数学模型与数学实验教学改革探索

数学模型与数学实验教学如何适应现代数学科学的迅猛发展,满足社会对高素质数学人才的需求,是高等理工科院校共同面临的课题。从教学观念的改变、教学内容的更新、教学模式的优化以及教学考核机制的完善等方面进行研讨,主旨在为数学模型与数学实验教学改革探索有效的解决途径。     

Students' mathematical modeling of motion

We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes, most students had difficulty using these concepts to characterize actual or hypothetical motions. Furthermore, some students developed their own nonstandard method of describing accelerated motion in terms of changes in the average velocity, from the start of the motion up to a given time. This is in contrast to the physics community's use of the acceleration construct, defined in terms of changes in the instantaneous velocity, to describe such motion. Although the change in average velocity is not typically identified as an important construct in traditional physics texts, some students found it intuitively appealing, and were able to use it successfully to describe and predict motion. We conclude that by focusing on standard constructs, and ignoring possible intuitive ways that students might view motion, standard kinematics instruction may miss an opportunity to maximize student understanding. © 2007 Wiley Periodicals, Inc. J. Res. Sci. Teach 45: 153–173, 2008.     

数学建模与数学实验

讨论了数学建模与数学实验的步骤、工具和目的，着重阐述3个观点：数学建模的核心步骤是建模，数学模型的求解隶属于数学，而非数学建模；数学建模的核心工具是数学，计算机作为数学之工具间接地用于数学建模；就数学实验自身而言，其主要目的是辅助做数学；就教学而言，数学实验的主要目的是培养学生运用计算机研究、学习数学的能力。     

化学竞赛中的数学建模思想

在化学解题过程中运用数学理念建立模型的方法是一种极其重要的思维方法,是培养学生实际应用数学方法的意识与能力的重要途径,也是在化学竞赛中培养学生创新思维的重要手段.     

探究数学建模中常微分方程的应用

自然界很多事物的运动和演变规律都是可以用数学模型来模拟的。但大多数问题在数学化的过程中,往往不能直接写出他们的关系式,而要借助微分方程来寻找满足规律的函数。微分方程常用来描述事物的瞬间运动,因此,数学建模中常微分方程的应用可以解决很多实际问题。     

数学建模在管理会计中的应用

数学模型在经济管理活动中有着广泛的应用。在管理会计业务中,利用会计资料及其他信息,运用数学基础知识,结合实际问题,建立数学模型,定量地解决企业管理方面的问题,对企业经营活动进行预测、规划、控制,为企业内部管理人员和决策者提供信息,数学无疑是一种很重要的工具。     

微分方程在数学建模中的应用

高等数学在很多领城有着成功的应用,因此,通过建立实际应用模型,将高等数学课程中的微分方程理论与实际相结合.可以增加学生学习新知识的兴趣,提高课堂授课效采.     

数学建模思想在高等数学教学中的应用

高等数学是高校理工科的一门公共基础课,是培养学生思维训练、掌握数学理论和方法的一门重要课程。将数学建模的思想应用到高等数学教学当中,使学生的学习积极性、主动性和创造性得到了充分的发挥,提高了学生应用数学知识解决实际问题的能力。     

矩阵在数学建模中的应用举例

矩阵作为一种认识复杂事物的简捷工具已经被广泛应用在各个学科领域中,在数学建模中也有许多应用。本文就数学建模中使用矩阵的情况做一些举例、小结,最后给出一个典型的数学模型。     

基于任务驱动的数学建模教学方法研究

通过进行数学建模竞赛的教学及培训工作,可极大地拓展学生的知识面,提高学生自己动手解决实际问题的能力,提高学生创新能力,增强学生的综合素质。主要介绍和讨论了基于任务驱动的数学建模培训及教学方法。该方法主要通过教师布置任务,鼓励学生自主地讨论并解决问题,通过自我评价和教师指导,使学生能掌握和拓展自己的知识。然后给出了具体的案例,并以淮南师范学院的建模辅导为例进行了相关的总结。     

特殊工件磨削加工的数学建模

特殊工件精密磨削是一个复杂的多变量影响过程,本文开展了精密磨削加工技术的优化研究。在利用已知加工外表面母线方程的基础上,采用了精密数控曲线磨削砂轮法向跟踪的方法,通过保证曲线轮廓上磨削点处的法线经过砂轮的回转平面,实现了砂轮与工件之间的恒定点接触,在分析砂轮与工件运动几何关系的基础上,建立了砂轮法向跟踪的数学模型,从而提高了加工精度,实现了对任意复杂曲线轮廓的磨削加工。     

The role of mobile technologies in shifting to digital

Educational technology research and development - In this section, we have responses to Joo, Kim and Kim (2016)’s study, from two scholars with international and inclusion perspectives. They...     

高校数学教学中数学建模思想方法的研究

随着社会的不断发展,数学在人们的生活中发挥着越来越重要的作用,甚至渗透到经济、科技、生物学、医学等各个领域。另外,当今时代数学思想的学习尤为重要,它不仅能够使枯燥的氛围变得有趣,也将抽象的问题具体化、简单化。因此,本文从高校数学模型的应用概述出发,对数学建模思想方法进行研究。     

蒙特卡罗方法在数学建模中的应用

蒙特卡罗方法是一个以概率模型为基础,利用计算机通过多次反复模拟实验完成问题求解的一种数值计算方法。它特别适用于用传统的解析法难以解决甚至是无法解决的问题。文章主要介绍蒙特卡罗方法及基本原理,并通过实例说明蒙特卡罗方法在数学建模中的应用。     

在中学进行数学建模教学的体会

从数学建模教学的重要性、数学建模教学存在的问题、数学建模教学的实践和数学建模教学的体会,这四个方面叙述了在中学数学教学中对数学建模教学的认识和实施策略。     

Developing understanding of mathematical modeling in secondary teacher preparation

This study examines the evolution of 11 prospective teachers’ understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include modeling as part of the school curriculum under current state standards. The module consisted of readings, analysis of the Common Core State Standards, carefully designed modeling activities, individual and group work, discussion, presentations, and reflections. The results show that while most prospective teachers had misconceived definitions of mathematical modeling prior to the module, they developed the correct understanding of modeling as an iterative process involving making assumptions and validating conclusions connected to everyday situations. The study reveals how the prospective teachers translated the modeling cycle into practice in the context of a carefully designed open-ended problem and the strong connections between modeling activities and promoting mathematical practices.     

The layering of mathematical interpretations through digital media

How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children’s mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital technologies in mathematics education is predominantly positioned within two theoretical perspectives, semiotic mediation and the instrumental approach. Meanwhile, within a contemporary hermeneutic position, mathematical learning comprises a process of interpretation, where understanding is seen as a formative process as the learner views events from fresh, ever-evolving perspectives. Concepts are then seen in ongoing formation. This paper examines learning through a contemporary hermeneutic frame and the contention is that this opens opportunity for learning to be perceived in alternative ways.     

数模竞赛与常规教学结合初探

本文阐述了数学建模竞赛活动与常规教学相结合的意义,构建了数学建模竞赛活动与常规教学相结合的教学运行体系,最后对如何克服教学中的困难提出了三条建议.