First, pay attention to the factors that can penetrate mathematical thinking methods in teaching materials.
Infiltrating mathematical thinking methods in primary school mathematics teaching refers to letting primary school students gradually understand the thinking methods of analyzing and solving mathematical problems in the process of learning mathematical knowledge through subtle influence. Therefore, in the process of preparing lessons, teachers should fully explore the factors that can infiltrate mathematical thinking methods into primary school students, and infiltrate them purposefully, planned and step by step. For example, from the first volume of primary school mathematics textbooks, the function thought has penetrated into many examples and exercises by filling in numbers and other forms; In fact, the area formula and volume formula of geometric figures in middle and high grade textbooks all express the functional relationship between variables by analytical methods; In the study of statistical charts, charts are used to visualize and concretize the core (correspondence) of functional ideas. For another example, the idea of set permeates the teaching of digital recognition, digital calculation, greatest common divisor and least common multiple. When we knew "1" in the first book, a venn diagram with only one element (a deer) first appeared, which intuitively expressed the meaning of the cardinal number "1". When understanding "0", the textbook shows that "0" means "nothing" through three sets of teaching with two teacups, one teacup and no teacups, thus infiltrating the idea of empty sets. When teaching "addition" and "subtraction" within 10, there is venn diagram with students playing games and chickens in the textbook. If the teacher explains with venn diagram, students can clearly see that the sum of two groups of objects should be calculated by addition; Remove a part from the total and calculate the rest by subtraction. This kind of teaching is not only intuitive, but also subtly permeated with the idea of combining and differentiating. When teaching the greatest common divisor and the least common multiple, the textbook also uses venn diagram to reveal the mathematical laws intuitively, and at the same time, it just permeates the idea of intersection. In short, there are many factors that can permeate mathematical thinking methods in primary school textbooks, and teachers should pay attention to mining them.
2. Pay attention to infiltrating mathematical thinking methods with intuitive methods.
Psychological research shows that the development of primary school students' thinking is characterized by the gradual transition from concrete image thinking to abstract logical thinking, but this abstract logical thinking still needs the support of perceptual experience to a great extent and still has a large concrete image component. Therefore, in the primary school stage, mathematical thinking methods should be permeated with various forms, vivid and interesting charts or pictures to make them intuitive and vivid, so as to adapt to the characteristics of primary school students' psychological development. As we all know, the set thinking method is the most basic mathematical thinking method, and the primary school mathematics syllabus also explicitly requires the combination of relevant knowledge to infiltrate the set thinking method. The method of collective thinking is a way of thinking to grasp and understand things as a whole. The concept of set did not appear clearly in primary schools, but permeated intuitively in various ways. For example, before recognizing numbers, some common objects (such as a pile of vegetables, a batch of cars, a flock of sheep, etc. ) often appears in the form of charts. By adding a circle to similar things, students are intuitively left with some concepts of class and whole. When we know the number 0 ~ 10, each number is equipped with a set legend, which further deepens students' overall concept of a group of things with certain properties and breeds the concept of empty sets. Through the practice of drawing, filling in numbers and formulas, students can further understand that the elements in a circle (set) have certain characteristics although they are different in size and shape. The elements in a circle (set) can be concrete things or abstract formulas or numbers, thus enriching students' perceptual knowledge of the set. Therefore, teachers should correctly grasp the teaching materials and infiltration methods in order to achieve the purpose of infiltration.
Third, seize the opportunity to infiltrate mathematical thinking methods in a timely manner.
With regard to the infiltration of mathematical thinking methods, teachers should pay attention to grasping the opportunity and timely infiltration, so as to develop students' mathematical thinking without increasing their learning burden. As far as primary school mathematics teaching is concerned, teachers can always seize a good opportunity to infiltrate mathematical thinking methods in the process of showing their thinking, such as the formation of concepts, the raising of questions, the search for methods and the derivation of conclusions. For example, in concept teaching, the introduction of concepts can penetrate the thinking method of observation and comparison; The revelation of concepts can penetrate the abstract and generalized thinking method; In the understanding and consolidation of concepts, we can infiltrate the commonly used mathematical methods such as induction, analogy, analysis, synthesis, abstraction and generalization. In the teaching of practical problems, by revealing the relationship between known conditions and problems, we can penetrate basic mathematical thinking methods such as correspondence, hypothesis, transformation and algebra. Modern mathematical thinking methods, such as set, correspondence and function, can penetrate into the mathematics of preliminary knowledge of geometry. For example, by solving the following application problems, we can penetrate the transformed thinking method.
For example, when a batch of goods is transported by car, the first transport is 65,438+00%, 2% more than the first transport, and the second transport is 65,438+0,065,438+0 tons. How many tons are there in this shipment?
Analysis: 2% of the problem is based on the tonnage of the first shipment, so the tonnage of the first shipment is "1", so the tonnage of the second shipment is the first shipment (1+2%), and the tonnage of the first shipment is 10% of the total, so the second transportation can be carried out.
101÷ [10%+10% (1+2%)] = 500 (ton)
In the process of thinking about solving this application problem, we actually completed the transformation from one relationship (the relationship between the second shipment and the first shipment) to another relationship (the relationship between the second shipment and the total number), thus making the solution of the application problem smooth.
Fourth, select exercises to let students actively discover mathematical thinking methods.
As we all know, for learners, the best learning effect is that learners take the initiative to participate and discover for themselves. The research of mathematical thinking method is no exception. In mathematics teaching, solving problems is one of the most basic forms of activities. The problem-solving process of mathematical exercises is a process of experiencing and acquiring mathematical thinking methods, and it is also a process of deepening understanding through application. Students' exercises will not only consolidate and deepen the mathematical knowledge and mathematical thinking methods they have learned, but also summarize and refine "new" mathematical thinking methods from them. Therefore, teachers should consider the design and selection of exercises from the perspective of mathematical thinking methods, and try to arrange some exercises that can make students of all levels of learning answer in simple terms, so that students can actively think, discover the key steps of solving problems themselves, form problem-solving methods, and then deepen them into mathematical thinking methods. For example, in the teaching process of mixed operation of fractions and decimals, students can be guided to master the most commonly used reduction thinking method in primary school mathematics teaching by doing exercises similar to the following.
1 1
For example, calculate 2.8 ÷ 1 × ÷ 0.7.
3 7
Analysis: the original question has both fractions and decimals, so it is more troublesome to calculate directly. Considering that the multiplication and division of fractions are more convenient than decimals, we can turn the decimals in the original problem into fractions, and turn the problem of mixing decimals and fractions into a single fractional operation, so there is.
1 1 28 1 1 7
2.8÷ 1─×─÷0.7=─÷ 1─×─÷─
3 7 10 3 7 10
For some students with strong learning ability, teachers can find and master mathematical thinking methods through some score calculation problems.
1 1 1 1 1
Example: Calculate (1+-) × (-+-)-
2 3 2 3 4
1 1 1 1 1
( 1+─+─+─)×(─+─)
2 3 4 2 3
Analysis: It is cumbersome and inconvenient to calculate the score directly. Through students' observation, it is found that there are the same parts between the reduction and the minuend. If some numbers are regarded as a whole and represented by letters, the calculation can be simplified.
1 1 1 1
Solution: Let A = 1+─ and B = ─+─
2 3 2 3
1 1
Then the original formula = a × (b+──)-(a+──) × b.
4 4
1 1
=A×B+─A-A×B-─B
4 4
1
=──(A-B)
four
1 1 1 1 1
=─[( 1+─+─)-(─+─)]
4 2 3 2 3
1
=─
four
Therefore, students can be guided to discover and master algebraic thinking methods.