小学数学单元整体教学设计策略——以“多边形的面积”为例

在小学数学教学中,以课时为视角进行的教学,往往只关注了单个知识点的理解和学习,这种教学方式下学生往往被繁杂的知识点所迷惑,造成学生在理解上只见树木不见森林,不能对知识进行融会贯通,在解题时不能举一反三.而单元整体教学则把教学目光放在单元内各知识点之间的关系上,强调数学知识点之间的融会贯通和相互生成,注重学生数学知识结构的建立,克服了知识之间彼此割裂的局限性.本文以“多边形的面积”单元为例,进行单元整体教学设计策略的探讨.     

“二元一次方程组”大单元结构化教学设计

大单元教学设计更注重教师根据学生心理认知的特征,从提高学生对知识点的系统性把握和对核心知识的角度入手,更加宏观地掌握知识点.对二元一次方程组单元教学设计的研究,利用布鲁姆教育目标分类学对目标进行叙写,根据UbD理论对本章进行单元教学设计,通过学历案落实目标,充分发挥大单元教学的实效.     

注重整体教学设计 提升数学核心素养

从教材来看,数学知识是分章节进行编排的,各章节之间的知识点看似孤立实则关联密切.教师要引导学生运用数学思维将所学知识串联起来,把握知识点之间的横向联系和纵向联系,不断提升自身数学核心素养.本文结合自己平时的教学案例,谈谈如何进行整体教学设计,从而提升学生的数学思维和核心素养.     

待定法在"高等代数"教学中的应用

在高等代数的教学中,“特定系数法”思想应用比较普遍.它不仅能够用以分析教材,理解教材中的知识点,还可以帮助我们理解教材中一些章节的知识结构,从而在更深的层次上把握教材.     

从AB与BA谈高等代数的教学串联

从矩阵AB与BA的基本关系出发,将高等代数教学中的若干重要知识点串联在一起.     

初三数学第二轮专题有效复习策略初探——以“以函数背景下特殊点的确定专题复习”为例

1研究背景 专题复习前学生已经进行了第一阶段的系统复习,掌握了较多的基础知识,但这时的知识是零碎的、孤立的,还没有从宏观上整体把握知识脉络.因此,还不能按教材顺序对知识进行再现复习,必须要对知识进行重组,把零散的知识归类、纵横串联、辨其异同、汇总起来形成知识网络.总复习的第二阶段,要特别体现教师的主导作用,对初中数学知识加以系统整理,依据基础知识的相互联系及相互转化关系,梳理归类,分块整理,重新组织,变为系统的条理化的知识点.故有必要由教师归类,对比讲解,分块练习与综合练习交叉进行,使学生真正掌握初中数学教材内容.因此,在经过第一轮复习后,应按中考试题题型进行整理归纳,即做到教学要有型,复习要有根.由此可见,对知识进行系统整理,怎样整理适合学生,是教师需要思考的问题.笔者主要针对中考试卷第18题、24题的类型进行专题复习.     

浅谈函数、方程、不等式之间的联系

<正>函数、方程和不等式是初中数学的主要内容,也是中考的必考知识点.新课程标准把此三部分的关系提到了十分明朗化的程度,因此,初中教学应该重视这三部分内容.总的来说,函数主线下的方程、不等式,本质上就是将研究方程、不等式这个局部的问题放在函数的整体性质中把握,将求方程根及研究根之间关系、求不等式解集这些静态的结果放在动态的变化过程中研究.即函数主线下的方程、不等式是整体与局部的关系,方程是函数的"点状态",不等式是函数的"区间状态",函数是"连续状态",函数统领方程和不等式.     

突破瓶颈,知识迁移——以全等三角形和相似三角形的教学为例

迁移理论可以在很大程度上帮助学生扭转传统的数学学习思维,简单讲即培养学生的发散性思维,锻炼学生的灵活转化能力、应变能力,切实提高学生的数学成绩,因此,迁移理论在数学教学过程中的重要性不言而喻.迁移理论固然有它本身系统的理论体系,但还要结合具体实际进行针对性的剖析,本文以全等三角形和相似三角形的教学为例,充分利用迁移理论逐渐打开学生的思维,帮助学生突破知识点瓶颈,建立正确的解题思路,充分学会利用各知识点的相似性及差异性实现知识的互通及整合,从而更好地把握整个数学学习的意义.     

跑台运动对慢性应激致抑郁模型大鼠学习记忆及前额叶皮质c-fos表达的影响

在数学教学中,教师掌握了学生学习各个知识点的思维过程与知识间的相互干扰,采用相应的教学方法,对杜绝不当的知识干扰,排除解题障碍,提高教学效果,有着重要的作用． 一、局部出发,轻易判断 学生解题过程中,对一些数学概念或数学原理的发生、发展过程没有深刻的理解,往往根据某些局部特征不作深入的审题,不弄清命题的本质涵义,没有摆脱局部事实的片面性而把握事物的本质,产生解题的片面性与主观性,造成解题的不当与失误．例如：     

单元视角下的课时教学设计的思考——以“画角的和、差、倍”的教学为例

核心素养视角下的单元教学设计非常必要,单元教学设计的整合有利于联合知识点与素养目标.笔者结合单元教学的思想,通过对教材的研读,在忠于教材的基础上,以“画角的和、差、倍”的教学设计为例,呈现知识点的结构化.     

谈线性代数与空间解析几何的整合

线性代数与空间解析几何的产生、发展,意味着它们是不可分割的两部分,本文分析和论述了线性代数与空间解析几何整合的必要性和可行性.     

逆矩阵的判定及计算方法

线性代数是大学教育中一门难度较高的基础必修课程,而逆矩阵是教学过程中一个主要概念,对研究其他线性结构有着非常重要的作用.本文通过对逆矩阵定义的分析,汇总若干个判定矩阵是否可逆的方法,同时提供了多种逆矩阵的计算技巧,包括利用计算机技术简化繁琐的计算过程,这些都是学习者在学习过程中需要掌握的重要内容.本文旨在协助教师在开展教学时,能够举一反三,以点带面来引导学生将所学知识融合,注重知识点之间的相关性学习;同时,也帮助学习者能够更加全面的认识逆矩阵这一重要概念.     

Quantization in $$*$$ ∗ -algebras and an algebraic analog of Arveson’s extension theorem

Positivity - In this paper our main goal is showing that many of quantization results in functional analysis are rather algebraic. Following Esslamzadeh and Taleghani (Linear Algebra Appl...     

On Spliced Sequences and the Density of Points with Respect to a Matrix Constructed by using a Weight Function

Ukrainian Mathematical Journal - Following the line of investigation in [Linear Algebra Appl., 487, 22–42 (2015)], for y ∈ ? and a sequence...     

On the largest kth eigenvalues of trees with n≡0 (mod k)

We consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue of trees with n vertices. In 1995, Jia-yu Shao gave complete solutions for the cases k=2,3,4,5,6 and provided some necessary conditions for extremal trees in general cases (cf. [Linear Algebra Appl. 221 (1995) 131]). We further improve Shao's necessary condition in this paper, which can be seen as the continuation of [Linear Algebra Appl. 221 (1995) 131].     

Motivating the concept of eigenvectors via cryptography

New methods of teaching linear algebra in the undergraduatecurriculum have attracted much interest lately. Most of thiswork is focused on evaluating and discussing the integrationof special computer software into the Linear Algebra curriculum.In this article, I discuss my approach on introducing the conceptof eigenvectors and eigenvalues, which I have used for the last3 years in my Linear Algebra course. I offer some examples onhow I have attracted the interest of our students via Hill ciphering,a method of cryptography. After emphasizing the effect of alinear transformation in a vector space and the importance ofeigenvectors, I show how students’ motivation and understandingtowards one of the abstract concepts in Linear Algebra; eigenvaluesand eigenvectors have grown positively.     

On some determinantal identities formation laws

We show that Muir’s law of extensible minors, Cayley’s law of complementaries and Jacobi’s identity for minors of the adjugate [Determinantal identities Linear Algebra and its Applications 52/53 (1983) pp. 769–791] are equivalent. We also show our generalization of Mühlbach/Muir’s extension principle [A generalization of Mühlbach’s extension principle for determinantal identities. Linear and Multilinear Algebra 61 (10) (2013) pp. 1363–1376] is equivalent to its previous form derived by Mühlbach. As a corollary, we show that Mühlbach–Gasca–(Lopez-Carmona)–Ramirez identity [A generalization of Sylvester’s identity on determinants and some applications. Linear Algebra and its Applications 66 (1985) pp. 221–234/On extending determinantal identities. Linear Algebra and its Applications 132 (1990) pp. 145–162] is equivalent to its generalization found by Beckermann and Mühlbach [A general determinantal identity of Sylvester type and some applications. Linear Algebra and its Applications 197,198 (1994) pp. 93–112].     

Minimum rank problems

A graph describes the zero-nonzero pattern of a family of matrices, with the type of graph (undirected or directed, simple or allowing loops) determining what type of matrices (symmetric or not necessarily symmetric, diagonal entries free or constrained) are described by the graph. The minimum rank problem of the graph is to determine the minimum among the ranks of the matrices in this family; the determination of maximum nullity is equivalent. This problem has been solved for simple trees [P.M. Nylen, Minimum-rank matrices with prescribed graph, Linear Algebra Appl. 248 (1996) 303-316, C.R. Johnson, A. Leal Duarte, The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, Linear and Multilinear Algebra 46 (1999) 139-144], trees allowing loops [L.M. DeAlba, T.L. Hardy, I.R. Hentzel, L. Hogben, A. Wangsness. Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns, Linear Algebra Appl. 418 (2006) 389-415], and directed trees allowing loops [F. Barioli, S. Fallat, D. Hershkowitz, H.T. Hall, L. Hogben, H. van der Holst, B. Shader, On the minimum rank of not necessarily symmetric matrices: a preliminary study, Electron. J. Linear Algebra 18 (2000) 126-145]. We survey these results from a unified perspective and solve the minimum rank problem for simple directed trees.     

矩阵方程X+A~*X~(-q)A=I(q>0)的Hermite正定解

1.引言 本文研究矩阵方程 X+A*X-qA=I (1)的Hermite正定解,其中I是一个n×n阶单位矩阵, A是一个n×n阶复矩阵, q是实数且q>0.q=1,q=2时的方程是从动态规划,随机过滤,控制理论和统计学中推导出来的,最近已有许多人对此进行了研究(见参考文献[1,2,4]),本文我们将研究方程(1)的解的存在性和解的性质,并讨论迭代求解及迭代解的收敛性. 对于Hermite矩阵X和Y,文中X≥Y表示X-Y是半正定的,X>y表示X-Y是正定的;对于方阵M,M*表示M的共轭转置,ρ(M)表示M的谱半径,λi(M)     

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014–2015 at the ‘ETSEIB'of Universitat Politècnica de Catalunya (UPC).