The Development Of High School Students'Mathematical Modeling Competencies

With the development of high school mathematics curriculum reform in China,mathematical modeling is gradually entered high school mathematics curriculum standards,and become a critical mathematical key competencies in the standards.However,many surveys have found that our country's high school mathematical modeling education is actually not satisfied,except for a few schools,most of them are in wait-and-see and even confused about mathematical modeling,and the relevant teaching experiences are extremely limited.Therefore,how to carry out high school mathematical modeling education in classroom,how to develop high school students' mathematical modeling competencies become a hotspot in academic research.There are two different perspectives on the understanding of modeling competencies,one is holistic,another is atomistic.Although there has been a lot of literature on the research of high school students' modeling competencies in China,it was found that Chinese scholars mainly discuss modeling competencies from holistic perspective,and the study from atomistic is quite rare.This study explores modeling competencies of high school students from atomistic perspective,and the purpose is to probe the performance characteristic and development characteristic of high school students' modeling competencies through empirical methods.The survey found that high school students' modeling competencies are generally very poor,most of the students' simplification abilities and formulation abilities are severely inadequate.There is a gender difference in high school students' modeling competencies.The boys' modeling competencies are superior to girls,and the difference is significant though there is a small effect size.High school students' modeling competencies have developed significantly with the rise of grade,but this is mainly due to the development of formulation abilities,and the modeling competencies of grade three is not satisfied.The development of high school students' modeling sub-competencies are not consistent,and the development of simplification abilities and validation abilities lag behind formulation abilities.The simplification abilities and formulation abilities of grade three and grade one have no significant difference in statistics.According to the survey results of high school students' modeling competencies and related literature review,some modeling competencies teaching intervention were designed,such as infiltrating model thoughts in daily mathematics teaching,strengthening the training of modeling sub-competencies,participating in real mathematical modeling tasks.Finally,an experiment has been conducted to examine the effects of mathematical modeling teaching interventions.It was found that:(a)daily mathematics teaching has a significant long-term effect on the development of high school students' modeling competencies,but the short-term effect is not significant;(b)special training for modeling sub-competencies and teaching of real mathematical modeling tasks have a significant short-term effect on the development of high school students' modeling competencies;(c)the teaching intervention of mathematical modeling has a significant promoting effect on the self-efficacy of high school students' mathematical modeling competencies,especially on the self-efficacy of simplification abilities and formulation abilities.Based on the analysis and discussion of understanding,assessment and cultivation of mathematical modeling competencies,this study explores the performance characteristic and development characteristic of high school students' modeling competencies by using a variety of educational research methods such as test,questionnaire and double-group experiment.All the works will lay down a good foundation for researchers of mathematical modeling education in China to further study high school students' modeling competencies,and it also have great usefulness and reference values for high school mathematics teachers to teach mathematical modeling in classroom.