Logical thinking is an advanced form of thinking, which is different from thinking in images. It reveals the essence of things with scientific abstract concepts and categories, and expresses the results of understanding reality. On the basis of perceptual knowledge, people reflect the objective reality with the help of concepts, judgments, reasoning and other forms of thinking, which is called logical thinking. Only through logical thinking can people grasp the essential provisions of specific objects and then understand the objective world. It is the advanced stage of human cognition, that is, the stage of rational cognition.
The development of children's thinking has certain rules, from concrete to abstract. Therefore, children cannot be asked to think like adults. However, proper education and training can promote the development of children's thinking from concrete to abstract, and also cultivate good thinking qualities, such as profundity, flexibility and creativity, thus improving children's thinking ability. For example, when Americans go to the supermarket to buy things, they don't even understand simple addition and subtraction operations. They have to hold a calculator for half a day to find a few cents. In international Olympic competitions, the winners are always China or Asians. However, we all see the reality that Americans who also received mathematics education in this country have trained a large number of scientists and inventors and led the development of science and technology in the world. Many people attribute this to American higher education and come to the conclusion that American elementary mathematics education is not good.
Creative thinking
This is our misunderstanding of American mathematics education. In China, the proportion and content of elementary mathematics teaching are biased towards calculation and operation. We recite multiplication and have been training mental arithmetic since childhood. We are used to measuring a person's mathematics learning by calculating ability. On the other hand, Americans think that mathematics is not equal to arithmetic. They pay more attention to how children know and apply mathematics in their lives. They encourage students to discover mathematics in life, and they cultivate children's logical reasoning ability from their mathematics learning. Therefore, although Americans' elementary computing ability is not as good as China's, their training in discovery, induction, deduction and reasoning in primary education has sown seeds and laid a foundation for the research and study of higher education, thus realizing creative thinking and logical thinking.
So, how do Americans cultivate children's logical thinking through elementary mathematics education? Hongtu Education Research Institute summarized the following characteristics through investigation:
Discover the world
First, cultivate children from an early age and guide them to be good at discovering.
Teach children the correct way of thinking: the characteristics of thinking are generality, indirectness and logicality. With the growth of age, children have more perceptual knowledge and life experience, and their language development has reached a higher level, which provides a conditional tool for thinking development. But only by mastering the correct way of thinking can we make better use of these conditions and tools. Children can't master it from the beginning. We should guide and teach them how to solve problems through analysis, synthesis, comparison, summary and logical judgment and reasoning. Teach children to master the correct way of thinking. Once a child has mastered the correct way of thinking, it is like plugging in the wings of thinking development, and the ability of abstract thinking can be developed and improved rapidly. This training mode requires children to observe and discover the arrangement law of figures, which is the initial form of logic training, mainly to cultivate children's observation ability and discovery ability.
Game entertainment
Second, games and entertainment to cultivate children's interest
Many parents who have just arrived in America are anxious because their children are "doing nothing" at school. As long as parents pay attention to cultivating their children's thinking ability in this respect and are good at guiding their children to think, there will be a bumper harvest. Play with toys, play games, guess riddles, raise small animals, raise flowers, and take part in housework. It can make children actively use their brains to carry out a series of logical thinking activities such as analysis, comparison, judgment and reasoning, thus promoting the development of thinking ability. For example, building blocks, spelling hexagrams and puzzles. , all need to use their brains, find out the law, to complete. Some intellectual games need not only brains but also speed to win. These exercises with certain regularity all embody the concept of pattern. But the process of children's practice is like playing games, and it is not easy to have pressure.
Close to the content of life
Third, content comes from life.
In teaching activities and practice, most of them are closely related to specific activities in life. For example, home tests. During the holidays, parents and children take turns as hosts and set up small prizes or other rewards. In order to enhance the atmosphere, friends and relatives or other small partners can be invited to participate. Guide children to discuss together, design ideas to solve problems, and participate in the process of solving problems. Parents should guide their children and discuss, design and implement solutions with them. This process needs analysis, induction and reasoning, and it needs to conceive methods and procedures to solve problems, which is of great help to improve children's thinking ability and problem-solving ability.
Mathematical calculation
Fourth, weaken calculation and strengthen understanding.
When teaching the concept of multiplication, we should first help students understand the meaning of multiplication. We can start with intuition, and through repeated observation and demonstration of objects or figures, we can relate the calculation problems of adding the same number, such as how many pandas are there in one set diagram and three sets diagrams? First, let the students calculate by addition, and then by multiplication. Finally, guide students to compare the results of the two algorithms. Then ask the students to calculate how many pandas there are in four sets and five sets. After several calculations, students can finally come to the conclusion that this kind of calculation can be calculated by addition or multiplication. But if there are many identical numbers, it is not as easy to calculate by continuous addition as by multiplication. So you need to use multiplication to calculate how many identical numbers are combined together. Multiplication is the operation of finding the sum of several identical addends. On this basis, students can be instructed to practice rewriting the formula of adding the same number into the formula of multiplication, or rewriting the formula of adding the same number into the formula of adding the same number, thus helping students to understand the meaning of multiplication more thoroughly. In teaching, the determination of multiplicand and multiplier must emphasize such concepts: how many are the same addend, how many are the multiplicand and how many are the multipliers.
think
Fifth, downplay the calculation process and attach importance to the guidance of reasoning and multi-level thinking.
When teachers introduce the relevant operating rules and skills to students, they need to guide students to understand and master the operating skills in principle. The purpose of doing this is to make students skillfully use calculation skills and methods on the basis of understanding and strengthen their operational ability. For example, in the process of calculating 20×3, most students replace 0 with 2×3-6 at first, and then add a 0 after it. When students come up with such an algorithm, the teacher should let them understand why they can calculate like this. The teacher can put a stick in front of the students to help them understand the reasoning. Bundle 10 bundles. Why count 2×3 first? It means that the 10 branch is regarded as a whole, representing a ten. Three bundles, two are six bundles. Since one bundle is 10 and three 20 s are 60, a 0 should be added after it. Only when students have a thorough understanding of this kind of arithmetic can they master the operation skills reasonably.
In the whole teaching activity, we should always make various assumptions, enlarge a topic, and constantly guide children to think and discover. Children can always open their hearts to discuss and put forward their own different questions and ideas from time to time.