Mathematical means and mathematical methods are different, teaching means more present what characteristics?

Chapter V Methods and Means of Teaching Mathematics in Elementary Schools

I. Methods of Teaching Mathematics in Elementary Schools

, I. An Overview of Teaching Methods

1. It has been defined in many different ways.

Some people think that "teaching methods are in the teaching process, teachers and students to achieve the purpose of teaching. To accomplish the task of teaching and learning and take the teaching and learning interaction of the activity of the way the general term. ", Li Bingde, ed. Teaching Theory, p. 197. People's Education Publishing House, 1991 edition,

Some people think that "teaching method refers to the working method of the teacher in the teaching process in order to complete the teaching task and the way of learning of the students under the guidance of the teacher. ", Shanghai Normal University, edited by the Pedagogical Sciences, page 156, People's Education Publishing House, 1979 edition,.

There are others who believe that "every teaching method is a series of purposeful actions carried out by the teacher to organize the cognitive and practical activities of the students and to ensure that they master the content of the education. ", see Foreign Educational Materials, No. 3, 1981, .

It is generally recognized that. "Teaching methods are the activities of teacher-student interactions that are carried out by using teaching means to achieve teaching purposes, guided by teaching principles and consisting of a whole set of ways. " , by Wang Cesan. Teaching Theory, a textbook for liberal arts in higher education. People's Education Publishing House, 1985 edition.

The above definitions reveal some of the essential attributes of teaching methods from different perspectives. That is, the teaching method is in order to realize the teaching objectives, to complete the teaching task adopted by the way of activity, teaching methods pay attention to the student's main position and the interaction between teachers and students. Teaching methods are different from teaching tools or instruments. Rather, it is the use of tools or means. Not a fixed way or action, but a series of purposeful action.

Teaching methods and teaching methods are two different concepts that are closely related and strictly different. Teaching method is the basic unit of teaching method. Teachers and students in the teaching process is a specific way of operating behavior, while the teaching method is composed of many teaching methods. It is not a separate way of operating behavior, but the language system, operating system, physical system and emotional system and other components of the activities of teachers and students system. Therefore, the teaching method is the basic unit of the teaching method, and the teaching method is an organic combination of many teaching methods. For example, the explanation method is a teaching method. In the lecture, the teacher explains and describes a concept. Explain a terminology or argue a proposition. Here illustrating, describing, explaining, arguing, etc. are teaching methods, and the same teaching method can be utilized in different teaching methods. Different teaching styles can also be utilized in the same teaching method.

2. Classification of teaching methods in elementary mathematics

In teaching methods. There are both methods of teacher teaching. Explanation, demonstration, guidance, etc., , and there are also methods of student learning, listening, observation, reading, discussion, practice, etc., . There is both teacher inspiration and student exploration.

Teaching methods can be broadly divided into five series and three levels.

Five series,

One is the transmission of acceptance type. Mainly through the teacher's systematic teaching to enable students to master knowledge, such as the explanation method.

The second is self-study tutorial type. The original part of the content explained by the teacher, changed by the students in the teacher's guidance, such as reading method, self-study method, counseling method.

The third is to guide the discovery type. Provide students with research materials, guide students to explore, discover the conclusions that should be drawn, such as the introduction of exploration teaching method, problem exploration method, guide the discovery method, migration teaching method.

Fourth, the mood of cultivation type. Through the emotional rendering of the teaching environment, the use of human suggestibility. Mobilize the potential of the unconscious field of the student brain, so that students in a spirit of pleasant atmosphere for learning. Such as the game method, contextual teaching method, enjoyable teaching method, suggestive teaching method.

Fifth, modeling and imitation. Through the teacher or textbook demonstration. Let the students to imitate the practice, so as to develop students' skills, techniques and abilities. Such as example teaching method, try teaching method.

Three levels,

The first level is the basic teaching methods, the main method of explanation, conversation, practice, demonstration, experimentation, etc., they are the basis of the teaching method system. Elementary school math teaching can be based on a few basic teaching methods, to create a number of distinctive teaching methods.

The second level is a comprehensive teaching methods, these teaching methods are actually a combination of several basic teaching methods. For example, the guided discovery method is a combination of conversation, experimentation, demonstration and discussion, and the self-study method is a combination of reading, practicing, explaining and discussing.

The third level is creative teaching methods. While learning and imitating various comprehensive teaching methods. Continuously summarize, be innovative, and create a teaching method with its own individual characteristics. Step into the seemingly unable to actually have the law of the free kingdom.

, second, the basic methods of teaching elementary school mathematics

The basic methods of teaching elementary school mathematics are mainly explaining the method, talk method, practice method, demonstration method, experimental method, reading method, visit method, discussion method, practice method and review method and other ten kinds. In terms of the degree of independence of students in acquiring knowledge. Basic teaching methods can be divided into three categories.

The first category, the teacher has to carry out more organization. Students' activities are less, such as lecture method, demonstration method, review method,

The second category. The teacher carries out the necessary organization, students' activities are more, such as conversation method, discussion method, visit method, practice method,

The third category. The main independent activities of students, such as reading method, experimental method, practice method. Three types of teaching method of student activities, the independence of a higher than one.

1. Explanatory method

Explanatory method means that the teacher explains the concepts, explains the rules and regularity of knowledge to the students through explanation. It is characterized by. Teachers can tell new knowledge systematically and with arguments.

The lecture method is mainly used to teach new knowledge and sometimes to review old knowledge. This method of teaching requires students to have a certain ability to listen and understand.

2. Talking method

Talking method is a method of teaching through purposeful and planned teacher-student conversations. It is characterized by. Through teacher questioning. Drive students' thinking, stimulate students' memories of old knowledge, communicate the link between new and old knowledge, so that students think according to the teacher's questions, so as to discover the law and draw conclusions. By studying the students' answers, the teacher will be able to understand their mastery of knowledge. It also develops students' language skills. Therefore, the talk method is commonly used in all grades, the implementation of heuristic teaching the most effective application of a wider range of teaching methods.

3. Practice method

Practice method is under the guidance of the teacher, the students through practice to consolidate knowledge, the formation of skills, techniques, and intellectual development. The practice method is a frequently used method in elementary school mathematics teaching.

4, demonstration method

The teacher demonstrates the teaching aids or objects to illustrate or confirm the knowledge taught, this teaching method is called demonstration method. Demonstration method not only provides students with distinctive perceptual material, helps to understand the abstract mathematical knowledge, but also helps to develop students' observation and thinking skills.

Mathematical concepts are abstract, sometimes. Teachers alone is difficult to make students master, must be demonstrated with the help of physical and teaching aids. It is the specific embodiment of the principle of intuitive teaching, therefore, in elementary school mathematics teaching. Should attach great importance to the application of the demonstration method.

5. Experimental method

Let the students under the guidance of the teacher through experiments. Mastery of mathematical concepts or laws, this teaching method is called the experimental method. Using the experimental method should be clear about the purpose of the experiment and the steps of the experiment.

Because the experimental method can cultivate students' hands-on ability, but also to develop students' intelligence and spirit of exploration. In recent years, has been the general attention of the educational community.

6. reading method

The reading method is characterized by. Under the guidance of the teacher, knowledge is acquired by reading textbooks. Reading is the most important method of learning in one's life. Teachers should constantly improve students' reading and self-learning skills.

In actual teaching, there are several forms of using the reading method,

, 1. Read first and then lecture Teachers first instruct students to read the textbook and then lecture. Before the students read, the teacher should put forward the requirements, and help the students to remove some of the obstacles in reading.

.2. Read before reading Teachers first explain, students then read. Clearly speaking the main points and the conclusion.

. 3, read while speaking Teachers explain. The teacher explains and the student reads.

, three, comprehensive teaching methods

1, discovery teaching method

Discovery teaching method is also known as the problem teaching method. It is characterized by. Teachers do not directly transfer ready-made knowledge to students. Instead, they guide students to use the teacher and the material provided by the textbook. Discover for themselves the conclusions that should be drawn.

The general steps in using the discovery teaching method are as follows.

, 1, put forward the problem to be solved, stimulate the students' desire to solve the problem.

, 2. Guide the students to utilize the materials provided by the teacher and the textbook, and formulate various hypotheses about the problem.

, 3. To express different views and opinions, and to start a discussion.

, 4. The teacher summarizes and draws conclusions.

The discovery teaching method used abroad allows students to discover knowledge entirely by themselves, which takes more time and is not easy to obtain complete and systematic results. Our country advocates the use of guided discovery teaching method, in order to play the leading role of the teacher and the role of the textbook, in the hypothesis to give students appropriate help. We call this the "guided discovery method".

The use of "guided discovery method" should pay attention to the following points.

, 1, play the leading role of the teacher.

To constantly inspire. Step by step to guide students to discover. And through the summary. Help students master the systematic knowledge.

, 2, play the role of textbooks.

Planned to guide students to use textbooks. Gradually "discover" the conclusion.

, 3, more conceptual, students lack of old knowledge as a basis for content. It is not appropriate to use the guided discovery method.

, 4, teaching to let everyone have enough time to think.

Can not be satisfied with the excellent students "discovery", to face the middle and lower students. Help them to "discover".

, 5, teaching to encourage students to ask questions.

2. Self-study tutorial method - emphasizing student self-learning, teacher tutoring.

3. Procedural teaching method - a method of teaching by using programmed materials and following certain procedures.

Four, the trend of reform of elementary school mathematics teaching method

According to the concept of the new curriculum, the reform of elementary school mathematics teaching method in China presents the following development trend,

1. Guiding students to learn mathematics in mathematical activities

The new curriculum concept that, "each learner should not wait for the transmission of knowledge, but should be Each learner should not wait for knowledge to be delivered, but should construct his or her own knowledge and give meaning to experience based on his or her own unique experience of interacting with the world.", Zhong Qiquan et al. ", Zhong Qiquan and other editors, "Basic Education Curriculum Reform Outline, Trial, Interpretation," page 24, East China Normal University Press, 2001 edition, . In elementary school mathematics learning, students discover and solve problems through activities such as manipulation, experimentation, inquiry and examination. Teachers should pay attention to the study of students' mathematical activities when researching the reform of teaching methods, focusing on the development and utilization of activity resources, actively guiding students to learn mathematics in mathematical learning activities, so that they can take the initiative to acquire mathematical knowledge in mathematical activities. Development of mathematical ability, but also to obtain a positive emotional experience.

2. Concerned about the students' experience of the learning process

Full-time compulsory education "Mathematics Curriculum Standards" , the experimental draft. In the learning objectives of mathematics for the first time in the "knowledge and skills goals" alongside the "process goals", that is, let students "experience. Feeling, experiencing, experiencing. Experience, experience, explore" mathematical activities, so as to better reflect the learning requirements of students in mathematical thinking, problem solving, as well as affective and attitudinal aspects. Not only should we pay attention to the results of students' learning, but we should also pay attention to the process of students' learning

The process of learning, the experience of students' learning of mathematics and experience. Therefore, the reform of teaching methods is largely reflected in the attention to the process of students' mathematical knowledge exploration and understanding, that is, the process of concept formation, the process of formulae and the process of exploring solutions.

3. Guiding Effective Exploration and Organizing Valuable Collaboration

Behaviorist view of learning is that learning is a change in behavior, a substantial connection between external stimuli and mental reflection, and cognitive view of learning emphasizes "understanding", which requires students to be able to explain knowledge in their own words. The constructivist view of learning sees learning as a process of student autonomy, exploration and practice. It emphasizes the role of students as subjects in practice. According to the theory of constructivism. Learning mathematics is a process of "doing mathematics". Students use their own activities to build an understanding of existing human mathematical knowledge. Mathematics teaching is the teaching of mathematical activities, and mathematics learning is not simply the acceptance of knowledge. Rather, it is a student-oriented mathematical activity. Therefore. They advocate that in classroom teaching, we should change the traditional mode of teacher teaching and student learning, and let students have the opportunity of self-reliance exploration, operation and experimentation, active thinking and cooperation and communication, so as to cultivate students' exploratory and innovative spirit, the ability to use mathematics to find problems, solve problems, and communicate and process information. Therefore. In the process of designing, arranging and organizing teaching, teachers should take realistic, interesting and exploratory subject learning activities as an important part of mathematics teaching. Teaching methods such as cooperative learning and classroom discussion have led to significant changes in the form of elementary math classroom teaching.

Under the influence of the above educational concepts. The reform of elementary school mathematics teaching method presents the following characteristics,

1. In the purpose of teaching, emphasizing the development of students' intelligence and ability, so that students not only grow knowledge, but also grow wisdom.

2, in the learning process. Emphasize the characteristics of the subject of mathematics and the psychological characteristics of students.

Student learning process is a special cognitive process, neither can completely repeat the human cognitive process. And not against the human cognitive process. Both to consciously arrange some content for students to research, discovery. And not everywhere to let the students to rediscover, neither from the psychological characteristics of children, ignoring the intuitive teaching, but also can not take into account the characteristics of the subject of mathematics, weakening the cultivation of abstract thinking ability.

3, in the relationship between teaching and learning. Emphasize the relationship between the leading role of the teacher and the main role of students.

Teachers should pay attention to explaining the meaning of learning, arousing students' motivation to learn, letting go of students' practice, cultivating students' hands-on ability, and. Guiding students to think positively.

4, in the choice of teaching method, emphasize the multi-method cooperation, improve the overall function.

Modern teaching theory advocates, according to the purpose of teaching, content and psychological characteristics of students to choose different methods. And use several teaching methods in conjunction with each other.

5, in the organization of teaching, emphasizing the variety of forms and adapt to the differences of students.

The combination of classroom teaching, group teaching and individual teaching. To do for all, but also to take care of individual differences.

6. In the classroom structure, emphasize the overall optimization and efficiency.

The design of classroom structure, in accordance with the law of teaching, according to the content, teaching requirements, classroom situation and children's age characteristics of the comprehensive consideration, deal with the relationship between teaching and learning, teaching and practicing, for all and tailored to the needs of the students, pay attention to the main tasks of the links arranged in the optimal time, and roughly stipulate the time used in each link.

Second, the means of elementary school mathematics teaching

, a type of teaching tools,

Teaching tools refers to "teachers and students in order to achieve the intended purpose of teaching, teaching activities. Mutual transmission of information tools, media or equipment. ", Tian Huisheng, edited by Teaching Theory, page 226, Hebei Education Publishing House, 1996 edition, .

Teaching means from the physical, graphic, modeling as the main tool of the traditional means of teaching, the development of today's computer as the core, including the network application of modern means of teaching, according to the sequence of its generation and development. Can be divided into the following three categories.

1, the traditional means of teaching. Mainly refers to teaching aids and learning aids, such as objects, specimens, models, charts, etc., they are used earlier in the teaching, is still widely used in elementary school mathematics teaching means.

2, electrochemical means of teaching, mainly refers to the slide, projection, audio, video and other power-powered means of teaching.

3, chemical means of teaching. It is characterized by the computer as the core, and includes the application of network technology.

, II. The role of teaching means.

1, the use of teaching means reflects the principle of intuitive teaching. It can provide students with perceptual experience, help them understand and master mathematical knowledge.

2, in line with the psychological characteristics of primary school students. Favorable to stimulate students' interest in learning. Elementary school students are curious, love to move the characteristics of new and different things can cause students' desire to learn, the image of vivid teaching aids introduced into the classroom, students can not only move the eyes, ears, brain, mouth, and can be operated, both active classroom atmosphere. Make teaching activities gamified. And greatly stimulate the students' interest in learning.

3, can break through the limitations of time and space, it is difficult for students to directly perceive the things and phenomena directly sound and colorful presentation.

4, can improve the efficiency of classroom teaching

Research in educational psychology shows that the human senses. The highest learning efficiency is visual, followed by auditory. In traditional teaching, most of the time by the teacher to speak, students listen, teaching efficiency can not be improved. In terms of memorization, the visual and auditory memory is the most effective. The retention rate after three days reaches 66%. While relying solely on visual three days after the retention rate of only 27%, relying solely on auditory three days retention rate of only 16%. Combining audio and visual will greatly improve the efficiency of classroom teaching.

. Three. The use of teaching aids, should pay attention to,

1, the use of teaching aids should pay attention to the following points,

, 1, so that students can see the process of teaching aids demonstration. At the same time with the explanation, guide students to observe, analyze, think.

, 2, correctly deal with the use of visual aids and the development of students' abstract thinking. Mathematics is characterized by a high degree of abstraction and rigorous logic. Due to the children's age, acceptance of abstract mathematical concepts have difficulties, the need to use visual aids as a means, but can not stay at the level of visualization. Teachers need to analyze and explain and abstract in time. For example, teaching the concept of volume, the teacher showed two glass cups filled with half a cup of water, let the students observe. Cup is not filled with water, the empty part can be called "space". Then put two pieces of iron of different sizes into the cups. Students observed that the water in the cup rose, indicating that the iron to "occupy" the space, and the height of the water rose differently, indicating that the two pieces of iron to occupy the space of large and small. Then let the students give examples of objects occupy space. Thus, the abstraction of the concept of volume.

. 3, visual aids to the appropriate size, color to be sharp. To help focus students' attention.

2, guide the operation of learning aids should pay attention to the following points,

. 1, the use of learning aids should be the right time, the right amount, the right degree. For example. Let the students fold a paper, draw a picture. Represented one-half, ? and other fractions, is to help students establish the concept of fractions. Once students have an understanding of fractions such as one-half, three-quarters, ? and other fractions have knowledge, should guide students to recall the operation of one-half, three-quarters, ? and other fractions is how to get, and then abstract the concept of fractions. If the abstraction is not timely, the pursuit of visualization, will hinder the development of abstract thinking.

, 2. In the process of learning tools. To guide students in time to observe, analyze, compare and master mathematical knowledge. Development of thinking skills.

, 3, in the process of learning aids operation, to pay attention to the development of students' language expression ability. Require students to operate while talking. After the operation, say the operation process, according to the results of the operation. Say the conclusion.

, 4, some learning aids can let students make their own. Such as the production of the prism length is 1 centimeter square. Through the production, you can deepen the students' understanding of the square.