It is clearly stated in the Curriculum Standard for Primary Mathematics that consciously teaching students some basic mathematical thinking methods can deepen their understanding of mathematical concepts, formulas, theorems and laws, and is an important means to improve their mathematical ability and thinking quality. There are many mathematical thinking methods in primary school mathematics textbooks, such as symbolic thinking, classified thinking, transformation thinking, statistical thinking, classified thinking and so on. In the process of learning, students not only learn knowledge and practice repeatedly, but also use mathematical thinking methods throughout. If the knowledge and skills in mathematics teaching are obvious, then the mathematical thinking method contained in it is a dark line. Therefore, in primary school mathematics teaching, teachers should pay attention to the infiltration of mathematical thinking methods, improve the teaching of mathematical thinking methods purposefully, selectively and timely, so that students can master mathematical thinking methods and lay a good foundation for their sustainable development.
First, the characteristics of effective infiltration of mathematical thinking methods in primary school mathematics teaching
Mathematical thinking method is a further generalization and refinement of mathematical knowledge based on mathematical knowledge, so it is a tacit knowledge, which needs students to understand and master through repeated experience in the practice of constantly solving problems. The characteristics of effective infiltration of mathematical thinking methods in primary school mathematics teaching generally include:
1. Turn recessive into dominant
In mathematics teaching, mathematical ideas and methods are hidden in knowledge, which is often just a vague expression. Even if "XX thought" and "XX method" are directly pointed out to students in teaching, good results may not be achieved.
Such as fractional addition and subtraction (extreme thinking)
Question 1: Calculate the following questions and find out the law of numbers.
Question 2: Write the numbers of the following formulas directly by applying the above laws.
Analysis: there are limited thoughts in the topic. Keep writing, and the number will get closer and closer to "1". However, it is difficult for students to understand extreme ideas because this is their first contact. Even if the teacher points it out to the students, the students may not understand it. Mathematical thinking methods are often hidden in knowledge, and teachers should consciously reveal these hidden thinking methods in teaching so that students can feel them more clearly.
2. Activities
The teaching process itself is a dynamic process, and the infiltration of mathematical thinking methods should also be dynamic, which requires teachers to carefully design teaching activities, communicate teaching materials with students' understanding, and make mathematical thinking methods with distinctive personality characteristics better presented in dynamic classroom teaching activities.
(1) Operating activities
Educator Suhomlinski said: "Children's wisdom is at your fingertips." Because hands-on operation can promote students' thinking development. Therefore, primary school mathematics teaching can combine the active and curious characteristics of primary school students, mobilize students' multiple senses to participate in cognitive activities through moderate operation activities, cultivate students' learning ability and promote students' learning of mathematical thinking methods.
For example, in the teaching of the area of a circle, students are guided to divide the circle into 8, 16, 32 ... equal parts, and then students can make a figure that we know. Through such an active process, students can fully realize that the more scores the circle divides, the closer the figure is to the rectangle, so that students can further understand extreme thoughts.
(2) Observation activities
Perception is the beginning of people's understanding of the essence of things, the window of people's thinking activities, and the process of understanding and determining a stimulating meaning. Primary school students' thinking is still dominated by image thinking, and gradually transition from image thinking to abstract thinking. At this stage, observation is an important way for students to find problems, ask questions and learn new knowledge. Organizing students to observe in order in primary school mathematics teaching can make students better master mathematical thinking methods.
For example, taking the teaching of circle area as an example, when students divide the circle into 8, 16, 32 ... by hand, they are guided to observe and compare in an orderly way, so that students can think about which figure of patched parallelogram is getting closer and closer to what we have learned, and then observe what the patched figure has to do with the original circle, and then gradually guide students through observation.
3. Strengthen language exchange activities.
Einstein said: "The development of a person's intelligence and the way in which he forms concepts depend to a great extent on the development of language". Because of their young age, inexperience and narrow language area, primary school students lack mathematics language. Moreover, each student may observe from different angles and think differently. Therefore, we should pay more attention to guiding students to observe and speak, operate and speak, listen and speak, and better promote students' learning of mathematical thinking methods through such teaching.
Second, the infiltration strategy of thinking method in primary school mathematics teaching
1, fully tap the mathematical thinking method in the textbook.
Because mathematical thinking method is a kind of hidden and essential knowledge content, teachers must delve into the textbook before teaching and fully explore the thinking method contained in the textbook. Teachers should not only prepare lessons carefully, but also consciously infiltrate mathematical thinking methods into teaching, and pay attention to them everywhere in normal teaching, so that many mathematical thinking methods will be found in the teaching content.
2. Purposefully and consciously infiltrate relevant mathematical thinking methods.
As a primary school math teacher, when teaching math thinking methods, we should first make clear all the math thinking methods in the textbook, and then decompose and refine some important thinking methods to make them more hierarchical and clear. In this way, teachers can consider how to introduce, infiltrate and highlight mathematical thinking methods in specific teaching content, and whether students should understand, grasp, master or flexibly use these mathematical thinking methods.
3. Infiltrate mathematical thinking methods in a planned and step-by-step way.
Students' learning is a gradual process. Therefore, when designing teaching, we must respect students' cognitive laws and infiltrate mathematical thinking methods in a planned and step-by-step manner.
(1) repeated infiltration
First of all, students' understanding and mastery of mathematical thinking methods is a cognitive process from individual to general, from concrete to abstract, from perceptual to rational, and from low to high. Moreover, compared with superficial knowledge, mathematical thinking methods are more abstract and generalized, so students' cognitive process is repetitive. That is to say, in primary school mathematics teaching, we should not be eager for quick success and instant benefit, but follow the principle of repetition, step by step, and infiltrate repeatedly for a long time.
For example, in the first grade, the symbolic thought is infiltrated, so that students can learn to use the origin to represent the quantity of things, use "()" to represent the unknown, draw "○" for statistics, and so on. After such repeated infiltration, students can not only strengthen their understanding of mathematical thinking methods, but also urge them to organically link mathematical knowledge.
(2) Step by step
Like the learning process of mathematics, the learning of mathematical thinking method is a cognitive process, from sensibility to rationality, from understanding to formation, from consolidation to application development. Therefore, in teaching, teachers can design the teaching process according to the method of "teacher's guidance-gradual infiltration-timely summary and waiting for an epiphany", implement the principle of step by step, from the outside to the inside, step by step and gradual infiltration, and combine the teaching contents at different stages.
For example, the combination of numbers and shapes, a mathematical thinking method, will be encountered when learning "addition and subtraction within 10" in senior one, but in senior three, numbers and shapes will be combined in the form of line graphs, so that students can understand the meaning of the questions faster and better and solve problems. When they are in senior grade, they often find the area and volume of graphics and solve complex math problems. Only by gradual infiltration in teaching can the mathematical thinking method be clearer, which has a very important influence on students' future study.
Three. Concluding remarks
If mathematical knowledge is compared to gold, then the mathematical thinking method is "golden touch". Mathematical knowledge can be remembered for a while, and mathematical thinking methods will always play a role and benefit us for life. This is the real power of mathematics. Therefore, from the beginning of primary school, we should pay attention to the infiltration of mathematical thinking methods to lay a good foundation for students' sustainable development.