【作者】 刘璐；

【导师】 杨泽忠；

【作者基本信息】 山东师范大学 ， 课程与教学论（数学）， 2020， 硕士

【摘要】 数学建模能够在数学理论与解决实际问题之间建立桥梁,对培养学生的逻辑思维、抽象思维及创新能力等方面有着重要意义,因此各大高校也十分注重学生数学建模能力的培养。回顾已有研究,研究者们对大学生数学建模能力的研主要包括数学建模的概念与作用、数学建模过程中现存问题、提升途径这些方面,其中提升途径是大多数学者研究的重点。对于如何培养学生的数学建模能力,各位学者专家也从不同的角度对培养大学生的数学建模能力提出了策略办法,主要集中在数学建模思想的渗透、课程建设、学生的能力素养的培养、搭建学习平台这些方面。对于研究方法,大多数学者都是在进行理论上的探讨,并没有采取实证性的研究,更没有数据来证明其观点,实施效果不得而知,文章整体的说服力较差。基于此,本文将运用结构方程方法,对数学建模能力的影响因素及路径这一问题给予量化分析,为高校培养学生的数学建模能力提供适当可行的参考方案。本文主要采用文献法、问卷调查法、结构方程方法等对问题展开研究。第一步,查阅大量文献,对数学建模相关问题进行整理综述。在有关研究中,按照数学建模的概念、数学建模的作用、数学建模过程中存在的问题、数学建模能力的培养途径进行了综述;第二步,按照文献中提到的培养途径,筛选出影响因素,做出假设,画出理论路径模型,编制调查问卷;第三步,将问卷随机发放给师范院校数学院,参与全国大学生数学建模竞赛的的同学;第四步,找出参与问卷调查的同学们的参赛论文,并请专业的数学建模老师对论文进行打分,编制得分表;第五步,将调查问卷结果进行赋分,结合数学建模得分表,将基本数据导入SPSS软件;第六步,运用结构方程方法对数据进行进一步的深入研究,做出分析和结论;第七步,对数据分析的结果进行解释说明,找出数学建模能力的影响因素及路径;第八步,进一步将影响因素进行分类,运用结构方程进一步进行分析,得到结论;第九步,基于结果分析,对本文所研究的问题做出回答,并结合实际教学工作,提出数学建模能力培养的有效途径。本研究得出的结论如下:数学建模能力的主要影响因素有6个,学生对数学建模活动的兴趣、学生对数学建模过程的基本了解、教师对学生的计算机能力的要求、教师对数学建模实际案例的讲解,以上这4个因素都对数学建模能力产生了正向影响,其中学生对数学建模过程的了解这一因素影响程度最大;另外,学生经常参加数学建模比赛、教师经常对数学建模能力进行考评这2个因素对数学建模能力产生了负向影响。基于以上分析,高校在培养学生数学建模能力时可以从如下几个方面进行:第一,教师应加强学生数学基础知识的学习;第二,教师应提高学生对数学建模基本过程的了解;第三,教师应提高学生对数学建模活动的兴趣;第四,教师应提高对学生计算机能力的要求;第五,教师应在课堂上增加数学建模实际案例的讲解;第六,教师应酌情制定数学建模比赛的次数;第七,教师应酌情制定数学建模水平考评的次数。更多还原

【Abstract】 Mathematical modeling can build a bridge between mathematical theory and solving practical problems,which is of great significance to the cultivation of students’ logical thinking,abstract thinking and innovation ability.Therefore,colleges and universities attach great importance to the cultivation of students’ mathematical modeling ability.Reviewing the existing research,researchers’ research on the modeling ability of college students mainly includes the concept and function of modeling,existing problems in the modeling process,and promotion approaches,among which promotion approaches are the focus of most scholars’ research.For how to cultivate students’ mathematical modeling ability,scholars and experts also put forward strategies and methods from different angles to cultivate students’ mathematical modeling ability,mainly focusing on the infiltration of mathematical modeling ideas,curriculum construction,students’ ability literacy,and building learning platform.For the research methods,most scholars are in the theoretical discussion,no empirical research,no data to prove their views,the implementation effect is unknown,the overall persuasion of the article is poor.Based on this,this paper will use structural equation method to analyze the influencing factors and paths of mathematical modeling ability,and provide a suitable and feasible reference scheme for the cultivation of students’ mathematical modeling ability in Colleges and universities.In this paper,literature method,questionnaire method,structural equation method are used to study the problem.The first step is to consult a large number of documents and summarize the problems related to mathematical modeling.In the relevant research,according to the concept of mathematical modeling,the role of mathematical modeling,the problems in the process of mathematical modeling,and the ways to cultivate the ability of mathematical modeling are summarized;the second step is to select the influencing factors,make assumptions,draw the theoretical path model,and prepare the questionnaire;the third step is to randomly distribute the questionnaire to the students who participate in the National College Students’ mathematical modeling competition;the fourth step find out the papers of the students who participate in the questionnaire survey,and ask the professional mathematical modeling teachers to grade thepapers and prepare the score table;the fifth step assign the scores to the results of the questionnaire,and import the basic data into SPSS software in combination with the score table of modeling;the sixth step is to use structural equation method to further study the data and make analysis and conclusion;the seventh step is to explain the results of data,find out the influencing factors and paths of mathematical modeling ability and answer the research questions;the eighth step is to further classify the influencing factors and use structural equation to further analyze;the ninth step,based on the analysis of the results,the author answers the questions in this paper,and combined with the actual teaching work,this paper puts forward an effective way to cultivate the ability of mathematical modeling.The conclusion of this study is as follows: there are six main influencing factors of mathematical modeling ability,including students’ interest in modeling activities,students’ basic understanding of mathematical modeling process,teachers’ requirements for students’ computer ability,and teachers’ explanation of actual modeling cases.All of the above four factors have a positive impact on the ability of mathematical modeling,among which students’ basic understanding of the process of mathematical modeling is the most influential factor.In addition,students often participate in mathematical modeling competitions and teachers often evaluate the ability of modeling.These two factors have a negative impact on the ability of mathematical modeling.Based on the above analysis,colleges and universities can cultivate students’ mathematical modeling ability from the following aspects: first,teachers should strengthen the learning of students’ basic mathematical knowledge;second,teachers should improve students’ understanding of the basic process of mathematical modeling;third,teachers should improve students’ interest in mathematical modeling activities;fourth,teachers should improve the requirements of students’ computer ability;fifth,teachers should increase the explanation of actual modeling cases in the classroom;sixth,teachers should make the number of mathematical modeling competitions as appropriate;seventh,teachers should make the number of evaluation of modeling level as appropriate.更多还原