I believe many of our teachers and classmates have seen the movie forbidden kingdom, which tells the story of a man who loves Kung Fu but has no foundation, and finally achieved great success by practicing peerless Kung Fu. Among them, when the silent monk played by Jet Li was teaching Jason Kung Fu, there was a wonderful dialogue: "The painter took splashing ink on mountains and rivers as kung fu, the butcher took the skill of understanding cows as kung fu, turned invisible into tangible, turned a deaf ear, learned all kinds of tricks, learned from the changes of thousands of families, created his own home, the musician took melodious as kung fu, and the poet took bold words as kung fu. This is also kung fu.
Applying the above dialogue, we can also say that students can create their own families by solving problems, learning the methods of various problems, from having tricks to not having tricks, and learning the changes of various problems. It reveals that learning is a process of self-knowledge, self-reflection, self-reflection and self-summary. So, how to realize "enlightenment" in the learning process?
First, mathematics learning is a process of learning to think independently. In mathematics learning, we should prevent the tendency of rote memorization and not seeking for a very good solution. In learning, we should ask more why, calm down and ponder, so as to draw inferences from others and achieve mastery. When listening to the class, you should think while listening, think about the knowledge system related to this class, think about the teacher's ideas and compare with yourself. Before the teacher makes a judgment or conclusion, try to judge and draw a conclusion by yourself, see if it is consistent with what the teacher said, and find out the reason for the mistake. Independent thinking ability is the basic ability to learn mathematics.
Secondly, the process of mathematics learning is a process that needs repeated practice, and it is also a process in which practice makes perfect. Repeated practice is to achieve the effect of enlightenment and cultivate the understanding and feeling of mathematics. The process of training needs to go through a process from quantitative change to qualitative change, an invisible process. Of course, due to the differences of everyone's knowledge structure, thinking level and understanding ability, the process and quantity of training are different, but in any case, we can't "solve problems for the sake of solving problems".
Third, the learning process of mathematics is the process of grasping the spirit of mathematics. The spirit of mathematics lies in thinking about problems with mathematical ideas, methods and strategies. No matter how many students practice mathematics, it is always difficult for them to find their own feelings about mathematics. This requires us to form a general conclusion from solving problems in the learning process and understand the application of mathematical ideas, methods and strategies in solving problems. This process will make it difficult for students to reach the sublimation of their thoughts only by teachers. Of course, this is not to weaken the role of teachers, but to reflect the importance of students' understanding. Only by embedding the understood knowledge into the existing knowledge structure can we truly understand and master it.
Fourth, self-confidence is a necessary condition for learning mathematics well. Self-confidence comes from enthusiasm for mathematics, self-recognition, persistent refusal to give up the spirit of mathematics, and solid basic skills in mathematics. Once a student explained his understanding of basic skills and said, "From today on, every question I do will definitely not be tested in the college entrance examination, but I can do every question well in the college entrance examination, which does not guarantee that I can do it right. I should pay attention to the right, not just know it. The best way to solve the problem is to repeat. Don't stop doing it just because it's simple, don't stop doing it just because it's been done three times, give up for difficult problems, and never give up for simple questions. These are basic skills. "
In a word, learning mathematics well is not only to cope with the college entrance examination, or to lay a good foundation for further study of related majors in the future, but more importantly, to accept the influence of mathematical thoughts and spirits and improve their thinking quality and scientific literacy. If so, they will benefit for life. Finally, I wish every student academic progress.