A Practical Study On The Effectiveness Of Problem-Based Teaching Mode In Teaching Mathematical Modeling In High Schools

Mathematical modeling is not only one of the six core competencies of mathematics,but also an important content of high school mathematics courses.The learning of mathematical modeling is crucial to the growth of students,and the teaching of mathematical modeling plays a very important role in students’ development.Through years of teaching practice,the teaching status of mathematical modeling is not optimistic,and the evaluation method is relatively single,so the innovation of mathematical modeling teaching mode and the improvement of evaluation method are imminent.Firstly,through reviewing the literature,the current situation of mathematical modeling teaching at home and abroad and the existing problems of mathematical modeling teaching in China are discussed in detail,and through the analysis of existing problems,combined with the practice and teaching characteristics of problem-driven(PBL)teaching mode,a "PBL teaching mode" that conforms to the teaching of high school mathematical modeling is proposed.Five processes of the "PBL teaching model" are given: first,through the problem situation,the introduction of teaching cases;Second,through the difference in grading,it is caused by students’ discussion;Third,through problem-driven,stimulate students to solve;Fourth,by combining reality,inspire the test results;Fifth,improve modeling literacy by improving models.These five teaching processes are applied to the three teaching cases of "distinguishing true from false","identifying species" and "peeling pineapple",and the teaching design is given.Then,the experimental research method is used to verify the teaching effectiveness of the "PBL teaching mode" through control experiments.The experimental class adopts the "PBL teaching mode" for mathematical modeling teaching,and the control class adopts the traditional classroom teaching mode,which lasts for two or four lessons.After the completion of teaching,the teaching effect is compared from two aspects: first,the test paper method is used to evaluate the teaching from the students’ mathematical modeling ability level,compare the difference in mathematical modeling ability before and after the teaching of the experimental class,and compare the difference in mathematical modeling ability between the experimental class and the control class;Second,using the questionnaire survey method,starting from the aspects of students’ mathematical modeling learning and mathematical emotional attitude,the evaluation framework of mathematical modeling teaching effectiveness from the four dimensions of "classroom culture","learning effect","learning motivation" and "self-efficacy" was constructed,and a questionnaire was designed according to the evaluation framework,from the students’ evaluation of the four dimensions,comparing the evaluation differences before and after the teaching of experimental classes,and comparing the evaluation differences after teaching in experimental classes and control classes.After two weeks of teaching practice,the mathematical modeling ability of the class in PBL teaching mode was significantly higher than that of the class in the traditional classroom teaching mode.The evaluation of classroom culture,learning effect,learning motivation and self-efficacy in the PBL teaching mode was significantly higher than that of the traditional classroom teaching mode.Through control experiments,it is shown that the PBL teaching mode is more effective than the traditional teaching mode for high school mathematical modeling teaching.