Assessment Of The Mathematics Application Problems In College Entrance Examination

The application of mathematics is valued all around the world today. From the perspective of mathematical modeling and representation, we make an exhaustive study of tne assessment of the application problems.We initially proposed evaluating indicators of application problems in college entrance examination on the basis of the literature review.then we examine these indicators from the point of mathematical modeling and representation and perfect these indicators according to the questionnaire survey and interview.Finally, a quantified evaluation index system of the application problems in college entrance examination is set up.Moreover, we give some concrete examples of assessing the application problems in college entrance examination.We set up a three-grade evaluation index system of the application problems in college entrance examination as following: first-class index: problem representation and mathematical modeling.problem representation sets target of 2 second-class: representation of stem and representation of question. Mathematical modeling sets target of 3 second-class: the background of the problem, build model and solve the model, reduction and inspection.The second-class index of representation of stem is divided into 3 third-class indexes:index 1:concise degree of expression,index 2:the accuracy of the expression, index 3:the accuracy of the graph. The second-class index of representation of question sets only a third-class index: index 4: hierarchy of questions. The second-class index of the background of the problem is divided into 5 third-class indexes:index 5:the popularity of the background,index 6:the fairness of the background,index 7:the positivity of the background index 8:the rationality of the data,index 9:authenticity of the problem. The second-class index of build model and solve the model is divided into 4 third-class indexes:index 10:the centrality of knowledge, index 11:the richness of knowledge,index 12:the level of mathematicilization,index 13:modest computation complexity. In the second-class index of reduction and inspection,we consider 2 third-class indexes:index 14 : the certainty of the outcome and index 15 : the reasonableness of the conclusion.In addition, we propose the final index from the view of overall situation and the whole process of problem solving. Index 16:the fundamentality of problem solving.In order to enhance the maneuverability of the evaluation index system of the application problems in college entrance examination, we refine every third-class index according to the actual condition.We divide every third-class index into two or three levels,then give weight to every index and every level,so that the assessment of the application problems in college entrance examination may be practicable.Last but not least, we propose some suggestions on compiling and teaching mathematical application problems, meanwhile, point out several shortcomings of this paper and some topics for further study.