Guide students to master the specific steps and methods of examining questions in teaching. The following is a sample essay on the opening report of 20 17 mathematics subject shared by J.L. ..

Model essay 1: topic: exploring the cooperative learning model of junior high school mathematics.

First, the significance and value of this topic:

Theoretical significance: The basic idea of national curriculum reform: student development-oriented, caring for students' needs, changing students' learning methods as a foothold, emphasizing that classroom teaching should be linked with students' lives, and emphasizing that students should make full use of their own experience potential for constructive learning. At the same time, the new curriculum standard of junior high school mathematics emphasizes the foundation, popularization and development, which makes mathematics education face all students, thus realizing: everyone learns valuable mathematics; Everyone can get the necessary mathematics; Different people get different development in mathematics. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. This shows that cooperation is really important in mathematics learning.

Application value: Effective mathematics learning activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. As a new teaching method, subject cooperative learning has become one of the focus issues in mathematics classroom teaching under the new curriculum standards.

Through the research of this topic, it is helpful to fully establish students' dominant position and establish the interactive, coordinated and consistent relationship between teaching elements; It can effectively improve students' learning methods and teachers' guidance methods in junior high school mathematics teaching, which is conducive to stimulating students' interest in learning and realizing the goal of happy learning in mathematics teaching. So as to improve students' learning effect, cultivate students' ability of cooperation, communication and innovation, and then improve their comprehensive quality.

Review of the present situation of similar research inside and outside the province: China began to explore cooperative learning in the early 1990 s, and there were studies and experiments on cooperative learning, which achieved good results. Many students have benefited from it, and teachers have also formulated some effective implementation strategies in practice. However, at present, the research on cooperative learning in China is mainly in colleges and universities, and cooperative learning in middle schools has just started. With the comprehensive promotion of quality education, cooperative learning needs further development in junior high schools, and primary schools have not seen the research topic of integrating mathematics and cooperative learning. Therefore, the research on the integration of junior high school mathematics and cooperative learning is forward-looking. At present, the domestic research on cooperative learning is more about putting forward some principles, and less about practical, concrete and operable ways and means. This topic focuses on the exploration of cooperative learning methods, which can make up for this deficiency.

Second, the research content, objectives and ideas

What is the form of cooperative learning? It is to encourage each student to share weal and woe through group goals, group division of labor, role assignment and transformation, and collective rewards. By infecting public opinion, collective honor experience and other activities, let every student realize that only by making efforts to contribute to the collective can everyone obtain the necessary mathematics.

Investigation and analysis on the present situation of learning style.

At present, there are various disadvantages in the form of mathematics teaching and learning, either learning has no goal or the goal cannot be achieved; Either the teacher is not responsible and indifferent to the students' problems, or the teacher is subjective and divorced from the students' reality. In short, the form of mathematics learning needs to be changed urgently.

The role of cooperative learning in mathematics learning.

Efficient use of time, so that students have more opportunities for active learning. It is more conducive to cultivating students' spirit of social cooperation and interpersonal skills. It can help students learn from each other's strong points and narrow the gap between students at both ends, and both sides can benefit, especially the underachievers. It is more conducive to cultivating students' spirit of active exploration, unity and cooperation and innovation.

The role and position of teachers in cooperative learning.

Changing ideas is the requirement of a learning society. In the open educational environment, the position and role of teachers have also changed. Teachers are not outsiders in the group, but makers of learning objectives, designers of programs, creators of situations, participants in discussions, coordinators, encouragers and evaluators.

How to guide students to cooperative learning?

The key to guiding students' cooperative learning lies in carefully designing discussion topics. From the teacher's point of view, the design topic should be interesting, situational, operable and creative.

Evaluation objects and methods of group cooperative learning.

The objects of evaluation include self-evaluation and peer evaluation. The contents of evaluation are mainly learning attitude, cooperative spirit, learning ability, teamwork and so on. As a systematic way of learning, cooperative learning must have corresponding evaluation mechanism. Establishing a reasonable evaluation mechanism of cooperative learning can change the competition among students into the competition among groups, change individual scores into group scores, and take the overall scores of groups as the evaluation basis, thus forming a pattern of cooperation and competition among members in groups. Shift the focus of the whole evaluation from isolated individual competition to cooperation.

This topic attempts to combine students' autonomous learning and cooperative learning organically by changing the practice process of group cooperative learning mode, so that students can truly feel, understand and master the formation process of mathematical ideas, knowledge and skills, stimulate students' interest in learning mathematics, promote the coordinated development of students' mathematical thinking ability and life ability, and cultivate students' ability to analyze, explain and solve real-life problems with mathematics, as well as their awareness and innovative spirit of operational research optimization.

Under the guidance of teachers, students gradually develop self-awareness, cooperation awareness and self-management ability. Really realize the integration of autonomous learning and group cooperative learning.

Changing ideas is the requirement of a learning society. In the open educational environment, the position and role of teachers have also changed. Teachers are no longer just imparting knowledge, but should be transformed into guides, consultants, designers, managers and participants of learners' learning. Through the research of the subject, we will cultivate a team of teachers with advanced educational concepts and a certain level of teaching and scientific research.

From the perspective of cooperative learning under the new curriculum standard, this topic takes group activities as the basic way, establishes multiple interactions of cooperative research, pays attention to the open cooperative process and emphasizes the construction of cooperative methods.

Research methods:

(2) Investigation: Through discussion, questionnaire and other means, learn about the current situation of mathematics learning from students and make a scientific analysis.

④ Experimental method: In the experimental stage of the learning mode, through the comparative analysis of the experimental class and the control class, the practical operation effect of this learning mode is studied.

⑤. Action research method: In the research process of project implementation, through study, practice, reflection, evaluation and analysis, the reasons for gains and losses are found, and the team cooperation ability is continuously improved.

6. Experience summary method: On the basis of teaching practice and research, according to the research focus of the subject, accumulate materials at any time, explore effective measures, sum up gains and losses, and find effective ways, methods and principles of group cooperation. The materials reflecting the facts in group cooperative learning are collected in various ways, and analyzed, sorted and processed to the height of rational understanding as the theoretical basis of cooperative learning.

Research stage

(1) preparation stage (April 20 15, May 20 15):

(2) Implementation process (June 2065438+June 2065438 +20051October)

According to the project design scheme, carry out action research in a planned and step-by-step manner. Keep practicing, summarize regularly, and have phased results every semester.

⑶ Summary stage (February 20 15, May 20 15)

On the basis of summing up the above achievements, the subject is comprehensively and scientifically summarized. Write a summary report and hold a report meeting on the results.

The second part: the realistic background and significance of the research;

Judging from the quality analysis of our school over the years and the quality analysis of the 20XX math quiz in Longsheng County, the main reason why students lose points is that they don't carefully examine the questions. In fact, in daily teaching, every time I do math homework or test questions, I can hear teachers complain that students are too careless and have not carefully examined the questions, and students regret that they have not carefully examined the questions. In the mid-term and final quality analysis, the teacher summed up the most sentence that the students were too careless and did not carefully examine the questions.

It can be seen that students' ability to examine questions puzzles every teacher and every student. Especially for rural primary school students, most of them can't do it carefully before they do it, because they have developed bad habits such as carelessness, lax demands on themselves and no sense of responsibility.

Through questionnaire survey, the most important step of examining questions is often ignored or despised by most students in practice, which directly affects the speed and correct rate of students' problem solving and indirectly leads to students' fear and panic about mathematics learning. It is very common for primary school students to solve wrong questions because of unclear exams. Students' ability to examine questions is weak and their habit of examining questions is worrying.

The ability to examine questions is a comprehensive mathematical ability. I want to promote students' analytical judgment and reasoning ability and creative thinking from scratch, from low to high, through the research on the cultivation of primary school students' ability to examine questions in mathematics learning, so as to improve students' ability to solve problems in mathematics.

Concept definition and theoretical basis

Theoretical basis:

It is clearly pointed out in the "Mathematics Teaching Syllabus for Primary Schools" that it is of great significance to make students learn mathematics well, cultivate their interest in learning and develop good study habits in primary schools, so as to improve the quality of the whole nation and cultivate socialist citizens with ideals, morality, culture and discipline. Examining questions is a kind of ability and a habit. The cultivation of primary school students' ability to examine questions in mathematics learning can promote students to develop good study habits.

Project implementation plan

research contents

To study the reasons for the weak ability of rural primary school students to examine questions.

This paper studies the training scheme of mathematics learning ability of rural primary school students.

According to the learning content, study the methods of students' examination of questions.

This paper studies the cultivation of the habit of examining questions in rural primary school students' mathematics learning.

Specific operational measures

To study the reasons for the weak ability of rural primary school students to examine questions. Through questionnaires and interviews, this paper investigates teachers' attitudes, methods, abilities and habits of cultivating students' ability to examine questions. In-depth understanding and analysis of individual students with particularly weak ability to examine questions in class, and find out the reasons for their weak ability to examine questions.

According to the learning content, study the methods of students' examination of questions. Based on different learning contents, the methods of examining questions will be different. Each grade of primary school mathematics is divided into four sections from the teaching content: number and algebra, space and graphics, statistics and probability, and practical activities (comprehensive application), which spiral upward, among which calculation and problem solving account for a considerable proportion. According to different contents, explore the corresponding effective examination methods.

The cultivation of the habit of examining questions in rural primary school students' mathematics learning mainly includes the habit of examining questions, solving problems and checking. Strengthen the training of reading questions and study reading methods. Reading questions is the first step in examining questions. When reading the questions, don't add words, don't miss words, read the questions smoothly, and form the habit of reading them two or three times. When examining questions, it is required to do mouth, eyes, hands and heart; Guide methods and cultivate good problem-solving habits.

Guide students to master the specific steps and methods of examining questions in teaching. For example, first read the question carefully, find out what the question says, which quantities are known conditions, what the question is, and accurately repeat the meaning of the question in your own language; Then you can underline the keywords and words in the question and understand their meanings correctly; Analyze and find out the quantitative relationship in the problem, know what conditions are needed to solve the problem, and how to find these conditions. When you don't understand, mark it in time and develop the habit of marking with symbols; Study and cultivate students' good habit of careful inspection.

Rural primary school students often have no good habit of checking, which requires the guidance of teachers, so that students can appreciate the benefits of checking and reward them according to their actual situation, forming an atmosphere. Inspection is the "last remedy" to check the problem.

Research steps and methods

The second stage: 20xx165438+1October 20xx July project implementation stage, analyze the reasons according to the plan, formulate countermeasures and put them into practice. First, investigate the causes of students' poor ability to examine questions, and then discuss the methods and matters needing attention with students. Through practical training, let students analyze their own gains and losses, organize students to exchange successful practices and experiences, strengthen training, and let students develop good habits of examining questions. Finally, the results are tested, compared with the results before the inquiry, summed up the experience, and extended the research results to the mathematics teaching and research group. At the same time, write papers that can be studied.

Selection of methods:

(1) investigation and research method. Through investigation, we can understand the reasons why rural primary school students are weak in examining questions. And the changes before and after the study.

(2) Case study method. Through the understanding of individual students with particularly weak ability to examine questions in the class, we can formulate corresponding measures, implement intensive training, observe the effect, explore the law and sum up experience.

(4) Literature research method. Through reading and searching related literature, the theoretical basis of this topic has been laid; At the same time, understand the current situation of similar research, provide reference for this study and lay the foundation for innovative research.

(5) Cooperative research method between teachers and students. Through discussion, research, training, analysis and summary between teachers and students, an effective way to improve the ability of examining questions is found.

Table of expected results and results of the study

(1) Explore ways and means for students to effectively examine questions, improve the ability of rural primary school students to examine questions through research, and cultivate good study habits of rural primary school students to carefully examine questions.

(2) Research report.

I will explore and implement it step by step according to the project implementation plan with full work enthusiasm. I want to explore the methods and ways for students to effectively examine questions through the research of this topic, and cultivate the good study habits of rural primary school students to carefully examine questions through research. I hope that under the guidance and care of my superiors, my research work can be a complete success through my efforts!

Model essay on the opening report of mathematics small topic Part III: Thesis title: On the application of Taylor formula.

The significance of subject research

Among elementary functions, polynomial is the simplest function. Because polynomial functions have only three operations: addition, subtraction and multiplication. If rational fractional functions, especially irrational functions and elementary transcendental functions can be approximated by polynomial functions, and the errors meet the requirements, obviously, it is of great significance to study the function behavior and approximate calculation of the function values. So what is the only condition for a function to be approximated by a polynomial function? What is the relationship between the coefficients of this polynomial function and this function? How about replacing this function error with polynomial function approximation?

Through the study of mathematical analysis, I feel that Taylor formula is an important content in calculus. Taylor formula is a useful tool in the estimation and approximate calculation of function value, approximation of function by polynomial, finding function limit and definite integral inequality, and equality proof.

Literature review

main content

Application of Taylor formula

Application of Taylor formula in limit calculation

It is very simple to calculate the limit of function polynomial or rational fraction. Therefore, for some complex functions, the limit problem of the original complex function can be transformed into a limit problem similar to polynomial or rational fraction according to Taylor formula. When the following conditions are met, Taylor formula can be considered to find the limit:

(1) When using Robida's law, there are many times, and the process of deduction and simplification is complicated.

(2) There is infinitesimal difference between numerator and denominator, and this difference is not easy to be converted into equivalent infinitesimal substitution form;

(3) It is not difficult to expand the encountered function into Taylor formula.

When Taylor formula is used to solve the limit, the key is to determine the order of expansion. If the denominator (or numerator) is 0, the numerator (or denominator) is expanded into an ordered McLaughlin formula. If both numerator and denominator need to be expanded, they can be expanded to the infinitesimal order of their same order, that is, the power of the first non-zero term after the merger.

Application of Taylor formula in proving inequality

Proof of general inequality

Type: It is suitable for the proposition that the function has second and above derivatives, the magnitude of the highest derivative or the upper and lower bounds are known. Prove the idea:

(1) Write a Taylor formula that is one order lower than the highest derivative;

(2) Scale and expand according to the given magnitude or upper and lower bounds of the highest derivative.

Proof of definite integral inequality

For formula: the second and above derivatives of the integrand function are known, and the sign of the highest derivative is also known.

The idea of proving the problem: write Taylor expansion directly, and then scale the expansion according to the meaning of the problem.

Proof of definite integral equation

For type: it is applicable to the proposition that the integrand has second or more continuous derivatives.

Proof idea: As an auxiliary function, Taylor expansion will be carried out at the required point.

The remaining items should be properly disposed of.

Application of Taylor formula in approximate calculation

When using Taylor formula to find the limit, the function should be expressed by Taylor formula with Peano remainder; If it is used in approximate calculation, the remaining term should be expressed in Lagrangian form, which is convenient for estimating the error.

research method

In order to write a good paper, I went to China Journal Network, China Knowledge Network and China Digital Journal Group to find out the publication date, title and author of relevant papers. Next, I went to the back room on the fourth floor of the library to find relevant literature, and then I went to the electronic reading room to find relevant periodical literature. Borrow relevant books from the library, read them carefully, analyze them carefully, and try to do a good job in graduation thesis through the patient summary, research, guidance and correction of teachers. Specifically using mathematical induction, analysis, reduction to absurdity, deduction and other methods.

Scheduled plan

In order to do my graduation thesis work well in a planned way, I have arranged a graduation thesis schedule for myself, and I will finish my graduation thesis work in time in strict accordance with my schedule.

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