By reading a large number of mathematical materials, it is not difficult to find that the arrangement of mathematical textbooks is a spiral arrangement system from easy to difficult. If you don't learn the previous knowledge, the latter knowledge will be difficult to understand. As time goes by, the snowball of "old knowledge" gets bigger and bigger, and finally it naturally gives up. Only by thoroughly understanding every knowledge point and introducing new knowledge with old knowledge can we learn better.
Second, step by step, there can be no leap ideas and practices.
Marx once said: "On the scientific mountain road, there is no smooth road to go. Only those who climb along steep mountain roads can reach the peak of glory. " This sentence tells us that the most important thing in learning mathematics is honesty. In the face of mathematical problems, knowing is knowing, not knowing is not, and you can't deceive yourself. Only by figuring out the origin of each number in a down-to-earth manner and making these mathematical knowledge logical and orderly can we really learn mathematics well. For example, there is a math problem arranged at intervals: how many minutes does it take to saw a piece of wood in half and how many minutes does it take to see it in six pieces? Many children get this question and intuitively think it is very simple, so they write 3×6= 18 (minutes), which is wrong and shows an error. But what is reflected behind the mistakes is that children have no patience, do not understand the problem scenarios, do not reason according to the problem scenarios, and do not analyze the problem scenarios in order.
The first step is to know the situation, that is, how to say the problem, we will do it. Describe the scene with pictures.
Everyone pays attention to the observation that this process, every number has its origin, which seems to be gradual, well-founded, and out of nothing. Let thinking visualization, let knowledge be structured. There are many such examples, for example, the knowledge about rectangles and squares is not thoroughly learned, and the knowledge about triangles, parallelograms and trapeziums cannot be learned.
Third, the key is to understand the "concept".
In mathematics, we must understand the definition of mathematics. In primary school mathematics, there are 54 basic concepts in number and algebra, and 32 concepts in figure and geometry. If a concept in it is not clear, it will have an impact on the later study. So in essence, mathematics plays with concepts rather than problem-solving skills.
For example, "the concept of reduction is to change a fraction into a fraction equal to it, but the numerator and denominator are smaller." If the child is not clear about the concepts of factor, common factor, greatest common factor, basic properties of fraction, prime number, etc. It will bring trouble to restore such a seemingly simple problem. Repeated mistakes will eventually cause a great blow to self-confidence and lose interest in math learning.
Fourth, after defining the concept, we should strengthen the practice until the concept is digested.
Look at the arrangement of textbooks. Every example is followed by "try or practice", which is the most basic exercise, and it is used to consolidate basic concepts, so it is necessary to strengthen practice. Otherwise, it is possible to eat "raw rice", which is not good for subsequent study.
If you don't practice repeatedly, you can't do this at all.
In short, if you want to learn mathematics well, you must be reasonable, and focus on the above four parts, and you will certainly gain something. Try it if you don't believe me. Mathematics is about concepts, not skills. Many questions are biased, which is putting the cart before the horse.