I. Historical background
Thorndike, a famous American educational psychologist, believes that the essence of learning is that organisms form the connection between "stimulus" (S) and "response" (R). And this connection is mainly established through trial and error. Therefore, learning is a process of trial and error, and teaching is a process of constantly correcting behavior. Bloom, a famous American educator and psychologist, believes that the main reason for the formation of underachievers is the accumulation of knowledge defects. If we can adopt the method of "trial and error" to correct constantly, we will avoid the appearance of underachievers in mathematics, thus promoting the fullest development of every student. In addition, constructivism holds that "mathematics learning is not a passive acceptance process, but an active construction process". Through trial and error teaching, teachers can help students better complete the process of knowledge construction.
Second, the common methods of trial and error teaching
1, trying to explore methods: looking for various strategies and ways, trying various methods in class.
(1) Let students feel "surprised" in the process of solving problems. Surprise comes from accidents. Once an accident happens, it will attract more attention and make people think. Once students solve problems, they will have a strong sense of pleasure and accomplishment. The role of teachers in teaching is to constantly create surprises and let students experience success.
(2) Set "traps" to induce students to make mistakes and improve their self-monitoring ability. Suhomlinski said: "Any kind of educational phenomenon, the less children feel the intention of educators, the greater the educational effect. We regard this law as the core of educational skills. " In view of the fact that students fail to judge, reason and solve problems because of their poor understanding of some mathematical concepts, laws, theorems and formulas, some confusing topics are selected pertinently, and "traps" are set in error-prone links to induce students to go astray, create thinking conflicts, induce inspiration and produce true knowledge, thus improving their self-monitoring ability.
(3) directly explain the students' wrong practices. In teaching, teachers can let students find mistakes through a "many mistakes" question, and cultivate students' critical thinking through the process of exposing mistakes. Critical thinking refers to the thinking quality that is good at strictly estimating the thinking materials and carefully examining the thinking process in thinking activities. In teaching, teachers can choose the right time to deliberately make mistakes according to students' "common diseases" and "frequently-occurring diseases", and expose the mistakes to students again, thus further promoting students' thinking, enabling students to distinguish the types of mistakes, find out the problems, and thus prescribe the right medicine and eliminate the root causes. This practice is conducive to cultivating students' discriminating ability and is also a kind of will education. "
2. Comparing questioning method: summarizing, analyzing and comparing each stage. Teachers can first analyze and compare what they have taught and put forward new problems for students to solve. For example, when we study permutation and combination, there are often many explanations for a problem, and the final result is mostly the same, but some methods and ideas are right, but different results are obtained. At this time, it is helpful for students to find out the causes of mistakes through analysis, which is conducive to improving their understanding of the problem-solving process.
3. Blackboard performance method: Let students come to the front to perform, which is conducive to finding mistakes in the process of solving problems in time. Because there is a big difference between doing the problems in front and asking students to do the problems in the exercise book. The blackboard writing performance can intuitively see the process of students' ideological changes in the process of solving problems, and help them find and solve problems. This problem may be caused by knowledge itself, problem-solving habits, long-term thinking patterns, or careless calculation errors. No matter what kind of problems, it is very beneficial to students as long as they are given correct guidance.
4. Quick answer method: Quick answer can find many questions of students, because this quick answer is a reflection of students' shallow consciousness, and can find problems that students don't pay much attention to. You may notice some ideas when you do the questions slowly, but mistakes will appear when you answer them quickly, which shows that students are not very skilled in some knowledge.
5. Look at each other's papers: Many students like to experience the feeling of being a teacher and look at other people's papers. Teachers can make use of their interests to let them find mistakes in others' learning process and avoid making the same mistakes themselves. But this practice should not be used often, because students can't play their due role when they feel tired.
Third, matters needing attention in trial and error teaching
1, the degree of teacher-student interaction. At present, the interaction between teachers and students is not enough. In order to really "move" between teachers and students, teachers need to keep learning, understand deeply and practice hard, so that teachers can change their roles. If our teachers are still in the traditional role, teaching in the traditional way, and students are still containers of knowledge, then I am afraid it is impossible to raise the requirement of equality between teachers and students a thousand times. It is hard to imagine that a senior teacher with a sense of dignity as a teacher will participate in teaching activities on an equal footing with students. Change the concept of education, change the way of learning, teachers and students participate in teaching activities equally, and realize the training goal of the new curriculum. Therefore, in order to achieve the effect of "teacher-student interaction" in class, we should spend more time communicating with students outside class, put down our airs and really become friends with students. Academic skills are the foundation, which must be solid and reliable and constantly updated; Teaching skills are means and must be vivid and intuitive; Teacher-student interaction is a platform, and both teachers and students must have a harmonious and equal dialogue. If we combine academic skills, teaching skills and teacher-student interaction, and constantly improve in practice, and gradually reach the point of perfection, then our teaching is perfect and our education is successful.
2. Guide correctly. Teachers should pay attention to guidance in the process of trial and error. The wrong direction may make students feel wrong. The teacher's purpose is not to make students make mistakes, but to let them learn knowledge and learn how to learn knowledge through mistakes. When students make mistakes in their studies, they should give priority to encouragement. High school students have not fully grown up, and their thoughts are in an immature to mature stage. They need teachers' care and encouragement more. The key and difficult points should be prompted in many ways. Teachers should make some language, tone, and even some important and difficult points in their lectures.
The quick action helps students solve problems and improve their confidence.
3. Teachers should arrange students' cognitive process according to the actual situation, and support and help students to gradually build a knowledge system. The arrangement of this process must be suitable for students' cognitive laws, and this process should be arranged through feedback and adjustment. In addition, in the process of trial and error teaching, teachers should pay attention to the accuracy of students, and combine general methods with special methods instead of blindly pursuing speed or skills.
In addition, teachers can stimulate students' interest in learning by setting inspiring and challenging questions. We should also pay attention to the treatment of teaching materials, the formation of knowledge and the pace of learning. Mathematics class is ineffective without a certain speed, and slow learning can't train thinking speed.
In a word, trial-and-error teaching conforms to students' psychological cognitive law and is conducive to the all-round development of students' thinking ability and learning ability. Trial and error teaching can also give full play to students' subjective initiative and creativity, and guide students to actively explore and discover, so as to achieve the purpose of actively learning knowledge.