Model essay on economic mathematics for freshmen: Practical research on hierarchical teaching of economic advanced mathematics.
Advanced mathematics is an important basic course for undergraduates majoring in economics, which plays a key role in mastering professional course knowledge and engaging in higher-level research in this major. In order to make the students of this major learn this course well, our school has tried out the teaching mode of layered teaching for the teaching of advanced mathematics. This paper analyzes and expounds the advantages of stratified teaching from the aspects of necessity, mode and effect.
Keywords: advanced mathematics; Hierarchical teaching; teach students in accordance with their aptitude
First, the necessity of implementing hierarchical teaching
Advanced mathematics is an important basic course for undergraduates majoring in economics. Its importance lies in that learning this course well is not only the basic guarantee for learning its specialized courses well, but also an indispensable tool for improving the quality of thinking and conducting higher-level research. Therefore, ordinary undergraduate colleges offer advanced mathematics courses to economic students from the beginning of their freshman year. However, after the enrollment expansion of colleges and universities, China's higher education has developed from elite education to mass education, which makes it an indisputable fact that the enrollment of various majors in colleges and universities has soared and the quality of students has declined. Moreover, students come from all provinces and cities in China, and their math scores and levels are uneven; Different students have different hobbies and development directions. However, the textbooks, teaching plans and syllabus used by the same major are the same, and students and teachers have basically no choice. This unified teaching mode has seriously hindered the development of advanced mathematics.
The quality of teaching has been further improved. At present, the biggest problem facing the teaching of this course is the decline of students' interest in learning and academic performance. There are many factors that cause this problem, one of which is the neglect of students' different needs for teaching methods and teaching contents. Therefore, according to students' math scores, hobbies and development aspirations, it is imperative to implement different requirements and different teaching methods for students with full respect for personal wishes. Based on the scientific theory and the teaching practice in our school, this paper analyzes and discusses the implementation methods and effects of hierarchical teaching.
Second, the theoretical basis of hierarchical teaching
The theoretical basis of hierarchical teaching is American psychologist and educator Bloom.
(Bloom)? Master's study? Theory. Bloom believes that as long as appropriate materials and teaching are provided, and each student is given appropriate help and enough time, almost all students can complete their learning tasks or achieve the prescribed learning goals.
Mark. Master's study? Does the theory need to be taught by the teacher? Should be carried out according to students' actual development level, learning style and personality characteristics? . Students from ordinary colleges and universities come from all provinces and cities in China. In recent years, the expansion of colleges and universities has also caused a decline in the quality of students. This has caused the students' mathematics level to be uneven and quite different, and hierarchical teaching can better reflect the above ideas. The layered teaching method is also based on the theory of multiple intelligences, respects the individual differences of students, attaches importance to individual development, follows the principle of teaching students in accordance with their aptitude, and regards the development of students as the starting point and destination of teaching, which truly embodies? Centered on student development, guided by social needs and based on subject knowledge? Only the requirements of educational reform can truly reflect the spiritual connotation of quality education. In addition, in fact, in ancient China, Confucius, an educator and thinker, had already put forward the importance of educating people? Deep, shallow, beneficial and respectful? , which is a risk-averse? Teaching students in accordance with their aptitude varies from person to person? . That is to say, the teacher's? Teaching? Must be suitable for students? Study? .
Third, the implementation of hierarchical teaching
Hierarchical teaching is to set learning objectives, design course content and create different teaching situations and teaching methods according to students' different learning levels and abilities, as well as students' own interests and requirements in mathematics, so as to teach students in accordance with their aptitude, promote students' all-round exercise and development, and then realize a more efficient and effective teaching model. Since the 2008 school year, with the strong support of the Academic Affairs Office of our university, we have tried the hierarchical teaching mode in the teaching of advanced mathematics for economic majors. Compared with the previous non-hierarchical teaching mode, the teaching effect has been improved obviously in the past two years. The specific implementation method is that for the two schools of the School of Economics, the School of Economics and Trade and the School of Business Administration, we adopt the method of not disrupting the departments, or we can divide classes by layers. The level is divided into two layers, namely, layer A and layer B. Layer A is a higher level in mastering basic knowledge, flexibly applying theory and combining theory with practice. The teaching plan and content are aimed at in-depth research in postgraduate entrance examination and professional fields. The corresponding requirements of layer B are lower, but the basic principle is to lay a solid foundation and make mathematics a powerful tool for subsequent professional courses. At the same time, due to the high requirements of Class A, it is not easy to grasp, and teachers with many years of teaching experience are responsible for teaching. The basis of stratification is objective and subjective. The objective basis is the students' mathematics achievement level. On the one hand, we should refer to the results of the college entrance examination; On the other hand, freshmen have to take a math class at the beginning of their enrollment? Found it? Exam. ? Found it? The test questions are given by teachers with rich teaching experience, most of which are average in difficulty, and a few of them are more difficult, which shows that students' math scores are high or low. The subjective basis of stratification is students' own interests and requirements for mathematics courses. For example, some students are very interested in mathematics, although their grades are average, or they are interested in continuing their research in this field, such as postgraduate entrance examination. We can consider dividing students into advanced classes. On the other hand, some students have high test scores, but they are not interested in mathematics, and just regard it as a compulsory basic course. Then, they can ask the students' opinions and divide them into class B. Considering the class size and teaching effect, we take quite three? Science class? The number of students is one class. The fundamental purpose of hierarchical teaching is to teach students in accordance with their aptitude. Therefore, after the end of the final exam of the first semester, some students' mathematics scores and interest in mathematics may no longer be suitable for the original class teaching objectives, which requires the adjustment of classes, that is to say, hierarchical teaching has certain mobility. Adjustment also follows the above hierarchical basis, because adjustment is hierarchical. On the one hand, it is the students' test scores, on the other hand, it also takes into account the students' subjective wishes. However, practice has proved that the fluctuation should not be too large, and it is appropriate not to exceed 5%.
Fourthly, the effect and thinking of stratified teaching.
Hierarchical teaching has achieved certain results. Compared with students who did not implement hierarchical teaching before Grade 08, the failure rate has been greatly reduced. The number of people with scores of 60-69 and 70-79 increased significantly, and the excellent rate above 90 increased slightly, and the average score increased significantly. The distribution of grades is normal. It can be seen that hierarchical teaching meets the wishes and requirements of most students and should be adhered to and improved. Hierarchical teaching is targeted and personalized, which can improve students' interest in learning and reduce the burden brought by the abstract and boring subject itself. Make some students who have no confidence in mathematics and lose interest in learning meet the requirements of the syllabus, and better solve the contradiction between the two levels of mathematics learning of college students. After Grade 08, students' recognition of hierarchical teaching is getting higher and higher, and their adaptability and confidence in learning mathematics are greatly enhanced. Practice has proved that hierarchical teaching ensures that all students teach students in accordance with their aptitude, and it has also been achieved? Top students eat well, middle students eat well, and poor students can eat? At the same time, it lightens students' schoolwork burden, which is an effective way to comprehensively improve teaching quality and implement quality education. Although the implementation of hierarchical teaching has greatly improved all aspects of higher mathematics teaching, there are still some problems to be solved urgently. Like different? Science class? Some students have math classes in the same class, which brings difficulties to classroom and homework management and puts forward new requirements for teachers and counselors. In addition, do you still need to press the students' grades after the exam? Science class? Ranking has also caused some trouble. Our work is just the beginning, and we will continue to improve the teaching methods of hierarchical teaching in the future practice. For example, when assessing students' grades, not only written test scores can be considered, but also other forms of assessment results can be considered; In the teaching process, multimedia teaching can be carried out with the help of computers to improve students' interest in learning.
References:
Yang Ni. Rational thinking on hierarchical teaching of college mathematics [J]. Higher Education Forum, 2007.
(5):87-89.
[2] Zheng. Theory and practice of mathematics teaching method in middle school in the new curriculum [M]. Beijing: National Defense Industry Press, 2006.
[3] Guo Dejun and Yuan Lee. Theory and Method of Cooperative Learning [J]. Research on Higher Normal Education, 1994, (3): 43-54.
[4] Fu Haifeng. Cultivating students' thinking ability in hierarchical teaching [J]. Middle School Mathematics Reference, 1997, (10).
Model essay on economic mathematics for freshmen 2: Teaching reform of economic mathematics course
This paper discusses the teaching reform of economic mathematics from the aspects of teaching content reform, teaching method reform, teaching means reform and examination method reform. Its leading idea is: economic mathematics teaching should be based on? Mathematics runs through the whole teaching. ? With the application practice as the main line, strengthen the understanding, application and supplement of knowledge points, and cultivate students' ability to establish mathematical models and solve practical problems.
Keywords: economy; Mathematics class; reform in education
Many people know that mathematics is very important, but they don't know where it is important. They only know that all kinds of exams have to take math. It seems that this is synonymous with exam-oriented education. What is the function of learning mathematics? How can mathematics teaching cultivate applied and innovative talents to meet the needs of the development of socialist market economy? It has always been a problem discussed in our teaching reform. This paper discusses the reform of teaching content, teaching methods, teaching means and examination methods of economic mathematics in higher vocational colleges. Its leading idea is based on? Applying mathematics runs through the whole teaching of economic mathematics. ? With the application practice as the main line, strengthen the understanding, application and supplement of knowledge points, and cultivate students' ability to establish mathematical models and solve practical problems.
First, what is the teaching philosophy? Apply? This goal runs through the whole teaching process.
Compared with ordinary advanced mathematics, economic mathematics has its particularity, and students should correctly understand the relationship between economy and mathematics. In the field of economics, mathematical analysis must serve economic analysis, not put the cart before the horse, and should be adhered to? Mathematics as the body and economy as the use? The principle of. Therefore, economy should be integrated into mathematics in teaching. At the beginning of each chapter, the hot issues in current economic life are used to stimulate students' interest in learning relevant mathematical knowledge, and the contents of each section are input. Take the economy as an example as far as possible, and mathematics and economy are gradually combined. Finally, combined with the relevant mathematical knowledge learned, the economic problems raised at the beginning of each chapter are analyzed. For example, when talking about function, we introduce the concept of function according to what the output of goods is affected and what the telephone bill is related to. After we finish the concept of function, we give the above functional relations with mathematical expressions, and finally give the functions commonly used in economic analysis (cost function, income function, profit function, demand function, etc.). ). When talking about derivatives and differentials, ask the students, have you ever seen a sudden drop in the price of a commodity and an increase in profits in your daily life? When students give many examples and their interest in learning is stimulated, the problem of change rate is introduced, that is, the derivative to be introduced. After writing this chapter, I will give the answer to why the price reduction of goods will increase profits, that is? Flexible? . In other words, appropriate price reduction will greatly increase demand, thus increasing income. This kind of teaching not only helps students understand the relevant mathematical principles and methods, but also helps students understand its application in economic management.
Second, what is the teaching content? Necessary and sufficient? For principle.
Economic mathematics is an important basic course and tool course for economic management majors in higher vocational colleges. By studying calculus, linear algebra and linear programming, students can initially have the ability to solve economic management problems and lay the necessary mathematical foundation for studying economic management courses and engaging in economic management work in the future. How to complete the teaching of so many contents in a limited time? Then it is necessary to closely combine the professional training objectives and press? Necessary and sufficient? The selection principle of economic mathematics content. Adding or deleting teaching content is to remove some abstract, theoretical and pure mathematical language concepts and theorem proofs and replace them with qualitative and popular descriptive definitions and geometric explanations. For example, the concept of function limit has a perceptual knowledge for higher vocational students, and it is enough to establish a concept and idea of limit. This paper mainly introduces the concept of function limit, and then simply describes the limit of integer function sequence as a special case of function limit. This treatment highlights the concept of function limit. Compared with the past, the concept and nature of sequence limit are introduced first, and then the function limit is introduced, which saves a lot of time and has good teaching effect. In teaching, power function, exponential function, linear function, matrix algebra, linear equations and so on are emphasized. , and deleted the concavity and convexity of the curve, the derivative of the function determined by the parametric equation, the volume of the rotating body, and some contents of the determinant. Instead, they spend their time on simple interest, compound interest, output, income, cost, minimum investment, maximum profit, elastic function and other things they will come into contact with in their future study and work. This will help the talents we have trained to be competent in future work.
Third, actively carry out the reform of teaching methods.
(A) the reform of teaching methods, so that students become the leading role in teaching. We actively implement the action-oriented teaching concept, change the traditional teaching mode in which teachers speak and students listen, and let students participate in classroom teaching. Teachers flexibly use action-oriented interactive teaching methods for a certain content and knowledge point, so as to realize the application of what they have learned? Want me to learn? Where to? I want to learn? The direction of change This course can be summarized and applied by various interactive teaching forms and methods such as brainstorming, special lectures, classroom discussion, scenario simulation and role practice. These methods can not only improve the teaching quality and effect, but also greatly stimulate students' enthusiasm and enthusiasm for learning this course.
(2) Realize the interaction between classroom teaching and concrete practice. In the teaching process of this course, the practical teaching methods of combining in-class practice with extracurricular practice and combining stage practice with curriculum practice are adopted. According to the teaching content, teachers not only carry out necessary classroom practice training, but also actively organize students to carry out social research and mathematical modeling, so as to cultivate students' ability to analyze and solve practical problems by using what they have learned.
(3) Case teaching in the whole process. This course carefully selects a large number of cases in content design, integrates theory with practice, and applies what you have learned. Through the analysis and explanation of cases, let students change from simple memorizing knowledge to applying knowledge to increase their skills.
Fourth, realize the renewal of teaching means and evaluation means.
Teachers make full use of modern educational technology in teaching, develop, make and use multimedia courseware and course network resources, enhance the intuition of teaching and help students understand and digest knowledge.
Examination is the baton of teaching, which plays a vital role in guiding students to correct their learning attitude and grasp the key points of learning. The main task of higher vocational education is to cultivate high-skilled talents, who should be able to use their brains as well as their hands. Therefore, we must use the talent quality view of vocational education to assess students and comprehensively evaluate their academic performance from all angles. To this end, we have carried out examination reform and changed the practice of marking grades. In the evaluation of students, one is to improve the comprehensiveness of evaluation with the flexibility of methods. Extend daily evaluation to project activities, economic mathematics papers, economic mathematics homework, group activities, self-evaluation, mutual evaluation, interviews, questions, daily observation, etc. The second is for what? Unification? Improve the reference of evaluation. The final exam will be re-composed and graded in a unified way.
In this regard, we have done a set of test questions to evaluate our ability, but we are still groping. Some principled opinions can be summarized as follows:
Attach importance to the foundation and highlight the key points. Mastering the basic knowledge is still an indispensable content in the exam.
Attach importance to thinking and downplay skills. Difficult skills should be diluted, and the universal mathematical ideas and methods in economic mathematics are the focus of examination.
Attach importance to application and examination ability. Emphasis should be placed on testing students' potential ability. Let students with high quality, strong ability and great potential have an advantage in the exam.
Various forms, flexible. Can you try it? Open? Test questions, test creative thinking ability, or try to combine written and oral tests.
Fifth, actively carry out the second classroom activities.
Carry out the second classroom activities and attach importance to the development of students' personality and ability. Mathematical modeling is the quickest and most effective way to directly apply mathematical knowledge to solve practical problems, and it is the best means to improve students' ability to analyze and solve problems, flexibly apply mathematical knowledge to solve problems, stimulate their interest in learning, actively consult materials, enhance their sense of cooperation and cultivate their innovative ability. So after studying calculus, we give some modeling training questions related to economic majors: product profit, continuous compound interest, optimization by marginal function, optimal batch size and so on. In the process of modeling training, students will read books carefully, look up information, often ask teachers for advice and discuss with each other, so that their comprehensive quality will be greatly improved. Of course, due to the poor foundation of higher vocational students, modeling homework will not be completed well, but teachers need to constantly infiltrate mathematical ideas into teaching to solve many economic problems and expand students' knowledge.
At present, the teaching of economic mathematics in our school has achieved good results, students' interest in learning economic mathematics has increased, and more and more students are diligent in learning and thinking. In a word, we closely follow the training goal, organically integrate basic theory with mathematical modeling, take the necessary mathematical theory as the basis, take rich practical problems as the background, and take mathematical modeling as the breakthrough, and achieve good results. Through the above teaching reform, we deeply realize that students' learning potential is unlimited, and the key is how teachers cultivate and explore, providing them with space to show their talents and develop. Therefore, we should establish innovative education and teaching concepts and firmly believe that others can do it, and we will certainly do it and do it better.
References:
[1] Gao Jiwen. The Present Situation and Countermeasures of Higher Mathematics Learning of Higher Vocational College Students [J]. China Vocational and Technical Education, 2005, (6).
[2] Liu Jianqing. Reform and Practice of Higher Vocational Mathematics Teaching in Petrochemical College [D]. Northwest Normal University, 2005:8- 1 1.
[3] Zhang Tuo. Discussion on the reform of mathematics teaching in higher vocational colleges [J]. Education and occupation? Theoretical Edition, 2008, (1).
Model essay on economic mathematics for freshmen III: Application of mathematical statistics methods in economics.
1 the integration process of economics and mathematical statistics methods
The application of mathematical statistics in economic research has been very common, and the relationship between them is getting closer and closer. Looking back at history, as early as the17th century, the integration of economics and statistics has shown an inevitable trend. At that time, the British classical economist William? Petty used mathematical methods to solve economic problems for the first time in the book Political Arithmetic, which is the first integration of the two. However, due to the limitations of social development at that time, the research methods were mainly qualitative analysis, and statistics were not fully used. 191920s, the combination of economics and statistics was further deepened. During this period, German economists put forward a conclusion in the paper published in 1854, pointing out that it can be deduced by mathematical statistics? Ghosn's law This also emphasizes the necessity and importance of the application of statistical methods in economics [1]. After that, the British economist Stanley? Wen Jie also made an in-depth study on the relationship between economics and mathematical statistical methods, and put forward a new idea in his book 187 1, that is, to establish an economic mathematical model through statistical methods [2]. Since then, the application of mathematical statistics in economics has been popularized and developed. After the 1940s, influenced by the third scientific and technological revolution, economics and statistics have made breakthroughs in practice and theory, and their integration has also made innovative progress and entered a new stage. 1955, American economist Morgenstein and mathematician Norman co-authored Game Theory and Economic Behavior, and the publication of this book became a milestone in the new cooperation between economics and mathematics [3]. Since then, statistical methods have been widely used in microeconomics and macroeconomics, and their importance has become more prominent. It can be seen that since the17th century, there has been a trend of integration between economics and statistics, and it has experienced a long-term development process. At present, the integration of the two has been very deep and mature, which has played a very important role in promoting the scientific development of economics.
2 the role of mathematical statistics in economic analysis
2. 1 mathematical statistics method can be used to solve economic problems.
Strict and precise analysis process and clear and accurate analysis results are the advantages of mathematical statistics methods, while analyzing and solving economic problems requires very high accuracy and scientificity of results. It can be seen that the application of mathematical statistics in economics has important practical significance. The application of mathematical statistics in the field of economics has a long history. With the combination and development of the two, many mathematical specialization theories have appeared in related research fields, such as econometrics and mathematical economics, which further provide a theoretical basis for the integration and development of the two [4]. What are the main application modes of mathematical statistics in solving economic problems? Economics-Mathematics? Economy? That is to say, firstly, a mathematical model is established based on realistic economic problems, then the mathematical model is analyzed by mathematical methods and the results are obtained. Finally, the results are evaluated by economic principles and theories, and corresponding conclusions are drawn, which can be used not only to guide economic activities, but also to predict the direction of economic development. Especially in the economic decision-making of modern enterprises, we can make a comprehensive analysis of economic activities from qualitative to quantitative through mathematical statistics methods, scientifically and accurately predict the results after the decision, and make full use of the existing conditions of enterprises to control and optimize the results. This can effectively improve the reliability and scientificity of economic decision-making and avoid the loss of financial and material resources of enterprises [5-6].
2.2 Mathematical statistics can be used as a tool for economic theoretical analysis.
From the initial integration of economics and mathematical statistics to the present, mathematical statistics has been applied to the research and analysis of various major economic issues. In addition, the integration of modern mathematics and modern economic theory is also deepening, and many theories of economic phenomena can be scientifically and reasonably explained by mathematical methods. Especially in recent years, the application of mathematical statistics to analyze economic phenomena and economic relations has been carried out continuously. In this way, we can not only determine the results from a quantitative point of view, but also make judgments from a qualitative point of view [7-8]. In this way, if there is no mathematical statistics method, it is difficult to effectively solve economic problems.
3 case analysis of the application of mathematical statistics in economics
In the GDP analysis model, we can find out the statistical indicators through quantitative analysis and statistical methods, design the corresponding indicator system, and study the calculation method and influencing factors of GDP value in combination with the current social situation. In the following study, we take a city 200 1? Taking the vertical distribution data model of GDP in 20 12 years as an example, this paper makes a statistical study by using regression analysis in the law of quantitative economy, and preliminarily predicts a certain stage after 20 14 years.
Table 1 is the statistical result of GDP data of a city. The regression analysis is used to process the data, and the F(y) model of the relationship between GDP and practice sequence is established. The scatter plot of data processing results is shown below. As can be seen from the figure, GDP shows an obvious non-stationary growth trend. Through the first-order difference between regression analysis and data processing, we can see that the scatter plot is in the form of a quadratic function, so we can get f (y) = AX2+BX+C, and we can get the regression statistical results by processing the years with regression analysis, as shown in Table 2. The regression equation is f (y) = 32.35x2-96.40x+1 6.5438+05.40, and the specified coefficient is R=0.9550, which is very close to1. Therefore, the regression equation has a good fit with the actual data and can be used to analyze the regression equation.
Generally speaking, the real GDP is influenced by many factors, and its change is unstable, so the predicted value will have some deviation. According to the actual GDP of a city in 20 13 years is 675,645,438+000 billion yuan, the theoretical error of the above forecast is:
w =(6756.402 1-6 105.5986)/6702 1？ 100%=9.63%
This error value deviates from the regression curve to a great extent, which may be due to the subjective attitude of the government, people's consumption of 100 million yuan, exchange rate, import and export tariffs and other factors that were eliminated when constructing the initial conditions of the model. Because there is no exact data for the years after grade 20 14, this paper is limited to the prediction of 20 13. As far as this model is concerned, although there is no overall consideration and analysis, it can be seen from the verification of its theory and practice that this prediction is not without any basis and is feasible.
4 Conclusion theory
Generally speaking, mathematical statistics play a very important role in economic prediction and summary. The application of mathematical statistics in economics has a profound impact on the prediction and evaluation of various economic indicators, as well as decision-making and reform. Taking a city as an example, this paper analyzes the methods of mathematical statistics. In the actual economic forecast, data collection should not be limited to the vertical, but also pay attention to the horizontal scope. Data collection should be comprehensive and screening should be scientific. Only in this way can the theoretical analysis be more reliable and the results have more theoretical effects. The application of mathematical statistics in economics will help them master the inherent regularity and essential changes of data, and improve the quality of data analysis and the scientificity and accuracy of economic forecasting.
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