What are the methods of selecting topics and writing mathematical papers? Understanding the topic selection and writing methods of mathematical papers is an important prerequisite for writing a good mathematical paper. Welcome to read the topic selection and writing methods of my math thesis, I hope it will help you.

Introduction to the topic selection and writing methods of mathematical papers 1

In the process of reviewing mathematics papers, I found that many papers are simple in content, or one or two exercises prove it, or the textbook content is combined with other papers, simply repeated, or even copied directly. Many people engaged in mathematics education think it is difficult to write a thesis on mathematics education. In fact, they have not mastered the writing rules of mathematical papers.

There are two kinds of mathematics test papers, one is called pure mathematics test paper, and the other is called mathematics teaching test paper. It is difficult for many mathematics educators to have a lot of time to engage in pure mathematics research, and the title appointment system needs to publish papers publicly, so many people sum up their work experience and write some mathematics teaching and research papers. Mathematics teaching and research thesis is to study curriculum theory, teaching methods, educational ideas, teaching materials and the psychology of educational objects. But no matter what kind of math paper, we must follow the paper format and writing rules.

1 Write a math paper with principles.

1. 1 innovation

As a style of publishing research results, it should reflect the new facts, new methods and new viewpoints provided by the author himself. The title of the paper is not novel and the experiment is worthless. Even with superb writing skills, it is impossible to write something new. Low-level repetition is the most taboo in basic research, such as subjects, therapeutic factors and observation indicators. The results are similar to those of predecessors, nothing new, and the paper is not worth publishing.

1.2 science

The life of scientific papers lies in their scientificity. No scientific paper is worthless, which may lead others astray and cause harmful results. Writing a thesis should have: (1) reflecting the truth of the facts; (2) the objectivity of the selected materials; (3) Rationality of analysis and judgment; (4) the accuracy of language expression.

1.3 standard

Standardization is an important feature of the paper's expression form. Scientific papers have formed a relatively fixed paper format, which generally consists of titles, generally no more than 20 words; Abstract (applied methods, obtained results, significance, etc.). ); Index keyword; Introduction; Research methods, discussions, results, etc. This standardized procedure is a summary of the experience of countless scientists. Its advantages are: (1) conforms to the cognitive law; (2) concise and lively, with less space to accommodate more information; (3) It is convenient for readers to read.

2. Taboos for writing mathematical papers

2. 1 big topic

The thesis is not a book. If the topic of the thesis is too big, it is inevitable to talk in general terms and discuss it briefly. The basic characteristics of mathematics education thesis are: it has mathematics content, talks about mathematics education problems, has the form of a thesis, is not greedy, is not empty, and has novel views. In this way, the author will choose a smaller topic and write out the characteristics.

2.2 Close the door to write a manuscript

Papers in academic journals are naturally independent and complete when read alone. As far as the whole system of magazines is concerned, there will be some connections, which will either constitute a small topic or deepen the discussion. In this way, the author should know something about the publication you are going to contribute, so as not to shoot at random. You can't fabricate facts out of thin air and exaggerate conclusions. First of all, you should know what others have done and written, and avoid duplication in your own paper. At the same time, we can learn from others' achievements and further study on the basis of others' research achievements to avoid doing useless work.

2.3 formal thinking confusion

With the development of science today, the basic format of scientific papers has become unified all over the world. The paper requires standardization and normalization. Some papers are patchwork and inconsistent, and it is difficult to teach people to understand. Therefore, writing a paper should abide by the basic laws of formal logic, and it is particularly important to correctly use logical reasoning methods.

3. About the topic selection of mathematics papers

Are you looking for "hot" or "unpopular" topics in your math thesis? There are many people engaged in the research on "hot" topics, which are developing rapidly. If the author's unit has a solid foundation and occupies a considerable position in this field, it is of course necessary to conduct in-depth research in this field or expand to related fields. If you have a poor foundation in this field and haven't found a new breakthrough since you started late, don't engage in low-level repetition behind others. It is a better choice to choose "unpopular", knowledge blank and interdisciplinary fields as research objectives. Whether you choose "unpopular" or "popular", you must follow the following principles:

(1) The necessary topic selection should proceed from the needs of social and scientific development.

(2) Innovative topic selection should be a problem that no one at home and abroad has studied or has not fully studied.

(3) Scientific topic selection should be based on the most basic scientific facts.

(4) The feasibility of selecting a topic should fully consider the subjective and objective conditions for engaging in research, and the research scheme is feasible.

4. About the writing style of mathematical papers

4. 1 language expression is accurate.

Words, sentences, paragraphs, chapters and punctuation should be correct.

4.2 Clear and concise language expression

The sentences are fluent, the context is clear, the writing is fluent, and the language is concise.

4.3 Simple language

Easy to understand language is the essence of scientific papers. There is no need to elaborate scientific problems with flowery words or exaggerated modifications. In short, writing a paper should be emotional, purposeful and purposeful. Learn from others' achievements, learn from others' strengths, put yourself into practice, refine new ideas, and express your true feelings in the paper. Don't simply repeat others' opinions, so that the paper can be published and accepted by readers. References (omitted)

Knowledge expansion: mathematical model essay

Topic: On the Instructional Design of Plane Vector

There are many basic knowledge of vectors, and they are related to many other parts of knowledge, such as the relationship between vectors and functions, the relationship between vectors and trigonometric functions, the relationship between vectors and solid geometry, and the relationship between vectors and analytic geometry. Therefore, it is necessary to strengthen the further research and summary of the chapter on vectors.

1. From the operational point of view, vectors can be divided into three operations.

(1) geometric operation

The textbook in this chapter gives the triangle rule, parallelogram rule and polygon rule. Using these laws, we can solve the geometric operation problem in vectors well, and experience the mathematical thought of combining numbers with shapes.

(2) Algebraic operation

1, arithmetic of addition and subtraction; 2. Multiplication law of real numbers and vectors; 3. Vector product algorithm.

(3) Coordinated operation

In rectangular coordinate system, the coordinate operations of vectors include addition, subtraction, number multiplication and product. Through the coordinate operation of vector, the geometric operation and algebraic operation of vector are organically combined, which fully embodies the idea of analytic geometry, enables students to solve practical problems by using "analytic method" initially, and lays the foundation for studying analytic geometry and solid geometry in the future.

Second, the teaching content, requirements, key points and difficulties

(1) The teaching content of this chapter can be divided into two parts: the first vector and its operation, and the second declination triangle.

1, basic knowledge of plane vector, vector operation. The specific teaching contents are: vector (5. 1 section), addition and subtraction of vector (5.2 section), product of real number and vector (5.3 section), product of quantity and algorithm of plane vector (5.6 section).

2. Coordinate operation of plane vector, connecting geometric operation and quantity operation. The specific teaching contents include: coordinate operation of plane vector (section 5.4), addition and subtraction operation of vector, product operation of real number and vector, and coordinate representation of volume product of plane vector (sections 5.4 and 5.7).

3. The application of plane vector, the specific teaching contents include: fixed point of line segment (section 5.5), translation (section 5.8), sine theorem, cosine theorem (section 5.9), application examples of declination triangle (section 5. 10), and practice.

(2) Teaching requirements

1, understand the concept of vector, master the geometric representation of vector, and understand the concept of * * * line vector.

2. Master the addition and subtraction of vectors.

3. Master the product of real numbers and vectors, and understand the necessary and sufficient conditions for the connection of two vectors.

4. Understand the basic theorem of plane vector, understand the coordinate concept of plane vector, and master the coordinate operation of plane vector.

5. Mastering the quantitative product of plane vector and its geometric meaning, understanding the quantitative product of plane vector can deal with the problems about length, angle and verticality, and master the conditions of vector verticality.

6. Master the distance formula between two points in the plane and the coordinate formula of the fixed point and midpoint of the line segment, and skillfully use it; Master the translation formula.

7. Master sine theorem and cosine theorem, and use them to solve oblique triangles.

8. Through the teaching of trigonometric solution, the ability to solve practical problems by using the learned knowledge is continuously improved.

(C) the focus of teaching

Geometric representation of vector, addition and subtraction of vector, product of real number and vector, quantitative product of plane vector, coordinate operation of vector, condition of vertical vector, distance formula between two points in plane, coordinate formula of bisector and midpoint of line segment, translation formula, sine and cosine theorems.

(D) Teaching difficulties

The concept of vector, the understanding and application of vector arithmetic and geometric meaning, the solution of oblique triangle, etc.

Three. Characteristics of this chapter

The characteristics of textbook arrangement determine that this chapter is different from other chapters in teaching.

1, the textbook fully embodies the idea of combining numbers with shapes in this chapter. First of all, the textbook introduces the vector by finding the displacement of the ship from A to B, according to the characteristics of students' thinking, from concrete to abstract, based on the knowledge of plane geometry. In editing concepts, rules and examples, arrange as many graphs as possible, and arrange more drawing exercises, drawing exercises and drawing verification exercises, which provide conditions for students to actively participate in teaching activities and give full play to the main role of students' learning. They can not only grasp the characteristics of plane vectors, but also enable students to understand new concepts through operational exercises. Secondly, a proper number of examples, exercises and exercises in each section of this chapter can make teaching have sufficient independent space, provide space for teacher-student interaction, provide opportunities for students to explore, discover and summarize, and also provide the possibility for teachers to reprocess teaching materials according to teaching objectives. 2. Solving practical problems with "vector method" is one of the remarkable features of this chapter. Vector is closely related to geometry; Vectors have operations such as addition, subtraction, product of numbers, product of quantities, and coordinate operations of plane vectors, so vectors have dual properties of geometry and algebra, which can link geometry and algebra, thus giving us a new mathematical method-vector method; Vector method can turn technical problem-solving into algorithm problem-solving, and use vector method to deduce sine and cosine theorems, laying a foundation for studying analytic geometry and solid geometry in the future.

4. Strengthening mathematical ability is another remarkable feature of this chapter. Because the essence of vector method in this chapter is to turn technical problem-solving ideas into algorithm problem-solving ideas; The ability to solve practical problems with what you have learned is an important teaching requirement of this chapter. In order to better cultivate students' ability of applying mathematical knowledge to solve practical problems and practical operation, the textbook also arranges "practical homework". Through practical measurement, students can use sine and cosine theorem to solve practical problems, which not only embodies the instrumental role and application of mathematics, but also promotes students' understanding and mastery of knowledge from another aspect. In order to strengthen students' correct operation, deformation and data processing according to laws and formulas; According to the conditions and objectives of the problem, find and design a reasonable and simple operation mode; It can estimate and approximate the data according to the demand, that is, computing power. In this way, students can comprehensively use the mathematical knowledge, ideas and methods they have learned to solve problems, understand the materials stated in the problems, summarize, sort out and classify the information provided, abstract practical problems into mathematical problems and establish mathematical models; Being able to apply relevant mathematical methods to solve problems and verify them, and being able to correctly express and explain them in mathematical language, that is, practical ability.

Fourth, teaching experience.

According to the teaching content, requirements and characteristics of this chapter, combined with students' cognitive level and teaching practice in recent years, we have the following teaching experiences on "plane vector":

1. Carefully study the examination syllabus, teaching requirements and objectives, analyze the characteristics of this chapter, and design the teaching plan, organize the teaching process and guide the learning methods according to the possible positive and negative transfer effect of students' original knowledge structure on learning this chapter.

2. Emphasis should be placed on basic knowledge, basic methods, basic skills, teaching materials, applications and tool functions. Don't overemphasize, don't choose off-topic and difficult questions, follow students' cognitive rules and follow the requirements of the syllabus.

3. Grasp the dual attributes of the combination of numbers and shapes of vectors and geometric algebra, improve the application ability of "vector method" and give full play to the tool role. In teaching, guide students to understand how vectors are represented by directed line segments, master three kinds of vector operations, understand the connection and difference between vector operations and real number operations, and strengthen the foundation of this chapter.

4. Training mathematical modeling by solving triangle application problems and combining with the teaching process, guiding students to remember, distinguish and understand the application scope of sine and cosine theorem, and the formula will be deformed; When solving triangles with formulas, triangle types will be classified and discussed; Guide students to master the relationship between the choice of sine and cosine theorem and the search for reasonable and simple operation methods when solving triangles, and summarize the application problems related to solving triangles.

5. Strengthen the combination of numbers and shapes, transformation, classified discussion and equation. Strengthen the cultivation and improvement of students' computing ability. Guide students to understand the relationship and difference between translation knowledge in this chapter and functional image translation; Understand the relationship between solving triangle and trigonometric function; Pay attention to the concept of distinguishing the angle between two vectors and the angle between straight lines.

Topic selection and writing methods of mathematical papers II. There should be a guide to writing math papers.

1. 1 anisotropy

As a style to announce the effect of the seminar, it should reflect the new reality, new methods and new opinions provided by the author himself. The title of the paper is not novel, which tests the effect of worthless reporting. No matter how good the writing ability is, it is impossible to write anything new. Basic research should avoid low-level repetition, such as the principle of subjects, processing elements, observation policies, etc. The results are similar to those of the predecessors, nothing new, and the paper is not worth publishing.

1.2 science

The life of scientific papers lies in their scientificity. Without scientific papers, it is worthless, and it may also lead others astray and cause adverse effects. Writing a thesis should have the following characteristics: (1) reflecting reality; (2) the objectivity of the selected materials; (3) analyzing the rationality of the conclusion; (4) Accuracy of speech expression.

1.3 standard

Standardization is an important feature of the paper. Scientific papers have formed a relatively fixed paper format, which generally consists of titles, generally no more than 20 words; Abstract (methods used, effects achieved, significance, etc. ); Index keyword; Introduction; Discuss methods, comments, effects and other parts. This standardized procedure is a summary of the experience of countless scientists. Its advantages are: (1) conforms to the cognitive law; (2) concise, short in space and large in information; (3) It is convenient for readers to read.

Second, the preparation of mathematical papers taboo

2. 1 act rashly

The thesis is not a book. If the topic of the thesis is too big, it is inevitable to talk in general terms and discuss it briefly. The basic characteristics of mathematics education papers are: having mathematics content, talking about mathematics education problems, having the form of papers, not being greedy, not empty, and having new opinions. In this way, the author will choose a smaller topic and write out the characteristics.

2.2 Close the door to write a manuscript

The papers in academic magazines are naturally independent and complete when taken out alone. As far as the whole magazine system is concerned, there will be some connections, which will either form a small topic or make the comments deeper. In this way, the author should know something about the publication you prepared, so as not to shoot it indiscriminately. You can't build a car behind closed doors, and you can exaggerate your conclusions without reality. First of all, you should know what others have done and written, so as to prevent your own papers from repeating. Learn from others' effects together, and discuss further on the basis of others' research results to prevent futility.

2.3 confusion of thinking mode

With the development of science, the basic format of scientific papers has become consistent all over the world. The paper requires standardization and normalization. Some papers are patchwork and inconsistent, and it is difficult to teach people to understand. Therefore, the writing of the paper should follow the fundamental law of pattern logic, and it is particularly important to correctly use logical reasoning methods.

Third, on the topic selection of mathematical papers

Is the topic selection of mathematics paper "popular" or "unpopular"? There are many people engaged in the discussion of "hot" topics, which are developing rapidly. If the author's unit has a strong foundation and occupies an appropriate position in this category, it is of course necessary to further discuss it from this category or expand it to related categories. If you have a poor foundation in this field and haven't found a new breakthrough since you started late, don't engage in low-level repetition behind others. It is better to choose "unpopular", blank common sense and interdisciplinary as the discussion policy. Whether you choose "unpopular" or "popular", you should follow the following criteria:

(1) Demand-oriented topic selection should proceed from the needs of social and scientific development.

(2) The topic selection of the opposite sex should be a problem that has not been discussed or fully discussed at home and abroad.

(3) Scientific topic selection should be based on the most fundamental scientific reality.

(4) The feasibility of selecting a topic should fully consider the subjective and objective conditions for discussion, and the discussion scheme is feasible.

Fourthly, the writing style of mathematical papers.

4. 1 is accurate in speech expression.

Words, sentences, stage, decoration and punctuation should be correct.

4.2 Clear and concise oral expression

The sentences are fluent, the context is clear, the writing is fluent, and the words are concise.

4.3 Simple words

Easy to understand is the essence of scientific papers. The discussion of scientific issues does not need to use rich vocabulary, nor does it need to be exaggerated and polished. In short, writing a paper should have feelings, intentions and purposes. Learn from others' effects, learn from others' strengths, enter into practice, refine new ideas, show your true feelings in the paper, and don't simply repeat others' ideas, so that the paper can be announced and accepted by readers.

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