1 how to cultivate students' mathematical thinking
Training students' mathematical thinking should be regular.
Laws in mathematical thinking include formal logic laws, dialectical logic laws and special laws of mathematics itself. They are interrelated. There are relations between form and content, concreteness and abstraction, particularity and generality. In order to make students learn effectively, it is necessary to reveal the internal relations and laws of knowledge. Such as integer, decimal, fraction and percentage; Five of the four kinds of calculation algorithms are the general formulas on which the number system is based. The four basic quantitative relations of sum, difference, multiplication and division are the basis of various application problems and so on. The more basic and general the law is revealed, the easier and more convenient it will be for students to understand and the better the teaching effect will be.
Therefore, when teaching new knowledge, teachers should make full use of the role of transfer, so that students can solve new problems with existing knowledge and thinking methods. For example, after teaching the multiplication formula of "5 times several", students can use this way of thinking to derive other multiplication formulas; After learning the derivation of "additive commutative law", you can also learn the multiplicative commutative law. After learning the derivation of "triangle area formula", you can learn the derivation of trapezoidal area formula in the same way and so on.
Cultivating students' mathematical thinking should be systematic.
Scattered and disorderly thinking can not correctly reflect the integrity of the objective world. "The so-called intellectual development is just a well-organized knowledge system." Considering the interaction between the logical system of mathematical knowledge itself and students' cognitive laws, mathematical knowledge should be integrated into a knowledge network that is constantly vertically differentiated, horizontally integrated and closely linked, so that the knowledge of numbers, shapes and shapes can be vertically and horizontally linked, mutually promoted and deepened. Practice has proved that the closer the knowledge, the wider the knowledge, the stronger the migration ability and the greater the possibility of creative thinking.
The multi-directional and multi-level overall structure is more conducive to the understanding, mastery, storage, retrieval and application of knowledge. However, due to the law of physical and mental development of primary schools, teachers can't impart knowledge to students at once, and teaching has certain levels and stages, which reflect different thinking levels and different thinking qualities. For example, there are four cycles of integer calculation and two cycles of fraction and decimal in primary school mathematics. And triangle knowledge. In teaching, teachers should make clear the requirements of students' thinking training at each level and stage from a holistic and systematic perspective, and carry out appropriate training.
2 Mathematical thinking training
We should be good at applying modern educational technology to cultivate students' mathematical thinking ability.
With the rapid development and popularization of information science and technology, people's ability and means to obtain, transmit, regenerate and use information have been greatly improved and enriched, which has changed people's way of life, study and work. Especially in teaching activities, it plays an increasingly important role. Information technology, which integrates text, sound, animation, graphics and images, can provide the best teaching situation, and plays an irreplaceable role in improving students' interest in learning mathematics, encouraging students to actively participate in rich and vivid learning activities, going through a process of practical innovation, and cultivating students' creative consciousness and innovation ability.
It will even greatly promote the value, goal, content and the way of learning and teaching of mathematics education. The application of modern information technology teaching means is an effective way to comprehensively implement quality education and improve the quality of education and teaching. Using modern information technology to assist teaching is a new and effective teaching means and method. The integration of information technology and mathematics teaching is the inevitable development of education facing modernization, the world and the future.
Training development
Carefully design open-ended questions to cultivate students' multi-directional and broad thinking. Open mathematical problems refer to those with incomplete conditions and uncertain conclusions. This kind of open question is extremely challenging, which requires students to think and explore, can open up a broad thinking space for students and has high creative education value. Design trap questions to cultivate and develop students' reflective ability. After the new curriculum reform, teachers pay attention to giving students time and space for independent thinking in classroom teaching.
When students make mistakes, teachers should not rush to correct them, but give students time to reflect, knowing that students' creative process is also a process of constant reflection. Therefore, the exercises designed by teachers should be conducive to the cultivation and improvement of students' reflective ability. Design outward bound exercises after class to extend students' thinking in life. The ultimate goal of people learning mathematics is to use mathematics to solve problems in life and production. The purpose of primary school students learning mathematics is to understand and master basic knowledge and skills, and to use the knowledge and skills they have learned to solve simple mathematical problems in life. It is impossible to achieve this goal by classroom teaching alone, and classroom learning must be extended to extracurricular activities. In the process of students' inquiry, guide students to capture life phenomena and collect life cases, so that students can have a pair of eyes that are good at discovering and guide students to think about mathematics in life.
3 Mathematical thinking training
Practice teaching cultivates mathematical thinking ability.
It is an important means to effectively improve the quality of classroom teaching to let students practice in primary school mathematics teaching. For example, after teaching the travel problem, I showed such a question: "It is known that the speed of passenger cars is 60 kilometers per hour and that of trucks is 50 kilometers per hour. Now two cars leave from A and B which are 200 kilometers apart at the same time. How many kilometers are the two cars apart after two hours? "
The heading does not specify the driving direction, so there is no standard for the distance between two cars for 2 hours. So, I organized two students to demonstrate in the classroom in four situations: 1. Two students walked towards each other at the same time; 2. Two students walk in opposite directions at the same time; 3. Two students walk in the same direction at the same time, and the fast student walks in front; Two students walk in the same direction at the same time, with the slow student in front. I will enlighten students on how to solve this problem. In this way, students quickly come to the conclusion that this problem should be discussed in the following four situations:
(1) Two cars are moving in opposite directions at the same time, and then they are separated after meeting: (60+50)? 2-200 = 20km
(2) Two cars driving in opposite directions at the same time: (60+50)? 2+200 = 420km
(3) The two cars are driving in the same direction, with the bus in front and the truck behind: 60? 2+200-50? 2 = 220km
(4) The two cars are driving in the same direction, with the truck in front and the bus in the back: 50? 2+200-60? 2 =180km
In teaching practice, teachers' hands-on operation or students' hands-on operation can arouse students' interest and keep their stable attention. For example, when deducing the volume formula of a cylinder, let students deduce and cut the cylinder into an approximate cuboid. After they master the volume formula of the cylinder, they can show such a topic: "After cutting the cylinder into an approximate cuboid, the surface area of this approximate cuboid increases by 40 square centimeters, and the height of this cuboid is known to be 1 decimeter. How many cubic centimeters is the volume of this cylinder? " Because the students have just deduced the volume formula of the cylinder themselves, they can quickly find out that the bottom radius of the cylinder is: 40? 2? 10=2 (cm), the volume of this cylinder is: 3. 14? 2? 2? 10= 125.6 (cubic centimeter).
Multimedia teaching to cultivate mathematical thinking ability
As an auxiliary means of conventional teaching, multimedia has been paid more and more attention by primary school mathematics teachers, which is inseparable from its positive role. One of the characteristics of slide show and projection is that the image is concrete, vivid and intuitive, which can provide students with vivid, vivid and clear visual images, stimulate students' interest and curiosity, and mobilize students' enthusiasm for learning.
For example, if the section "Understanding and using protractor" is explained according to book illustrations or model teaching AIDS, the visibility is too low, which will affect students' learning enthusiasm. If the transparent protractor is placed on the projector stage and explained by projection, it can meet the visual and intuitive needs of students and make them concentrate on their learning activities with interest.
4 Mathematical thinking training
Change students' learning style
Break students' cognitive thinking pattern, let students have cognitive conflicts and cultivate students' thinking independence. Thinking set not only affects the solution of problems, but also limits students' thinking space. Therefore, in the process of solving problems, teachers should encourage students to solve problems in various ways, guide students to think from different angles and different ideas, and try to evaluate the differences between different methods. Teachers should affirm the problem-solving methods summarized by students and guide them to use them when solving practical problems in life. Students' multi-directional thinking can be trained, not limited to books.
Guide students to reflect and let them experience the whole process of their own thinking. Reflection is one of the important contents of students' mathematics learning activities. In the process of mathematics learning, students should be consciously guided to reflect on their own thinking activities. The contents of reflection are: where is the key to solving the problem? What are the basic thinking methods and skills used? Whether we can find other faster ways to solve the problem, whether there are better and more interesting ways to solve the problem, and so on.
Push the boat with the current and expand your thinking.
In classroom teaching, because each student is a different individual, there are many learning situations that cannot be preset. However, these unexpected learning experiences can become valuable hidden resources in teaching. If you follow the students' thinking, teachers can set doubts appropriately, which can often promote students' thinking to a deeper level. For example, in the process of teaching "Understanding Parallelism", the teacher found that some students drew a straight line with the hypotenuse of the triangle, and then leaned against a vertex on the left side of the hypotenuse of the triangle with a ruler, and found that something was wrong, but did not know where the problem was (see figure 1). At this time, the teacher caught it in time: put this painting on the physical projection and let the students observe what is wrong with this painting. The student said to draw a straight line with one right-angle side of the triangle, and the ruler was close to the other right-angle side, but he didn't use the right-angle side.
At this time, the teacher guides the students to think, so if you draw parallel lines with this hypotenuse, how can the ruler draw parallel lines with the same method? What role does a ruler play in drawing parallel lines? Students' thinking is naturally deeper. Through discussion and practice, students are happy to find that parallel lines can be drawn as long as the ruler is inclined to the right angle. The key is to ensure that the ruler is close to one side of the triangle and the other side of the triangle can be translated, so that parallel lines can be drawn correctly (see Figure 2). So as to further understand the method and principle of drawing parallel lines. A detail that seems to deviate from the preset track has triggered a deeper exploration. In this kind of teaching, students are no longer afraid of making mistakes, and teachers are no longer afraid of students exceeding the preset. Because of these "derailment", mathematics learning is more attractive and the thinking space is higher and farther.
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