Investigation On The Universality Of Mathematical Modeling Competency Cases Of The New Curriculum Standards In High School

"High School Mathematics Curriculum Standards(2017 Edition)" is the framework document of high school mathematics education in our country,and is a leading navigation mark of high school mathematical modeling education.It divides it into several levels,and provides 7 mathematical modeling cases in the 37 teaching and evaluation cases.Mathematical modeling key competency cases aim to help teachers better understand the curriculum standards and the implementation.But whether these mathematical modeling cases have universality,as whether they are suitable for the evaluation of the ordinary high school students' mathematical modeling key competency,lack of corresponding empirical research.This paper selects three mathematical modeling cases of the new curriculum standards(foot length and shoes numbers,packing color rope,weight and heart rate)to test.On the basis of literature analysis,building a high school mathematical modeling key competency evaluation model from the situation,content and process dimensions.Then using the evaluation model to analyse experiment edition and 2017 edition curriculum standards,which finds that there is no mathematical modeling problems,and seven mathematical modeling problems in the new curriculum standards,5 mathematical modeling problems are at the highest level of evaluation model(application level),which indicates the highest level of mathematical modeling requirement increased significantly,harder.Meanwhile,370 college students and 1827 high school students are selected to analyse the levels of students to solve the three typical cases of mathematical modeling,and to explore the universality of mathematical modeling cases.Using the classical measurement theory,item response theory to analyse,the result shows that the reliability,validity,differentiation are low,and cases are difficult.High school students,college students are all understand level,thus three typical cases are not universal,the reasons mainly have four,one is the mathematical modeling cases are designed to help teachers understand mathematical modeling teaching and evaluation,rather than the daily study of the ordinary high school students.The target of the academic quality evaluation of the new curriculum standards is high school graduates,rather than ordinary high school freshmen and sophomores.Three typical cases of mathematical modeling are all from the Beijing mathematical knowledge application competition,which are very difficult.Through statistical analysis of the mathematical modeling strategies of college students and high school students,it is found that the tendency of high school students and college students to solve problems is relatively consistent.In terms of testing strategies,high school and college students tend to use data testing strategies and intuitive judgment strategies rather than theoretical deduction strategies.In the process of modeling hypothesis,the number of students adopting feasibility hypothesis strategy,balance hypothesis strategy,and accuracy hypothesis strategy decreases successively.In terms of visual representation,the more difficult the problem is,the more people will use visual representation,and the characteristics of the problem affects the choice of visual/non-visual representation.Empirical investigation finds that three typical mathematical modeling cases are difficult,and not a universal practice,this paper puts forward adaptation of mathematical modeling cases,implement visual suggestions to solve the problems of the mathematical modeling teaching.But in view of building the evaluation model,design process of case adaptation,empirical research,and the data processing and so on is an exploratory attempt,this paper need further thinking,such as repeating validation to extract the samples failed to nationwide,the lack of the research process,etc.As a result,in a follow-up study,is committed to expanding the scope of the study,constantly improve mathematical modeling key competency evaluation model.