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How to give lectures on primary school mathematics and "do mathematics" in practice
According to teacher Zhao's arrangement today, the topic I want to communicate with you is "How do primary school math teachers conduct research? To tell the truth, subject research is a heavy topic, but also a slightly boring topic. Let me sit here and talk to you about how to carry out the research, which is really a bit daunting. I can only talk about my own experience and feelings. Please criticize and correct the shortcomings.

Mainly divided into three parts:

First, pursue the "root" of educational research. Thinking about the significance of research from the perspective of a primary school math teacher.

Second, grasp the "method" of subject research. Combined with the research topic of "Rational use of Jiangsu Education Edition primary school mathematics textbooks to improve students' learning style" presided by Mr. Zhao, this paper talks about the general process and methods of school research.

Third, highlight the "soul" of education life. If we compare our educational career to a trip, we hope to change a teacher's walking style through educational research.

First, pursue the "root" of educational research.

When talking about "educational research", it is necessary for us to ask: What is a "topic"? What is the value of "project research"? School education, or specifically, as an ordinary primary school math teacher, is it necessary for us to engage in educational research? If these problems are not solved, even external forces (such as the expectations of leaders, the pressure of assessment, the needs of personal career, etc. Push us to devote ourselves to educational research. Our thoughts are like water without a source and trees without a root. Our spirit will lack the motivation for sustainable development, and we will lose our direction. Our work on the subject research will eventually dissipate our passion and lead to a dead end.

As far as I am concerned, from the point of view of a primary school math teacher, I understand the subject research like this:

What's the topic? From the text sense, English is a task, a job, or a problem, a difficult problem; The definition of Modern Chinese Dictionary is the main problem that needs to be studied or discussed, and it is also the main problem that needs to be solved urgently. In teaching and research, the so-called "subject" is a research project, which is established from the problems indicated by the research direction.

Aside from these literal restrictions, we might as well examine and interpret them from everyday words. First of all, the so-called "subject" is the problem explored in the study. Moreover, the process of project work is essentially a process of constantly focusing on problems. For example, the key project of Yangzhou City, "Mathematical Practice Activities and the Cultivation of Primary School Students' Mathematical Literacy", which was presided over by Teacher Zhao, found that the content was comprehensive and complicated, and it was impossible to conduct in-depth research. After careful consideration by the research group and the guidance of experts, we decided to focus on one of them: "Mathematical practice and the cultivation of students' non-intelligence factors", which was in 2002. This part of the research content coincides with the three-dimensional goals of implementing knowledge and skills, processes and methods, emotional attitudes and values proposed by the curriculum reform. Therefore, the research group timely put forward the research on promoting the development of emotional attitude and values in mathematical practice. Through the efforts of the research group, some training strategies have been formed, and the resulting research paper won the first prize of "Teaching and Exploring the Sea" in the history of Baoying County. It is a process of constant focus from cultivating primary school students' mathematical literacy to cultivating non-intellectual factors and then cultivating emotional attitudes and values. Focus is a physical term, and problem focus is to constantly focus on the most innovative, practical and groundbreaking problems. This kind of problem research is the most valuable.

The so-called "subject" is the subject of research and discussion. Furthermore, the so-called "subject" is the central concept of research thinking. One interpretation I appreciate is that the topic is a research platform that is problem-oriented, accumulates everyone's wisdom and generates sparks of thinking.

(2) What is the significance of the project? For a period of time, many people, including ourselves, will feel it necessary to engage in teaching and scientific research in primary and secondary schools. A hint of discrimination against primary school teachers or our own inferiority.

My idea is: it is necessary. There are two reasons:

Conditional. As front-line teachers, we devote ourselves to education and teaching practice every day, so we have the most vivid and valuable education and teaching resources. There is a need. Teachers' professional growth needs research. Although we have the freshest and most precious resources, jade is rough and abrasive. The best diamonds must be cut. Accumulate (k? One step, to a thousand miles. For a teacher who never thinks or studies, teaching for decades is just repeating what he did in the first year dozens of times. There is a good saying: "there is no scenery in the repeated place." At best, he can only be an authentic "teacher".

The new era calls us to become research-oriented teachers. At the same time, from the utilitarian point of view, it is necessary to become a backbone teacher quickly, participate in and ultimately undertake the project independently.

Second, grasp the "method" of subject research.

Although school education and scientific research are different from research in scientific research institutes. But we must also follow certain methods and steps. Formally speaking, it includes topic selection, topic opening, mid-term detection and topic selection conclusion.

Focus on the following steps:

(1) Determine the research topic.

Educational scientific research is to study and discuss a specific problem in the form of a topic. Therefore, the determination of the subject has become the primary problem. To determine a scientific research topic, you must first be able to ask questions. Asking a problem is often more important than solving it. Putting forward a novel, creative, feasible and good question and forming a topic can be said that the research on the topic is half finished. On the contrary, some topics are of little value just by looking at their names. Generally speaking, it takes a long period for us to do the project, about two years, and we put in more energy. Therefore, we must choose the project carefully and don't start blindly, otherwise it will lead to the "unfinished building" project.

So, how to properly determine the topic?

First of all, we should choose innovative topics. Where is innovation reflected?

1. Problems that others have not studied.

For example, after Huang Aihua, a teacher from Shenzhen, moved from Jinhu to Shenzhen, he keenly felt the great influence of computer technology on mathematics teaching, so he initiated the research work of "Applying Multimedia Computer to Assist Mathematics Teaching", which was later approved as a national project. The "understanding of circle" and "understanding of rectangle and square" have become the precedent and classic pen of multimedia computer-aided teaching, which has triggered a revolution in modern educational technology in the national education sector. At that time, it was an innovative topic, but today, when we talk about the influence of multimedia computer-aided teaching and even network technology on teaching, we have learned from it. On this topic, we must consider whether our research ability can surpass others, or we must re-select the entrance to carry out research, otherwise it is best to find another way.

2. Although others have studied the problem, but the conclusion is incomplete or inappropriate, re-study it from a new angle.

For example: theoretical and practical research on the application of discovery learning in teaching. We often mention Bruner's discovery method in our own teaching, which is actually a kind of "guided discovery method". Bruner, a famous American cognitive psychologist in the late 1950s, believed that in all human lives, the greatest feature of human beings is their ability to find problems. He regards students as "discoverers" and even discovers them like scientists. The teacher doesn't give any inspiration or help. When this concept was first put forward, it was "acclimatized" in China, and everyone questioned: Do students need the guidance of teachers in teaching? How much guidance do you need? Later, after research, educators in China extended the "discovery method" to "guided discovery method", thinking that teachers can give students some guidance when necessary, which is somewhat different from Bruner's "pure discovery method". This view has been widely recognized in China's educational circles. This is a re-study from a new angle.

3. Problems found in general teaching practice.

For the average person, the teaching work completed every day and the phenomena seen seem to have no special feeling, and they don't even want to think about it. But keen thinking can often see the problems, and most of these problems are valuable problems that we can solve.

For example, after the implementation of mathematics curriculum reform, Xu Bin, a special-grade teacher in Suzhou, encountered such a problem in practice: Is it more important to create situations or review old knowledge in computing teaching? This seemingly nonexistent problem may have never been considered in our minds. Reviewing old knowledge is traditional teaching, and creating situations is new concept teaching, which is of course subordinate to creating situations. But the review of the so-called traditional teaching methods is not without its merits. It plays a very important role in the migration and analogy of calculation methods. However, the situation of the so-called new ideas is not perfect. In teaching, we often pay too much attention to situations and downplay reasoning. How to deal with the relationship between inheriting tradition and reform and innovation to maximize the benefit of computing teaching? Another example is diversification or optimization algorithm. With a carry addition, more than 20 algorithms are given, and even the method of wrench pointing is given, which deserves our deep thinking: Is it necessary? Is it a kind of ideological degeneration? How to optimize? When will it be optimized? This leads to a topic: computing teaching: research on basic contradictions and handling strategies.

Secondly, we should choose feasible topics. In other words, do you have the conditions and ability to choose a topic well? Is there any condition to do it. It includes hard conditions and soft conditions. For example, the school doesn't even have an internet. What should you do? This refers to hard conditions. Soft conditions are the main aspect of the contradiction, that is, the problem of teachers. Even with the Internet, without a group of teachers with high professional quality and computer skills, the research on the subject cannot be carried out in depth.

Have the ability to do it. The scope of the topic should not be too large. For example, the strategy of quality education, such a topic for the Ministry of Education to organize, primary school math teachers should also "retreat from difficulties." For example, some topics have high theoretical requirements. For example, a topic I have been thinking about recently has encountered such a difficulty: I found in my own teaching and lectures that many teachers do not have enough professional knowledge background for the contents of the textbook of Jiangsu Education Edition, especially the newly added space and graphics, statistics and probability, which leads to superficial understanding and brings many problems to teaching. For example, when teaching axisymmetric graphics, students ask: Are people axisymmetric graphics? Teachers are speechless, specious and difficult to judge. Another example is the possibility of teaching. Two red balls and a white ball in the bag have been pulled out continuously. When the students agreed that the next time it must be a white ball, it happened that the red ball was drawn for the seventh time. What's the point? The little cloth bear facing the observer has several triangles on the left and right. How many triangles are there to the left of the bear? Should observers be the standard or bears the standard? So I want to declare a practical interpretation of the basic theory of mathematics in primary and secondary schools in the textbook of Jiangsu Education Edition. However, doing this job requires a deep academic foundation in mathematics. I think I must have at least a bachelor's degree in mathematics, so that I can really and thoroughly review the whole set of teaching materials, sort out the ins and outs of the theory and put forward reasonable teaching suggestions. So, I put it on hold for a while.

(2) The compilation of experimental scheme.

When we choose the subject of experimental research, the next job is to write the experimental research plan. This is also a basic work of project declaration, and the project declaration evaluation book can be filled out accordingly.

Generally speaking, a relatively complete project experimental research scheme includes eight aspects. The following is the specific writing method combined with the research of "Rational use of Jiangsu Education Edition primary school mathematics textbooks to promote the improvement of students' learning methods" hosted by Teacher Zhao. It also gives you a preliminary understanding of the subject.

1. Question raised. The reason why we do experimental research is because we find or encounter a certain teaching problem, so we need to make clear the background of the problem, that is, the various factors that cause the problem.

For example, the background of our topic is:

At the turn of the century, the world gradually entered the era of knowledge economy, which put forward higher requirements for people. The call of the times: "65.438+0.3 million teachers need to change their education methods, 300 million students need to change their learning methods, and more than 600 million parents need to change their family education methods." Therefore, one of the six specific objectives of the basic education curriculum reform in the Outline of Basic Education Curriculum Reform points out: to change the current situation that the curriculum implementation overemphasizes learning, rote learning and mechanical training, to advocate students' active participation, willingness to explore and hard work, and to cultivate students' ability to collect and process information, acquire new knowledge, analyze and solve problems, communicate and cooperate. This round of curriculum reform is the eighth curriculum reform since the founding of the People's Republic of China. The first seven curriculum reforms have led to changes in teachers' educational concepts and teaching methods. If you ask the front-line teachers casually now: What kind of educational concept does the new curriculum advocate? I will know more about the three new ways of learning, the change of the roles of teachers and students, and the change of evaluation concepts. At the same time, in terms of curriculum, according to the concept of Mathematics Curriculum Standard, the national standard textbook of Jiangsu Education Edition takes effective measures to provide students with basic contents, basic clues and exploration opportunities, which provides a good platform for promoting the transformation of students' mathematics learning methods. It can be said that the reform of the new curriculum has created good external conditions for the improvement of students' learning style. However, looking at the classroom after the new curriculum reform, there is no domino effect in the curriculum reform. Curriculum implementers have a superficial understanding of the concept of new curriculum reform, such as simply thinking that students' seats are changed from "sitting in rows" to "sitting in squares" which means cooperative learning and group discussion; Changing the past "you sit down" to "you are great" is to respect students' personality and improve their self-confidence; Vulgarization, the new concept is only used for public class performances, and the usual teaching returns to tradition, "new wine in old bottles", and students' learning methods have not changed essentially.

We find that the key to promoting curriculum reform and ultimately changing students' learning style is teachers. The key for teachers is to master the essence of new learning methods and deeply understand and surpass the text of teaching materials. There are many new educational ideas in the national textbook of Jiangsu Education Edition, but these vivid educational ideas are statically attached to the text and pictures of the textbook, which requires teachers to deeply understand the textbook, creatively explore and use it, so as to maximize the educational value of the new curriculum content and achieve the established training goals.

In recent years, many researchers and teachers at home and abroad are trying to explore new learning methods, and many good learning forms have indeed appeared. But it is often too theoretical and not closely related to teaching practice; Some teachers also consciously explore in practice. Although it is operable, it is not deep, comprehensive and systematic enough.

Based on the understanding of the above problems, we put forward the research topic of "Rational use of primary school mathematics textbooks published by Jiangsu Education Publishing House to promote the improvement of students' learning style", aiming at fully tapping the advantages of textbooks published by Jiangsu Education Publishing House, deeply understanding the compilation intention of textbooks published by Jiangsu Education Publishing House, improving teachers' ability to grasp textbooks, and creatively using this textbook as a carrier to provide students with opportunities for independent, cooperative and inquiry learning activities, thus improving students' learning.

2. Hypothesis (or subject definition) of experimental research.

Make a "conceptual definition" of the contents specified in the "hypothesis" and give a hypothetical answer to the questions of the topic.

For example, the title of this topic is "Rational use of primary school mathematics textbooks published by Jiangsu Education Press to promote the improvement of students' learning style", so we have grasped the key words of "learning style", "rationality" and "improvement", thus defining the concept:

"Learning style": In fact, there are as many theorists as there are in the definition of learning style. However, different definitions have one thing in common in essence: the essence of learning style is the learning strategy that learners like or often use. The Outline of Basic Education Curriculum Reform (Trial) advocates "active participation, willingness to explore, and diligence in hands-on", and the mathematics curriculum standard clearly puts forward three important ways for students to learn mathematics: independent exploration, hands-on practice, and cooperative communication.

"Improvement" refers to the improvement of students' learning strategies, attitudes, consciousness and habits. To fully understand.

"Rationality" refers to objectively grasping the textbook system and intention, and scientifically designing teaching based on the textbooks published by Jiangsu Education Publishing House, which is not only a textbook, but also does not violate the textbook. The former is obedient, the latter is illegal.

Hypothetical answer is the answer to what the research really wants to do. This question is answered from three aspects: teaching materials, teachers and students. Through the research of this topic, this paper expounds the influence and function of Jiangsu Education Edition primary school mathematics textbook on improving primary school students' learning style from both theoretical and operational aspects, which will provide a successful case for improving students' learning style; Teachers can have advanced ideas, be good at organizing and using the contents of textbooks scientifically, provide students with an open, practical and active learning space, and create a math classroom suitable for children's development.

3. The basic content of experimental research.

Summarize first and then describe separately. For example, the basic contents of this study are as follows: there are three contents: teaching materials, rational use; Teachers, change the way of education; Students, improve your learning style.

The specific research contents are as follows:

(1) The current situation of students' learning styles in classroom teaching. Although the national textbook of Jiangsu Education Edition is used, the change of students' learning style is still not optimistic.

(2) The arrangement characteristics and intentions of primary school mathematics textbooks published by Jiangsu Education Press, and the influence of textbook arrangement on students' learning style. Including the analysis of the material structure of textbook compilation, the summary of the influence on students and the way of action, and the combing of the enlightenment influence of textbook compilation on teachers' learning style transformation.

(3) Relying on textbooks published by the Soviet Union, scientific design can promote the improvement of students' learning style. Including how to carry out the secondary development of teaching materials.

4. The goal of experimental research.

It is also a summary first and then a description. This paper expounds the goal of changing students' learning style from three aspects: teaching materials, students and teachers, and will not repeat them.

5. The cycle and steps of experimental research.

The so-called "cycle" refers to the start and end time of your research. The so-called steps are that you divide the research into several stages and what to do in each stage. Generally speaking, the research cycle is always divided into three stages, namely, preparation stage, experiment stage and summary stage. The work to be done in the preparatory stage mainly includes scheme writing, pre-test of students' experiment (or investigation of students' situation), theoretical study (or teacher training) and so on. The work to be done in the experimental stage mainly includes action research, data accumulation, problem investigation, lesson paper display and so on. The work to be done in the summary stage mainly includes project effect test (also called post-test), writing research report and accepting expert appraisal.

For example, the cycle and steps of this study are as follows: the cycle of this study is two years.

06. 1~06.4 is the preparation stage, and the main tasks are: (1) study deeply, find problems and determine the research direction. (3) Select experimental schools and teachers for theoretical training. (4) Formulate the experimental scheme, complete the project demonstration and participate in the application review. The experimental period is from 06.5 to 08.3, and the main tasks are: (1) experiment as planned. (2) Accumulate experimental data, and organize excellent teaching design and excellent paper display. (3) Demonstration of typical courses. (4) Stage research summary and mid-term detection. 08.4 ~ 08.7 is the summary stage. The main task is: (1) to write the experimental report. (2) Prepare relevant materials for appraisal and acceptance and classroom display, and apply for appraisal and acceptance. (3) Popularize the research results.

What we are doing now is still the first stage: the preparation stage. Today can also be said to be a training activity for experimental teachers.

6. Analysis of experimental conditions.

Mainly explain the research level and time guarantee of the host and participants, as well as the guarantee of information, equipment and scientific research means. For example, the analysis of the experimental conditions of this topic is as follows: this topic has been paid attention to by the leaders, and the moderator is the leader of mathematics in Yangzhou primary school and a full-time teaching and research staff in the teaching and research department of Baoying County Education Bureau, with strong educational, teaching and research capabilities. The key members of the project are all academic leaders and key teachers in cities and counties, with certain theoretical basis and practical experience. In addition, they also absorbed the students from the training class of county minority backbone teachers as the main participants in the experiment, and they had the time and ability to ensure the in-depth development of the project research and achieved good results. The experimental school has a large-scale reading room and library, equipped with advanced computer classrooms and educational local area networks, which creates conditions for researchers to learn, communicate and consult materials.

7. The form of experimental research results.

After the research is finished, what form it will be displayed should also be written into the plan. Generally speaking, the common forms of achievement are: first, the teaching structure (displayed by typical classes); Two, experimental research papers (based on published or award-winning papers, can be made into collections, teaching plans, etc ... ); Third, students' test scores; Four, the subject of experimental research report; Fifth, research results related to other topics.

The results of this project include teaching design set, case analysis set, suggestions for textbook revision, classroom presentation and experimental report.

8. Organizational structure of experimental research. Includes experimental leading group and experimental research group.

Of course, if it is a large-scale project research, the source of experimental research funds and how to guarantee it must also be indicated, which should also be written into the experimental plan.

(3) Operation of the theme experiment. That is, how to conduct research.

There are many methods, mainly literature method (mainly used for theoretical study), educational observation method, educational investigation method (such as questionnaire survey method), educational experiment method, experience summary method and case study method (in-depth study by one person). At present, it is recognized that the research methods that are more suitable for primary and secondary school teachers are action research and case study. The following is the key introduction.

The so-called "action research method" means learning through action and acting through research. Action research requires teachers to constantly turn research topics into actions from finding problems to solving them. Look at an example of action research method: (1) Find the problem: every new lesson in the junior textbooks of Jiangsu Education Publishing House has a rich theme situation map, which really attracted students' attention at first, but after a long time, students are not fresh and interested in the situation map. What should they do? (2) Teachers' reflection: After carefully studying the theme maps in the textbooks, teachers found that the scene maps in the textbooks can be roughly divided into two categories. One is to provide us with teaching resources that can be developed, such as the campus map provided in Counting in Grade One. The other is to provide some activities or operation methods for teachers and students in the teaching process. (3) Take action: With the above understanding, teachers have consciously adjusted their teaching methods, and situational diagrams are no longer simply used as wall charts. Our teachers should creatively use and deal with them, make them active and realistic, and give them vitality. (Primary school math teacher 05.3. )

Case study method. Educational cases are typical events in real educational activities and vivid educational stories around them. A class, an educational activity, an educational scene, a dialogue between teachers and students, a wonderful teaching detail and so on are all educational cases. When writing educational cases, teachers should not only describe facts, but also reflect on educational theories through facts, phenomena and materials in order to improve their educational practice.

Let me cite an educational case I heard at a training meeting. It may have nothing to do with mathematics, but it is very telling: in a music class, a young music teacher wore a beautiful skirt. What attracts children's attention is that there are five-pointed stars of various colors on the skirt. Children know that whoever listens carefully, uses his brain actively and answers accurately will get a five-pointed star and stick it proudly on his forehead. In this music class, the children study very hard.

The accident happened within 30 minutes of this class. The music teacher, who was rendered by the warm atmosphere in the classroom, accidentally dropped a five-pointed star from her skirt while walking around excitedly. The five-pointed star was picked up by a child sitting next to it. He didn't have a five-pointed star yet and wanted to have it very much, but he finally gave it to the teacher and said in a childish voice, "Teacher, you lost a five-pointed star. Here you are. " If at this time, the teacher can praise the child and say, "You are an honest child, and this five-pointed star will be awarded to you!" " "Then stick the five-pointed star on the child's forehead, how appropriate! However, the music teacher replied in an unexpectedly dull and even indifferent tone: "Oh. "After that, I put it back on the skirt without saying thank you.

At the end of this class, another five-pointed star fell from the music teacher's skirt. It happened that it was a child who didn't even get the five-pointed star. Similarly, he also took the initiative to hand it over to the music teacher respectfully. But what I didn't expect was that the music teacher actually said, "Class is over. It's no use. Throw it away! " The child suddenly froze. He didn't expect that he thought the most precious five-pointed stars were useless rubbish, but our education was so hypocritical and pure. What kind of negative impact it will bring to children may never be made up. After the meeting, I wrote, "Teacher, what did you ask the students to throw away?" Published in the July 2004 issue of Jiangsu Education.

(4) The conclusion of the theme experiment.

When the research of the subject has completed the predetermined content and achieved the predetermined goal, it is necessary to summarize the subject. The conclusion is not only a summary of the subject, but also an evaluation of the research results. The following materials should be prepared to complete the topic: 1. Complete the application report of the project; 2. Project declaration report; 3. Notice of project approval; 4 project opening certificate (project research plan); 5. The mid-term test certificate of the project (phased summary of the project research); 6. Final conclusion report of the study; 7. Attachment: (1) Project achievements; (2) Relevant research materials of the subject, etc. The final report can be divided into: education investigation report, education experiment report and education experience summary report.

Third, highlight the "soul" of education life.

If we compare our educational career to a trip, I think educational research is enough to change our way of walking. First, let me tell you a story:

The most effective way to make a teacher constantly reflect and accumulate bits and pieces of thinking is writing. Writing educational papers and teaching cases in project research.

Limited by time, I won't go into details about how to write educational essays, how to write teaching cases and how to improve the hit rate of submission. I will communicate with you again when I have the opportunity.

At this stage, I hope everyone will devote themselves to this research and write down their own research. According to teacher Zhao's request, we will set up a special post of Baoying Research Group "Rational use of Jiangsu Education Edition primary school mathematics textbooks to promote the improvement of students' learning style" in the research column of "Primary School Mathematics Teaching Network" forum. Each student is required to send 1 article every two weeks, each with more than 400 words. Excellent articles will win prizes or be made into essays. This post was built on Sunday. Everyone must register first. If there is an error in the dialog box, please click it several times. There are landing steps on the outline in hand.

Finally, I send you two sentences: The first sentence Einstein said: "The difference between people lies in their spare time." The other sentence is what Suhomlinski said: "In order to make teachers' work bring fun to teachers and make classes not a monotonous obligation every day, teachers should be guided to the road of happiness in research. "Encourage with everyone and make progress with everyone! Thank you!