CTI模式:知识迁移应用的教学策略

<正>“知识的迁移应用”是CTI教学模式的一个环节,这个环节在整个教学过程中起到承上启下的作用^[1].数学知识教学一般分为三个内容:概念教学、命题(规则)教学、解决问题教学.无论是概念教学还是命题教学,其中都有解题教学环节,因为概念应用和命题应用都涉及将新学习知识用于解决问题.另一方面,解决问题又可以是独立的课型,而且这种课型在数学教学中占有很大比重.知识的迁移应用和知识的创新应用均属于解决问题教学范畴,两者可以在一堂课中同时体现,也可以独立体现,这要根据教学内容的多少和教学时间的限制而定.但是在单元教学中,知识的理解应用、知识的迁移应用、知识的创新应用三个环节都必须有体现.     

关于在概率统计课程中改进教学方法的若干思考

通过结合教学实践与理论,阐述了概率统计教学改革的几点看法．提出了在教学过程中加强数学美学教育,应用情景教学法和适当应用反例教学与软件教学．     

应用数学教学中加强素质教育的三个环节

应用数学是一个发展和使用新的或现成的数学理论来解决对社会有益的问题的研究领域。应用数学教学的目的是以培养非数学工作者的数学思维及应用数学技术促进生产力发展。多年来 ,应用数学教学虽然不存在严重的应试教学的不良偏向 ,但教学中以黑板为中心 ,以教员为中心 ,以讲灌为中心的现象仍然不乏存在 ,特别是应用数学教学没有应用的特色。应用数学教学如何突出学员的中心地位 ,突出素质培养的中心地位 ,突出数学应用的中心地位 ,这是应用数学教学中突出素质教育 ,培养学员能力的核心问题。近几年我们经过反复的思考、一年一年的摸索试验 ,…     

初中数学教学中应用意识培养的策略研究

作为一门重要的基础性学科,数学在科学技术中的应用极其广泛,为提升科学技术水平发挥了重要作用.所以,在数学教学中应当注重培养学生的应用意识.在当前的初中数学教学研究领域,关于应用意识培养的成果大多集中在理论层面上,落实到实践中的指导策略相对较少.基于此,本文探讨初中数学教学中应用意识培养的研究背景,结合文献资料和自身工作实践总结了应用意识的基本内涵,并提出在初中数学教学中应用意识培养的策略.     

信息技术在高中数学教学中的应用

近年来,随着科学技术的不断提升与优化,大量新型技术在我国教育教学中得到了广泛的应用与普及,从而进一步推动了新时期教育教学工作模式的多元化发展.在此过程中,信息技术凭借良好的应用效果受到了广大教育工作者的密切关注.实践表明,通过积极做好信息技术的引入与应用,教师可以有效促进“互联网+教育模式”的充分构建,对于新时期我国教学工作的合理优化具有重要的指导意义.本文中,结合教师在教学过程中的感受对信息技术的教学价值进行总结,并积极分享了日常教学工作中如何应用信息技术开展教学活动.     

圆锥曲线的光学性质及其应用的教学设计

以数学学科核心素养为教学理念,采用“情境—问题—猜想—探究—证明—应用”的学习方式与教学流程,借助多媒体设备与动态数学软件演示圆锥曲线的光学性质,增强信息技术的应用意识,通过中国“天眼”的介绍渗透数学学科育人,对“圆锥曲线的光学性质及其应用”作了教学设计.     

多媒体与大学数学教学

分析多媒体手段在大学数学教学中的应用情况.数学本身有它的独特性,在应用多媒体进行教学时,要结合具体的情况,使多媒体能真正为数学教学服务,同时,又能使得数学教学没有失去它的特点和规律.     

《初等数论》课题化教学方法研究——以中国剩余定理为例

以中国剩余定理在密码学中的应用为例,引入课题化教学方法.将理论教学、应用实践和科学研究融为一体,形成了立体化的教学结构.     

以题理知:回顾概念的有效方法——两则教学案例的对比分析及感悟

概念教学中,融合入网是学生认知必须经历的一个环节.只有经过系统认知后的数学概念,才会在学生分析问题和解决问题中发挥它的应用价值.在学生获取概念后,对概念进行简单的应用在教学中是最常见的.这样的应用将会推动新知迅速“入网”,实现与其他数学知识、技能进行关联与融合.然而,在实际教学中,仍然存在一些老师在对已学概念进行回顾时,立足于概念本身的陈述,忽略了概念的应用与延伸,这样的教学,“纯”概     

管理专业与数学专业运筹学课程教学比较与分析

运筹学是管理专业和应用数学专业的重要课程,但是不同的专业特点、教学目的、学生知识基础等情况,决定了运筹学这门课程的教学内容和教学重点的不同.本文就此进行了对比和分析,提出管理专业的运筹学应侧重应用性,应用数学专业的运筹学课程应理论、应用并重,另外应加强该课程的实践教学环节.     

关于高校科技管理队伍建设的思考

本文主要讨论了在社会主义市场经济体制下高校科学管理队伍建设的有关问题。     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

Measure and integration: The basic extension and representation theorems in terms of new inner and outer envelopes

The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals.     

Separated and Connected Maps

Using on the one hand closure operators in the sense of Dikranjan and Giuli and on the other hand left- and right-constant subcategories in the sense of Herrlich, Preuß, Arhangel'skii and Wiegandt, we apply two categorical concepts of connectedness and separation/disconnectedness to comma categories in order to introduce these notions for morphisms of a category and to study their factorization behaviour. While at the object level in categories with enough points the first approach exceeds the second considerably, as far as generality is concerned, the two approaches become quite distinct at the morphism level. In fact, left- and right-constant subcategories lead to a straight generalization of Collins' concordant and dissonant maps in the category of topological spaces. By contrast, closure operators are neither able to describe these types of maps in , nor the more classical monotone and light maps of Eilenberg and Whyburn, although they give all sorts of interesting and closely related types of maps. As a by-product we obtain a negative solution to the ten-year-old problem whether the Giuli–Huek Diagonal Theorem holds true in every decent category, and exhibit a counter-example in the category of topological spaces over the 1-sphere.     

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

his paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda’s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance.     

小区域科技实力及其评估体系

科技实力是运作主体能够进行并完成科技活动的能力。科技实力是一个评估性概念，它反映了科学技术的创新，发展，转移，推广，储备条件以及管理，效果等不同层面的综合性的特征，科技实力由科技潜在能力（科技势能），科技显现能力（科技动能）构成，它包含了对科技资源及分布状态，科技资源保障能力，科技创新能力，科技开发能力，科技转移能力和科技活动运作能力的综合描述。     

Study of the size-flux relation of pores and spots

Using the vector magnetic field data from the Huairou Solar Observing Station of National Astronomical Observatories, a statistical study on the size-flux relation of photospheric magnetic features without any assumption is given. The selected data here include mature sunspots, as well as protosunspot (with a partial penumbra) and pore. We studied not only their size-flux relations of pore, protosunspot and mature sunspot, but also that of umbra and penumbra of the mature sunspots. The size-flux relationship of mature sunspots and their umbra and penumbra is found to be in different indexes of power-law. No evident relations are found between size and flux of the pores and protosunspots. We found that there is a threshold of 1×1012 Wb or (3-4.03) × 107 km2 for the transition from a pore to a protospot. Such results may be useful for understanding the physical conditions and dynamical processes of magnetic flux tubes in solar plasma during sunspot's formation. In addition, their characteristic size is also given.     

有限区域求解流函数和速度势的迭代调整方法及其收敛性分析

全球区域求解流函数和速度势的解是唯一的,但有限区域内,由于受区域边界条件限制,流函数和速度势的计算以及风场的分解不是唯一的,减小或消除边界不确定对结果的影响是有限区域求解流函数和速度势以及分解风场最重要的问题．该文在Endlich迭代调整思想上,提出了能准确求解有限区域流函数和速度势且对边界条件要求较低的迭代调整方法．该方法也能准确地分解和重建风场,且风场重建的误差非常小．对该迭代方法的收敛性进行分析,发现其收敛性与不同方向网格的格距和调整系数有关．最后将该方法应用到Arakawa A-D网格和不规则区域,验证了该方法的可靠性．     

Some Results for Large Closed Queueing Networks with and without Bottleneck: Up- and Down-Crossings Approach

The paper provides the up- and down-crossing method to study the asymptotic behavior of queue-length and waiting time in closed Jackson-type queueing networks. These queueing networks consist of central node (hub) and k single-server satellite stations. The case of infinite server hub with exponentially distributed service times is considered in the first section to demonstrate the up- and down-crossing approach to such kind of problems and help to understand the readers the main idea of the method. The main results of the paper are related to the case of single-server hub with generally distributed service times depending on queue-length. Assuming that the first k–1 satellite nodes operate in light usage regime, we consider three cases concerning the kth satellite node. They are the light usage regime and limiting cases for the moderate usage regime and heavy usage regime. The results related to light usage regime show that, as the number of customers in network increases to infinity, the network is decomposed to independent single-server queueing systems. In the limiting cases of moderate usage regime, the diffusion approximations of queue-length and waiting time processes are obtained. In the case of heavy usage regime it is shown that the joint limiting non-stationary queue-lengths distribution at the first k–1 satellite nodes is represented in the product form and coincides with the product of stationary GI/M/1 queue-length distributions with parameters depending on time.