Lecture 1: How to prepare lessons
What should I pay attention to when preparing lessons?
1. Where to? -designing teaching objectives. We should focus on the concept of curriculum standards and design teaching objectives according to our teaching materials. Our goal is where we are going and what is our direction?
2. Where are we? Pay attention to students' reality. That is, pay attention to students' existing knowledge base and life experience. What do the students already know? What difficulties and problems do they have, and what ways and methods do they prefer to learn knowledge? We should pay attention to all these.
3. How to get there-writing teaching design. Design teaching process and teaching links.
4. Have you arrived yet-self-reflection. Can this design achieve our teaching goal?
What is the important basis for preparing lessons?
The important basis for preparing lessons is curriculum standards, teaching materials and students. In other words, the design is based on the content of teaching materials, the requirements of curriculum standards and the reality of students.
Now let's talk about how to prepare lessons from the following three topics:
First, how to design teaching objectives and teaching contents according to the requirements of curriculum standards and textbooks.
The basis for determining teaching objectives is curriculum standards and teaching materials. (regardless of the current situation of students' foundation)
Three-dimensional target:
Knowledge and skills: the key words to describe this goal are knowing, understanding and flexible use.
Process and method: The key words to describe this goal are experience (feeling), experience (experience) and exploration.
Emotional attitude and values: mainly refers to curiosity, thirst for knowledge, self-confidence, successful experience, will to overcome difficulties, scientific and rigorous attitude, habit of questioning and independent thinking, and understanding the connection between mathematics and real life.
Some teachers have heavy classes, mainly designed according to three-dimensional goals, so the classes are full.
Video lesson: the "circle" clip of Mr. Sun from the primary school affiliated to Peking University.
The teaching goal of this class is not only to know how to calculate pi and pi. It also pays attention to students' exploration process, the infiltration of mathematical thinking methods, such as extreme thinking, turning joy into straightness, etc. It not only pays attention to the level of subject knowledge, but also pays attention to mathematical thinking and methods, and the cultivation of students' scientific inquiry attitude and scientific research consciousness is also in place.
How to determine three-dimensional goals according to curriculum standards and teaching materials?
1. How to implement knowledge objectives? When preparing lessons, look at what knowledge the textbook has, think about what requirements the curriculum standards have in this respect, interpret the contents of the textbook with the ideas in the curriculum standards, and design the teaching objectives. Teacher sun's knowledge goal in class is not very consistent with the original, not only to let students know what is the circumference formula of a circle? In other words, students should not only understand and master the formula of pi, but also explore the relationship between the circumference and diameter of a circle, which puts mathematical activities on how to discuss pi, and the knowledge goal falls on the understanding of the meaning of pi. As a teacher, we should deeply understand the textbook and the editor's intention, and design the teaching objectives by grasping the core concepts and essential problems of mathematics. It is easy to grasp the knowledge goal. You can know what you have mastered by reading textbooks. We mainly think about how to make students understand, and then dig behind.
2. How to achieve the process and method objectives? The method and process of inquiry are often more important than simply acquiring knowledge. Paying attention to process and method is a problem that teachers need to solve hard. In the process of exploring pi, teachers give students a platform to explore, feel and discover, which lays an important foundation for the formation of students' scientific inquiry attitude and methods, rather than a superficial understanding of knowledge. According to the relationship between the length and width of a rectangle and the circumference of a square, let students explore whether the circumference and diameter of a circle are also fixed through measurement and calculation. Teacher Sun didn't rush to the conclusion of pi, but helped students analyze the causes of measurement errors. In the process of analyzing the mistakes, the students put forward better methods to solve the problems. The teacher asked: What should I do? The students also said very well, "Take more tests". In particular, a classmate suggested that it is a statistical idea to measure several times to calculate the average value, and the average value is used to describe the overall state of a group of data. Circumcision embodies the idea of limit. In the process of leading students to explore pi, Teacher Sun gave them a platform for exploration and discovery. It is far more important than letting students acquire the knowledge of pi or knowing that pi is about 3. 14 times the diameter. Why? Because it undoubtedly laid an important foundation for the formation of students' attitude and method of scientific inquiry. The teaching objectives of mining process and method can be considered in this way, such as parallelogram area teaching. Many teachers think like this: What do students already know? Knowing the area of a rectangle, what else do you need to know now? Now we need to know the area of the parallel polygon. How do you know? At this time, I thought of the mathematical thinking method of transformation; Numbers and algebra, we thought: What can we do in this section to cultivate students' sense of numbers and symbols? Space and graphics, we should cultivate students' concept of space; Statistics and probability, we just want to cultivate students' statistical consciousness, and so on. That is, how to implement the concept of curriculum standards according to teaching materials.
In each learning section, the standard arranges four learning fields: number and algebra, space and graphics, statistics and probability, practice and comprehensive application. The study of course content emphasizes students' mathematical activities and cultivates students' sense of number, symbol, space, statistics, application and reasoning. There are also some requirements for process methods and mathematical thinking methods.
The sense of number is mainly manifested in: understanding the meaning of number; Numbers can be expressed in many ways; Be able to grasp the relative size relationship of numbers in specific situations; Able to express and exchange information with numbers; Can choose the appropriate algorithm to solve the problem; Can estimate the result of operation and explain the rationality of the result.
The sense of symbol is mainly manifested in: it can abstract the quantitative relationship and changing law from specific situations and express it with symbols; Understand the quantitative relationship and changing law represented by symbols; Will be converted between symbols; Can choose appropriate programs and methods to solve the problem of symbol representation.
The concept of space is mainly manifested in the following aspects: geometric figures can be imagined from the shape of an object, and the shape of an object can be imagined from the geometric figures, and the geometric body and its three views can be transformed from the unfolded diagram; Can make three-dimensional models or draw graphics according to conditions; Can separate basic graphics from more complex graphics, and can analyze basic elements and their relationships; Can describe the movement and change of physical objects or geometric figures; Can describe the positional relationship between objects in an appropriate way; Can use graphics to describe problems vividly and use intuition to think.
The concept of statistics is mainly manifested in: being able to think about problems related to data information from the perspective of statistics; Be able to make reasonable decisions through the process of collecting data, describing data and analyzing data, and realize the role of statistics in decision-making; Can reasonably question the source of data, the method of processing data and the results obtained from it.
Application consciousness (mainly problem solving) is mainly manifested in: recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in the real world; In the face of practical problems, we can actively try to use the knowledge and methods we have learned from the perspective of mathematics to find strategies to solve problems; When faced with new mathematical knowledge, we can actively look for its actual background and explore its application value.
Reasoning ability (mainly to explore new knowledge and use knowledge to judge and reason) is mainly manifested in: being able to obtain mathematical guesses through observation, experiment, induction and analogy, and further verify, prove or cite counterexamples; Be able to express your thinking process clearly and methodically, and be reasonable and well-founded; In the process of communicating with others, I can discuss and ask questions logically in mathematical language.
3. How to implement the goal of emotional attitude and values? Emotion, attitude and values should be organically infiltrated into the teaching process and naturally integrated with other goals. Some teachers' emotional, attitude and values goals are like labels, which are completely compiled for the goals and cannot be implemented in the teaching process. Even some teachers have no goals of emotion, attitude and values at all, but have goal designs that focus on one thing (knowledge goal) and two things (desalination process and method goal) and three things (no goals of emotion, attitude and values), and two or three goals are precisely the goals that embody the concept of the new curriculum standard. Like the teaching of pi, teachers usually introduce Zu Chongzhi and find that pi is between 3.1415926-3.1415927, and then ask: How do you feel? Students say that our Chinese nation is great, and Zu Chongzhi is great, as if they love the nation without any worries. See how Teacher Sun implements the goal of emotional attitude and values. When he introduced historical facts, he did not mention Zu Chongzhi alone. First of all, he told everyone that the constant of scientific inquiry did not come from China, but from Archimedes, who introduced history objectively. Then, he introduced Liu Zheng with the combination of numbers and shapes, and introduced Liu Zheng with a small courseware. He asked the students; You said it was wrong. Is there any way to explore the relationship between the length and diameter of a circle? Under the background of such problems, the students are very focused. He introduced Liu Zhenghe's circumcision, and the third one talked about Zu Chongzhi. How did he get Zu Chongzhi out? He said that Zu Chongzhi stood on the giant arm of his predecessors, and today he made brilliant achievements in making the numerical value accurate to the seventh place after the decimal point. Why did he introduce it like this? Zu Chongzhi did not rise from the ground, and a scientific exploration needs a long and arduous process. He added: Later, many Chinese and foreign mathematicians worked hard, and some of them came to the conclusion that pi is an infinite acyclic decimal after a lifetime of exploration and proof. Teacher Sun's four-level introduction is not a simple introduction to the historical facts of pi, but an objective and fair introduction to history. In the process of introducing history, students not only learned about China's mathematical culture, but also talked about human's pursuit of truth. The pursuit of perfection is endless. He is telling students with his heart that the road to exploration in the future is still difficult. You should keep pursuing it. We are latecomers, and we have historical responsibilities. I think this kind of education is to moisten things and enter students' hearts silently. The three-dimensional goal is not isolated, but you have me and I have you, which is very well integrated.
The teaching goal of Zhang Qihua cognitive score;
1. Make students know the scores preliminarily and learn to compare the scores with intuitive methods.
2. Let the students know the names of each part of the score and read and write the score that represents a score correctly.
3. Combine observation, operation, comparison, association and other activities to enrich students' experience in mathematical activities, guide students to exchange the achievements of mathematical thinking with their peers, and gain positive emotional experience.
4. Make students realize that mathematics comes from the actual needs of life, feel the connection between mathematics and life, and further develop their curiosity and interest in mathematics.
Where 1 and 2 are the goals of knowledge and skills, the third is the goal of process and method, and the fourth is the goal of emotional attitude and values.
Let's sum up: how to set teaching objectives;
The important basis for preparing lessons is curriculum standards and teaching materials, and a comprehensive understanding of curriculum standards.
Respect teaching materials, understand teaching materials, use teaching materials creatively, and fully tap curriculum resources.
Grasp the three-dimensional goal as a whole and cannot be separated.
Different teaching objectives will produce different teaching designs and teaching effects.
Second, how to analyze students and determine the teaching methods and methods of a class.
Our curriculum concept puts forward that students' development should be the foundation and our teaching should serve students' development. The starting point and destination of all teaching are students, not to lower the goal to adapt to students, but to design our classroom teaching according to students' learning reality and lead students to achieve our teaching goals.
It's important to know students. Know what? Whether you blame it or not can be understood from four aspects: First, what is a student? What knowledge background and life experience do students have? For example, if a student wants to learn fractional division, he already knows integer division. How to consider life experience, we should consider whether life experience is helpful for students to learn mathematics, such as decimal addition. It is easier for students to figure out what 1 yuan 2.3 points +2 yuan 3.6 points is. They have such life experience, but it is easy to make mistakes when calculating 1.23+2.36. At this time, with the help of yuan, jiao and Dian, it is not easy to make mistakes, that is, prepare lessons. Second, we should know what students don't know. In other words, in what aspects do students have difficulties? Don't repeat what students already know. What students don't know needs teachers to explain or guide students to explore. Third, what do students want to know? That is, students' interests and needs. When preparing lessons, teachers should think about what content or methods students are interested in and what needs they have. For example, what is the significance of the distribution of pre-class ratio? Why are you learning this? The introduction of new lessons has a great relationship with the cultivation of students' interest and their desire to explore this lesson. You don't understand, son. If you teach with the eyes of adults and the idealized things of teachers, students may turn a blind eye to some wonderful problems. Faced with materials that you think are good, students may get bored. There is a generation gap between teachers and students. Nowadays, teachers often treat students with their own experience. How did I go to school at that time, or later teaching changed my own experience, thinking that I learned this way, and so did the students. In fact, this is not the real situation of students. Fourth, we should know what methods and ways students like to learn mathematics. Hands-on operation, independent inquiry and mathematical activities are students' favorite learning methods.
How to understand students? 1. Classroom observation, the observation of students' learning situation, learning attitude and learning effect, is an important channel to understand students. Teachers should feel every change of children in the classroom with their heart. 2. Questionnaire survey. For example, how many students know pi through questionnaires before teaching pi? How many students can find the circumference of a circle? 3. Homework feedback. See what students have mastered better and what problems exist through homework. Homework design is very important, and it is necessary to comprehensively test the knowledge, skills and goals of a class. 4. Interview between classes to find out what students need. After class, the teacher talked with the students and caught several questions. What do you think of this course?
What if the students know?
When a teacher was teaching multiplication of 9, he made careful preparations before class, but the students became less and less interested. After class, she interviewed two students: Son, how do you feel after this class? The student replied: I can recite the multiplication formula of 9, and the class is a bit boring. Teacher: Then how did you get your multiplication formula 9? Health: My parents are tutoring me. The teacher asked himself in his mind: Can students really learn? How far will they go? The teacher tested another class that had not been taught, and the statistical results are as follows:
Percentage of classified population to total population
All written to 25 people, 56.8%
5 people who have written all of them, but their expressions are not standardized 1 1.4%
Write most (to 69 or 79) 1 1 25%
Write a few 3 6.8%
Are we going to teach such a course that most students know? What should be taught to students? What students learn belongs to rote learning, for example, the formulas of 5945 and 6954 are easy to be confused, and the formulas of 79, 89 and 99 are unclear. Faced with this situation, teachers should guide students to memorize formulas and apply them to solve practical problems. Teachers adjust their teaching ideas as follows: first, let students freely say the multiplication formula of nine, then lead students to study the formula, remember the formula by finding the method and practicing with their fingers, and finally apply the formula.
Let's take a look at the teaching clips after the teacher adjusted his teaching ideas. (video clip of multiplication formula of nine), teachers should teach where students need to teach, so as to be conducive to the development of students.
What will students not do for more difficult content?
Let's watch a teaching video (two practical problems of two-step calculation with known conditions 1).
It's really difficult for students to have problems. What adjustments have been made to the teacher? She set up a scaffold for students, and guided them to explore by drawing pictures, which is a relatively intuitive method, to help students understand this 8. It takes twice. Let's take a look at her adjusted teaching video. (Practical Problems of Two-step Calculation 2)
The teacher used the line graph and tree technique graph to let the students intuitively understand the quantitative relationship of the two-step application problem and why they used 8 twice. If students' problems are found, they should be redesigned. When redesigning, you should design practical teaching methods according to students' actual problems. There are of course other methods besides graphic method. Different classes, different teaching contents and different teaching methods, such as operation, demonstration and so on. In short, practical teaching methods should be adopted according to the teaching content and the needs of students.
It's important to know the students, knowing what they know and what they don't know. We should set up a scaffold for them, such as charts, calculations and demonstrations, to help students with difficulties understand basic mathematical concepts and quantitative relations. After understanding the students, the teaching design is carried out.
How to set feet and hands?
1. Make good use of materials. 2. Create a good situation. 3. Give students a platform for independent thinking. 4. Give students a chance to communicate.
Understanding students is an important prerequisite for us to prepare lessons well. Students are the starting point and destination of all teaching.
Third, how to design teaching plans and determine the teaching process and links of a class.
How to determine the teaching process and teaching links of a class? Let's take the new teaching practice class as an example to talk about how to carry out teaching design.
New teaching
The traditional new teaching consists of five links, which are called five-step teaching method, review, Protestantism, consolidation exercise, summary and assignment. Under the new curriculum concept, how to continue to innovate and develop on the basis of previous good experience? The new curriculum pays great attention to students' learning process. Should we also pay attention to students when designing a class? How to pay attention to students and design their activities? What changes have taken place in the classroom teaching process?
1. Situation creation. Some experts say: Situational creation is a load-bearing wall. Not dispensable.
2. Mathematical activities. Including students' inquiry, cooperative learning and teachers' explanation. What the teacher said in the past has become a process of mathematical activities in which teachers and students explore and communicate with each other.
3. report and exchange. After group discussion and individual independent thinking, the whole class communication and communication process is once again an interactive time. Students listen carefully to others' views, accept others' views and correct their own.
4. Expand the application. Apply the mathematical knowledge gained in the exploration to solving problems.
5. Class summary.
6. assign homework.
These are all new ideas that inherit and develop traditional teaching methods on the basis of original experience.
How to design the teaching process of a class? Let's look at a lesson first (a video clip of the teaching of "Numbers with Letters" by Zhao Dong, a teacher at Changping Central Primary School)
Teacher Zhao Dong's class focuses on the essence of mathematics, focusing on the creation of situations, students' learning methods and students' learning activities.
What should we pay attention to when designing a new class?
1. Situation creation is very important. The box created by teacher Zhao Dong is in excellent condition. What's so good about it? There are several characteristics: First, it is close to students' life and students like it. Second, it has the taste of mathematics. The input is a number, and the output is also a number, which is directly related to mathematical problems. Third, students can extract math problems from situations. When students see the input number and output number, they will immediately think: How did this output number become? How did it become such a number? Fourth, it can promote students' development and is challenging. Students are curious and want to explore in this situation, so they must find a way to solve it. What is the relationship between the output number and the input number, and how to express it?
Situational creation has become a beautiful landscape of mathematics classroom teaching reform.
Creating a situation should take into account students' interests, be mathematical and challenging, reflect the situation of mathematical thinking and activities, and be meaningful.
Add one more thing:
Life situation: It is also possible to bring children with real life and realistic and interesting life situations closely related to study materials and mathematics in life.
Cognitive conflict situation: asking an interesting question at the beginning of class is like throwing a boulder on a calm lake, causing ripples in students' thinking and asking questions. What's going on here? You must explore.
The situation of knowledge transfer: the situation created according to the development of mathematical knowledge,
Fairy tale situation: presenting mathematical problems in fairy tales.
In short, the creation of situations should serve teaching and mathematics learning, and its effectiveness is particularly important.
2. Grasp the essence of mathematics and reflect the formation process of knowledge. In Zhao Dong's "Representing Numbers with Letters", the teacher always grasps the meaning of representing numbers with letters. The magic box inputs a set of numbers and comes out with another set of numbers. You always go in and out one by one like this, and students will find that the numbers entered on the left are arbitrary, while the numbers output on the right are not random, but are regular and constantly changing. At this time, letters appeared, which highlighted the role of letters.
3. In teaching design, we should pay attention to mathematical thinking methods. For example, there is a one-to-one correspondence between a series of numbers input on the left side of the magic box and a series of numbers output on the right side. Through one-to-one correspondence, it is actually the function idea of middle school, which the teacher has not talked about, but is actually contained in it. Students will be the easiest to understand when learning functions.
4. In teaching design, to highlight a main line is to highlight key points and break through difficulties. What's the point of using letters to represent numbers? Letters are used to express the meaning of numbers. Through the game of the magic box, the students are exploring: how can I express the output numbers in the simplest and most common way? The teacher asked the students such a question. Students use their own methods to express the number of inputs and the number of outputs, and this method is diverse, so there will inevitably be collisions and exchanges. What the teacher has done particularly well here is to use students' mistakes as resources, so that this key point can reach a breakthrough point, and the difficulty can reach a breakthrough point, so that students can understand that the formula containing letters can not only represent a number, but also a quantitative relationship, with the emphasis on knowledge. The difficulty is considered from the cognitive perspective of students. It may be difficult for students to learn this problem, that is, to find the key points and break through the difficulties. When a teacher designs a class, as long as he is careful, flowers are everywhere.
Practice class
How do we usually have practice classes? Arrange the students to do exercises, comment on the students' problem-solving situation after they finish, and then practice. We turn the practice class into a problem-solving class and an error-correcting class. Teachers have no passion and students are not interested. Let's take a look at the video clip of teacher Wang Wei's "practice class of addition and subtraction within 100" in Beijing primary school.
Teachers create queues for students, then describe them as little soldiers, let them find friends with each other, and make students very motivated, active and interested. Whether it is a practice class or a review class, it contains the teacher's careful design, queuing for numbers, and a certain law permeates it. Some laws are related to the teaching of this class, so it is revealed through students' eyes that some laws are not directly related to this class, but they are a kind of gestation. For example, with the expansion of its digital team, there is actually a group of arithmetic progression, but teachers respect students' cognitive ability. Finally, the teacher concluded by encouraging the students to say that there are many secrets in the digital family, and you can only discover them by mastering solid skills. Practice class should not only consolidate the effect, but also have the effect of further development. Looking for friends such as 16, 19, 35 unconsciously reviewed the relationship between addition and subtraction. The position of the big ruler to find the number is very intuitive to the interval between two numbers, which cultivates students' sense of number.
Practice class is not a simple skill exercise of repeating old knowledge. It should be novel, interesting and challenging, pay attention to the creation of situations, the implementation of basic knowledge and skills, further infiltrate mathematical thinking methods, pay attention to the comprehensive application of knowledge, and cultivate students' ability to solve problems.
Summary: How to prepare lessons well?
1. Determine the teaching objectives and contents according to the curriculum standards and teaching materials. 2. According to the students' reality, determine the teaching methods and means. 3. Carefully design the teaching process and write lesson plans.
Now let's talk about the basic framework of preparing lessons for three classes.
The new teaching plan should be changed: teaching content (textbook), teaching goal (three-dimensional), teaching focus, teaching difficulty, teaching preparation, teaching process and blackboard design.
The exercise lesson plan should include: teaching content (textbook), teaching objectives (three-dimensional), teaching preparation, teaching process [new lesson review, organization exercise (basic exercise-comprehensive exercise-expansion exercise), summary and evaluation].
The lesson plan of a structured review class should include: teaching content (textbook), teaching objectives (three-dimensional), teaching preparation, teaching process [arrangement and review, practice and practice (consolidating applied knowledge, infiltrating mathematical thinking methods, paying attention to the challenges of mathematical problems), summary and evaluation, blackboard design].
Teaching reflection: each unit has a comprehensive reflection, reflecting on the teaching situation of a unit, summing up successful experiences, analyzing existing problems, and thinking about measures to improve teaching in the future.
According to the query information of Fujian Putian Education Network, the admission of students ma