Key words: examples of mathematics teaching, misunderstandings in mathematics teaching, and matters needing attention. In the middle school mathematics teaching, the example teaching occupies a very important position and plays an important role in the teaching process. Textbook examples are not only classics for solving problems with knowledge, but also models for thinking training. Although there is only one example in a class sometimes, it is its exemplary role that enables students to learn how to think with mathematics, how to think and solve problems with mathematical knowledge, and how to express their own problem-solving process. However, in the current teaching process, many teachers' teaching methods are too old, traditional teaching methods are dominant, and examples are unclear. The main reason is the misunderstanding in example teaching, which affects the cultivation and improvement of students' mathematical quality and the teaching effect. The following is an analysis of several misunderstandings in teaching.
First, teachers talk more and students participate less.
From the examination to the solution, the teacher contracted a person, and at the end, he finished a problem with great enthusiasm and high spirits, but the students were dumbfounded and didn't understand it in the fog. Here, teachers ignore students' dominant position and most students' participation. Teaching has become a personal performance, students have become bystanders, and the leading role has not been fully exerted.
Second, teachers' teaching methods are single and students are boring.
Teachers do not practice the new curriculum concept when teaching examples, and the teaching methods are old and single, relying on experience and focusing on teaching. Students lack passion and thinking in class, which leads to poor classroom atmosphere and boring students. It is often said that there are laws in teaching, but there are no fixed laws. It is important to get the correct laws. Teachers should choose teaching methods reasonably according to different examples and use a variety of teaching models comprehensively. The main reasons are: indifference to the new curriculum concept, weak awareness of curriculum reform, insufficient preparation of lessons or insufficient excavation of teaching materials. Deal with in a hurry, take care of
Benxuanke If you don't prepare lessons or don't prepare lessons adequately, the example teaching will have to be scripted, and students don't understand why. Third, the topic is not refined, ignoring the foundation and being greedy for more and less.
When teachers choose topics, they are often greedy for perfection, which leads to large capacity, overlapping examples or mechanical repetition. After a class, the teacher was hoarse and sweaty, but the students were confused and unintelligible, and the teaching effect was not good. This is mainly caused by the unclear purpose and function of teachers' teaching examples. Concept teaching is an important part in mathematics classroom teaching. In order to make students clearly understand mathematical concepts and solve problems by using the concepts they have learned, a certain number of examples are arranged in the textbook, which are generally typical and targeted, and are good materials for understanding and consolidating basic concepts. But some teachers abandon these easy-to-understand examples and blindly pursue some obscure and eccentric problems. I don't know that these strange questions have confusing meanings, complicated processes and abstract conclusions. Taking them as an example to help students master what they have learned is tantamount to scratching their boots.
Fourth, we can't give students enough time to think and ignore the teaching of thinking process.
After the teacher puts forward the topic, if he does not wait for the students to think, or when the students' thinking is just beginning, he is eager to prompt, or reread the topic, or take out the key sentences in the topic, or directly put out the ideas and methods, so that the topic can be solved quickly. On the surface, it saves time and avoids mistakes, but in essence, it replaces students' thinking with teachers' experience, students' thinking with teachers' lectures and students' active exploration with teachers' lectures. Many reasons for this situation are that the teacher presupposes the solution of the example when preparing the lesson, thus forming a mindset. In the classroom, it shows that the thinking of solving problems lacks flexibility. The analysis of examples only leads students to their own prepared solutions, and their thinking cannot be opened. Some even finished the analysis in a few words, and the students haven't figured out why. Obviously, this ignores students' voices and ideas, and also limits students' mathematical thinking, which is extremely unfavorable to students' mathematical problem solving and mathematical thinking training.
Fifth, there is a lack of extension and reflection on the topic.
There is no need to summarize the correct conclusion of the problem after the lecture. Just staying on how to solve this problem cannot be sublimated into how to solve this kind of problem, nor can it be sublimated into how to connect with other knowledge. Teachers should accurately point out the advantages or disadvantages of students in concept understanding, formula application and strategy determination, and give necessary affirmation and timely correction; Guide students to exchange experience in solving problems, sum up methods and skills of solving problems, sum up mistakes that are easy to be confused, sum up the differences between similar exercises and heterogeneous exercises, highlight key points, promote migration, and truly achieve the purpose of solving one problem, knowing one problem, and understanding one problem. In the teaching of mathematical examples, it is often the teacher who finishes solving the examples, rather than summarizing the examples (such as questions, thinking methods, expressions, etc.). ) or mining examples (such as changeable questions, multiple solutions to one question, multiple uses to one question, etc. If the teacher solves the problem in this way, the students will not be affected by the reflection on solving the problem, and of course, the students will not have the consciousness of reflection after solving the problem. Sixth, there is a lack of optimal treatment of examples, and the topics are arbitrary.
After each math knowledge point is finished, some examples are usually explained to help consolidate knowledge and deepen understanding. However, when choosing examples, there is a phenomenon, that is, the right example; No in-depth research, lack of optimization, and random choice. Some topics have problems due to the writer's lack of in-depth thinking. Some topics are not wrong, but are they typical? In addition, all kinds of problem-solving ideas and methods also need to be considered by teachers, so. In problem-solving teaching. We must attach importance to and do a good job in optimizing the topic selection, make it more reasonable, combine theory with practice, and try to avoid the randomness of the topic selection.
In view of the above situation, I think we should pay attention to the following points in the teaching of mathematical examples:
First, pay attention to quality and give good examples.
Teach examples well. Through the active interaction between teachers and students, students and some math activities, the examples are analyzed clearly and thoroughly, so that students can understand why they should solve it like this and how to express it.
Mathematics teaching is the teaching of mathematics activities, and it is a process of reflection, interaction and common development between teachers and students. Effective mathematics learning process can not only rely on imitation and memory. Teachers should guide students to actively engage in mathematical activities such as observation, experiment, guessing, verification, reasoning and communication, so that students can form their own understanding of mathematical knowledge and effective learning strategies. In example teaching, teachers should focus on teaching students the ideas and methods of analyzing problems, so that students can learn to explore problems by deduction and induction.
Second, study teaching materials and make good use of examples.
Make good use of examples, tap the potential educational value of examples, infiltrate moral education in example teaching, and cultivate students' mathematical emotion in example teaching. This is also one of the main teaching objectives of the new curriculum. Mr. Ye Shengtao, an educator in China, warned us long ago: "Teaching materials can only be used as the basis for teaching. To teach well and benefit students, we must rely on the good use of teachers. "
Third, teach students in accordance with their aptitude and choose a good example.
Choose good examples, and if necessary, replace or supplement the textbook examples according to the students' actual situation, but the selected examples should reflect the current mathematics teaching objectives, including the basic ideas and methods of mathematics, rather than blindly pursuing the difficulty and quantity of examples and problem-solving skills.
Fourth, the teaching method is flexible and the examples are well solved.
Solving examples well means thinking from multiple angles, exploring solutions or developing examples, and making them vivid and thorough. This requires us to use teaching, discussion and inquiry reasonably in teaching, so as to guide students to discover new ideas and find new solutions, thus cultivating students' innovative thinking ability. Mathematician Friedenthal put it well: "The only correct way to learn mathematics is' re-creation', that is, students discover and create what they want to learn. The main task of teachers is to guide and help students to do this kind of re-creation work, rather than instilling existing knowledge into students. " In addition, it is necessary to form habits and reflect on examples. Reflect on the solution of examples, whether the solution is rigorous, whether there is a new solution, whether the expression of the solution is clear and concise, whether the answers to such questions are regular, and so on. rise
It is very important for us to form the habit of reflection. Mr. Ye Shengtao, an educator in China, once said, "What is education? Simply put, education is to cultivate habits. " Only when our teachers form the habit of reflection after solving problems can students have the habit of reflection after solving problems. Even excellent students will get together with books and find something else to do after getting the answers to the questions and writing down the whole argument concisely. In fact, reflection is the key to mathematical wisdom, which embodies the rigor of mathematical thinking. Regular reflection can cultivate our good habit of being rigorous and considerate. Therefore, teachers should do a good job of students' reflection in example teaching. We should pay attention to multiple solutions to one problem and expand the teaching of examples.
Mathematics example teaching not only requires students to master the basic knowledge and skills of mathematics, but also requires students to develop their own abilities through example teaching. In the process of realizing mathematics teaching, properly solving a problem can stimulate students' strong desire for discovery and creation, deepen their deep understanding of what they have learned, and exercise the universality, flexibility and creativity of thinking, thus cultivating the quality of thinking, developing creative thinking and cultivating divergent thinking ability. Teachers should strive to create an encouraging and tolerant classroom atmosphere, create an educational environment that can guide students to actively participate, get rid of boring preaching, and be good at listening to students' understanding and ideas during lectures, giving students room for thinking.