A case is a description of the actual situation, which contains one or more difficult problems and may also contain solutions to these problems. Teaching cases describe teaching practice, and show people some stories containing typical behaviors, thoughts and feelings of teachers and students in rich narrative forms. The case of primary school mathematics teaching should describe the typical vivid communication state and external behavior of teachers and students in the classroom teaching situation of primary school mathematics, and portray their rich and delicate mental state and inner world.

Second, the characteristics of primary school mathematics teaching cases

1, authenticity of materials

The case should reflect a real event, that is, it describes real people, true feelings and insights, and should stimulate everyone's thinking.

2. Typical selection of materials

The case of primary school mathematics teaching describes a typical mathematics teaching case, which should have a complete plot from beginning to end and contain some dramatic conflicts, mainly focusing on the conflicts between mathematics teachers and students, and between students and students' mathematical thinking.

3. Specific circumstances

The narrative of primary school mathematics teaching cases should be specific and special, and it should be able to vividly describe mathematics teaching and students' mathematical thinking activities. For example, reflecting a bilateral activity between a math teacher and a student around a specific math teaching goal and specific math teaching content should not be an abstract summary description of the overall characteristics of the activity, but a detailed and interesting description of the specific plot of the bilateral activity.

4. Spatio-temporal extensibility

The description of primary school mathematics teaching cases should put the cases in a time-space framework, that is, explain the time and place of the events. The description of the case should be placed in the real life scene, which makes people feel immersive.

5, the goal is comprehensive.

Behavior description in primary school mathematics cases should reflect the characteristics of teachers and students' teaching and learning, cover all teaching objectives and reveal the inner world of characters. Such as thinking activities of mathematics cognition, attitude and emotion towards teaching, motivation and need of learning mathematics, etc.

Third, the function of primary school mathematics teaching cases

The writing cases of primary school math teachers have the following functions:

1. Recording function-Case writing provides an opportunity for primary school math teachers to record their teaching experience. Case writing is actually a record of some puzzles, joys, problems and so on in the teaching profession. If a math teacher mainly shows his life value in class, in school and in communication with students, then the case is a record of the light of the teacher's life to a certain extent. In the case, there is the teacher's emotion and infinite vitality. Cases can reflect the evolution of education, on the one hand, as a reflection of personal development history, on the other hand, as a process of educational reform under the social background.

2. Guiding function-case writing can make primary school math teachers more deeply aware of the key and difficult points of their work. The fact that can become a case is often a lingering problem or unforgettable event in the work of primary school mathematics teachers. If writing cases has become a habit and a way of working, then with the increase of case materials, you will gradually find out where the difficulties are in your work and what the direction of future efforts is.

3. Reflective function-Case writing can promote primary school math teachers to reflect on their own behavior and improve the professional level of teaching. If reflection is regarded as an organic part of mathematics teaching, rather than impulsive or year-end behavior, it can greatly promote the professional development of primary school mathematics teachers and upgrade them to professional level.

4. Communication function-The case provides an effective way for teachers to share experiences and strengthen communication. Teachers' work is mainly reflected in a personalized labor process, and there is relatively little communication at ordinary times. Case writing reflects the educational and teaching experience of one or several teachers in written form. It can help other teachers effectively understand the thoughts and behaviors of colleagues, and make personal experiences become everyone's wealth. At the same time, through personal analysis and group discussion. I can realize the complexity of my work and the diversity and fuzziness of the problems I face, and I can improve my original silent knowledge, my knowledge, values and attitude. , can only be expressed in a self-evident or self-evident way, through discussion and critical analysis, from perceptual knowledge to rational knowledge.

Fourth, the compilation of primary school mathematics teaching cases

1, compilation principle

(1) principle of objectivity. A case is a description of an actual situation, which cannot be replaced by "facts fabricated in a rocking chair" or "facts derived from abstract and generalized theories". Insist on seeking truth from facts and try to record cases objectively in the order of time development. Putting an end to adulteration will not be a "reasonable idea". Don't play with words, and don't distort or change the facts because of the need of words.

(2) the principle of uniqueness. In case writing activities, teachers should be encouraged to do creative work, not to be have it both ways like others, but to have individual observation, practice, reflection and expression.

(3) the principle of value. The purpose of writing cases is to promote teaching reform. Therefore, the advanced and practical value of the selected case is directly proportional to the practical significance of the case itself. Therefore, we should choose cases from the height of the times and face the actual needs of teaching.

2. By analyzing relevant cases, it is not difficult to find the general format and writing method of the case. At present, the main format of expert case writing is "case+analysis", and its variants mainly include "prompt-case-analysis" and "prompt-case-interview-analysis". Hint mainly introduces the basic theories of education involved in Case and Analysis, which can promote the integration of theoretical knowledge and teaching examples. Interview Record records interviews with relevant teachers in the form of dialogue, externalizing teachers' tacit knowledge, so that others can understand the background, process and practice of the case more comprehensively and deeply. The main format of teachers' case writing is "fragment+reflection", and its variants mainly include "background-fragment-reflection" and "fragment-evaluation-reflection". It can be seen that the case mainly consists of two parts, namely "case+reflection". Cases are fragments of teaching behavior intercepted for a theme, and these fragments contain certain educational theories. It comes from practice, but it is higher than practice. The case is based on real teachers and events, but it is not a simple mechanical classroom record. It is a teacher's description of his typical teaching events. It can describe a lesson or a fragment, or it can overlap related fragments of several lessons around a theme. From the manifestation of the case content, there are mainly "narrative" and "dialogue"; Judging from the arrangement of case contents, there are mainly "single type", "contrast type" and "progressive type". On the one hand, reflection is based on cases, which combines theory with practice and proves theory with examples; On the other hand, it is higher than the case, so we should put forward new problems and new viewpoints from the analysis of the case.

09-05-03 | Add a comment

Simple love, love, love

1. Students' enthusiasm for math class.

It mainly reflects whether students are in the best psychological state in their learning activities.

Performance: (1) The best state of attention: concentration, concentration, concentration and stability.

(2) The best cognitive state: clear perception, keen observation, active thinking, rich imagination and firm memory, and the brain is in the best state of excitement.

(3) The best emotional state: serious attitude, enthusiasm for learning, strong interest and liveliness.

(4) Best will: strong motivation, curiosity, initiative, overcoming difficulties, self-control and perseverance.

2. The degree of students' participation in learning.

It mainly evaluates whether the teaching design conforms to the actual level of students and whether the thinking space left behind can stimulate students' cognitive needs. American educational psychologist Brula's "Mastery Learning Theory" holds that: "As long as there are suitable learning conditions, the learning ability, learning efficiency and motivation of most students will become very close. The three variables that cause students' individual differences are: the degree of students' experience and ability, the degree of students' active participation, and the degree of teachers' adaptation to students' teaching. "It shows that any student can exert his greatest potential in his own situation, get the least help in his own way and achieve the same learning goal.

3. The display space of students' innovative consciousness and exploration spirit.

It mainly evaluates the reasonable transfer of students' self-study ability structure and creative thinking level in learning activities. Including: reading mathematics textbooks independently and solving new problems with existing knowledge and methods, self-organizing learning activities and the unity of feedback divergence and aggregation thinking, the organic combination of intuition and analysis, and the participation of creative imagination.

4. Master basic knowledge and skills.

It mainly evaluates whether the way students master the "double basics" is scientific and reasonable, and whether the formation process is efficient, time-saving and independent in building a knowledge body. Mastering knowledge should include four aspects: what it is, where to find it, how to learn it, and what is the use. It is not the same as memory or imitation.

5. Students' ability to use mathematical knowledge to solve problems around them.

It mainly evaluates students' understanding of mathematics from life, discovering and refining mathematical laws from collected information, and observing and answering practical problems in life with mathematical eyes. Including: collecting life information before class, exchanging, sorting and analyzing information in class, and re-understanding and imagining innovative practice information with what you have learned. It truly embodies that mathematics comes from life and mathematics serves life.

The key to students' enthusiasm for math class is that teachers respect students' personality. Try to reduce the prescribed behavior of teachers in the classroom. As long as teachers pay attention to students' words and deeds, they must encourage students. Teachers should be good at discovering students' learning personality, guiding and developing it, and avoiding the formulation of the learning process; Reasoning is integrated into life situations and childishness to overcome monotony and boredom. According to the survey data, primary school students like a teacher because they like the subject taught by the teacher, and then show the best psychological state in class.

"The optimization of teaching is that all the activities designed by teachers can inspire students' thinking and get the maximum gain with the least time and energy. "Teaching design should be based on students' life examples, provide students with materials to participate in the learning process in the form that students are most interested in, and ensure the content and time of students' activities. Learn what? How to learn? Back to students, teachers can provide learning materials instead of explanations, and sort out original information instead of processing; We should believe that every student can learn math well at different levels with different speed and methods. Teachers should encourage students to think independently, learn from each other and dare to express new ideas and practices. Only by truly forming an open classroom and designing open questions can students take the initiative to participate and cultivate their awareness of exploration, innovation and practice. Primary school mathematics should be regarded as applied mathematics rather than pure mathematics, and abstract book contents should be visualized and boring exercises should be gamified in teaching; Let students use mathematical thinking methods to solve the problems around them and feel that learning mathematics is the need of life. Change "I want to learn math" to "I want to learn math".

The experiment shows that changing the object of teaching evaluation can promote the change of teachers' educational concept and guide a new mode of preparing lessons and attending classes. It can better reflect that teachers are organizers, guides and collaborators in the teaching process. To sum up, the implementation of the new curriculum standards of primary school mathematics classroom teaching evaluation quantification is as follows:

I. Teachers' activities

1. Be able to grasp the internal relationship between old and new knowledge and stimulate students' thirst for knowledge by creating scenarios.

2. According to the key points, difficulties and doubts, effectively organize group cooperative learning, design substantive collective learning content, guide learning methods with correct mathematical terms, and infiltrate mathematical thinking to cultivate ability.

3. Join the study group and give individual counseling.

4. Attempt, practice and innovative practice of thinking training closely related to goals.

5. Be able to use questions and inquiry, group communication, collective evaluation, self-revision and mutual revision of homework, sampling inspection and other methods to get timely feedback and give appropriate evaluation.

Second, student activities.

(A) the status quo of autonomous learning

1. Make full use of your mouth, hands and brain to actively collect, communicate, process and process learning information.

2. Independent thinking, mastering learning methods, bold practice, self-evaluation, self-examination and self-correction.

(B) the status quo of cooperative learning

1. Have the courage to express your opinions, listen to and respect others' opinions, and implement division of labor and cooperation, with respective responsibilities.

2. Debate and be harmonious, and help and learn from each other effectively in groups.

(C) the state of creative learning

Observe from all directions, be good at asking questions, think differently, draw inferences from others and practice flexibly. The new curriculum reform has gone through more than five years. Teachers actively participate in the exploration of classroom teaching according to the concept advocated by the new curriculum standards, which makes mathematics classroom full of passion and vitality and makes mathematics teaching more exciting. However, in the actual classroom teaching, we often encounter such a situation: the teacher throws questions and lets the students discuss and solve them in groups. Suddenly, the classroom was full of people. In some groups, when you say something, everyone is opening their mouths, and no one can hear clearly who is saying what; Some group leaders sing a one-man show, and the rest of the students are listeners, without adding anything; In some groups, students with learning difficulties do their own things absently; Some groups disagree, but in the discussion, instead of using their own reasons to convince students with different opinions, they argue endlessly. After a few minutes of discussion, feedback and exchange of views, the students raised their small hands and kept shouting, "Teacher, me!" " Me! Me! "When the teacher called a classmate, all the other students sighed. In the sighs of some students, the named students began to speak: "I am ..."

"Teacher, I have different opinions." Before this classmate finished, another classmate shouted below.

"I also have different opinions. I am ... "The other students also cried. After these students made a scene, the following students talked about their own methods. The whole classroom is in a mess. I have come across the example just now many times, so I thought: Is this teaching effective?

The whole process of cooperation and exchange is lively on the surface, and behind the excitement is more laissez-faire, randomness and inefficiency. Communication is just an expression process without listening, which greatly reduces the effect of communication. The common phenomenon in our classroom now is that many students love to talk and express themselves. However, it is not enough for students to express themselves in an active math class. The most important thing is listening. Listening is a means to acquire knowledge, and listening to others' opinions is also an important learning skill. Effective listening can help us learn from others and make up for our lack of consideration; It also allows us to draw inferences and get inspiration; This also enables us to cultivate the good quality of respecting others. Then, how can students express themselves correctly and learn to listen according to their age and psychological characteristics? Let me briefly talk about how I cultivate students' listening ability in mathematics classroom teaching.

First, cultivate students' listening ability and let them "listen".

Listening is an ability and a quality. As a basic human skill, it can be continuously improved and perfected through training. In my usual math teaching, I mainly cultivate students' listening ability through the following four points:

1. Listen.

In teaching, I often put some confusing concepts and laws into judgment questions. The teacher dictated the meaning of the questions, and the whole class used gestures to indicate "right" and "wrong". For example, in the consolidation exercises of rectangles, squares and parallelograms, I ask students to listen carefully and judge carefully to see whose ears are pointed: "A figure with four corners at right angles and four equal sides is a square; All four corners are right angles, and the equilateral figure is a rectangle; Four sides with equal opposite sides and equal diagonal angles are flat quadrilaterals. " Through these judgment exercises, on the one hand, students can identify, analyze and strengthen their understanding of knowledge, on the other hand, they are forced to listen carefully and make correct judgments. This virtually strengthens students' listening comprehension.

2. Monitoring algorithm.

Calculation is an indispensable part of mathematics teaching. In normal teaching, I try to practice oral arithmetic for 3 minutes every day to improve students' computing ability. In oral arithmetic practice, I not only practice visual arithmetic, but also often practice listening and calculation. This not only changes the monotonous practice mode, but also helps to stimulate interest in practice, and at the same time gradually improves students' listening comprehension ability. Through listening and calculating, let students understand that we should not only learn to calculate, but also pay attention to listening. Only when you listen clearly can you be correct.

3. Listening and speaking method.

The favorite activity of junior students is learning in games. After teaching division with remainder, I designed a fragment like this:

Teacher: Next, let's play a password game to compare which child is right quickly, but we can't repeat it. The teacher reported the remainder as 1. Can you tell me a formula equal to it?

Health1:15 ÷ 2 = 7 ...1health 2: 10 ÷ 3... 1 health 3: 25 ÷ 8 = 3 ../kloc- ...

Teacher: Too many. The remainder below is 3.

Health 1: 15 ÷ 4 = 3...3 Health 2: 27 ÷ 6 = 4...3 Health 3: 33 ÷ 5 = 6...3 ...

In this link, only after students listen carefully to other people's answers will they not let their answers be the same as others', which will also prompt students to keep thinking about whether there are other answers.

This practice not only enlivens the classroom atmosphere, but also stimulates the enthusiasm of all students to participate. At the same time, students can calm down and listen patiently. There is stillness in movement, and there is movement in silence. Multiple senses participate in learning, which greatly improves the learning efficiency.

4. Report and summarize.

"Learning to listen" has two meanings. First of all, you need to listen to others attentively and carefully. Another meaning is "listening", thinking while listening, thinking about what others say, and remembering the main points that others say. Therefore, in the usual teaching, I often ask students to paraphrase and summarize others' speeches and process them on the basis of listening to others' speeches. For example, in group cooperation and communication, when each student is asked to speak, he should first say what the previous speaker said, then evaluate what he heard, and then make his own point clear. In this way, students can relay others' speeches, gradually learn to grasp the essence of others' speeches, and reach the degree of real understanding; Also get inspiration from it, reach analogy and learn to listen.

In addition, every time the teacher assigns homework, he only says it once and asks the students to listen carefully. Then ask the students who have not listened carefully enough to repeat it. If you are not clear, please ask another student to relay it.

It is obviously time-consuming for students to report, but it is very helpful to cultivate listening comprehension. As long as students' good listening habits are cultivated from a low level, they will get twice the result with half the effort in the future classroom teaching, so they should spend less time.

Second, form a good habit of listening and let students "listen well".

People's growth is actually the accumulation of some habits. To cultivate students' listening ability, we must cultivate students' good listening habits. So in classroom teaching, how to use the limited time to cultivate students' good listening habits?

1. Explain the importance of listening.

Listening is a conscious and active listening. Because students are young and psychologically immature, they can't make them understand the importance of listening by hard indoctrination, but should infiltrate in a harmonious atmosphere. In teaching, I always seize the opportunity to emphasize that listening is as important as speaking. Say it is to express yourself and let others understand; Listening is to respect others and understand what others mean. Speak boldly and listen attentively; We should not only dare to speak, but also listen, so as to be a good student. Of course, it takes more than one sentence to make students understand the importance of listening. It depends on our teacher's patient guidance and every available opportunity to make students understand the importance of listening from experience.

The protracted nature of conscious listening.

Learning to listen is an ability and a habit; Listening carefully is a good quality and a kind of respect for others. It was not built in a day. Because students are young, psychologically unstable and have relatively low comprehension ability, it is difficult for them to really learn to listen, which requires us to be conscientious people in daily teaching and gradually cultivate them carefully. In the usual teaching, I mainly let students express their opinions after listening, so as to cultivate listening habits. No matter whether a student answers "right" or "wrong", I will educate the students, let others finish their sentences, and then raise their hands to express different opinions. This is a sign of respect for others. At the same time, guide students to put themselves in other's shoes. What would you think if you were interrupted while talking? Let the students put themselves in the speaker's shoes and respect the speaker. Ask students to restrain their excitement, even if they have opinions on other people's speeches, they should wait until others have finished speaking before expressing their opinions. This can not only satisfy the students' desire for expression, but also allow each student to express his own opinions. The formation of habits is a slow process, which is repeated during the period, but it can be achieved as long as it is orderly and persistent for a long time.

3. Give play to the exemplary role of teachers.

Cultivating listening habits is not only a problem for students, but also a task for teachers. Many habits of students can be found in teachers. In order to let students learn to listen, teachers should pay special attention to words and deeds inside and outside the classroom.

(1) Understand students' voices.

When talking with students, teachers should listen attentively and occasionally give hints. No matter whether the child's speech is right or wrong, fluent or hesitant, he must never interrupt the student's speech. When a teacher treats a student's speech, he should first see his bright spot, strive for affirmation and then correct it, with encouragement as the mainstay and criticism as the supplement.

② Evaluate students appropriately and timely.

Pupils are very emotional, especially juniors. They often talk loudly because they are emotional and don't listen to their classmates. At this time, I immediately praised those students who could listen to others and actively raised their hands or answered questions: "Look, XXX listened carefully today!" " ""You see, XXX not only understood other people's speeches, but also added his own ideas. Great! " "XXX is really something. I can hear the main meaning of the students' speeches at once. " In this way, it not only praised the students who listened carefully, but also pointed out the direction of efforts for other students.

Through the above attempts, students in our class have gradually developed the habit of speaking actively and listening to others' opinions in class; I also have a strong interest in mathematics, and my learning efficiency has been improved to a certain extent. This makes me further clear that autonomy in the classroom is not equal to randomness. Under the modern educational concept of advocating individuality, "respect, democracy and equality" are the core, and learning to listen is based on this concept. Only by listening carefully to others' speeches can we understand what others mean and achieve the purpose of communication. Efficient classroom should not only encourage students to "love talking", but also guide students to "listen", "listen well" and "think more".