Project 1: Proposition and background of the "Investigation and Research on the Errors of Primary School Students in Solving Application Problems" (1). According to the data, students are generally afraid and indifferent to the application. In order to cope with the exam, they simply apply "types" to solve problems, lack the analysis of the quantitative relationship of application problems and the mastery of problem-solving strategies, and neglect the cultivation of students' excellent thinking quality, which leads to mistakes in solving problems. It is difficult to achieve the goal of "let students get different development in mathematics". In primary school teaching activities, the cultivation of problem-solving ability is also at the core. However, many teachers still use traditional methods in the teaching of mathematical application problems in primary schools, and students can often solve basic conceptual problems by mechanically copying. Teachers inadvertently strengthened students' thinking habits of mechanical imitation and not thinking deeply. Although it takes up a lot of teaching time and energy, the correct rate of students' problem solving is still very low. This fully exposes the defects of exam-oriented education in the cultivation of thinking ability. (2) In view of this phenomenon, we should realize that it is an important content of mathematics teaching and the need of new curriculum reform to pay attention to the guidance of students' problem-solving methods and the cultivation of their abilities. To cultivate students' ability to solve practical problems, we must know how students' problem-solving ability is. Therefore, our math group put forward the inquiry activity of "investigation and research on the mistakes of primary school students in solving application problems" Through the investigation and analysis of right and wrong problems, we can find out the causes of the problems, seek countermeasures and improve our thinking ability. 2. The problem to be solved (1) changes the phenomenon that "teachers are difficult to teach and students are difficult to learn" in the teaching process of mathematical application problems. Cultivate students' interest in solving problems and develop good math study habits. (2) Through investigation, master the situation of students solving application problems. In the research process, the problems existing in solving application problems of three types of students are analyzed through cases to shorten the cognitive distance. (3) Through investigation and analysis, change the traditional teaching methods and practice. Establish an open and vivid classroom learning mode combined with life. Effectively improve students' ability to analyze and solve practical problems and promote students' personalized development. (4) Through investigation, analyze and understand students' mastery level of knowledge and skills, problem-solving knowledge and skill classification level. Enable students to answer various application questions on the basis of understanding, and gradually improve their ability to analyze and solve problems. (5) Establish a diversified evaluation system. Pay attention to their learning process and results, pay attention to their feelings and attitudes in mathematics activities, and help students know themselves and build confidence. (6) Through the activities and practice of teachers and students, we can further understand the structure of application problems, so as to improve the classroom teaching quality of application problems in primary schools. Second, the significance of research. Theoretical significance: The research project "Investigation and Research on the Errors in Solving Primary School Students' Application Problems" analyzes the errors in solving primary school students' application problems, which not only helps to improve teaching methods and teaching quality, but also helps to diagnose the learning obstacles of poor students and improve their thinking ability. It is beneficial to reform the situation of single and closed classroom teaching and students' passive learning, and rejuvenate the mathematics classroom. It is beneficial to cultivate students' innovative consciousness and practical ability, and to cultivate students' ability to solve application problems. Strengthen the exploration of theory and practice, put people first, pay attention to human development, and let students actively participate in learning activities. Practical significance: the research and implementation of this topic will explore the effective ways and methods of mathematics application problem teaching in primary schools under the new curriculum standards; Find the best way to cultivate students' practical ability and innovative spirit in the teaching of mathematical application problems in primary schools. It has operability and application value. In practice, it can promote the development of mathematics application problem teaching in primary schools, thus improving the quality of application problem teaching. Make students learn to observe the life and things around them from a mathematical point of view, and then put forward mathematical problems, analyze and solve them. 3. Analysis of the current situation and situation in the same field at home and abroad: Since 1980s, problem solving has become a trend in international mathematics education. Since 1980s, the United States has attached great importance to solving problems. The first suggestion in the action agenda issued by the American Association of Mathematics Teachers in 1980 is that "problem solving must become the core of school teaching". In the latest curriculum standard, it is also one of the five teaching objectives and the first standard in its 13 curriculum standard. There have been studies on the causes of errors in one-step or simple two-step calculation of application problems in China. Researchers believe that the main reason for the mistakes in solving application problems is that students can't correctly understand the structure and types of application problems and the narrative of time and space in application problems. Trend analysis: solving problems has always been an important goal of mathematics courses at home and abroad. In the Mathematics Curriculum Standard for Compulsory Education, the goal of cultivating students' problem-solving ability is clearly put forward, whether it is the overall goal or the sub-goal. The connection and difference between this topic and it are as follows: (1) This topic is the same as their research on giving full play to students' main role. (2) We can learn from some successful methods and experiences. Difference: (1). This topic studies the causes of "students' mistakes in solving application problems". The research of other topics is the teaching method of "cultivating students' ability to solve problems" (2) At present, there is a certain distance between the teaching of mathematical application problems in primary schools and the trend of educational reform and development, so it is very necessary to study this topic. ⑶ In the teaching process, this topic, through investigation and analysis, intends to explore the teaching mode under the new curriculum standard on the basis of investigating and studying the causes of difficulties in solving primary school students' application problems, and break the mode that teachers classify application problems and use problem-solving formulas. Pay attention to teaching methods, not only by teachers, but also by students' active perception, understanding, practice and re-practice. The purpose of mobilizing students' enthusiasm is to improve their ability to analyze and solve practical problems and promote their personalized development. ⑷. The study of this topic is learner-centered, student-centered, with the change of students' behavior as the external symbol and the study of their thinking process as the starting point, aiming at improving students' ability to solve practical problems. Theoretical basis: 1, modern educator Tao Xingzhi: "I think a good teacher is not teaching, but teaching students to learn." Ye Shengtao, a famous contemporary educator, has repeatedly put forward that "teaching is for not teaching" and advocated that students should learn to learn. 2. Bruner, a famous contemporary American educator, thinks that "learning how to learn is much more important than learning what". 3. Educator Rousseau believes that teaching should allow students to learn from life and various activities, gain direct experience by connecting with real life, and actively learn, and oppose letting children passively accept adult lectures or simply learn from books. He believes that the teacher's duty is not to teach children all kinds of knowledge and instill all kinds of ideas, but to guide students to learn directly from external things and the surrounding environment and combine them with students' real life, so as to obtain useful knowledge. 4. Innovative teaching contains two meanings: one is teaching students to learn how to learn. Second, it refers to how teachers innovate and optimize students' learning methods, and then cultivate teaching methods with innovative learning as the core goal. 5. Dialectical and unified teaching concept of "teaching as the leading factor and learning as the main body". Teaching activities are the organic combination of teachers' teaching and students' learning. The leading role of teachers should be reflected in putting forward learning objectives and requirements, arranging learning plans and contents, and guiding students' learning methods. Students' dominant position can only be realized through their active learning. 6. Constructivism learning theory: knowledge is not directly taught to students by teachers, but is actively constructed by learners themselves. It is constructed through meaning under a certain cultural background with the help of certain strength (including teachers) and necessary learning materials. Policy support: The standard divides students' mathematics learning objectives into four aspects: knowledge and skills, mathematical thinking, problem solving, emotion and attitude. Specific requirements are put forward for "solving problems" and "knowledge and skills", "mathematical thinking" and "emotion and attitude". Ask students to use the knowledge and methods they have learned to observe the strategic world of solving problems from a mathematical point of view and ask various questions; Able to flexibly use different methods to solve simple mathematical problems in life; Security system: 1. At present, there is a certain distance between the teaching of mathematical application problems in primary schools and the development trend of educational reform, so it is necessary to study this topic. 2. The members of the research group are of high quality, all of whom have junior college degrees. Many of them are studying for undergraduate courses, and some teachers have participated in the research of the subject many times, with rich research experience and strong business ability. 3. School leaders attach importance to teaching and scientific research and provide reliable policy and funding guarantee. Our school has a strong scientific research atmosphere, which is conducive to experimental research. Our school is located in the economic development zone, and it is the political, economic and cultural center of Tongshan County. Parents of students generally attach importance to education. The purpose of this study is to attach importance to the cultivation of students' innovative spirit and practical ability, which is supported by society and parents. On June 2nd, 2006, 1 1, our school held a signing ceremony with Ji Zheng Experimental Primary School in Tongshan County, and officially became a friendly school for teaching and research. We once formed a sister school with Pavresh Suhomlinski School in Ukraine. Our school is also the educational experimental base of Xuzhou Normal University. Therefore, all our projects will be guided by many educational experts, who can provide us with theoretical support and we will have opportunities for support and cooperation. Fourthly, the purpose and content of the study, through the methods of investigation, interview and classroom analysis, collect the general strategy "conditions and problems" to solve application problems. Analyze the quantitative relationship. Draft a solution. Answer. Inspection and evaluation. "These five aspects have made descriptive records and analysis of students' ability to solve mathematical application problems, and found out timely remedial strategies according to the causes of problem-solving errors. It aims to provide rich and detailed research materials and some teaching suggestions for the implementation of curriculum standards. Lead the majority of mathematics teachers in our school to constantly update their educational concepts, actively promote curriculum reform, and strive to change teaching methods, so as to urge teachers to continuously improve their scientific research ability in research and practice. So as to improve the quality of mathematics teaching in our school. Content: 1. Content design strategy of engineering application problems. Second, the effective way to solve the error cause analysis in engineering application problems. 1, for different types of engineering application problems, organize the whole class test. 2. Take out the poor students and analyze them according to different types of application questions to find out the reasons for the mistakes. Test students' methods and process of solving application problems, and make a comprehensive and detailed analysis of students' mastery and application level of problem-solving knowledge and skills. 3. Establish students' personal mathematics learning files. After a comprehensive and meticulous investigation, we should have a deep understanding of our own students, but we still need to establish a group of students' learning files, make appropriate classification and comparison, and make a table. 4. Students' mistakes in solving engineering application problems. Thirdly, the learning evaluation strategy of primary school students to solve engineering application problems. V. Research object and research method Research object: Primary school students in grade five or six. Research methods: (1) Literature method: Seriously study constructivism theory, modern cognitive psychology, New Curriculum Standards and other related theories or document spirit, extract theoretical knowledge that can guide the research of this topic for learning and reference, and do a good job in data collection and archiving. (2) Action research method: In mathematics classroom teaching, I diligently translate the teaching ideas obtained from the research into teaching behavior, constantly sum up, reflect, modify and practice in the actual teaching process, and gradually accumulate experience. (3) Survey method: Taking all students as the research object. Under the guidance of scientific methodology and educational theory, relevant data and information are collected purposefully, planned and systematically by using scientific methods such as questionnaires, interviews and measurements. (4) Observation: Through a comprehensive, detailed and profound observation of the performance of primary school students in the process of mathematics classroom learning, we can obtain more substantial and objective factual materials and determine the conditions for their development. (5) Case analysis: Take individual students as the research object, establish a case, analyze the answers to their application questions, track and record, and conduct a comprehensive and profound analysis of individual situations to provide a basis for verifying the subject. (6), experience summary method; Carefully write periodic reports, summarize the gains and losses of each stage, constantly adjust the research rhythm, and finally complete the conclusion report of the subject research in the form of summary. The research of this topic also adopts the methods of written test, interview and classroom analysis. The concrete measures of intransitive verbs: the first stage: (May 2006-September 2006): the preparation stage. (1), determine the subject name, discuss and write the subject plan, and draw up the examination plan. (2) set up an experimental research group; ⑶ Collect relevant theoretical data. (4) The members of the research group make experimental plans, and make preparations for declaration and project demonstration; 5], do a good job of testing before the project. The second stage: (September 2006-June 2006 12): Determine the research implementation plan (1), start the experiment, and train the teachers involved in the research in theory and practice. At the same time, we should seriously study the programmatic documents of the new curriculum reform, such as "National Basic Education Curriculum Reform Outline (Trial)" and "Mathematics Curriculum Standard for Full-time Compulsory Education (Experimental Draft)", as well as the theories and methods of educational research and relevant theories of case studies, so as to prepare for the implementation of this experiment. (2) Carry out research work according to the scheme and project implementation plan, and decompose and refine according to the characteristics of each discipline. Compile the research goal refinement scale. (3), carefully recorded and phased summary. (4) Hold regular meetings of project members to solve the problems in the research. The third stage: (2006, 12—2007, 7) The specific implementation stage of the research (1) discusses the applicability of the subject; Demonstration and guidance of constructing sub-project mode; Full participation; Popularize and deepen [2], modify the research plan and adjust the research direction. ⑶. Construct a sub-topic model of the discipline and conduct all-round research. (4) Promote phased research results and deepen research. 5. Identification and promotion of phased results, and construction of sub-project mode. (6) Hire relevant experts for theoretical argumentation. The fourth stage: (September, 2007-2008, 1) Re-study the unexpected situation in the process of revision, achievement summary and popularization. ① Re-study the difficult problems in the research process. (2) Hold a promotion appraisal meeting. ③ Qualitative evaluation of the research object. Statistical data, write relevant summary materials. The fifth stage: (2008.3-2008.7) the summary stage of the model research. (1), write a research report. 2. Apply to the superior for project completion acceptance, and evaluate and summarize the promotion of scientific research achievements. Seven. Division of project leaders: Qin Wen is responsible for the design of research plan, the organization and writing of research report. Other members of the research group are responsible for the implementation of the plan and the collection and arrangement of research cases. Eight, expected research results: 1, excellent courses, courseware (CD); 2. Teaching design works and essays; Case set. 3. Research report.