The Outline of Mathematics Education clearly points out that mathematics teaching should "cultivate students' good personality quality". It can be seen that it is necessary and important to consciously infiltrate frustration education in mathematics teaching and pay attention to the cultivation of quality, which should become the consensus of mathematics teachers. How to effectively infiltrate frustration education in mathematics teaching?
Improving students' understanding of setbacks by using mathematical historical materials
A correct understanding of frustration is the premise of implementing frustration education. Many materials on the history of mathematics are good teaching materials for educating students, which need to be explored and studied by the majority of mathematics educators and creatively used in teaching.
1. The history of mathematical development is full of setbacks.
Mathematics is an ancient basic natural science, and the road of its birth and development is uneven. This historical process embodies the unremitting pursuit and exploration of countless mathematicians at home and abroad. From the generation of numbers to the discovery of irrational numbers, from the invention of analytic geometry to the advent of calculus, from the discovery of non-Euclidean geometry to the generation of computers, every difficulty has been successfully overcome from countless failures. It can be said that the history of mathematics development is the history of scientists' continuous struggle to overcome setbacks.
2. The struggle history of mathematicians is full of setbacks.
In the history of mathematics at home and abroad, many mathematicians dare to face up to setbacks, and their spirit of overcoming setbacks is touching. Let's look at the history of the great mathematician Euler! His profound knowledge, endless creative energy and unprecedented research results are amazing and amazing, thus becoming a world-famous mathematician. However, due to overwork, he was blind in his right eye at the age of 28, and then his left eye vision decreased until he was completely blind. Soon, his bedroom and his research results were burned by the Petersburg fire and hit one after another, but he didn't fall down and was completely blind in 17. With amazing memory and indomitable perseverance, he dictated dozens of monographs and about 400 papers. Another example is the death of hippasus. Hippasus, the great disciple of Pythagoras, first discovered the existence of incommensurable line segments, that is, the objective existence of irrational numbers, which is the truth. However, this discovery supported the foundation of the mathematical kingdom built by Pythagoras and his disciples, including hippasus. The tutor asked him to keep a secret and stipulated the discipline of death penalty. But for the truth, hippasus bravely "leaked" this great epoch-making discovery, and he was fired. However, the discovery of irrational numbers has opened up an infinitely broad bright road for the development of mathematics! The teacher's brief and vivid introduction in class will enable students to truly understand the meaning of the sentence "There is never a smooth road to science, and only those who dare to climb can hope to reach the glorious peak" by understanding the setbacks experienced by mathematicians in the process of scientific research.
Educating students to correctly understand setbacks is one aspect of cultivating students' initial dialectical materialism. Through the education of the history of mathematics, students should understand that setbacks on the way forward are inevitable at any time and under any conditions. Success is of course a good thing, but setbacks are not necessarily useless. Frustration has a dual nature, which may produce destructive power and depression, and may also produce regenerative power, so that people can learn from mistakes and failures. Become stronger and more mature. As the saying goes, "failure is the mother of success". Brown, a British psychologist, also said, "If a person has no obstacles, he will always be satisfied and mediocre." Setbacks can also produce self-tension, that is, tolerance and humility, but they become more calm and tolerant because of setbacks. Therefore, it is necessary to educate students to treat setbacks dialectically and regard setbacks as a good opportunity to exercise themselves.
Expose the thinking process and teach students how to overcome setbacks.
The development of mathematics and the path taken by mathematicians are full of setbacks. The discovery and proof of every proposition is often based on the intuitive thinking of mathematicians, making various conjectures and then confirming them. In this process, it is full of setbacks and ways to overcome them, but it is impossible to write all textbooks, and we can only write them in the mode of "definition, axiom, theorem and example" and give the results directly. But the tortuous process of mathematicians' exploration, induction, fantasy and discovery is hidden. If teachers only talk about the correct method and ignore the analysis of the wrong method, they always get the right guess, the right choice and the right proof in class, and students can only see a magician's performance when using it. Students will be helpless when they encounter setbacks. Therefore, in mathematics teaching, teachers should pay attention to the exposure of thinking process. In the stage of knowledge generation and cognitive arrangement, let students participate in the formation of concepts, the acquisition of mathematical principles and rules, and the choice of mathematical methods. Second, we should expose teachers' thinking process. For the answers to examples and exercises, teachers should always expose the real thinking process, try to reveal the thinking and selection process of methods, and pay special attention to the analysis of bifurcation. Sometimes teachers might as well learn from the great mathematician fuchs and put themselves in danger in class. How did the initial idea of solving problems hit a wall? Let's take a look at how the teacher adjusts the problem-solving plan after encountering setbacks, and gradually find the correct countermeasures to overcome setbacks, so as to teach students how to face up to setbacks and overcome them.
Creating problem situations and cultivating students' ability to resist setbacks
It is not easy to acquire knowledge and improve quality. It takes long-term efforts and unremitting pursuit to complete. Although success can bring people a sense of satisfaction and happiness, consistent success is unfavorable to students, which easily makes students feel proud, thus reducing their interest in mathematics learning. Especially some students who are competitive and complacent, sometimes immersed in self-appreciation, and occasionally successful, will mistakenly think that they have a super group. Once frustrated, they often become self-doubt and lack self-confidence. Therefore, it is necessary for students to experience certain setbacks in order to exercise their will, their correct attitude towards failure and their ability to deal with failure, that is, their ability to resist setbacks.
The great mathematician Paulia pointed out: "Difficulties and problems belong to the same concept: without difficulties, there is no problem." Therefore, in mathematics and mathematics, teaching students to solve problems is to teach them how to overcome setbacks through hard work. Therefore, Paulia said: "Teaching students to solve problems is the education of will ... If students don't have the opportunity to taste the ups and downs of fighting for solving in school, then his mathematics education will fail in the most important place." Therefore. Teachers should pay attention to creating problem situations and carefully designing problems with moderate difficulty, so that students at all levels can experience setbacks by solving problems. The so-called "moderate difficulty" means starting from reality, making students "jump up and pick peaches", which requires courage and perseverance, and "being able to pick peaches" means making students experience success and pleasure through tempering. The topic is too difficult, which easily makes students cringe and feel frustrated. Even losing confidence in learning, the topic is too easy, not only will it not produce happiness and enhance interest after success, but it will also make students feel "boring" and dampen their enthusiasm. Facts have proved that the success achieved through our own struggle to overcome setbacks is the most inspiring and inspiring. Frustration education is not to let students circulate in a bitter circle, but to stimulate students' confidence and determination to strive for self-improvement and success.
Teaching practice has proved that frustration education in mathematics is an important means to improve students' quality. The majority of mathematics teachers should actively explore, purposefully and systematically infiltrate frustration education in teaching, and turn mathematics teaching into a practical activity to improve students' will quality.