Problems Should Be Focused on in Curriculum Construction of Mathematical modeling in Institution of .doc

1、1Problems Should Be Focused on in Curriculum Construction of Mathematical modeling in Institution of Abstract. Introduce the development and current situation of mathematical modeling，disscus five problems that should be focus on in the curriculum construction of mathematical modeling in the institu

2、tion of higher education，the aim of this paper is to promote the curriculum construction of mathematical modeling and the development of subject. Key words： institution of higher education； mathematical modeling； curriculum construction. 1. Introduction Mathematics is one of the basic subjects in sc

3、hools， it is increasing united relation closly with other fields，and it is a powerful tools to promote the development in these fields.Setting mathematics models with the help of mathematical theory is an important means to realize this applicating function of mathematics.The idea of mathematical mo

4、deling originated from the U.Kand U.S since 70s in 20th century.Then it spreaded fastly across the whole word.Many colleges setted curriculum for mathematical modeling successively. So far some 2achivement is attained in building of curriculum，but there are still some problems to be sovled.For examp

5、le，how to deal with the relation between the modeling curriculum and the teaching skills，and it is obscured to the content in the curriculum，and so on.The next part of this paper is devoted five problems which should be pay attention to at present stage in the building of mathematical modeling curri

6、culum in Institution of Higher Education. 2.The relation between mathematics modeling curriculum and other basic curriculum. 2.1 The targets of curriculum are the same The basic curriculum pay more attention on the basic knowledge and skills that students should learn.While the mathematical modeling

7、 curriculum pay more attention on initiative and cretivity that students should learn in the process of connecting the theory and practice during they apply mathematical knowledge. 2.2 It is complementary in content of curriculum There is rigorous logicality in scheduling of the basic curriculums co

8、ntent，an it has a strong stability and a certain degree of closure.While the content of the modeling curriculum is of great openess and flexibility，and it can 3include more valuable new knowledge as it needs.For example，the content of the Least Square Method which involved very little in Mathematica

9、l Analysis and Higher Mathematics is added and expanded appropriately in mathematical modeling curriculum. 3. Some difficulty would be met in the process of specific practice since the mathematical modeling curriculum is a new one.So it should be noted 3.1 It is the emphases and objiectives of mathe

10、matical modeling curriculum to develop students practical abilities The mathematical modeling curriculum has its own characteristics and requirements，it should not need advanced mathematical theory，and it should focus on such fields as stimulating the studentsinterest in learning the curriculum，deve

11、loping their appling consciousness and practical ability.So teachers who teach students the curriculum should guide them to combine their knowledge with some specific application in their own daily life.For example，the teachers can give some examples for appling of mathematics in phsics，chemics，biol

12、ogy and computer and so on.These will promote greatly the students formation of practical ability and achieve good teaching and learning results. 43.2 Theory with practice is the difficulty of mathematical modeling curriculum The mathematical knowledge used in many mathematical modeling problems is

13、not at all profound，but students meet constantly difficulty in modeling because they lack the ability of abstracting practical problems to mathematical ones.So the modeling curriculum should focus on sovling the commom phenomenon of out of touch in theorettical knowledge and practical problems，obvio

14、usly this is not an easy thing. Mathematical modeling is a product of a combination of theoretical knowledge，experience and inspiration，so there are some techniques and methods that we learn. 3.2.1 Guide students to do more exercise with help of existing results in the related fields Mathematical mo

15、deling is an open area and it requires a certain breadth of knowledge for the participants.So the teachers should guide students to do more modeling exercise in the learning process of this course and make them familiar with some basic knowledge and techniques.This will be very helpful for students

16、themselves later when they face new problems.For example，the second problem in National Mathematical Modeling Contest of China in 2000 is similar to calculate the minimum of 5Graph Theory，so it is a good choice to model it by taking advantage of the Dijkstra Method. 3.2.2 Absorb some experienced tea

17、chers and students to take part in in some research projects This not only can increase the application of mathematical modeling in the projects，and make teachers and students get the opportunity to practice and be trained，but also promote greatly the ideas of mathematical modeling. 3.2.3 Actively c

18、arry out internal competition in schools This not only meets the modeling enthusiastsentry requirement，but also train and selecct participating students，and the instuctorsleve have been improved.It is helpful to promote the construction and development of mathematical modeling subjects to do the abo

19、ve. 4. Teach the commomly idea of modeling and method is as important as the same while the basic knowledge for mathematical modeling is taught 4.1 Carry out logical thinking In most cases，the modeling problems are expressed in the form of narrative，so we should translate the relationship implicited

20、 in the text into mathematical language or symbols.It also requires us to understand the title firstly，and then 6identify the relevant factors ，confirm which are variables，parameters and constants according to the objects and purpose of mathematical modeling.Finally make reasonable assumptions to bu

21、ild mathematical modeling by applying some methods such as reasoning，analogy and logical thinking and so on.For example，for the problem of water saving washing machines，we can divide the whole process into 3 stages：water-laundry-dehydration，and express the amount of water and dirt in mathematical si

22、gns，then express the relationship in water and residnes with mathematical formulas.Of course it is necessary to make reasonable assumptions and simplify under the actual situation. 4.2 Build a preliminary model ，then examine and modify it if necessary Mathematical modeling is a complex process of in

23、novation.we can try to build a preliminary model after confirmming the basic relationship of every quantity.Generally the preliminary model is very crude.The purpose to build a preliminary model is to distingiush further between primary factors and secondary ones，and outstand the key issues.After a

24、preliminary model，it is necessary to test whether the model is reasonable，if not，we have to modify the hypothesis and rebuild new 7models.Furthermore，it is also necessary to test the stability of the results and sensitivity of the parameters in order to further improve and optimize the model.In a wo

25、rd，a good mathematical modeling is built well in the process of checkingg，improving and re-establishing. 5. Its important to select appropriate textbooks Textbook is the carrier of teaching content and the medium of communication between teachers and students，it play an important role in the constra

26、ction of curricucum.At present there are many mathematical modeling textbooks，but some of these books contain too more profound principles and methods such as game theory，operational research and computer simulation and so on.Generally a teacher feel difficulty to read these books，so its more diffic

27、ulty for students.A good textbook should be easy for readers to understand the knowledge in it.Generally we shall select a book in which the knowledge is basic but difficulty is moderate as the basic textbook， and then select one or two books as auxiliary. 6. Teachers are the key The mathematical mo

28、deling curriculum need the teachers not only have a good base of mathematics， but also have a broad range of knowledge and rich modeling experience，and are able 8to use the advanced teaching techniques and teaching methods.So a good teacher is key to achieve the goal of mathematical modeling curricu

29、lum. 6.1 Mathematical modeling problems involves generally in all areas of social life This want teachers to learn various branches of mathematics.For the same problem，the teacher should be good at inspiring students to model with different methods.Of course，to do this it requires th teacher a highe

30、r level of knowledge. 6.2 Teachers should have applying awareness In modeling classes teachers should break away from tranditional teaching model to guide students to explore their own knowledge，give them a thinking space，and encourage them to express their views. 6.3 Do well in changing own roles I

31、n the process of leaarn modeling， a teacher is the person to teach knowledge and also is the study participants，the information consultant and the jury of dispute.A good teacher should make the students play fully their own initiative，maximize their potential.Teaching practice shows that it is a goo

32、d teaching method with the combination of 9teaching，studying and disscussing. Any curriculum would meet difficulties in the process of its constrction and development.The five of problems mentioned above should be paid special attention in curriculum constrction of mathematical modeling in instituti

33、on of higher education.And they would have direct impact on the teaching effect and future development of modeling curriculum. References 1.Jiang Qiyuan，Mathematical Modeling.Higher Education Press，1996 2.Sun Yuepeng，Reflection on the establishment of mathematical models.1rd ed，Vol 3.Journal of Beij

34、ing University of Posts Telecommunication（social science） ，2001，p.44-46 4.Yuan Yanfei，Li Xine，Set up modeling course in institution of higher learning. 2rd ed，Journal of North China Institute of Technology（social science） ，2001，p.29-31 5.Blum W， ICMI study 14：application and modeling in mathematics

35、education- Discussion document.2rd ed，Vol. 51， Educational Studies in Mathematics， 2002，p.149-171 6.Li Mingzhen，Pang Kun，The problems and countermeasures of mathematical modeling in normal university. 4rd ed，Vol. 1042，Journal of Northwest Normal University（natural science） ，2006，p.109-113 7.Li Mingz

36、hen，Pang Kun，Thinking and probing about the cinstruction of “mathematical modeling”textbook in anvanced normal university.1rd ed，Vol. 15，Journal of Mathematical Education，2006，p.64-66 8.Zeng Guobin， On Mathematical Modeling and Advanced Mathematics Teaching. 3rd ed， Vol. 21， Journal of Hunan Institu

37、te of Science and Technology（Natural Science） ，2008，p.92-94 9.Lin Yuanhua，Lu Yusong， Reflections on the Infiltration of Mathematical Analysis Class in Mathematical Modeling Thought. 4rd ed， The Science Education Article Collects，2011，p.72-73 10.Wang Rufa， Introducing Mathematics Culture and Mathematical Modeling Into The College Mathematics Curriculum. 4rd ed， Vol.3， Joumal of Education Culture，2011，p.90-93