Many parents report that their children did well in math in grade one or grade two, but their grades began to decline in grade three. What is the reason? It turns out that parents and teachers ignore the cultivation of children's mathematical thinking and limit themselves to learning new knowledge and doing exercises mechanically. It turns out that when learning new knowledge, old knowledge is constantly forgotten. This inefficient learning mode actually leads to children's understanding and application ability of mathematics getting weaker and weaker with the growth of grade.
Some parents may ask, is there a good way to learn math? Teacher Leng Yue will tell you that there are ways to systematically cultivate children's mathematical thinking, but you haven't done any collection and sorting. Today, I will make a list first, starting with the cultivation of primary school students' mathematical thinking.
However, before formal study, parents and friends must solve a cognitive misunderstanding, that is, the quality of children's mathematics learning is related to the teaching ability of mathematics teachers! If you always think like this, then you ignore the important role of family education classroom, because parents who are interested in cultivating their children's mathematical thinking ability often do not stick to the study of textbook knowledge, but also apply textbook knowledge to their lives. Even jump out of the textbook itself and cultivate children's mathematical thinking ability independently.
First, mathematics learning starts from the primary school stage, and it is the last word to lay a solid foundation of mathematical thinking.
Mathematics is a highly applied subject, and the learning of mathematical knowledge is a process from easy to difficult. If parents look at the mathematics textbooks of different grades in primary schools, you will find that in primary schools, basic training is basically to cultivate children's mathematical thinking. In this case, parents must pay full attention to cultivating children's mathematical thinking. But the problem is coming again. What exactly is mathematical thinking? Leng Yue, a cold stone teacher, gave a definition: Mathematical thinking refers to the whole process of combining mathematical logic modules and mathematical formulas with spatial order at a certain time to build a mathematical model. Modules are tangible, but the thinking process is intangible. Invisible thinking can be embodied through tangible modules, thus realizing visualization. Ask parents and friends to understand this definition again and again. Only when you understand it can you continue reading the following.
Second, mathematical thinking training starts with the construction of digital three-dimensional space, so that children's brains are very sensitive to numbers.
What is the biggest problem in elementary mathematics teaching? Leng Yue, a cold stone teacher, can tell you that what math teachers and parents lack most is to cultivate children's sense of digital three-dimensional space. Maybe parents didn't understand the meaning of this sentence. To put it simply, children's visual thinking and auditory thinking in learning mathematics are seriously inadequate. For example, when you show an apple to a child, the average child will only see the apple in his eyes and want to eat at most. But for a particularly clever child, he may judge what kind of apple it is by color and switch, and even his brain will quickly reflect whether the apple is sour or sweet, crisp or soft from the known life experience. Obviously, the two types of children have completely different cognition and judgment on a simple apple, while the latter's brain thinking develops better. In the aspect of mathematical thinking training, the training of digital three-dimensional space has laid a good foundation for children to be very sensitive to numbers in the future. I will write a special article in the future, please continue to pay attention to it.
Third, mathematical thinking training begins with oral and written calculation training, so that children are particularly skilled in digital calculation.
When it comes to mathematics, parents may be familiar with it, but do you know why children have to be trained a lot from primary school? Smart parents will immediately say that it is to lay a good foundation for mathematical calculation for their children. The parents' answer is correct, and indeed it is. However, some parents can't fully understand the purpose of doing this and think that their children will naturally be older. However, when you miss the best training period of grade one or two, children will quietly form lazy behavior in mathematical oral and written calculations. That's why parents often see their children making mistakes in calculations, and even don't want to write calculations. They just want to save trouble by verbal calculation. It is understandable to say that the oral arithmetic training is really perfect, but most children can't do it. To this end, parents must pay special attention to the basic training of oral and written calculations for their children, and devote special time and energy to the interactive mode of parent-child games, so that children can enter the training state with fun.
Fourth, mathematical thinking training begins with reading questions, so that children can develop a good habit of paying close attention to reading questions.
In primary school, children who get good or fail in math often have * * * learning behavior, that is, they have not been systematically trained to examine questions. The most important first step to solve the problem was to miss the training. In this way, children will develop the impetuous psychology of solving problems, either skimming the surface or misreading words or numbers, and then they will not fully understand the meaning of the problem, and even misunderstand, especially misreading the numbers to ensure that there will be wrong results in the calculation. Reading training, as one of the basic skills of mathematical thinking training, often requires parents to use their children's time outside of study, especially in combination with extracurricular reading time. If they don't arrange it, they will make their children suffer big losses in this respect until they finally develop a bad habit of being lazy to think. As we all know, bad habits are extremely stubborn and it is very difficult to correct them. Therefore, parents are advised to seek truth from facts when cultivating their children's mathematical thinking.
Fifth, mathematical thinking training starts with the concept of constructing mathematical modules, so that children can easily master mathematical logic reasoning and operation.
Have parents and friends ever heard of "math module"? Maybe most of them don't know. If parents and teachers ignore the idea of teaching children to build math modules from primary school and don't do quite special training, it can be said that this is the biggest mistake in math teaching. The reason for this is that mathematical logic reasoning and operation only begin with the construction of mathematical modules. What is a math module? Let me show you a picture below, and you will see it clearly.
Have parents found that the meaning of modular math problems has become more stereoscopic and intuitive? As long as you master this method, teach children and ensure that they will understand the questions, the brain will subconsciously arrange all the module numbers, write logical formulas easily and correctly, and perform logical operations quickly. Now please parents think about it. You usually help your children with their math. Do you teach children a sense of mathematical logic thinking? If not, you might as well make up this lesson now.
Sixth, mathematical thinking training starts with problem-solving process and step training, so that children no longer find mathematics difficult to learn.
Mathematics problem-solving pays great attention to complete steps and strictly abides by the problem-solving process, but many teachers and parents just don't cultivate their children's study habits in this respect. In this way, children gradually developed the bad habit of answering questions at will. Even those children who can get more than 90 points in the exam are not because they can't answer the questions, but because they haven't got strict problem-solving process and step-by-step training, which leads to carelessness in the answering process. For children under 90, there are more problems, not only careless problems, but also that mathematical thinking has not been systematically cultivated and intuitively reflected. At this point, parents may feel anxious about the problem-solving process and step-by-step training methods. Don't worry, this is not the focus of this article. In the future, Teacher Leng Yue will write an article to explain it in detail. What you have to do now is to establish the concept of mathematical thinking.
Seven, mathematical thinking training starts from the basic knowledge link, so that children can build a complete mathematical knowledge chain in their brains.
There are a lot of knowledge points in both primary school mathematics and middle school mathematics. With the growth of grade, if children don't develop the good habit of connecting knowledge points in series, they can't establish a complete mathematical basic knowledge chain, and naturally it's easy to forget the old. Especially after the fifth and sixth grade of primary school, until entering junior high school, if children have not developed this good habit, it is very easy to understand new knowledge in mathematics learning. To this end, helping children master the basic knowledge chain has become a compulsory course for parents. When children master the method, they will improve the knowledge chain in stages, remember it in their brains, and gradually learn to learn new and old good habits. Speaking of knowledge chain, we have to mention "knowledge tree" here. I wonder if my parents and friends have contacted each other. In fact, this is a way to build a knowledge chain. If necessary, you can look up relevant information online after reading this article, so that you can further understand the concept of knowledge chain.
Eight, mathematical thinking training starts with the speed and quality of operation and inspection to improve the accuracy and efficiency of children's problem solving.
In order to reduce children's correct rate of solving mathematical problems and improve the efficiency of solving problems, parents must strengthen the training of operation and checking speed and pay attention to quality in the process of cultivating children's mathematical thinking. There is no practical significance to have a fast time chart, but the ultimate pursuit is fast and accurate. In this link, the most prone to problems is that many children are unwilling to check the completed calculation process because of the bad habit of being lazy in their hands and brains, which can easily lead to wrong judgments and calculation results. To this end, parents need to devote special extra-curricular time, such as training their children in this area on weekends or holidays. Don't underestimate these basic skills training, which is a compulsory course for the cultivation of mathematical thinking and absolutely indispensable. Otherwise, children will not want to learn math well as long as they develop lazy thoughts.
Nine, mathematical thinking training starts with overcoming the fear of difficulties in mathematics learning, thus ensuring children's concentration when solving problems.
I don't know if parents and friends have found that children sometimes have a fear of difficulties in math learning. Whenever children are afraid of difficulties, they will sincerely resist writing math homework, and even if they do, they will make many mistakes. Why do children have such negative learning emotions? The most critical reason is that parents and teachers criticize inappropriately, assign too much homework, and pursue achievements excessively. If children want to learn math well easily, they must lower their expectations for grades. No matter how many times your child takes the exam, you should give affirmation and encouragement. Only when your child feels the recognition of teachers or parents can he be motivated, willing to study mathematics harder and cooperate with you in mathematical thinking training. The most important thing is that parents should be clear about their children's mathematics learning ability, mastery of basic knowledge points, mastery of mathematical logic modules, and mastery of problem-solving processes and steps. When they find out which part of their children have not learned well, they must strengthen counseling and training to help them overcome difficulties, thus enhancing their self-confidence.
Conclusion: How to learn mathematics well requires parents to pay attention to the cultivation and training of children's mathematical thinking. Although there is a lot of work to be done by school teachers, when school teachers can't do it, parents must do it independently. There may be parents who are also afraid of difficulties, but please remember one sentence: what children can learn, you can certainly learn! As long as you are willing to be a concerned parent and spend more time studying and improving your counseling ability, why not? When we say that fathers love their mothers, it is precisely because they can make sacrifices, including a comfortable rest, and always take responsibility. This paper only summarizes the cultivation of mathematical thinking.
Difficulties: How to determine the point M? Because the side lengths of the left right-angled triangle are 3,