数学建模课内容和教学方法的探讨

拟就以下内容进行了探讨：（i）该课程究竟应该讲什么内容，怎样讲，才能使学生在较短的时间内，掌握数学建模的基本知识和基本方法；（ii) 该课程怎样与数学实验更好地结合起来，以培养学生的动手能力；（iii)该课程应采用什么样的教学手段和教学方法，才能加大课堂信息量，加强直观性和趣味性等，我们的解决办法是：（i)以介绍建立数学模型为主，按数学知识内容的不同来选取数学模型的典型案例，通过案例介绍，使学生学会怎样建立模型；（ii)适当介绍数学软件包，让学生掌握运用软件包来求解模型能力。(iii)做大作业，教员给出题目，学生自己收集资料，讨论，上机求解，最后写出报告。（iv)开展多媒体教学，对主要的教学内容进行模块化教学，将建模分成14个专题，做成14个多媒体课件。     

对高师数学专业课程教学改革的思考

高师数学专业课程教学改革的成功与否,直接关系到我国高素质数学教师的培养质量.为了更好完成高师院校的培养目标,本文认为以下三点值得思考:(i)改变原有陈旧教学内容,使学生熟练掌握专业类课程,提高自身数学素养;(ii)教学内容上应尽量挖掘高等数学类课程与中学数学其根叶相连的关系,让师范生能在中学教学中学以致用,高屋建瓴;(iii)加强"数学建模"课的学习,让师范生亲身体验开放式、探究研讨型数学活动,为以后指导中学生开展研究式学习、创造性开展教学打下基础.     

数学建模素养在课堂中的实践及反思

在日常教学中,教师要加强对学生数学建模能力的关注,充分利用一些来自学生生活中的素材和实际问题,引导学生主动构建合理的数学模型,加强此方面能力的培养,以使学生能更好地形成数学建模素养.本文结合实际案例介绍数学建模的课堂实践,并给出对于培养学生数学建模素养的思考.     

安全渡河问题的计算机求解和模拟

本文介绍利用数学软件包来求解和利用计算机多媒体制作工具来模拟数学模型课程中安全渡河问题的方法     

安全渡河问题的计算机求解和模拟

本介绍利用数学软件包来求解和利用计算机多媒体制作工具来模拟数学模型课程中安全渡河问题的方法。     

突出建模过程 培养模型意识——一道高失分题引发的思考

在数学解题中发现,学生常因模型意识不强、对模型理解不深而出现“懂而不会”的情况.为了培养学生的模型意识,提高学生的建模能力,在教学中应带领学生经历数学模型的“形成—建立—求解”的全过程,以此帮助学生认识数学的本质,提高学生解决实际问题的能力,提升学生数学素养.     

关于数学模型评价的思考与实践

重视数学模型的评价对于全方位提升数学建模能力具有举足轻重的作用.数学建模的假设应遵循目的性、简明性和真实性准则;数学模型的选择要符合适合性、基础性和可行性准则;提出模型算法评价的3项指标;给出粗略及细致检验模型求解结果的策略.这些准则和策略在数学建模实践中的合理应用,有助于数学建模教学和参赛的成功.     

基于可信性理论的模糊离差MADM模型研究

针对属性值以模糊变量形式给出的特点,运用2004年基础数学领域完成的研究模糊现象数量规律的一个新的数学分支——可信性理论的原理,我们做了以下三点研究:(i)结合模糊变量之间的距离,定义模糊离差,构造了模糊属性值之间离差最大化的算子;(ii)得到了计算属性权重值的模糊规划期望值模型(EVM);(iii)考虑到属性的重要性程度不同,利用信息熵最大化原理,构造了具有平衡能力的权重计算模型,从而得到基于可信性理论的模糊离差多属性决策(FD-MADM)模型.最后结合实例进行分析和计算,显示该模型的可行性和有效性.     

数学建模思想渗入代数课程教学的试验研究-短周期课堂教学试验与分析

通过短期教学试验与分析方法研究数学建模思想渗入代数课程对学生学习效果的影响。对试验数据进行分析建模求解可知数学建模思想渗入代数课程对提高学生知识的直观理解、直观到抽象的理解和数学知识的实际应用的认识有较大的影响,对数学模型的认识和学习兴趣有一定的影响,但需要长期的熏陶。     

浅谈中学数学建模教学

当前由于社会经济迅速发展 ,以及面向生活、面向大众的国际教育浪潮的冲击 ,中学数学开始重视数学应用的教育和训练 ,这在全国高考和各地中考试题中都有明显的体现 .如何在中学的数学课堂教学中提高学生的数学建模能力 ,还有待中学教师进一步的探讨 .数学模型是实际问题的简化和抽象 ,数学模型方法就是借用数学模型处理各类问题 (包括数学学习和实际应用等方面 )的方法 .数学模型方法的学习与掌握、运用与深化 ,一般是按模型模仿———模型转换———模型构建的主线进行和发展的 .因此对于中学课堂的数学建模教学 ,本人认为应从三个层次进行…     

深入开展数学建模活动，培养学生的综合应用素质

数学建模时大学生综合应用素质培养的一种有效途径。本文首先分析数学建模在大学生实践创新能力和综合应用素质培养中的作用,在此基础上从数学建模的数学理念更新、数学模式和教学内容设计,教学方法运用等多个方面,研究了以培养学生综合应用素质为牵引的多焊接、全方位的数学建模教学模式,提出了一些创新性的实践做法,为教学建模数学与组织竞赛活动的开展提供参考。     

Faces of mathematical modeling

In this paper I will discuss and exemplify my perspectives on how to teach mathematical modeling, as well as discuss quite different faces of mathematical modeling. The field of mathematical modeling is so enormous and vastly outspread and just not possible to comprehend in one single paper; or in one single book, or even in one single book shelf. Nevertheless, I have found that the more I can illuminate some of the various interpretations and perceptions of mathematical modeling which exists in the world around us when introducing and starting a course in mathematical modeling, the more benefit I will have during the course when discussing the need and purpose of mathematical modeling with the students. The fact that only some models fit within the practical teaching and assessing of a course in mathematical modeling, does not exclude the importance to illustrate that the world of today cannot go on without mathematical modeling. Students are nevertheless much more charmed with some models of reality than others.     

概率统计课程教学方法的几点体会

通过教学实践与理论思考,并结合目前大学生的特点,对概率论与数理统计课程的教学方法阐述四点看法.主张在教学中引人历史典故,引进多媒体辅助教学,将教学与数学建模活动相结合,运用案例教学法以培养学生分析问题和解决问题的能力.     

浅议创新思维在高等数学多维立体教学中的应用

本文探索了高等数学的多维立体教学方法,即结合多媒体课件、案例教学和实验教学,实现以教师为主导,学生为主体的主客体相结合的教学思想．     

Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology

The study reported in this article deals with the observed actions of prospective Swedish mathematics teachers as they were working with a modeling situation. These prospective teachers were preparing to teach in Grades 4 to9 or in the gymnasium (Grades 10 to 12) and were students in a course in mathematical modeling. The larger study of which this study was a part focused on these students' understanding of modeling and how they related mathematical models to the real world. This article also attempts to illustrate how mathematics is intertwined with many other subjects, in this case medicine. This revised version was published online in July 2006 with corrections to the Cover Date.     

Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course

While models are an important concept in statistics, few introductory statistics courses at the tertiary level put models at the core of the curriculum. This paper reports on a radically different approach to teaching statistics at the tertiary level, one that uses models and simulation as the organizing theme of the course. The focus on modeling and simulation??along with inference??was facilitated by having students use TinkerPlots? software for all modeling and analysis. Results from a 3-month teaching experiment suggest that a course focused on modeling and simulation through randomization and resampling methods in which students learn to think using a powerful and conceptual modeling tool can foster ways of thinking statistically. Furthermore, such an approach seems to help students develop experiences with and appreciation for the science and practice of statistics.     

将数学建模思想融入工科“概率统计”教学中

提出‘概率统计”课程的一种教学改革思路,注重理论联系实际,强调应用案例中融入数学建模思想的新的教学法.改革课堂教学方法,探索新的教学模式.加强学生的实践性教学环节,培养学生的应用能力和创新能力.     

概率统计类课程多维立体教学的实践与认识

针对概率统计类课程不同于其它确定性数学的特点,作者从教学内容及教学方法两个方面进行了探索与实践.在教学内容上,强调点面结合,拓展一些现代的与本学科密切有关的面上知识.在教学方法上,强调多维立体教学方式,即结合多媒体课件,案例教学,软件演示,实验教学,实现以教师为主导,学生为主体的主客体相结合的教学思想,以期达到使学生受益最大化的目标.     

How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to ‘make maths relevant’ for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources.     

浅谈蒙特卡罗法在概率统计教学中的应用

在概率统计教学中利用蒙特卡罗法设计适当的模拟实验,结合多媒体在课堂教学中实时演示,能很好地加深学生对概率统计概念、思想的理解,进而培养学生的统计思维能力.