The first hurdle: regard "Olympiad Mathematics" as a new subject divorced from mathematics.
In fact, the Olympiad Mathematics is an extension of general mathematics, and it is not an independent subject for in-depth study based on the mathematical knowledge learned in school.
Some students think it's useless to learn Olympic Mathematics, so they don't take school exams. Later, most problems can be solved by equations in junior high school. They think that learning Olympic Mathematics is just a waste of time. In fact, apart from the utilitarian function in everyone's eyes (junior high school, cup competition), Olympic Mathematics can also develop intelligence and exercise logical thinking ability, which is of great help to future study and life.
Because most of the mathematics learned in school is based on the application of formulas, learning the knowledge points in a textbook, exercises and exams are just substituting the numbers in the questions into the formulas and calculating the numbers. Basically, children don't need to think about how to solve problems by mathematical methods. The main purpose of Olympic Mathematics is to solve complex problems with simple mathematical methods, so that children can know how to find the path to solve problems in the appearance of problems. Especially for primary school students, it is very helpful for brain development.
Many college students are not good at high numbers, probability, etc. Still suffering from primary school mathematics learning is not deep enough! I have been used to doing simple math learning by substituting numbers and writing answers since primary school, which will be a great obstacle to the development of science in the future.
The second hurdle: knowledge learning is not systematic.
Some children, when asked about him, will say,' I studied Olympiad for two years.' "I learned the olympiad of 1 year." I started to learn in the third grade of primary school. In fact, after reading these students' diagnosis questions and asking some questions, I found that many children were very unsystematic when learning Olympic Mathematics. For example, a sixth-grade freshman said that he learned the travel problem and memorized the formula skillfully at night, but he could only solve the problem with a few formulas in the book, and he was at a loss when he came up with a problem that only gave the distance.
Another example is a fifth-grade student in a new primary school. I asked him about chickens and rabbits, and he answered fluently, so I asked him a question:
The exam is divided into two times: the first time, 24 questions, 5 points for answering one question correctly, and 1 point for answering one question wrong or not; The second time 15 questions, if you answer one question correctly, you will get 8 points, and if you answer one question incorrectly, you will get 2 points. Xiaoming answered 30 questions correctly in two tests. The first test is more than the second test 10 points. Ask how many points you got in each of the two tests. He can't see that this is actually a chicken and rabbit problem.
Most of the reasons for this situation are to talk about topics and recite formulas. So that students only wrote down the formula when they studied the Olympic Mathematics, but they didn't learn how to apply it. I can do the questions the teacher said, but I can't figure out which formula to use if I change the form a little. There are also some students who missed some chapters in their study. For example, if they don't learn the difference clearly, they will learn the following knowledge directly, such as travel, chickens and rabbits, so there is no way to learn the following knowledge well.
The third level: the writing process is not serious and the drawing time is not enough.
As I said before, Olympiad Mathematics is a knowledge of solving complex problems with simple methods, so the process of natural needs is very rigorous. Many children don't like the writing process when doing problems, or many large numbers are calculated by heart. I'm not saying that my mental arithmetic is not good, but I need to think about solving problems when I do problems, and doing mental arithmetic on large numbers is easy to cause confusion. Moreover, even if you can't think of a solution at the moment, you can often find a breakthrough to solve the problem as long as you carefully record the process. The most obvious thing is that children who come to diagnose can't do it. I often just need to say "write down the whole process carefully!" He knows what to do in the future.
The content of most Olympic math problems can be displayed intuitively with pictures, and the quality of pictures directly affects the thinking of solving problems. The most typical problems are travel, age, planting trees and differences.
The fourth level: quick success and instant benefit
Learning Olympic Mathematics can develop intelligence, exercise thinking and improve the ability to solve various problems. However, learning Olympic Mathematics is definitely not the more classes you take, the more time you spend, the better. Just like physical exercise, Olympiad is the exercise of thinking. The long and arduous learning task will only make the child's body unbearable, completely counterproductive, and will not play the role of exercise at all.
Mathematical olympiad is the extension and expansion of mathematics, so the necessary condition for learning mathematical olympiad well is solid mathematical knowledge. For example, if a child is vague about the concept of score, learning to split the score in the Olympic Mathematics will only lead to drawing water with a sieve, which will eventually make the child lose interest in mathematics.
Mental exercise is the same as physical exercise. A man who becomes a Hercules without exercising for a day is also a man who becomes a genius without studying Olympiad for a semester. The study of Olympic Mathematics should be gradual, based on school textbooks and aimed at cultivating interest. There are no children who are not suitable for learning Olympic Mathematics, only learning methods that are not suitable for children.
Most of the parents who talked said: I don't want my children to be too tired. He or she has studied enough courses.
The fifth level: I don't like thinking.
The study of Olympic Mathematics is the exercise of thinking. If children don't want to think about their own problems and seek solutions, simply waiting for the teacher to teach them is tantamount to doing physical exercise without thinking about activities. The movements are not in place and they can't play the role of exercise at all.
In summer school, a child was very reluctant to use his brain at first. I said, let's do this problem. He immediately said, I won't do it. Let the teacher announce the answer. Classroom teaching is also step by step, and learning is very passive. Seeing that the topic is a little more complicated, I gave up my choice to solve the problem and waited for the teacher to explain the method.
So in order to solve this problem, I will spend more time standing next to him and watching him write after each class. He said no, so I asked: Where do you know? Then gradually guide him from what he doesn't understand. When he thinks through every step, I will praise him for doing well. After two classes, his interest in learning improved obviously and he was willing to think for himself. When I gave my students a few questions, he was the first to solve them.
Many children are not good at math and are not stupid. In fact, no child is stupid, and cleverness is exercised. Children don't want to use their brains, and they don't get the correct guidance to improve their interest in learning. Finally, it shows that he can't do problems and doesn't like thinking.
The sixth level: the learning attitude is not serious.
When it comes to the word attitude, most children are disgusted. In fact, the attitude mentioned here only refers to how children treat math problems.
The solution of mathematical problems, especially the Olympiad problem, is a very rigorous and interlocking process. If anything goes wrong at any step, the rest will be written in vain. This hurdle is somewhat the same as the "not writing seriously" hurdle mentioned earlier. It is the attitude towards mathematics and whether it is serious about mathematical problems. Many students are very casual when calculating, thinking that the process is right and it is a trivial matter to calculate the wrong number. In fact, the accuracy of miscalculation is very important! Strict learning attitude is a necessary condition for learning mathematics well.