构建数学辅助解题工具的问题解决模型——以线段图在小学数学教学中的作用为例

在数学教学中,合理地利用数学辅助解题工具可以更有效地帮助学生解决问题,提高学生的学习兴趣.然而,关于解题工具如何发挥作用,目前还缺乏详细的介绍.从认知心理学的角度出发,可以将数学辅助解题工具解决问题的过程视为开启了一个新的视角,通过线段图的作用来解决小学数学过程中存在的难题,构建模型来分析线段图如何解决学生的难题.研究表明,线段图能够有效地减轻学生的记忆负担,提高学生解决问题的效率.     

关于分配格的判定问题

针对分配格判定时容易出错这一教学难题,提出可以利用学生专业特点从而结合计算机这一工具来帮助解决,并通过一个典型例子来具体说明,该例子同时也指出了教材习题解答书中的一处错误.认为本文提出的这一教学思想对于离散数学的教学有一定的启示.     

向量法的运用

<正>向量是高中数学的重要知识,是沟通几何与代数的工具.教材中不少公式、定理都可以用向量的方法推导与证明.因此利用向量思想可以帮助我们解决问题提供不同的思路.1向量在线性规划中的运用     

加減算尺及乘除算筹

一、引言在本文內作者介紹两种簡单的計算工具。第一种叫做“加减算尺”,可以帮助小学生做加減法,熟练加減法口訣,还可以分解二次式的因子。第二种計算工具叫做“乘除算筹”,它是化乘除为加減的一种准确的工具。利用它可以比較快而准确地做多位数的乘法及除法。1951年孙克定同志在教速成算术的乘除法时就用了这种算筹帮助笔算,获得出色的效果。后来上海財經学院又研究了怎样用算筹来配合珠算,多次的試驗证明效果是很好的。二、加减算尺市面上有一种供小学生用的20厘米长的木尺(北京第三木制文具生产社出品)。每一个一年級小学生都应当有一根这样的尺。这种尺不但可以用来划线、打格子、量測,而且还可以用来认数。尺上有从1到20     

合作博弈的粒子群算法求解

随着局中人人数的增加,利用传统的“占优”方法和“估值”方法进行合作博弈求解无论从逻辑上还是计算上都变得非常困难。针对此问题,将合作博弈的求解看作是局中人遵照有效性和个体理性提出分配方案,并按照一定规则不断迭代调整直至所有方案趋向一致的过程。依据该思路,对合作博弈粒子群算法模型进行构建,确定适应度函数,设置速度公式中的参数。通过算例分析,利用粒子群算法收敛快、精度高、容易实现的特点,可以迅速得到合作博弈的唯一分配值,这为求解合作博弈提供了新的方法和工具。     

如何使用信息技术帮助学生学习几何

在数学课内外 ,学生使用信息技术的机会越来越多 .信息技术确实有纸笔工具无法比拟的优势 ,例如呈现丰富的图例 ,描绘复杂的图形 ,展现不同数学表示之间的关系 ,提供动态的数学学习环境等等 .当我们将信息技术的使用整合到几何课程中去的时候 ,应当考虑一个问题 :如何使用计算机工具帮助学生有效地学习几何 ?一般地 ,我们可以从发挥信息技术工具两方面的功能来考虑 ,即图形显示、制作功能和交互功能 .1　图形显示制作功能1 1　图形显示功能几何和图形密不可分 ,每一个几何概念都可以用图形表示 .理解几何概念在一定程度上就是确定某类图形…     

群体多指标决策的偏好集结方法

研究多个指标条件下,利用个体决策结果形成群体一致偏好的方法、假设个体有加性效用函数,将个体多指标效用函数表示成单个指标评价函数的加权和,群体指标评价函数表示成个体指标评价函数的加权和.通过协商指标权重、指标评价函数、支付意愿三个参数,成对个体达成双方一致.提出了(n-1)对个体之间达成双方一致,从而得出群体效用函数的决策方法,这种分析框架同样可以扩展到联盟协商一致中.     

解读2007年高考试题中的导数问题

导数进入中学数学教材,成为一个很好的工具,在解决高中数学问题时应用极为方便,尤其是利用导数来解决函数的单调性问题,求函数的极值、最值问题,也可以利用导数来解决几何、物理及实际生活问题.……     

一类非线性Burgers方程组的基于Hopf-Cole变换的直接间断Galerkin有限元方法

<正>1引言Burgers方程可以作为描述许多物理现象的数学模型,如交通流、激波、扰流问题和连续的随机过程.它还可以用于检验数值方法的效率.由于其具有较广的实用范围,一些学者对其近似解进行了较多的研究.如Adomian分解方法、混合有限差分和边界元方法、样条有限元方法、精确显式有限差分方法、Douglas有限差分格式,直接变分方法和变分迭代方法被用于Burgers方程近似解的研究~([1-13]).Hopf-Cole变换~([14,15])是研究Burgers方程较好的分析工具,利用它可以获得Burgers方程一些精确解.近年来,人们意识到该变换也是一个很好的数值工具并利用其得到了一     

Mathematica软件快速上手指南(1)——Mathematica系统的基本概念

Ｍａｔｈｅｍａｔｉｃａ是由美国Ｗｏｌｆｒａｍ公司研究开发的一个交互式数学软件.利用这个软件,能够完成符号运算、数学图形绘制甚至动画制作等多种操作,是制作数学课件的一个极好工具.我们将在一系列文章中以Ｍａｔｈｅｍａｔｉｃａ2.2版(操作系统:Ｗｉｎｄｏｗｓ98中文版)为例,就如何使用这个软件进行介绍.1　Ｍａｔｈｅｍａｔｉｃａ的数学功能Ｍａｔｈｅｍａｔｉｃａ是一个强大的数学专家系统,它能帮助你解决复杂的数学计算、公式推导,能作出数学函数的图形等,归纳起来主要有如下几点:1.1　数值计算它的意义读者易于了解.它可以当作一…     

作弊因素的统计分析

针对目前高校校园里大学生的作弊问题,本文通过对调查问卷的统计分析对其原因进行了分析。通过对名义数据和有序数据的相关性分析,我们首先找出影响大学生作弊的因素。然后用逐步回归法和Logistic回归模型得出影响大学生作弊的主要因素。最后分析了性别和不同年级对作弊的影响,得出了许多意料之中和意料之外的答案。这些分析结果对如何进行大学生素质教育有一定的参考价值。     

A Decision Aid for Structuring and Evaluating Career Choice Options

A decision aid for helping ICI personnel in assessing future career options is described. Its rationale is to help users clarify their own thinking about possible careers, by raising their awareness of the current subjectively relevant factors (or attributes) for assessment of careers and by encouraging them to generate a more complete and realistic set of attributes. Career options can then be evaluated using this modified attribute set. A computer program, MAUD, is employed for structuring and evaluating options, and the design of a simple aid, HISTRA, which helps users to generate a more complete understanding of the career decision problem and to clarify relative importances of conflicting attributes, is described.     

First year mathematics undergraduates’ settled images of tangent line

This study concerns 182 first year mathematics undergraduates’ perspectives on the tangent line of function graph in the light of a previous study on Year 12 pupils’ perspectives. The aim was the investigation of tangency images that settle after undergraduates’ distancing from the notion for a few months and after their participation in university admission examination. To this end we related the performances of the undergraduates and the pupils in the same questions of a questionnaire; we classified the undergraduates in distinct groups through Latent Class Analysis; and, we examined this classification according to the Analytical Local, Geometrical Global and Intermediate Local perspectives on tangency we had identified among pupils. The findings suggest that more undergraduates than pupils demonstrated intermediate perspectives on tangency. Also, the undergraduates’ settled images were influenced by persistent images about tangency and their prior experience in the context of preparation for and participation in the examination.     

成也萧何,败也萧何？——高管金融经历与公司债券融资

基于印记理论和高层梯队理论,本文以2008至2018年发行公司债券的上市公司为研究对象,考察高管金融经历对公司债券融资的影响机理。结果表明:首先,高管金融经历在提高公司债券发行成功率的同时也会增加债券融资成本和违约风险,而对发债规模与期限并不会产生显著影响,在控制可能的内生性问题后结论依然成立;其次,具有金融经历的高管所任职公司会通过盈余管理来提高债券发行成功率,但也会增加债券的融资成本和违约风险;最后,具有证券公司或商业银行工作经历的高管对公司债券融资的影响更为显著。本文有助于实务界和理论界理解高管异质性特征对公司债券融资的影响机制,为监管部门制定防范金融风险的政策提供可靠的理论依据。     

学生学习《高等数学》困难原因调查及统计分析

为分析学生学习<高等数学>学习困难原因,提高新建本科院校<高等数学>教学效果,我们对一所新建本科院校2005级至2007级全部本科学生进行调查.本研究主要采用问卷调查方式进行,并应用统计学方法,研究学生学习<高等数学>困难原因,探讨解决办法.     

大学生综合素质的问卷调查与结论

本文给出的大学生综合素质问卷调查的若干结论,是通过对武汉大学、中国科技大学等18所高校参与的大学生综合素质问卷调查所获统计数据,进行了多层次、多方面、多视角的比较与分析所得。我们期望这些研究结果,能给大学的领导与广大教育工作者进一步了解在校大学生的现状、特点、问题以及对如何全面提高大学生的培养质量等提供帮助。     

Reflective Pathways: Analysis of an Urban Science Teaching Field Experience on Noyce Scholar‐Science Education Awardees' Decisions to Teach Science in a High‐Need New York City School

Awardees of the National Science Foundation's Noyce Scholars funds are required to teach science in high‐need urban or rural school districts upon graduation. The purpose of this research was to analyze the reflective considerations that distinguish preservice Noyce Scholar science education majors committed to teaching in high‐need New York City (NYC) schools from those committed to high‐need rural careers. Essays designed to expose their (n = 22) considerations of teaching in NYC written before, immediately after, and two weeks following a one‐week cultural and science teaching internship experience were coded to reveal distinguishing reflective thought patterns. The results showed that those (16/22) whose final essay showed commitment to NYC teaching viewed themselves positively as NYC teachers and that increases in positive self‐perceptions were paralleled by increases in affinity toward living in NYC and NYC schools. Those not inclined to NYC teaching (6/22) expressed increasingly negative views of themselves as NYC teachers, NYC life, and urban education generally. The research provides insights into what Noyce Scholar undergraduates in science education think about when considering a teaching career in urban school districts.     

Learning to Teach Inquiry: A Beginning Science Teacher of English Language Learners

Early career science teachers are often assigned to classrooms with high numbers of English language learners (ELLs). For the underprepared early career science teacher, these circumstances are challenging. This study examines the changes in beliefs and practices of an early career science teacher who taught high numbers of ELLs in an urban setting. Victoria participated in the Alternative Support for Induction Science Teachers (ASIST) program during her initial two years of teaching. Our research team followed her over a three‐year period, and the data collected included classroom observations and interviews about her beliefs and practices. In addition, documents such as teacher evaluations and classroom artifacts were collected periodically for the purpose of triangulation. The analysis of the data revealed that with the support of the ASIST program, Victoria implemented inquiry lessons and utilized instructional materials that promoted language and science competencies for her ELLs. Conversely, standardized testing and her teaching assignment played a role in constraining the implementation of inquiry‐based practices. The results of this study call for collaborative efforts between university science educators and school administrators to provide professional development opportunities and support to build the capacity of early career science teachers of ELLs.     

Innovation capabilities measurement using fuzzy methodologies: a Colombian SMEs case

The main aim of this paper is to establish the hidden incidences that can improve specific aspects of beekeeper Small and Medium Enterprises (SME) innovation capabilities in Boyacá-Colombia. The methodology is focused on the use of the expertons model, adequacy coefficient and forgotten effects theory. A questionnaire of 58 items about different innovation management areas is distributed to 14 beekeeper SMEs in the area of Boyacá-Colombia. The findings suggest that there are two specific actions that can improve innovation culture. These actions are related to marketing strategies and product innovation. The innovation strategy has a significant influence on the development of an innovative culture in the beekeeper SMEs; one must have a clear orientation to the innovation objectives in the marketing strategy, which is transferred to the product. Likewise, the utility of fuzzy methods for analysis when information is limited, subjective and scarce is highlighted. Finally, this research can be useful to practitioners and academics because the findings can serve as guidelines to understanding sources and enablers of innovation. In addition, the findings show how fuzzy methods help in contending with incomplete and subjective information, highlighting the meaning of the information rather than its measurement.

     

Researcher,Teacher, Education Researcher: The Evolution of a University Geoscience Instructor

This case study describes a professor's evolution from geoscience researcher to effective teacher to education researcher. The article details his initial beliefs about teaching, looks at the factors that prompted him to seek a different teaching approach, and enumerates the supports and challenges that he had on his journey. Factors essential to this evolution are early career success in discipline research, an institutional climate to reward teaching, mentoring support by colleagues, access to professional development opportunities, and involvement in action research activities. The case study is linked to education literature about teaching and education research and makes recommendations based on the findings of the study.