线性代数课程思政教学案例的设计与实践

在线性代数课程中进行课程思政教学案例的设计,应以课程内容为源头,综合运用学习的课堂、文化的课堂、实践的课堂.在学习的课堂,通过深入挖掘知识点,帮助学生理解线性代数知识体系中蕴含的马克思主义哲学观;在文化的课堂,通过数学史料的讲解,帮助学生树立文化自信,激发爱国情怀;在实践的课堂,通过应用实例的分析和实践,激励学生学以致用,报效祖国.     

线性代数课程实践教学网络平台的研究和探索

本文针对借助Blackboard平台,从用实际问题驱动线性代数课程教学,介绍与线性代数课程内容相关的数学软件(MATLAB数学软件),增加线性代数课程在实际问题中应用的内容等方面,探讨线性代数课程实践教学网络平台问题.     

论非数学专业线性代数的内容改革

为了弄清线性代数中哪些理论是非数学专业(下简称工科)学生必学的,采用了逆向追踪的方法,把后续课和工程中遇到的问题加以归纳,找到其最低限度需要的理论.从大一学生的知识水平出发,用工科语言来讲解.提出了简化理论的几条原则,写出了面向应用、形象易懂、采用机算的普及型教材《实用大众线性代数(MATLAB版)》,达到"用最少的理论,解决最多的应用问题"的目标.     

矩阵特征体系与化学动力学参数估计

矩阵的特征系统在线性代数知识体系中作为最重要的一环,在实际教学中却面临学生无法直观体会其价值的困境.面对化学化工专业的线性代数课程教学中,针对矩阵特征体系在化学动力学中的应用,开辟与专业结合的应用专题.其目的在于阐明线性代数作为分析与计算工具的基础作用,同时也实现和专业课程的无缝衔接,以促进学生专业课程的学习.     

新工科背景下线性代数课程教学改革与实践

在新工科背景下探讨线性代数课程教学内容、教学模式和考核方式改革,通过优化知识体系、建设丰富的网络资源和课程思政内容、构建多元化教学模式、采取多元化评价方式等,充分发挥学生的主体作用,强化线性代数知识的应用,培养学生的数学素养、实践能力和创新能力,切实提高线性代数课程教学效果和人才培养成效．     

线性代数课程改革的探索与思考

本文主要分享了在“以学生为中心”和“全面育人”等教学理念下，将课堂创新改革和思政元素融入线性代数课程教学过程的探索和实践以及初步成果.本课程改革坚持以学生为中心，师生共同体，在知识讲解中步步递推，层层深入，引导学生的思考和讨论，在教学过程中融入品质的培养，对价值观的塑造，实现全面育人，师生共同进步.     

“以学生为中心”基于多平台的线性代数在线教学探索与实践

本文从“以学生为中心”的现代教育理念出发,充分利用各种平台的优势开展线上的教与学,建立线性代数课程分层次人才培养模式,增大过程评价考核的比例,保障线上教学质量.以求提升学生利用数学知识解决实际问题的能力,激发学生兴趣和学习动机,把线性代数课程的知识体系学习、应用能力提升与品德修养育成有机统一.     

线性代数课程思政建设与教学实践

探讨了线性代数课程思政建设与教学实践.通过优化课程思政教学目标,从线性代数相关历史人物、课程知识点及教学拓展案例三个方面,积极挖掘课程思政元素切入点.加强课程思政教学团队建设,将思想政治教育融入到线性代数课堂混合式教学,增加对学生思政学习的过程性评价.教学实践表明,线性代数课程思政教育有利于培养学生的综合素质,受到学生...     

从一道线性代数试题的几种证明方法谈起

本文以一道线性代数试题的几种证明方法为例,指出线性代数相关教学过程中应加强主线与构架的讲解,以培养学生分析问题的独特视觉及全方位多层面的分析问题的能力.     

信息大类专业《线性代数》课程教学改革的研究与实践

分析了《线性代数》课程的授课现状与困境,探讨了针对信息大类专业特点的教学内容改革,以及应用案例库建设示范.提出应突出线性代数的思维和方法在信息大类学科中的应用、对概念的几何直观展示,以及加强MATLAB编程训练,以培养和提高学生的线性代数思维,全面提升教学效果和学生素质.     

大类招生线性代数教学方法初探——以浙江大学为例

根据探究式学习理论,让学生在教师的指导下自主地解决教师预先提供的大量问题,称之为基于问题的探究式教学法.这种教学法可以在有限的时间内让学生掌握大量的知识并锻炼解决问题的能力.相比传统的教学模式,该方法能更好的培养现代社会发展所需要的人才.我们给出了该方法在线性代数课程上的实施过程.     

Understanding the Development of Flexibility in Struggling Algebra Students

The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote flexible use of solution strategies. Assessments were designed to capture both knowledge and use of multiple strategies. The students were interviewed in order to understand their rationales for choosing particular strategies as well as their attitudes toward instruction that emphasized multiple strategies. Findings suggest that students gained both knowledge of and appreciation for multiple strategies, but they did not always use alternate strategies. Familiarity, understandability, efficiency, and form of the problem were all considerations for strategy choice. Practical and theoretical implications are discussed.     

线性代数是蓝色的——大学非数学专业《线性代数》的课程设计

线性代数不仅是处理多元问题的有力工具,而且具有强烈的思辨性.大学本科教育应该是"泛专业的高等素质教育",作为公共基础课之一的《线性代数》,也应着眼于学生综合科学素质的培养,注意对学生进行思维训练.本文提出线性代数的教学理念:"提出处理多元问题的新要求,沿着多元整合的集成化思路推进,逐步把学生引上线性变换和线性空间的思维平台."为此,本文进行了"五模块、两阶段、三层次"的课程设计,希望对讲授该课程的教师有所裨益.     

线性代数教学中的几个问题

从线性代数教学实践中,选取3个学生提出的问题,进行分析,予以解答.     

Lack of set theory relevant prerequisite knowledge

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students’ mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a group of linear algebra students’ mistakes on a set of linear algebra questions. The paper also details an in-time intervention (a pedagogical approach) to enhance students’ understanding of linear algebra concepts through advancing their set theory knowledge. Mathematics teachers can consider similar approaches to address their students’ mistakes.     

面向独立学院学生的线性代数课程“可视化”教学研究

针对独立学院培养目标和学生的特点,研究如何通过案例教学,具体将线性代数的概念、定理、应用、习题"可视化",完成将枯燥数学知识由抽象到直观的转化,使得线性代数理论与数学建模紧密结合,培养应用型人才.     

The learning and teaching of linear algebra: Observations and generalizations

This paper is about a teaching experiment (TE) with inservice secondary teachers (hereafter “participants”) in the theory of systems of linear equations. The TE was oriented within particular social and intellectual climates, and its design and implementation took into consideration a series of findings concerning the difficulties students have in linear algebra. The questions we set for this study were: (1) Did the participants in the particular TE climates construct viable knowledge in the theory of systems of linear equations? Our criteria for viable knowledge consist in evidence for the ability to (a) generate non-trivial conjectures, judged so subjectively by a mathematician, (b) prove such conjecture, and (c) move upward along the APOS conception levels. (2) What difficulties and insights did the participants experience as they constructed such knowledge?The potential contributions of our investigation into these questions to researchers and practitioners include (a) a detailed depiction of the participants’ achievements and challenges in dealing with theoretical questions concerning linear systems in an authentic learning environment and under a tutelage oriented in a particular constructivist perspective; and (b) a field-based hypothesis about the consequences of a particular learning environment vis-à-vis construction of knowledge in linear algebra.All of the participants had taken a linear algebra course as part of their undergraduate studies, on average 17 years prior to the TE, with an average grade of about 80%. Thus, a third question set for this study concerns retention. (3) What did the participants retain from their linear algebra courses vis-à-vis concepts, ideas, and problem solving pertaining to the theory of systems of linear equations, assuming they had constructed such knowledge during these courses?     

关于数学分析在线性代数中某些应用的数学札记

线性代数中有不少难度较高的问题,若从代数学内部系统出发处理起来,相当繁冗.但是若从另一角度出发,运用数学分析的方法去处理这些代数问题,可能有着事半功倍之效.为此,本文运用数学分析的有关知识和方法论证线性代数中的某些问题.供大家在教学时参考,不妥之处,敬请斧正.     

线性代数课堂中的“教”与“学”

结合教学实践经验,从人才培养的角度阐述线性代数课堂教学中的思维培养问题.指出课堂教学中要善于创设和营造和谐民主、积极向上、与学生心理相融的良好的课堂氛围;设置有利于学生参与认知的教学环节,通过采用灵活的教学方式,激发学生思考;尊重学生主体地位,让他们在教学活动中获得最大的情感体验;充分利用直观形象思维,教学中贯穿直观的几何形象,激发学生学习的兴趣,激发他们的求知欲.     

线性代数教学中的归纳与演绎方法

针对线性代数概念多、内容抽象、逻辑性强等特点，介绍归纳和演绎方法在线性代数教学中的应用，并借助具体案例加以说明．