked, "Who hasn't finished their Chinese and math homework?" No one raised their hands. How many people in this class have finished their Chinese and math homework?

When you look at this problem, you will find it relatively simple to use venn diagram to calculate. Draw a rectangle to represent the complete set, the set of students who have completed Chinese homework (A) and the set of students who have completed math homework (B), where A and B have an intersection.

Because the sum of the two parts in A indicates the number of people who have finished their Chinese homework (37), the parts outside A and inside B indicate the number of people who are 48-37= 1 1 (people), or the number of people who have finished their math homework but have not finished their Chinese homework. So the number of people who have finished both Chinese and math homework is 42- 1 1=3 1.

When teaching the content of common divisor and common multiple, we usually use the idea of intersection, such as:

The divisor of 12 is the divisor of 18.

3. The application of integration thought in primary school mathematics teaching.

In the textbook of the first grade of primary school, the meaning of addition is illustrated by combination. For example, page 22 of the first year of Beijing Normal University solves the problem of "how many pencils are there". In a picture, a young friend holds two pencils in his left hand and three pencils in his right hand. In another picture, a young friend puts his hands together, that is, the pencils of his left hand and his right hand are put together. 2+3 = 5 (only)

There is also an understanding of the numbers 1 1 ~ 20 in the first grade of Beijing Normal University Edition (Volume I). For "1 1", first stick 10 in the tenth place to form "1", and then count 65438. Similarly, when teaching numbers 12, 13, 14 and 15, we should also adopt the idea of union.

Another example is the first grade of Beijing Normal University Edition (Volume I), page 72: 9+5 =? The textbook shows that five sticks are divided into 1 and four sticks, 1 and nine sticks are combined to form ten sticks, and "1" is used in the tenth place, which is also the idea of union.

4. The application of difference set in primary school mathematics teaching.

In the textbook of the first grade of primary school, the difference set is used to illustrate the significance of subtraction. For example, on page 26 of "Picking Fruits" of Grade One in Beijing Normal University, two apples were picked by children, leaving three apples (elements) (sets) on the tree: 5-2 = 3 (pieces).

Another example is "Do it" on this page: there are always five circles in the picture, four of which are crossed out by lines, which means that only 5-4 = 1 (1) is removed. In teaching materials, what is generally crossed out by lines or circled by imaginary lines is the part to be cut.

5. The application of empty set in primary school mathematics teaching.

An empty collection means that this collection has no elements. The application of the idea of empty collection mainly appears in the teaching of "0", such as "Cat Fishing" on page 8 of the annual collection (Volume I) of Beijing Normal University Edition. Each kitten's bag represents the scenery, and the fish in the bag represents the elements. In the first picture, there are three fish in the bag, and there are three elements in the collection; In the second picture, there are two fish in the bag, and there are two elements in the collection; In the third picture, there is a fish in the bag, and there are 1 elements in the collection; In the fourth picture, there are no fish in the bag, and there are no elements in the collection, which is an empty collection.

Three, the application of one-to-one correspondence in primary school mathematics teaching

The idea of one-to-one correspondence is reflected in many textbooks. When comparing the number of elements contained in two sets, it must be solved by establishing a one-to-one correspondence. At the same time, the idea of one-to-one correspondence is also the basis of modern function thought. The idea of one-to-one correspondence is mainly presented in two forms in primary school mathematics textbooks: the first is the ratio, and the second is that one group gets the other group through the corresponding law.

In contrast teaching, teachers should first arrange the elements in the collection one by one. Such as Beijing Normal University Edition Grade One (Volume I) Page 43:

exceed

absent

In the second case of teaching, when one set gets another set through the corresponding rules, the teacher should clearly explain to the students that the corresponding rules work on every element in the given set.

For example, page 23 of the third day of the People's Education Edition (Volume II)

This pairing of formulas is also the application of the idea of one-to-one correspondence.

Paulia, a math educator, said: "The primary responsibility of math teachers is to develop students' problem-solving ability as much as possible. "Teachers can't talk about topics in the teaching of question inquiry. Teaching them "fish" is far more important than teaching them "fish". This "fishing" refers to the mathematical thinking method implied in the exploration of mathematical problems. Only when students gradually form thinking activities guided by mathematical thinking methods will they have a well-planned plan when they encounter other problems. The new curriculum standard also points out that: combining with the teaching of related knowledge, the mathematical thinking methods such as set and function should be properly infiltrated to deepen the understanding of basic knowledge. As math teachers, we should boldly apply set thought in teaching, so that students can gain perceptual knowledge of set thought in their study and gradually form the concept of using set thought.