Development And Application Of Mathematical Modeling Ability Assessment Tools For High School Students

With the in-depth development of mathematical modeling,paying attention to mathematical modeling ability has become the consensus of the international mathematics education community.In China,from 1983,when mathematical modeling courses first appeared in university classrooms,to 2018,high school mathematics curriculum standards listed mathematical modeling as the core literacy of mathematics disciplines.Cultivating students’ mathematical modeling ability has become one of the important goals of mathematics education and teaching in China.In actual education and teaching,the cultivation of high school students’ mathematical modeling ability is still insufficient compared with the requirements of mathematics curriculum standards.To ensure the cultivation of students’ mathematical modeling ability in high school,scientific and reasonable assessment tools are a strong guarantee.Based on this,this study developed assessment tools based on the relevant requirements of mathematical modeling ability in the "General High School Mathematics Curriculum Standards(2017 Edition and 2020 Revision)",combined with the existing research foundation,and applied the assessment tools to explore the current status of high school students’ mathematical modeling ability.Firstly,this study defines the connotation of mathematical modeling ability by combing the literature related to mathematical modeling ability,and determines the sub-dimensions of mathematical modeling ability: model establishment ability,model solving ability,interpretation and verification ability.At the same time,referring to Yu Ping’s division of mathematical modeling ability levels,each modeling sub-ability is divided into three levels:knowledge understanding,knowledge transfer and knowledge innovation,which are recorded as level 1,level 2 and level 3 in turn,and the specific performance of each dimension at different levels is given,so as to obtain the mathematical modeling ability assessment framework of high school students in this study.Secondly,this study develops a mathematical modeling ability assessment tool for high school students according to the framework of mathematical modeling ability assessment of high school students.Based on the corresponding levels of the assessment items and the assessment framework,combined with the project design principles: the assessment items are based on mathematical knowledge,the context of the assessment items meets the authenticity,and the questions of the assessment items meet the openness,and the mathematical modeling ability assessment items for high school students are initially formulated.Experts are then invited to review the mathematical modeling sub-ability and corresponding level of the assessment project and give revision suggestions,and then make preliminary revisions to the assessment items according to the revisions to form an assessment tool.On this basis,the assessment tool is tested.Winsteps software was used to analyze the answer data,test the evaluation tool from the aspects of reliability and validity,determine whether the assessment tool meets the quality requirements of the Rasch model,and revise the abnormal items.Until the formation of a good quality high school students’ mathematical modeling ability assessment tool.Finally,this study uses assessment tools to investigate the current situation of mathematical modeling ability of senior and second-year students in a middle school in Chongqing.The results show that:(1)The students’ mathematical modeling ability level is low,and the average level is at level 1.In terms of gender differences,boys performed slightly better than girls,but there was no statistically significant difference.In terms of grade difference,the performance of the second grade was significantly better than that of the first grade,and it was statistically significant.(2)The level of students’ mathematical modeling sub-ability is low and shows the characteristics of uneven development.From the perspective of the proportion of students at higher levels(level 2 and level 3),the performance of students in model building ability is better than that in interpretation and verification ability,and model solving ability.Further considering the group differences at each sub-ability level,the gender difference was only significant at the level of model solving ability,which was manifested as girls being better than boys.The grade difference was significant in the level of model establishment ability and the level of interpretation and verification ability,and both students performed better than the first grade of high school.Based on the above research results,focusing on cultivating the mathematical modeling ability of high school students,the following suggestions are put forward for teachers’ teaching: mathematics teaching shifts from knowledge transfer to ability training;Try to teach mathematical modeling in stages;In the teaching activities of mathematical modeling,according to the group differences of students,teaching according to aptitude.