大学生数学建模竞赛与教学策略研究

【作者】 刘冬梅；

【导师】 傅海伦；

【作者基本信息】 山东师范大学 ， 课程与教学论， 2008， 硕士

【摘要】 本文从调查分析我国高校传统数学教育存在的问题入手,在考查我国大学生数学建模竞赛与教学发展状况的基础上,提出大学生数学建模活动是创新高校数学教育的有效途径。论文较深入分析了大学生数学建模竞赛的特点、理论基础,指出大学生数学建模竞赛对提高大学生创新能力和对高校数学教育改革的重要意义。本文重点从学生能力、教师素质、教学实施及学校管理与组织等四个方面总结阐述现行大学生数学建模教育存在的突出问题,在此基础上,本文提出了大学数学建模教学策略,并结合例题对如何提高大学生的建模思维意识和建模相关能力进行了详细论述。论文还对大学数学建模教学模式进行了初步构建,对大学数学建模教学的层次性和数学建模选题原则进行了深入分析,最后,提出了在实施大学数学建模教学中应注意的几个问题。文章主要采用资料、文献研究和调查分析的方法。具体来说,全文重点阐述了以下几个问题:1、本文在对师生进行问卷调查和个别访谈的基础上提出了我国高校传统数学教育存在的问题,即当前高校的数学教育中还不同程度存在着“重理论,轻实践”的教育模式,以及单一的教学方法、考试方法,这些现状严重影响着学生的全面发展,这与当前国际高校数学教育改革的基本趋势——重视数学的应用性不相适应。同时,大学生数学建模竞赛和教学在各大高校的蓬勃发展之势说明了数学建模教育与当前高校数学教学改革的必然联系,从高校数学建模教学已经取得的成效可见大学生数学建模竞赛是创新高校数学教育的有效途径。2、本文深入分析了大学生数学建模竞赛的特点和理论基础,结合山东师范大学数学科学学院本科生近几年参加数学建模竞赛所取得的成绩,对70余名参赛选手和部分指导老师的调查分析,尤其是对部分选手的跟踪调查,以第一手数据资料的形式论述了大学生数学建模竞赛对学生科学素养的培养和提高作用,同时,分析了大学数学生数学建模活动对高校数学教育改革的重要意义。3、本文重点从以下四个方面总结分析了现行大学生数学建模教育存在的突出问题,即:学生方面的问题集中表现在缺乏良好的思维品质、数学阅读能力、把实际问题数学化的能力和处理数据的适当方法;教师方面的问题主要表现为教育教学观念有待更新、知识体系需进一步拓展、创造能力和科研意识还待提高、敬业精神需要加强、还要自觉转变教学过程中的角色;教学实施方面的突出问题是大学数学建模教育在高校中的普及性不够和数学建模思想在高校数学课堂教学中渗透的力度不够。另外,从学校管理与组织方面来看,部分高校对数学建模活动缺乏足够的重视和支持,少数学校在数学建模竞赛的组织中存在功利意识,大多学校对数学建模活动缺乏规范的制度建设。4、针对以上问题,本文提出了大学数学建模教学策略,通过举例论述了如何在传统高校数学教学中提高大学生的建模思维意识和建模相关能力,包括双向翻译能力、解模能力、观察和猜想能力、逻辑思维能力、创造能力、自我评价能力。在此基础上,本文对数学建模教学策略进行了初步构建。一方面,论文在分析了各国数学建模教学类型之后重点对我国高校针对大学生四年三阶段的一种新型数学建模教学模式——“KK”整合模式进行了分析评述;另一方面,本文按照数学建模的模仿、转换、构建三个阶段的顺序进行了大学数学建模教学层次性分析。同时,论文还提出并分析了大学数学建模教学的选题原则,即价值性原则、以问题为中心原则、客观可行性原则和趣味性原则。最后,论文提出了在实施大学数学建模教学中应避免的几个误区和应处理好的几个关系。更多还原

【Abstract】 Beginning with the investigation and analysis of problems in our country’s traditional higher mathematical education,based on examing of our undergraduate Mathematical Modeling Competition and its teaching development,this article puts forward that the undergraduate mathematical modeling activity is an effective way of innovating or higher mathematical education.The article analyzes undergraduate Mathematical Modeling Competition’s characteristics and the theory foundation thoroughly, and points out the significance of this competition both in improving colledge students’innovation ability and in higher mathematical education reform. The article also concentrately summarizes and expatiates the prominent problems in present undergraduate Mathematical Modeling education from four aspects:students’ability, teachers’quality, teaching facilities and the management and organization of the school, on basis of this,the article puts forward teaching strategies for undergraduate Mathematical Modeling,and also dwells on how to improve the thinking principles and capabilities about undergraduate Mathematical Modeling by examples. The article also establishes the teaching mode of colledge mathematical modeling and thoroughly analyses the hierarchy of mathematical modeling’s teaching and basic principles for selecting titles. At last, the article proposes several questions which we should pay attention to about colledge mathematical modeling teaching.The article mainly uses methods of materials and document research and investigation.In more specific terms, the article highlights several questions as follows:1. Based on questionnaire survey and individual interview to teachers and students,the article puts forward some problems in our country’s traditional higher mathematical education,existing in varying degrees in our present higher mathematical education.That is the educational model of“put more emphasis on theory than practice”and the single methods of teaching and examination,which puts back students’all-round development badly,and is incompatible with the present international mathematics education reform’s primary trend-----valuing mathematics’application. At the same time, the vigorous development of undergraduate Mathematical Modeling Competition illustrates the definite link between mathematical modeling education and higher mathematics teaching reform.It can be seen that university student mathematics modelling competition is an effective way of innovating colledge mathematical education from the achievements that the higher mathematical modeling teaching have gotten.2. The article analyzes China’s Undergraduate Mathematical Modeling Competition’s characteristics and the theory foundation thoroughly.Academy of Mathematical Science of Shandong Normal University have continuously attended China Undergraduate Mathematical Contest in Modeling during the past few years.Combining with their achievements,the article makes analysis about more than 70 competitors and some instructors,especially tracking down information about part of the competitors.By those first hand date,the article discusses the Mathematical Modeling Competition’s action for training and improving colledge students’quality of science,and, also analyzes the significance of the undergraduate mathematical modeling activity in higher mathematical education reform.3. This article also concentrately summarizes and expatiates the prominent problems in present undergraduate Mathematical Modeling education from four aspects as follows:problems about students ,which focus on lacking upstanding thinking quality,mathematical reading ability,the ability of turning a practical problem to a Mathematical problem and also the appropriate manners for processing data; problems about instructors,which are mainly on education or teaching ideas , knowledge hierarchy, creative ability and scientific research consciousness, professional dedication and also on transferring roles during teaching ;problems about teaching process,which is that The undergraduate Mathematical Modeling Competition’s popularity is not enough, and the efforts for the teaching of Mathematical Modeling toughts in higher mathematical classes are not enough ;moreover,from the aspect of the management and organization of the school,it can be found that,some colleges lack enough attention and support for higher mathematical modeling activity, a few schools have serious tendency towards utilitarianism during the organisation of Mathematical Modeling Competition,and most schools lack standardized system for Mathematical Modeling activity.4. Aiming arrectly at the above problems, the article puts forward teaching strategies for undergraduate Mathematical Modeling, and also, by examples ,dwells on how to improve the thinking principles and capabilities about undergraduate Mathematical Modeling, including bidirectional translation ability, modeling ability ,observing ability,guessing ability,logical thinking ability ,creative ability and self-evaluation ability; The article also establishes the teaching model of colledge mathematical modeling:on the one hand, after the analysis of different mathematical modeling teaching types in various countries,the article mainly discusses a new teaching model of maths modeling-------“kk intergrative model”;on the other hand,the article proceeds hierarchy analysis about the teaching of higher mathematical modeling according to three stages.Besides,the article analyzes the basic principles for selecting titles in the teaching of colledge mathematical modeling,that is, valuable principle, problem-centered principle,objectivity and feasibility principle and interest principle;at last ,this article proposes several avoidable pitfalls and relations that should be well treated during colledge mathematical modeling teaching.更多还原