The development of modern science and technology and the progress of society put forward a new task of cultivating "innovative" talents for the education front. In order to adapt to the new situation of educational reform and development and build a new system of primary school mathematics teaching in 2 1 century, we have conducted in-depth analysis and research on a large number of primary school mathematics classroom teaching, and found that most classroom teaching has not jumped out of the traditional teaching mode and is not suitable for the cultivation of "innovative" talents and the full implementation of quality education. There are some main problems: teachers explain more and students think less; Ask more questions and answer more, and discuss and communicate less; Practice memory more and encourage innovation less; Adhere to more consistency and less personality development; More scripted subjects, less intellectual activities; More explicit content and less implicit content; Dealing with more tasks, less spiritual fun and so on. In a word, we attach importance to imparting systematic book knowledge and neglect the cultivation of curiosity, innovative consciousness and exploration spirit. In order to completely change this situation, under the guidance of innovative spirit, we have designed a comprehensive and systematic reform plan for primary school mathematics teaching from the aspects of teaching evaluation, textbook application, organizational form, teaching methods, teacher-student relationship, exercises and homework design, teaching means, lesson preparation methods and teaching management. As a special research topic, we named it "Experimental Research on Innovative Learning of Mathematics in Primary Schools". 1March, 1998, an experimental site was determined, and two experimental areas (a school, a county-level city and a prefecture-level city) conducted organized, planned and led exploratory experiments. The exploration in the past two years has achieved remarkable results, and classroom teaching presents a new situation centered on students' autonomous learning. During the period of 1999, the observation class of the experimental class recommended by the national and provincial primary school mathematics teaching professional committees and the observation activities of the evaluation class were affirmed by experts and teachers inside and outside the province with the first prize, and the mental outlook, learning interest, learning ability and academic performance of the students in the experimental class were well received by the society. Parents and leaders at all levels recognized. At the end of last semester, 1500 students in the experimental class of Jason Wu Road Primary School in Jinan were investigated. Survey results: 97.9% like and like math very much, 90.8% are willing to solve math problems by themselves, 98.3% think group learning is helpful and helpful to learning, and 92.9% have improved their learning ability and language expression ability obviously. Because students are interested in mathematics, their learning ability is enhanced, and they are generally not afraid of exams, and their academic performance has been greatly improved. At the end of last semester, the math test scores (grade system) of a real class and a non-experimental class in grade six were compared and counted. Roughly speaking, the excellent rates of oral calculation, written calculation, concept and application in the experimental class are 97.5%, 92.5%, 97.5% and 87.5%, which are higher than those in the non-experimental class by 17 percentage points, 14 percentage points, 22 percentage points and 33 percentage points respectively. The students' real progress in mathematics learning, from interest, ability to grades, has laid our confidence in further exploration. The following focuses on teaching evaluation, textbook use, organizational forms, teaching methods and other aspects of exploration, and briefly introduces some immature practices for joint research with teachers. With the advent of the era of knowledge economy, people are increasingly aware that whether the educated can succeed in their future life, study and work depends not only on their knowledge, skills and general intelligence level, but also on their non-intellectual factors such as interest, motivation, attitude, willpower and self-confidence, as well as their ability to analyze and solve problems. Based on this understanding, we roughly determine the evaluation criteria of primary school mathematics classroom teaching as five aspects: whether students like mathematics class; The degree of students' participation in mathematics learning; The present situation of cultivating innovative consciousness and exploring spirit; The development of mathematical communication and problem-solving ability; Master basic knowledge and skills. Whether students like math class or not, this index mainly evaluates whether the relationship between teachers and students is harmonious. Whether the psychological freedom and psychological safety environment for students to learn mathematics are formed, and whether students' interest and emotion in learning mathematics are well cultivated. The degree of students' participation in learning, this index mainly evaluates whether the teaching design conforms to the actual level of students and whether the left thinking space can arouse students' cognitive needs. Reflected in the cultivation of innovative consciousness and exploration spirit, this indicator mainly evaluates whether students' intellectual potential has been better played through the performance of students' independent thinking, mutual inspiration and daring to express new ideas and practices. The development of mathematical communication and solving mathematical problems, this index mainly evaluates students' ability to respect others, learn from each other's strong points, study habits in cooperation and apply knowledge flexibly and comprehensively, especially students' ability to construct new knowledge independently. Mastery of basic knowledge and skills. This index mainly evaluates whether the way students master basic knowledge and skills is scientific and reasonable, whether the formation process is time-saving and efficient, and whether the mastery level is deep and solid. The purpose of the evaluation index is to promote the achievement of the index and play a clear guiding role for the experimental teachers. In order to highlight the key points, at the beginning of the experiment, we focused on the first two indicators. Instructors and experimental teachers study almost every week, and each time they go deep into the specific design intent and actual effect of the experimental class. After seven rounds of repeated evaluation and research on 29 classes, the experimental teachers gradually accepted new teaching concepts in step-by-step practice. Because these five evaluation indicators are interrelated and mutually promoting, it will greatly promote the realization of the last three indicators in the process of strengthening the evaluation of the first two indicators. Evaluation is supervision and guidance. In the process of continuous evaluation, a group of high-quality experimental teachers have been trained. They have new teaching ideas, constantly improve the level of classroom control and student management, and are very interested in the reform, thus ensuring the smooth progress of the experimental work. Second, reform the teaching materials boldly and cautiously. The nine-year compulsory education mathematics textbook published by People's Education Publishing House should be said to be a very good set of textbooks seven or eight years ago, but with the development of the times, it has obviously shown a lag. It is certainly not objective and unreasonable to demand it with new standards. Because the compilation of teaching materials is the product of the times, teaching materials will inevitably develop with the development of the times. Only by analyzing and studying it from a historical and developmental perspective can we have a scientific attitude. Therefore, on the basis of repeatedly studying the mathematics textbooks for nine-year compulsory education published by People's Education Publishing House, we have taken five measures and carried out bold and prudent reforms on the textbooks. 1. Change the presentation of mathematical content. Try to turn the content suitable for the teacher to explain into the material suitable for students to discuss and study problems. For example, in the section of "quantity is inversely proportional", the original long explanation content is changed to only present a few examples of inverse proportion, so that students can analyze the quantitative relationship, find the law and draw conclusions by learning the thinking method of "quantity is directly proportional". For another example, the application problems of middle and lower grades try to present things with pictures, so that students can ask their own questions and solve their own problems, infiltrating the idea of "problem solving". 2. Put forward real and thoughtful questions in combination with the actual production and life, so that students can experience the value of mathematics and learn problem-solving strategies in the process of solving specific problems around them. If you study the content of percentage application, guide students to investigate in banks and shops, ask questions such as interest and discounts, and learn to answer them in groups. In the process of solving problems, understand concepts and learn methods. For another example, when middle school students learn to solve integer and decimal application problems in three-step calculation, some classes are to copy some real invoices, so that students can investigate the prices of familiar items, and students can understand the quantitative relationship and solve problems in life by filling out invoices themselves. By doing so, students not only learn to solve problems, but also get in touch with society. 3. Expand the thinking space of examples, let students think independently and learn how to construct knowledge. For example, learning fractional engineering problems is not paved with examples of integer engineering problems, but with pictures showing the scene of two engineering teams completing projects, giving time conditions and solving them by students. For another example, after learning the addition of 9 plus a few, simplify 8 plus a few, 7 plus a few and so on, so that students can finish their research. 4. Strengthen the basic and backbone knowledge, and weaken and delete complex content. For example, the understanding of numbers within 10 is too detailed and repetitive. We combine the knowledge of L ~ 5 appropriately and divide it into two categories. After students have mastered the basic methods of number recognition, compress the following contents. Another example is integer multiplication and division. On the basis of strengthening oral calculation, estimation and multiplication and division of two digits, the multiplication and division of multiple digits is listed as an elective course. 5. Set aside appropriate time to carry out mathematical practice activities, mathematical speech activities and intellectual interest topic exchange activities. In these activities, statistics, mathematical history, mathematical appreciation and other aspects have been infiltrated. Because of the reform of teaching content, it broadens teachers' horizons and thinking space, helps teachers organize teaching activities, and greatly promotes the reform of classroom teaching. Third, explore new forms of classroom organization. Large-scale classroom teaching is conducive to teacher-centered explanation, but not to student-centered autonomous learning. It is difficult to really put students at the center of learning without changing the long-term organization of large-scale classroom teaching. To this end, we should actively explore the organizational form of combining classes, groups and individuals with various learning methods, focusing on strengthening the learning method of group discussion and relatively weakening the learning method of large-scale classroom explanation. In this class, students are provided with sufficient space for independent activities and opportunities for extensive exchange of ideas, and students are guided to explore independently, learn from each other and boldly express innovative opinions. In the process of exploring the reform of organizational form, we deeply realize that it is an arduous task to cultivate students' ability to discuss problems, practice and cooperate with each other. We should not only have the kindness of teachers, but also have scientific guidance methods, establish incentive mechanisms and well-organized management measures to adapt to students' psychological characteristics. After good training, students can give full play to their learning potential and management ability in the group. The backbone members of the group can not only organize students together well, but also grasp the direction and depth of discussion, which greatly improves the teaching efficiency. For example, in a math class teaching "Fractional Engineering Problems", students listed two formulas according to international problems and their own understanding level: L \u+ and L \u( L \u 10+L \u 15). Each of them made his own formula clear and clear, and the debate was fierce, and it was not convenient for the teacher to draw conclusions too early. At this time, suddenly a classmate, with the support of several classmates, expressed such an opinion in time: "Our grade has mastered the knowledge of fractions, why not solve problems in a simple way and return to the middle grade level?" Our view should adopt the first formula. "In a few words, the whole class was silent and soon unified their opinions. With the change of classroom organization, the leading role of teachers is more important. This is mainly manifested in the design of teaching scenes that can arouse students' enthusiasm for learning, and the timely and appropriate grasp of "temperature" such as guidance, explanation, dispelling doubts and theoretical sublimation in the learning process. Therefore, teachers are required not only to have solid and generous basic knowledge, but also to have high teaching wit, teaching art and moral cultivation. We also have this lesson: the teacher has done a lot of work, and the enthusiasm of students to discuss problems has been mobilized. The teacher asked a lot of questions and didn't know how to end it. There was a phenomenon of "temporary prosperity" and "flashy". The more open students' learning is, the more important the leading role of teachers is. How teachers play a leading role is the key to the success or failure of classroom teaching reform. Fourth, gradually implement inquiry and discussion teaching methods. Regarding the reform of teaching methods, a very important issue is the change of ideas. At present, many teachers still regard the teaching process as a process in which students "accept" book knowledge. To be more specific, the teacher makes the contents of the book clear, or asks questions clearly, and the students carefully remember that they can finish their homework on time to cope with the exam, even if they have successfully completed the teaching task. In doing so, we have actually lost all the "invisible" and precious things-curiosity, thinking method, exploration spirit, and especially the cultivation of innovative consciousness. Through exploration, we realize that the teaching process should be like this: in the problem scenario designed by the teacher, students are closely attracted by the problem, consciously and wholeheartedly engage in learning activities, concentrate on thinking, communicate sincerely, sometimes confused, sometimes happy, and independently complete the construction of knowledge in the ups and downs of emotional experience. In this learning process, students not only have a deep understanding of knowledge, but also "create" methods to acquire knowledge and experience the pleasure of acquiring knowledge. At the same time, in the harmonious and sincere communication, fully display their personality and talent. On the basis of this understanding, we gradually promote exploratory and discussion learning methods. It is realized from three aspects. 1. From the reality of students and teaching content, creatively organize mathematical intelligence activities, so that students can construct knowledge, learning methods and increase their wisdom in the experience of real thinking and innovation. The intellectual activity mentioned here is to create a practical activity that allows students to operate, observe and think independently, to stimulate students to learn and innovate independently, to complete the information processing process through group communication, and to turn knowledge into students' own spiritual wealth. For example, in the course of "Understanding Circle", the teacher gives every four people a set of special tools for drawing a circle-thumbtacks, short ropes and pencil tips, so that students can draw a circle by themselves. Because it seems simple to draw a circle with this set of tools, it is difficult for a person to draw it. It is cooperation. There are still many tricks in the comprehensive operation and use of thumbtacks, strings and pen tips. It is difficult to draw an ideal circle with a little carelessness. It is precisely because of overcoming the difficulties repeatedly that I finally drew a circle, which increased the attraction and deeply experienced the functions of various elements when I painted it back. Therefore, when students discuss the characteristics of radius and diameter, as well as the function of center and radius, they feel something, say something, and show unusual enthusiasm. When I switched to learning to draw circles with compasses, I felt a heartfelt need. Under the guidance of my teacher, I am constantly looking for the law and eager to master it. Such a class is a pleasure and enjoyment for both students and teachers. 2. Really establish the idea that students are the main body of teaching activities. This sentence is easy to mention as a slogan, but it is not easy to really implement it in the classroom. First of all, teachers must change their roles from authoritative lecturers to good friends and instructors who discuss problems with students. After a long period of experiment, exploration and summary, we feel that to solve this problem, we should completely change the traditional classroom teaching structure and establish a new classroom teaching structure. The initial teaching idea of the experimental class is "problem scenario-operation, discussion, communication-summary, application and expansion". After repeated practice, good teaching results have been achieved. For example, in the review class, the teacher systematically combed the knowledge, and the students finished some corresponding exercises and summarized it after listening, even if the review was over. For many years, the reform of review course has been a difficult point. However, in our experimental class, we have greatly changed the previous teaching methods. The context of knowledge is arranged by students in groups, and exercises are designed and communicated with each other under the guidance of teachers. Let's have a review lesson on fractional application problems. Students use tables, branch diagrams, maze diagrams and physical diagrams to express their ideas. No matter which form, it clearly reveals the knowledge connection and problem-solving law of this unit. In the process of communication, students are also allowed to ask and answer questions, and the key links can be illustrated by examples. In particular, a group designed a colorful tree diagram, using roots, stems, branches and leaves to show the internal relations and basic laws of fractional multiplication and division application problems in knowledge and problem-solving methods, so as to master the knowledge base of this unit in front of everyone. Coupled with clever exercise design, it won the unanimous praise of teachers and classmates, making this review lesson interesting and profound. The outstanding performance of students in learning potential and learning methods has profoundly educated teachers. 3. Actively create a natural and harmonious learning atmosphere so that students can open their hearts and participate in learning activities. Children are lively and active by nature, willing to learn knowledge in games and activities, and have a strong thirst for knowledge. However, in the traditional classroom, the enthusiasm for learning is often suppressed by the overly serious rhetoric of "discipline" and "stereotyped writing". In order to change this situation, we advocate that teachers should do three things well: first, ensure that students have a relaxed atmosphere when discussing problems, and if necessary, they can lower their posture, regroup and even argue loudly; The second is to understand childlike innocence and let students express their thoughts and exchange opinions in natural and childlike language; The third is to encourage students to ask questions boldly and express their unique opinions. In this way, students and teachers can be greatly liberated, and the classroom presents a new scene of positive, natural and harmonious. For example, in the teaching of "How to find one application problem with more numbers than another" in the experimental class, students understand the quantitative relationship in various ways and establish their own problem-solving ideas. When exchanging ideas with each other, some students don't use words like "as much" and "divided into two parts", but take a long piece of paper and a short piece of paper, align them at one end, and then loudly say, "Remove this piece from the long piece (as much as the short piece), and subtract it." Although the language is not so accurate and complete, it can be seen that he understands the essence of finding differences. The teacher nodded happily, indicating that as long as the students understand. He proudly exchanged eyes with the students, and his expression revealed his confidence in understanding the problem. When the teacher guided the class to make a systematic summary, he was very active. On the basis of constantly absorbing other people's expressions, he established a reasonable problem-solving idea with fluent and clear language. Another example is that in the class of learning "Ten MINUS Nine", a student with learning difficulties encountered difficulties when trying to add and subtract to calculate the subtraction of "Ten MINUS Nine" because he could not skillfully remember the addition number of "Nine plus Several" he had just learned. But he boldly put forward to the teacher: "I use 10 to do subtraction first, and then add a few, and it will be right." Instead of stopping him, the teacher encouraged him to calculate what was right. The student quickly learned the subtraction of "ten MINUS nine" in his own way. Later, when the addition is mature, you can also add and subtract at will to learn the following knowledge. Give another example of students freely participating in learning activities. In a math class on "Knowing Rice and Centimeter" for junior pupils, a young female teacher with long braids designed a link to know rice and centimetre by measuring the length of objects around her. After measuring the length of books, pencil boxes, tables and other objects, students began to exchange the measured values of many parts of the body freely between their deskmates. Suddenly, two students proposed to measure the length of the teacher's braid, and both the teacher and the students laughed. The teacher didn't mind, and naturally turned around and asked them to measure. The whole class watched intently. Two students, one kneeling on the pedal and the other standing on a high place, measured the length of the teacher's braid one by one, very happy. But once compared, the measurement results are different. The teacher immediately asked a question: "Why do two students measure the same braid of the teacher differently?" According to the experience of measuring the length of an object and observing the scene with one's own eyes, the students had a very heated discussion and further deepened the method of measuring the length of an object. The result of doing this for a long time has greatly changed the situation of stiffly instilling knowledge in the classroom, and enabled students to deepen their understanding of knowledge and consciously learn the methods of constructing new knowledge in vivid, friendly and harmonious intellectual activities full of emotion and fun. The above contents are some immature practices of mathematics classroom teaching reform in research-oriented and experimental primary schools in the past two years, and they are presented to you systematically. I sincerely hope that all experts and teachers will put forward valuable opinions and communicate together to further deepen this experimental research.