How to talk about class?

Lecture is a new form of teaching and research. It refers to a teaching and research form in which teachers systematically and verbally express their teaching design and theoretical basis for a class (or a unit) in front of judges, peers or teaching and research personnel on a specific occasion, and then the audience comments and the speaker defends, so as to communicate and learn from each other, so as to continuously improve the teaching design. In a narrow sense, lecture refers to the teaching research activities conducted by teachers in the form of oral expression, based on the theory and teaching materials of educational science and aiming at the specific characteristics of a class.

Speaking lessons is a new topic in today's teaching reform and a new form of teaching research. The development of lecture has aroused widespread concern and attention of the majority of leaders and teachers, and injected new vitality and vitality into teaching research. In recent years, there are more and more young teachers in schools, and school leaders attach great importance to the cultivation of new teachers. For a new teacher who has just taken up his post, he can't figure out what to say and how to say it during the lecture. Because there is a certain time requirement for lectures, I only see the speaker "speeding" in a hurry, talking, talking and talking; The audience couldn't keep up with the trip in the fog. It is difficult for this kind of lecture to achieve the expected effect and purpose. In order to help young teachers understand the lecture, let's talk about some personal views on the lecture.

First, get out of the misunderstanding and understand the "lecture" in essence.

1, one of the misunderstandings: giving lectures is just repeating teaching plans.

There is a certain connection between handouts and lesson plans, but there are also obvious differences, so don't confuse them. The lecture notes should be written on the basis of personal study of textbooks, and should not be too long, and the time should be controlled within 10 ~ 20 minutes; The lesson plan only says "how to teach", but the focus of the lesson plan is "why to teach like this". Teaching plan is a summary of the complicated thinking process of preparing lessons for teachers. It is mostly a list of specific teaching processes, a record of the results of preparing lessons for teachers, and an operation plan for teachers to carry out classroom teaching. It focuses on setting the specific content and behavior of teachers in teaching, that is, reflecting "what to teach" and "how to teach".

The lecture focuses on expounding targeted theoretical guidance. Although it also contains the essence of lesson plans (lesson plans are mostly used as first-hand reference materials in the preparation of lecture notes), it is more important to reflect the teaching ideas, teaching intentions and theoretical basis of the lecturers, that is, the core of thinking. To put it simply, the lecture notes should not only accurately state the contents of "teaching" and "learning", but more importantly, specifically explain "why should I teach like this" from the combination of theory and practice. The teaching plan is one-way, while the lecture is three-dimensional and multi-dimensional. The lecture notes are the deepening, expansion and perfection of the teaching plan.

2. Myth 2: Speaking class is to reproduce the class process.

Some teachers have been eloquent in the process of giving lectures, and they are very excited to give lectures to the audience: explaining the difficult points of knowledge, analyzing teaching materials, demonstrating teaching AIDS, introducing blackboard writing and so on. And tell the students what they said to the judges and colleagues sitting below. In fact, if the contents and courses they prepare are for students, it may be a very successful demonstration class. However, lectures are by no means classes. There are substantial differences between the two in objects, requirements, evaluation criteria and occasions, and they cannot be treated equally.

Talking about lessons is the track of teachers' teaching thoughts. How to design the teaching plan, what are the advantages of the design, what is the basis of the design, and what kind of teaching objectives are scheduled to achieve? This is like a feasibility report of a project, not the construction project itself. It can be seen that attending classes is a kind of teaching research activity between preparing lessons and attending classes. It is a deepening and testing of preparing lessons, which can make preparing lessons rational and is a more rigorous scientific preparation for attending classes.

3. Myth 3: The teaching method is too general and the learning method is not standardized.

"Teaching design and teaching of learning methods" is an essential link in the course of lectures. Some teachers can sum it up in one sentence: I use heuristic and intuitive teaching methods, and students use independent inquiry and cooperative discussion. As for how teachers inspire students and how to operate, I won't say much below. Even some teachers misunderstand "learning instruction" as: answering students' questions, cultivating students' habits and simple skill training.

4. Myth 4: "I am poor and white", and there are no auxiliary materials and means in the process of speaking.

Some teachers have neither written speeches nor any auxiliary means during the lecture. Some teachers clearly say that they have designed multimedia courseware to assist teaching, but in the teaching process, they can't see the true face of Lushan Mountain all the time, which makes listeners doubt its authenticity. Therefore, teachers can use some auxiliary means, such as making multimedia courseware, physical projectors, lecture scripts and so on. Explain the lesson clearly and tell it to peers and judges in a limited time.

Second, the basic content of the "lecture".

Mathematics lecture is a professional exchange between mathematics teachers, and its fundamental purpose is to pursue the optimization of mathematics classroom. Preparing lessons well is the premise of speaking lessons. Speaking lessons must be scientifically analyzed and understood from the theoretical height, thus proving that preparing lessons is orderly rather than blind, rational rather than perceptual. What should I say to my peers in math class? I think the content of the math lecture mainly includes the following four aspects:

1, oral teaching material

In teaching, the teacher should first explain his understanding of the teaching materials, because a thorough understanding of the teaching materials can make a more complete teaching plan. Said the textbook includes three aspects:

Analysis of (1) teaching materials. The textbook of any course will form a system from its knowledge content to its arrangement form. To grasp the teaching materials as a whole, it is necessary to make clear the position and role of this topic or chapter in the teaching materials system of the whole school period and a school year. Only by clarifying this point can we attach importance to the internal relationship between the knowledge before and after, accurately identify the key points and difficulties of the teaching materials, and thus improve the efficiency of classroom teaching.

(2) Put forward the specific and clear teaching objectives of this class. The teaching goal is the teaching result to be achieved at the end of a class planned in preparing lessons. The clearer and more specific the classroom objectives are, the more fully teachers understand the lesson preparation and the more reasonable the design arrangement of teaching methods. Attention should be paid to avoiding the cliche that "students can correctly calculate ×× exercises through teaching", and the teaching objectives should be analyzed from four aspects: memory, understanding, mastery and application. When making class objectives, we should also put forward the training objectives of thinking ability and non-intelligence factors, including the infiltration of ideological and moral education and the training objectives of interest habits. The basis of establishing teaching objectives is: first, the provisions of teaching syllabus; Second, the unit chapter requirements; Third, the task of classroom teaching; Fourth, the reality of the teaching object. We should combine these four points and consider them as a whole, and then determine the starting point and end point of teaching, so as to clearly put forward the specific teaching objectives of this lesson.

(3) Analyze the compiling ideas, structural features, key points, difficulties and keys of the textbook. Explain clearly what knowledge points are included in the teaching content of this course, how to show the teaching content through teaching examples, how to match the narrative language of teaching materials with examples, what is the distribution order of examples and exercises, and what are the key and difficult contents.

In addition, on the basis of the regular contents of the above-mentioned "teaching materials", the highlights of teachers' personal thinking can be added. For example, the reorganization and adjustment of teaching materials and the design idea of alternative treatment of teaching materials.

2. Oral teaching method

Mainly explain the question of "what to teach" and the reason of "why to teach these". That is, on the basis of personal study of the textbook, this paper expounds the main characteristics of the teaching content of this lesson, its position, function and connection in the whole textbook, and tells how teachers determine the teaching purpose, goal, emphasis, difficulty and emphasis of this lesson according to the requirements of the syllabus and textbook content. For example, the classroom teaching mode of completing teaching tasks and its theoretical basis; Means and reasons for highlighting key points and breaking through difficulties; Strategies and measures taken to deal with the exercise. What kind of teaching method to choose depends on the teacher's grasp of the characteristics of teaching materials and students' cognitive laws, but no matter which method is adopted, the principles of "enlightening", "highlighting subjectivity" and "paying attention to thinking gender" should always be implemented. Therefore, the lecturer should proceed from reality and choose the appropriate teaching methods. In addition, with the deepening of teaching reform, new teaching methods should be creatively used.

3. Speaking and learning methods

Talking about learning methods should not stop at introducing learning methods, but should focus on how to implement the guidance of learning methods. Mainly explain the truth that students should "how to learn" and "why to learn like this". It is necessary to explain how teachers can stimulate students' interest in learning, mobilize positive thinking and strengthen students' initiative consciousness; It is also necessary to talk about how teachers guide students to learn according to the characteristics of grades and the age and psychological characteristics of students. Especially in today's new curriculum reform, changing students' learning style and advocating a learning style characterized by "active participation, willingness to explore, exchange and cooperation" is the top priority of this new curriculum reform, which will also become the "baton" for all our teachers. To learn how to learn, we must first study students deeply, deal with the relationship between teachers and students in classroom teaching, and rearrange the position of teachers and students. To change the old teaching mode of "you ask me and answer me", the teacher speaks on the podium, his facial expression is dull, "I speak and you listen", and the scholar sits below. Secondly, we should pay attention to the explanation of the guiding process of a method, such as how teachers design situations, what good study habits students have developed in what activities, and what scientific learning methods have been realized, that is, not only let students "learn", but also let students "learn" and "enjoy learning".

4. Talking about teaching procedures

The basic connotation of the teaching process is the classroom structure, which should be the essence and climax of the whole process of teachers' lectures. It is said that the teaching process is the key link of the lecture, because only through the analysis of this process can we see the unique teaching arrangement of the lecturer, which embodies the teacher's teaching thought, teaching personality and style. Only by expounding the design of teaching process can we see whether the teaching arrangement is reasonable, scientific and artistic. Usually, the following questions should be clarified in the teaching process.

1, teaching ideas and teaching link arrangement. Instructors should explain their understanding and treatment of teaching materials according to the students' reality, and organize the basic teaching ideas by what teaching means. It is said that the basic links of design in the teaching process should be made clear in the teaching procedure. But the specific content only needs a brief introduction, as long as the listener can clearly understand "what to teach" and "how to teach". You can't talk according to the teaching plan like giving lessons to students. It should also be noted that when introducing the teaching process, we should not only talk about the arrangement of teaching content, but also explain the theoretical basis of "why to teach like this" (including syllabus basis, curriculum standard basis, teaching method basis, pedagogy and psychology basis, etc. ).

2. Explain the arrangement of bilateral activities between teaching and learning. This paper expounds how to use modern teaching concepts to guide teaching, how to embody the harmonious unity of teachers' leading role and students' main activities, the harmonious unity of teaching methods and learning methods, the harmonious unity of knowledge imparting and intelligent development, and the harmonious unity of moral education and intellectual education.

3. Explain the handling of key points and difficulties. It is necessary to explain how to highlight the key points, solve the difficulties and use what methods to solve the difficulties in the teaching process.

4. Explain what teaching methods are used to assist teaching. When and where to use it, and why?

5. Clarify the blackboard design and design intention of the subject.

When talking about teaching procedures, we should also pay attention to the use of summary and report language, do not copy the teaching plan directly, and use the original words of teachers and students in class as little as possible to reduce the length of records.

Third, the methods and skills of teaching.

1, say "quasi" textbook; 2. Say "Ming" teaching method; 3, say "will" learn the law; 4. Say "clear" teaching intention; 5. Say "clear" training level.

Fourth, the basic principles of lecture

According to modern teaching philosophy and methodology, successful lectures should follow the following principles:

1, incisive reasoning and outstanding theory.

Lectures are not about preaching teaching plans, nor are they about concentrating the classroom teaching process. The core of the lecture lies in reasoning and explaining "why to teach like this". Because there is no teaching practice under the guidance of theory, I only know what to do and don't know why to do it. It will always be experiential teaching, which can only be costly and inefficient. Therefore, teachers must seriously study the theory of education and teaching, take the initiative to accept the new information and achievements of education and teaching reform, and apply them to classroom teaching.

2. Objective reproducibility and operability.

The content of the lecture must be objective, true, scientific and reasonable, not mysterious and difficult to understand, and not mechanically copy some professional terms of education and teaching theory. To truly reflect how you did it and why. Even if it is unscientific and incomplete, it should be said truthfully. Arouse the listener's thinking, form * * * knowledge through mutual learning, and then improve the speaker's teaching design.

Lectures serve classroom teaching practice, and every step of lectures should be operable. If lectures are just for the sake of speaking and cannot be implemented in actual teaching, it is empty talk and boasting, which makes lectures a mere formality.

3. Informal and flexible

Lectures can be conducted according to the content of a class, or around a unit or a chapter; You can talk about the determination of goals, the choice of teaching methods, the guidance of learning methods and all the contents of the program at the same time, or you can just talk about one of them, or you can just talk about how a concept is derived, or how a law is drawn, or how to demonstrate the design of experiments, etc. It is not easy to say that the Lord does not say twice, the big one is not small, the thin one is not thick, and it is difficult; In the future, we should adhere to the principle of long words, short words and informal sections to prevent dogmatism. At the same time, as long as we reflect the characteristics of teaching design and show our teaching expertise.

Attachment: Draft lecture series (first class)

The topic I want to talk about today is "sequence (first class)"

Firstly, the structure and content of the textbook are briefly analyzed.

The position of this section in the whole book and chapters: "Series (the first category)" is the first section of the third chapter of the first volume of the new mathematics textbook for senior high school. Sequence is the content immediately after function in Chapter 2. A sequence is a function whose domain is a set of positive integers (or its finite subset). When the independent variable takes the value from small to large, it corresponds to a series of function values. It plays a connecting role in teaching materials. On the one hand, it can deepen students' understanding of the concept of function, so that they can not only understand the function with continuous change of independent variables, but also understand the function with discrete change of independent variables. On the other hand, we can study some problems of sequence in a changeable and intuitive way from the perspective of function, so as to further understand the essence of sequence. Sequence has a very wide range of practical applications; Sequence is also a good subject to cultivate students' mathematical ability. Therefore, sequence is one of the important contents of high school mathematics.

Analysis of mathematical thinking method: As a mathematics teacher, we should not only teach students mathematical knowledge, but also teach students mathematical thinking and mathematical consciousness. Therefore, this class tries to show students mathematical thinking methods such as observation, induction, analogy and association.

Second, the teaching objectives

According to the analysis of the structure and content of the above textbooks, and taking into account the psychological characteristics of students' existing cognitive structure, I have formulated the following teaching objectives:

1, basic knowledge goal: to form and master the concept of sequence and understand the general formula of sequence. And through the comparison of sequence and function, we can deepen our understanding of sequence.

2. Ability training goal: to cultivate students' general methods such as observation, induction, analogy and association.

3. Emotional goal: let students feel the fun of learning in democratic and harmonious activities.

Three. Teaching emphases, difficulties and keys

In line with the curriculum standards, on the basis of thoroughly understanding the teaching materials, I think this lesson is the first lesson of this chapter and the basis for students to learn this chapter. To learn the knowledge behind this chapter well, we must first master the concept of sequence, and then the general formula of sequence is the soul of arithmetic progression and geometric progression, so I think the concept of sequence and its general formula are the focus of teaching. From the special to the general, from the phenomenon to the essence, students are required to observe, summarize, analogy and associate a general term formula of a series from the previous items or adjacent items. Students must find out the relationship between the general term an and the number n through their own efforts, which requires students' ability. So I think it is difficult to establish the general term formula of series. I think the key to teaching is to teach students to overcome difficulties. The method is to let students learn to observe the characteristics of the first few items of the series and reveal the changing law of the series through observation and comparison.

Next, in order to clarify the key points and difficulties, so that students can achieve the teaching objectives set in this section, I will talk about teaching methods and learning methods:

Fourth, teaching methods.

Mathematics is an important subject to cultivate and develop people's thinking. Therefore, in teaching, students should not only "know why" but also "know why". In order to reflect the students' development-oriented, follow the students' cognitive rules and embody the teaching principle of gradual and heuristic, I designed such a teaching method: under the guidance of teachers, I created scenarios, inspired students to think through the setting of open questions, and experienced the mathematical methods involved in the formation of mathematical concepts in thinking, so that they could get their inner feelings.

V. Studying law

We often say: "Modern illiterates are not illiterate people, but people who have not mastered learning methods", so we should pay special attention to the guidance of learning methods in teaching. With the promulgation and implementation of the Outline of Basic Education Curriculum Reform (Trial), the curriculum reform has formed a good trend from point to surface and gradually spread out. Among them, changing students' learning style is one of the focuses of this curriculum reform. One of the specific objectives of the curriculum reform is to "change the current situation that the curriculum implementation places too much emphasis on learning, rote memorization and mechanical training, advocate students' active participation, willingness to explore and diligence, and cultivate students' ability to collect and process information, acquire new knowledge, analyze and solve problems, communicate and cooperate". Mathematics is one of the core courses of basic education. Changing students' mathematics learning style is not only conducive to improving students' mathematics literacy, but also conducive to promoting the change of students' overall learning style. Guided by constructivism theory, supplemented by multimedia means, heuristic teaching methods based on students' exploration and research are adopted to discuss and summarize with teachers and students. In the classroom structure, according to the students' cognitive level, I designed six levels of learning methods: ① Creating situations—introducing concepts—observing and inducing—forming concepts—discussing and researching—deepening concepts—instant training—consolidating new knowledge—summarizing and reflecting—raising awareness—postponing tasks—exploring independently, interlocking and deepening at different levels, thus successfully completing the teaching objectives.

Next, I will talk about the teaching process of this course in detail:

Six, teaching procedures and ideas

(A) the creation of situations-the introduction of concepts

I often think: why have our students been not interested in mathematics for a long time, or even afraid of it? One of the important factors is that mathematics is too far away from the reality of students' lives. In fact, mathematics learning should be combined with students' life. Starting from students' life experience and existing knowledge background, let them discover mathematics, explore mathematics, understand and master mathematics in their lives.

1, introduced by specific examples of series in life:

A, time: clock, calendar b, plant: plant stem

2. The introduction of ancient legends about chess accords with the characteristics that senior one students like to explore novel and mysterious things. It is beneficial to stimulate students' interest in learning.

(B) observation and induction to form a concept

Get a few columns from examples, and then design purposefully, such as natural numbers, reciprocal of natural numbers, even numbers greater than zero, switches (0, 1, 1, ...), "one foot pestle, take half every day, never exhaust." And from 1984 to 2004, the number of gold medals won by China athletes in the six Olympic Games were 15, 5, 16, 16, 28 and 32 respectively. The teacher guides the students to summarize the new knowledge of this lesson: the definition of sequence.

Discussion and research-deepening the concept

Before class, I carefully designed several series, including finite series, infinite series, increasing series, decreasing series and constant series, waiting for students to master the above concepts through observation, discussion and communication. Related concepts of series: each number in a series is called an item of the series, followed by the first item (the first item), the second item, … the nth item, …. The general form of the sequence can be written as: a 1, a2, a3, …, an…, abbreviated as {an}, where an represents the nth item of the sequence.

Then guide the students to observe the relationship between the items in the above series and the number of items. If the relationship between the nth term an of the series {an} and the serial number n can be expressed by the formula an = f (n), then this formula is called the general term formula of this series.

Finally, through the comparative study of series general formula and resolution function, students can draw the conclusion that the image with series general formula an = f (n) is a group of isolated points.

In the series, there is a corresponding relationship between the number of terms n and the term an. If the number n is regarded as an independent variable, then this series can be regarded as a function of natural number set (or its finite subset {1, 2,3, ... n}) as its domain. When the independent variable takes the value from small to large, it corresponds to a series of function values. The general term formula of sequence is also the analytical formula of corresponding function. When we regard the abscissa of rectangular coordinate system as n term and the ordinate as an term, the obtained image is a group of isolated points.

Instant training-consolidating new knowledge

In order to deepen students' understanding of knowledge, so as to achieve the effect of consolidation and improvement, I specially designed a set of instant training questions, integrating examples from textbooks into instant training questions, and consolidating new knowledge through students' observation, discussion and research, as well as teachers' guidance.

Summary and reflection-raising awareness

Ask the students to summarize the main contents of this lesson: (1) series and its related concepts; ⑵ Find any item according to the general formula of sequence; ⑶ Find the general term formula of the sequence according to some adjacent terms of the sequence; (4) The relationship between sequence and function (sequence is a special function). Through the summary of knowledge content, let students transform the knowledge taught in classroom teaching into students' quality as soon as possible; Through the summary of mathematical thinking methods, students can understand the position and application of mathematical thinking methods in solving problems more deeply, and gradually cultivate students' good personality quality goals.

(vi) Deferred mandate-independent investigation

After the study of the above five links, students have mastered the general method of exploring the law of sequence, which needs to be further improved. Therefore, according to the differences of students' quality, I designed layered training questions to let them explore independently after class, to let students master the basic knowledge, and to improve students with learning ability, so as to achieve the goal of top-notch and "burden reduction".

Seven, briefly describe the blackboard design.

End: Above all, I only explained "what to teach" and "how to teach" from the aspects of teaching materials, learning situation, teaching methods, learning methods and teaching procedures, and made clear "why to teach like this". I hope that all the experts and leaders will put forward valuable opinions on this lecture.