Theory And Practice Of Mathematical Modeling Teaching In Senior High School From The Perspective Of STEAM

Under the background of the country’s in-depth implementation of the following three strategies,i.e.,invigorating China through science and education,the strategy on developing a quality workforce,the innovation-driven development strategy,the fundamental goal of education is to cultivate innovative talents.Mathematics is not only the foundation of natural science,but also the basis of major development of innovation and technology.From the history of human science and technology,almost all major discoveries are related to the development and progress of mathematics.Applying methods to solve real-world problems has become an essential ability of innovative talents.Research has shown that STEAM education can effectively cultivate students’ innovative thinking and creativity by reforming the form of classroom teaching and education,as well as creating the new paradigm of curriculum development on the basis of the concept of interdisciplinary education and integration.As one of the core qualities of high school mathematics,mathematical modeling is a key carrier for people to recognize,understand and express the world,which reflects the applied characteristics of mathematics and plays an important role in the early training of innovative talents.Therefore,the localization research of STEAM education and the teaching research of mathematical modeling in senior high school have become a heated spot in the academic sphere.This research focuses on the strong correlation between mathematical modeling and multiple disciplines in the core literacy systems at senior high schools,following the research route of "theoretical learning-status investigation-curriculum design-practical testing-literacy evaluation-college entrance examination analysis-summary and outlook".It aims at the blank of current STEAM education and mathematical modeling courses in senior high schools,to build a STEAM based senior high school mathematical modeling curriculum system,evaluation mechanism and activity platform.The typical mathematical questions of the college entrance examination with model recognition situation are classified and analyzed,and the future direction of the college entrance examination on mathematical modeling literacy is prospected.On the basis of summarizing experimental experience,this research proposes a theoretical framework and practical path to cultivate students’ mathematical application ability,cooperative spirit,innovative thinking and core literacy through the advanced curriculum system of mathematical modeling in senior high school.The advanced curriculum system of mathematical modeling in senior high school consists of the elementary mathematical modeling compulsory course,the intermediate research-based learning course and the advanced STEAM-based course,i.e.,“the three levels of mathematical modeling course"or "MRS course" for short.This research integrates the STEAM education concept into the whole process of the research.The research content involves five questions.First,how to implement high school mathematical modeling teaching and STEAM education? Second,how to design and implement the high school mathematical modeling course for students at different levels? Third,how to organize and practice high school mathematical modeling activities?Fourth,how to evaluate and apply the level of senior high school students’ mathematical modeling core literacy? Fifth,what are the implications of the college entrance examination questions characterized by model recognition situations? This research is carried out around the above five research questions and comes to the conclusions of three levels: investigation,theoretical research and practical research,First of all,the investigation and research found that the teaching of mathematical modeling in senior high school needs to be emphasized,and teaching,learning and examining need to be strengthened;The proposition of the core literacy of mathematical modeling in the college entrance examination needs to be reformed and improved;Mathematics teaching in senior high school still focuses on "problems solving teaching",and the college entrance examination needs to strengthen the guidance of basic activity experience;the implementation of STEAM education is insufficient,and teachers’ training in interdisciplinary disciplines needs to be strengthened.In addition,through expert interviews with Professor Shi Ningzhong,this study clarified the educational value of mathematical modeling teaching in senior high school,the direction of examination and evaluation of mathematical modeling literacy,and the difference and relationship between "mathematical inquiry activities" and "mathematical modeling activities" in the textbooks.Secondly,there are three conclusions in the theoretical research.First,this research proposes the MRS curriculum education theory,that is,with the interdisciplinary integration concept of STEAM education,the problem-based and project-based teaching methods,the advanced curriculum of mathematical modeling in senior high school were carried out,mathematical modeling activities were organized,to guide students to apply mathematics to solving practical problems,and cultivate students’ mathematical application awareness,cooperation spirit,innovative thinking and core literacy,which further promote in-depth learning and early cultivation of innovative talents.Second,this research constructs an evaluation index system for senior high school students’ mathematical modeling literacy based on the level division of mathematical modeling core literacy,STEAM education concept and the main process of mathematical modeling activities in the high school mathematics curriculum standard,through the expert consultation and the analytic hierarchy process to obtain the quantitative formula of mathematical modeling literacy level.Third,this research proposes to integrate the STEAM concept into the college entrance examination questions,which leads to develop mathematical experiment questions with model recognition situations,reading and writing questions,map recognition and mapping questions,discrimination and discussion questions,etc.,Finally,the practical research provides two experiences.One is about the implementation of the "three levels curriculum of mathematical modeling".The elementary curriculum is aimed at all senior students.Through two mathematical modeling cases in senior high school mathematics textbooks,students are guided to fully understand all aspects of mathematical modeling activities and popularize mathematical modeling education;The intermediate level course is aimed at senior one and senior two students who take the elective mathematical modeling research study,and carries out mathematical modeling activities with the hot issues in real life as the research object.The content involves the introduction of common computer software,the learning of mathematical modeling methods and mathematical modeling cases,aiming to enrich students’ knowledge and ability structure;The advanced curriculum is aimed at senior two and senior three students with innovative potential and certain experience in mathematical modeling activities.With the innovative STEAM problems proposed by students as the research object,it promotes students’ innovative ideas to transform into tangible innovative achievements by providing with curriculum content related to high-level information technology software,engineering structure design and students’ personalized needs.The second is to carry out regional joint research activities on mathematical modeling as the carrier,and guide students to experience the six stages of "curriculum learning-posing problems-presenting problems-solving problems-reviewing papers-displaying questions and debates",which not only provide a platform for teachers and students to exchange mathematical ideas,demonstrate mathematical modeling literacy and innovation ability,but also provide useful reference for the early training of innovative talents.The practical accomplishments so far have been remarkable.