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What are the common teaching methods?
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The difference between teaching means and teaching methods
What are the types and means of teaching methods?
Commonly used mathematics teaching methods
First, the independent inquiry learning method
Self-inquiry is a kind of classroom teaching mode that allows students to study independently, explore independently and learn independently, which fully embodies students' dominant position. Since the implementation of the new curriculum standard, it has been widely used in various disciplines, which can better stimulate students' enthusiasm and initiative in teaching, let students explore the source and characteristics of new knowledge and explore its application value in real life. Train students' thinking ability and understanding ability, and enhance students' self-confidence in learning mathematics well. Students will regard the result of autonomous learning as success, thus generating a sense of accomplishment and joy, stimulating students' strong self-confidence in the whole learning process and their interest in independent exploration and conscious research, and cultivating innovative spirit. If students want to understand the seemingly abstruse knowledge in mathematics, they can solve it quickly as long as they actively explore and think seriously. Mathematics comes from life and is better applied to life.
Second, group discussion learning method
This model takes students as the main body, allowing students to discuss and discuss the problems raised by teachers in groups, thus forming an interactive way with teachers. Group discussion is conducive to cultivating students' collectivism, and classroom group discussion is conducive to cultivating classified thinking, comprehensive thinking ability and understanding ability in the process of learning mathematics. At the same time, it can also cultivate the communication ability between students, students and teachers, and enhance the feelings between classmates and teachers and students. Through group discussion, we can get ideas and ways of thinking to solve problems from many angles, and often integrate discussion and communication, understand in discussion and deepen our impression in communication. This can enhance the effect of classroom teaching, which is much better than direct teaching by teachers, promote students' learning, and teachers can also get unexpected gains from it.
Third, the discovery learning method
Discovery learning is another student-centered teaching mode and method after independent inquiry learning and group discussion learning. By reading textbooks, we can find new knowledge, new problems, new ideas and methods for solving problems, mathematical laws and places where students are prone to problems. In this way, students have priority in mastering new knowledge and are deeply impressed by the knowledge, problems, ideas and methods they have discovered, which is very important for students to master knowledge and find channels to discover knowledge. Sometimes it may make students have a whim and ask some strange math questions like some mathematicians. It will also promote students' enthusiasm for learning mathematics and help improve the quality of classroom teaching.
Fourth, demonstration and performance learning method.
Demonstration teaching method is the most basic and commonly used model in mathematics teaching and even in all disciplines. Mainly teachers demonstrate classroom teaching content and tell new knowledge content. Some teaching contents do not need students to explore and discover, such as definitions, concepts and axioms. These contents directly describe or demonstrate or explain the formation of theoretical knowledge by means of teaching tools.
Fifth, the game learning method of entertaining.
The content of the new mathematics textbook is lively and interesting, and the topic is like a piece of sweet cake, which is very attractive. Such as: interesting puzzles, equations in the calendar, how big is a million, and so on. The teaching content has also become very interesting, such as the corner on the table of billiards, changing fish. Many teaching contents are interspersed with game contents, such as: is the game fair, are you sure you can touch the red ball, and so on. The content of the textbook is more in line with the psychological characteristics of middle school students who are active and fun. Using games can not only exercise students' courage and stimulate their enthusiasm for learning, but also cultivate collectivism. Games can make students relax their study pressure, enter the study state with a relaxed mood, acquire knowledge from the game and apply it to the game.
Sixth, problem-based teaching methods.
Problem-based teaching method is to arrange the new knowledge to be learned into closely related questions, so that students can think, discuss and finally answer each question. During the discussion, students also ask related questions. The more questions you ask, the stronger your knowledge, and the teacher plays a guiding role.
Seven, feedback training teaching method
In order to test students' mastery of classroom knowledge, it is necessary to give timely feedback according to the mastery and application of what they have learned. Feedback training is an important part of classroom teaching, and the design of feedback questions is very important. The design of feedback questions should be moderate and difficult. Feedback training questions suitable for each student can be designed according to the learning level of different students. Students can also design feedback questions according to their own learning level, answer them themselves, and find and solve problems in time during the feedback process.
Feedback training can make up for the shortcomings and mistakes in students' study. When students have difficulties with new knowledge, it will be reflected in feedback training. The forms of feedback include observing oral expression, hands-on operation, demonstration process, reasoning and argumentation, etc. Feedback can correct students' learning attitude (careless and one-sided thinking) and enhance students' understanding of knowledge, which is easy for students to accept and has a good effect. There are rules in teaching, but there are no fixed rules. A good class is not a single method, but a variety of teaching methods according to the characteristics of knowledge and students' psychological characteristics. Under the new curriculum standards, students should be the main body of adopting new teaching modes and methods, and should be required to do more work and use their brains. Apply mathematics knowledge in life to real life and solve related problems in real life. There are various teaching methods, and the above methods are only superficial. More teaching methods need to be explored and summarized in the long-term teaching, so that I can enter the new curriculum with the same look.
How to improve junior high school students' mathematical thinking ability
Mobilize students' inner thinking ability
1. Cultivate students' interest in learning mathematics and promote the all-round development of mathematical thinking. Interest is always the best teacher for students to learn, and it is also the internal motivation for every student to consciously seek knowledge. Therefore, we should carefully design each class, make each class vivid, deliberately create moving situations, set attractive suspense, stimulate students' thinking sparks and desire for knowledge, and let students realize the important position and role of mathematics in real life. Students are often guided to explain their familiar practical problems with the mathematical knowledge and methods they have learned. The "thinking" and "reading" arranged in the new textbook can not only expand the knowledge, but also improve students' interest in learning and stimulate students' thirst for knowledge.
Disperse difficulties appropriately and create conditions for students to think. For example, solving application problems with equations is one of the contents that students generally find difficult. The main difficulty lies in mastering the idea of not using algebraic method to analyze problems. In primary school, I used to use arithmetic solution, so I couldn't find the equivalence relationship and couldn't list the equations. Therefore, when I teach series algebra, I consciously make some preparations for the teaching of series equations, and inspire students to find the internal relationship between the known and the unknown from the complex quantitative relationship. By sketching a certain number of examples and exercises, let students gradually find out the equivalence relationship and list the equations. On this basis, it is pointed out that different equations can be listed for the same topic because of different ideas. In this way, most students can list equations smoothly and make positive analysis and thinking when they encounter problems. Encourage students to think independently. Influenced by experiential thinking, junior high school students have the same thinking tendency and lack the spirit of exploration. Therefore, students should be encouraged to express different views.
How to improve junior high school students' mathematical thinking ability
We should teach students the method of thinking.
Confucius said: "Learning without thinking is useless, thinking without learning is dangerous". Only by properly handling the relationship between learning and thinking can we achieve good results. In order to make students think actively in mathematics learning, we must teach them the basic methods of analyzing problems, which is conducive to cultivating students' correct thinking mode. To be good at thinking, students must attach importance to the study of basic knowledge and skills. Without a solid foundation, their thinking ability cannot be improved. Mathematical concepts and theorems are the basis of reasoning and operation, and accurate understanding of concepts and theorems is the premise of learning mathematics well. In the teaching process, we should improve students' cognitive ability of observation and analysis, from outside to inside, from here to there. The discovery process of solving (proving) problems should be regarded as an important teaching link in the example class. Not only should students know how to do it, but also let them know why they should do it and what prompted you to do it and think so. This discovery process can be completed by teachers guiding students, or by teachers telling their own search process.
In mathematics practice, we should carefully examine the questions and observe them carefully, and have the ability to dig out the hidden conditions that play a key role in solving problems. Learn the positive and negative analysis methods from conditions to conclusions or from conclusions to conditions. For a mathematical problem, we must first be able to judge which interval it belongs to and which concepts, theorems or calculation formulas are involved. Try to learn the use of mathematical language and mathematical symbols in the process of solving problems (proving). The research objects of junior high school mathematics can be roughly divided into two categories, one is to study the quantitative relationship, the other is to study the spatial form, that is, "algebra" and "geometry". Make students master some important mathematical methods, including collocation method, method of substitution, undetermined coefficient method, synthesis method, analysis method and reduction to absurdity.
Stimulating students' thirst for knowledge in junior high school mathematics teaching
Interest is the best teacher. As long as students are curious, their enthusiasm will be improved and their thinking will be more active. If teachers can fully stimulate students' interest in learning and stimulate their positive thinking, it will be more conducive to promoting and developing students' creative thinking ability. In classroom teaching, teachers should be good at combining the characteristics of junior high school students, stimulating and catering to their psychology, making them produce * * * sounds, and guiding them to think deeply and explore constantly. For example, before talking about the linear equation, choose the quoted example: "One hundred monks have one hundred buns, one big monk eats three, and the other three little monks eat one right after eating. Ask how many monks and young monks have been exposed to simple equations since their students started primary school. Because of the humor of the example itself and the curiosity of the students themselves, they will actively participate in finding solutions, and their enthusiasm for learning new knowledge will be fully mobilized. This not only aroused students' interest and thinking, but also deepened their impression of the content to be studied in this section and their understanding of the significance of learning each small concept well. In this way, students will be more interested in learning this lesson. Junior high school students have great creative potential, but this potential needs constant encouragement to produce.
Cultivating students' observation ability in junior high school mathematics teaching
Observation is the channel of information input and the door of thinking exploration. First of all, before observation, students should be given specific goals, tasks and requirements. Secondly, give students guidance in observation. Third, guide students to analyze and summarize the observation results. For example, students have difficulty in understanding "closure" when learning "triangle understanding". Teachers can ask students to prepare a stick of 5cm, 8cm, 4cm and 3cm, and choose three sticks to form a triangle. In the pendulum, the students found that they could make a triangle with 5, 8, 4 cm and 5, 4, 3 cm. When choosing 8, 4 and 3 cm sticks, the two ends can't be connected and can't be put together into a triangle; When you choose a stick of 5, 8 or 3 cm, you can't put it together to form a triangle. With the help of graphics, students can intuitively perceive that the sum of two sides of a triangle cannot be less than the third side, so that they can understand that a triangle is not composed of three line segments, but is surrounded by three line segments, so that students can define a triangle more clearly. Therefore, in concept teaching, teachers should strive to create conditions, provide students with opportunities for independent exploration and sufficient thinking space, so that students can draw conclusions in the process of observation, operation and analysis, which is helpful to cultivate students' creative thinking ability.
Imagination is the wing of thinking exploration. Guiding students to imagine mathematics in teaching can often shorten the time of solving problems, gain opportunities for mathematical discovery and exercise students' creative thinking ability in mathematics. For example, when learning the area of parallelogram, the teacher can let the students look at the blackboard (usually rectangular) and let them calculate its area. Students can use what they have learned to solve this problem quickly. Then take out the prepared parallelogram and ask the students to calculate the area of the parallelogram. According to junior high school students' natural curiosity and enthusiasm for exploring unknown areas, we can make the following guesses based on previous knowledge: 1, and the area is the product of the length of long side and short side. 2. The product of the long side and its height. 3. The product of the short side and its height. At this time, the teacher writes one by one on the blackboard, and students will have a sense of accomplishment when they see their thinking results affirmed, thus inspiring students to take the initiative to imagine and explore.
Pay attention to practice and cultivate students' thinking ability
Paying attention to hands-on practice is one of the most effective ways to develop students' thinking and cultivate their mathematical ability. One of the characteristics of the new textbook is to attach importance to intuitive teaching and increase students' practical activities and hands-on operation content. Therefore, homework activities become an important link in the process of classroom teaching. This is especially true in junior high school mathematics teaching. Obtaining knowledge in operation practice is the core of each class. For example, when teaching math composition, I ask students to put a stick first. "Eight sticks are divided into two piles, how to divide them? Let's work together to see which team scores more points and which team takes the red flag. " The students are full of interest and act quickly. While posing, chatting and taking notes, some are still arguing and trying to convince each other.
In this way, students' thinking has been fully developed and their language expression ability has been exercised. Another example is teaching "how to calculate how many plus nine". I'll let two people at the same table put a stick first and talk about how to calculate it while putting it. Then, speak your mind and communicate with the whole class. Some said that they should be counted one by one; Some say 9 doesn't count, count back from 9; Some say that if you give another pile of 1 to 9, it will become ten, and a few will be added next to it; Others say that subtracting a few from nine will make the pile next to it become ten, and adding nine will make the rest become more than a dozen. The teacher wrote their ideas on the blackboard. Organize a discussion to see which method is the simplest and fastest, so as to draw the best conclusion.
Students' mathematical thinking should be trained according to certain laws.
Laws in mathematical thinking include formal logic laws, dialectical logic laws and special laws of mathematics itself. They are interrelated. There are relations between form and content, concreteness and abstraction, particularity and generality. In order to make students learn effectively, it is necessary to reveal the internal relations and laws of knowledge. Such as integer, decimal, fraction and percentage; Five of the four kinds of calculation algorithms are the general formulas on which the number system is based. The four basic quantitative relations of sum, difference, multiplication and division are the basis of various application problems and so on.
The more basic and general the law is revealed, the easier and more convenient it will be for students to understand and the better the teaching effect will be. Therefore, when teaching new knowledge, teachers should make full use of the role of transfer, so that students can solve new problems with existing knowledge and thinking methods. For example, after teaching the multiplication formula of "5 times several", students can use this way of thinking to derive other multiplication formulas; After learning the derivation of "additive commutative law", you can also learn the multiplicative commutative law. After learning the derivation of "triangle area formula", you can learn the derivation of trapezoidal area formula in the same way and so on.
Let students prove their conclusions independently and cultivate their thinking.
Modern teaching theory holds that students are the main body of learning. The traditional teaching proof process is completed by teachers, which does not conform to the principle of student subjectivity. As the saying goes, "Seeing is believing, seeing is believing." We think some students can prove it through their own exploration and thinking. At this time, students should be allowed to do it independently and give them the opportunity to discover, which not only increases students' participation, mobilizes students' enthusiasm for learning, and actively completes the proof, but also truly reflects students' sense of ownership. When students see the achievements made through their own labor and realize the joy of success, they will also have a strong desire to explore mathematical knowledge and confidence in learning mathematics, prompting them to further explore mathematical knowledge. So as to cultivate students' ability to explore and solve problems independently.
Training methods of junior middle school students' mathematical thinking ability
Create thinking situations to inspire students' thinking.
"Teachers are the guides and organizers of students' learning process", which requires teachers to fully mobilize students' initiative and enthusiasm in the classroom. In order to enable students to participate in teaching activities to the maximum extent, teachers should explore the thinking factors of teaching materials according to the key points and difficulties, accurately grasp the students' cognitive level, create thinking situations, and ask students seemingly incomprehensible and incomprehensible questions, so that students feel both unexpected and reasonable. Just like an apple on a tree, you can't pick the apple at your head, but you can easily pick the apple on the tree with a jump, so that students can pick it. This can fully mobilize the initiative and enthusiasm of students and inspire their thinking.
Guide students to reflect after solving problems and cultivate students' thinking.
Friedenthal, a mathematical educator, once pointed out: "Reflection is an important mathematical activity, it is the core motivation of mathematical activities, a positive thinking activity and exploration behavior, and it is assimilation, exploration, discovery and re-creation." After solving the problem, we should guide students to review and reflect on the inquiry process, make the successful experience clear, and organize students to summarize the general conclusions about mathematical thinking methods, knowledge and skills. Then, through the intensive reading teaching of teachers, the overall relationship between these conclusions is revealed, so that the knowledge learned is systematic, which helps students to think about the mathematical model contained in objective things, thus helping students get rid of the sea of questions and understand the problems more clearly. It is helpful for students to consolidate and assimilate new knowledge, accurately grasp the internal relationship between old and new knowledge, and find new laws to popularize and extend; It is beneficial to improve students' mathematical thinking ability. If we don't reflect on every process of solving problems, then the problem-solving activities will stay at the experience level and get twice the result with half the effort.
Four Basic Principles of Mathematics Teaching
I the principle of combining abstraction with concreteness
High abstraction is one of the basic characteristics of mathematical theory. Mathematics takes the spatial form and quantitative relationship of the real world as the research object, so mathematics abandons all other characteristics of objective objects and only conducts systematic and theoretical research on its spatial form and quantitative relationship. So mathematics is more abstract than other disciplines. This abstraction is also manifested in a high degree of universality. Generally speaking, the higher the abstraction of mathematics, the stronger its universality.
Second, the principle of combining rigor with ability.
Stiffness is one of the basic characteristics of mathematics. Its significance mainly refers to the rigor of mathematical logic and the accuracy of conclusions. In the theoretical system of middle school mathematics, it is mainly manifested in the following two aspects: first, it is necessary to define concepts (except original concepts) and prove propositions (except axioms); Secondly, the arrangement of mathematics content should conform to the inherent logical structure of the discipline.
Third, cultivate the principle of combining "two basics" with strategic innovation.
Mathematics "double basics" refers to the basic knowledge and skills of mathematics. The basic knowledge of mathematics, that is, the "nodes" in the mathematical knowledge network, includes concepts, theorems, formulas, rules and methods in middle school mathematics. Basic skills refer to the operation methods related to the basic knowledge of mathematics according to certain procedures and steps, including mental activities such as operation, reasoning, data processing, drawing and table drawing. A correct understanding of mathematical concepts is the premise of mastering mathematical knowledge, while a firm grasp of mathematical laws such as definitions, properties, axioms, theorems, formulas, rules and proof methods for solving problems is a necessary condition for learning mathematics well.
Fourth, strengthen the principle of combining teaching with self-construction.
Intensive teaching and more practice is the main method of mathematics classroom teaching at present. Intensive teaching is put forward for teachers' explanation, which requires teachers to choose typical problems to explain and explain the key points in mathematical concepts and theorems incisively. Explanations should be few but precise, targeted, representative and universal, and individual problems should be taught separately. More practice requires students to practice solving problems in a certain amount.
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