关于“三角函数的诱导公式”的教学比较

1问题的提出在扬州市2011年度师能建设"百千万工程"中,有一项活动是千名骨干教师科研引领下"我的教学研究"展示,对象为全市在职特级教师、学科带头人、中青年教学骨干,形式为以基于课题研究的教学设计评比和说课展示相结合的形式进行.笔者选择了"三角函数的诱导公式的教学比较"这个课题参加了     

关注学生个体差异，实施有效教学——一道工程应用题的教学反思

2012年,笔者参加了某中学召开的课堂教学设计与案例研讨会．本小组研讨的课题是人教版七年级第三章实际问题与一元一次方程中的“一元一次方程的应用——工作量问题”．     

三角函数在中学数学中的核心地位

笔者于2008年10月17-19日应邀参加人教社中教室的"中学数学核心概念与思想方法教学设计研究"课题组的活动,笔者长期从事数学教育实践,直觉感到这一课题具有深远意义.本文基于笔者从1978年开始对三角函数概念系统改造的实践,借探讨三角函数在中学数学中的核心地位来阐述个人对中学数学核心概念研究的一些思考.请同行批评指正,希望有助于课题研究的深入,推动我国的数学教育改革.     

一节“自主、合作、探究”的课题学习课——“心率的调查”教学实录及其评析

在江苏省南京市教学研究室举办的初二年级数学"课题学习"研究课教研中,笔者执教"课题学习"研究课"心率的调查",给与会教师留下深刻的印象.教学时感慨很多,现将本节课的教学及评析整理记述如下,与同行共同探讨.一、活动准备(一)知识准备通过上网了解,查阅资料,采访老师和医务工作者等途径,获得心率概念、心率的测量方法,以及测量心率受到哪些因素影响等相关知识.(二)实践准备1.方案的确定     

“数列的概念”的教学反思

在一次教研员教学实践活动中,笔者到一个数学基础相对薄弱的班级上课,课题是"数列的概念".围绕数列的概念,师生进行了"长时间"的数学活动,可谓是历经"九九八十一难"修得"正果",其间有一些精彩的意外生成,也留下诸多遗憾.课后评课中,听课教师提出了很多宝贵的意见.之后,笔者静下心来,回顾教学设计、     

学生预习后课堂教学策略转变与优化实践研究

笔者读了文[1]与[2]后,想起了2000年在华东师大参加中学骨干教师国家级培训时,一位老师计划进行"学生课前学习行为的调查与研究"的课题实验,在与专家组讨论中,实验老师总是想说明课前预习是有效的,应该大力提倡;专家组却质疑预习的有效限度,认为预习的负面影响也是不容忽视的.这引起了笔者对课前预习的思考与研究.     

基于核心素养的高中数学作业设计

在基于核心素养的课程改革的背景下,高中数学教学出现了许多新的特点,对高中数学作业的布置也提出了更高的要求.如何根据学生的实际认知水平,遵循数学教学的基本原则.设计符合学生发展的数学作业,提升学生的数学核心素养,已成为每位数学教师必须面对与思考的课题.笔者基于实际教学经历,从作业布置的时间和类型进行阐述.     

行程问题:从历史到课堂

<正>作为华东师范大学与宝山区沪太路新农村教育发展区合作项目"HPM与教师专业发展"的学员,笔者接受了开观摩课的任务,选定的课题是"一元一次方程的应用:行程问题".这是笔者任教以来第一次尝试HPM教学.意大利学者Furinghetti曾提出了数学史融入数学教学的一般过程:了解历史资料→选择合适话题→分析课堂需要→设计课堂活动→实施教学计划→评价课堂活动.按照上述过程,首先需要查阅、搜集有关行程问题的历史材料;然后对历史材料进行加工,用于教学设计,最后实施于课堂.     

谈初中数学课题的生成策略

生成适于教学的数学课题是学习教学设计的基础,因此,教师应当明确好的数学课题的标准,平常注意积累适合设计成课题的信息资源,并尝试依据不同的教学要求自主生成丰富多彩的数学课题.只有自己学会如何生成有效的数学课题,才能将数学课题学习这一形式为我所用,更好的为教学服务.以下笔者结合自身的体会对初中数学课题的生成进行分析.     

研究性学习的选题案例

案例1　关于货物包装设计的研究.高中数学课本(试验修订本—必修)《不等式》一章的引言中提出如下问题:“某工厂要建造一个长方体的无盖贮水池,其容积为4 80 0平方米,深为3米.如果池底每平方米的造价为1 50元,池壁每平方米的造价为1 2 0元,问怎样设计能使总的造价最低?”课本提出这个问题,旨在为学习不等式的必要性提供铺垫.以此为引子,可提出这个研究性学习课题.在课题方案中,要求学生通过实际调查写出自己的研究论文,并列出下列问题供学生参考:1 )请你实际测算一下健力宝饮料罐的包装是否是最节约成本的设计?2 )猫在冬天为什么总缩成一团?…     

Structuring resource allocation decisions: A framework for building multi-criteria portfolio models with area-grouped options

Multi-criteria portfolio modelling has been extensively employed as an effective means to allocate scarce resources for investment in projects when considering costs, benefits and risks. Some of these modelling approaches allow the grouping of projects into organisational areas, thus also supporting the decision of resource allocation among organisational units in a way that is collectively efficient for the organisation. However, structuring in practice a portfolio model using this latter type of approach is not a trivial task. How should areas be defined? Where should new projects be included? How should one define the criteria to evaluate performance? As far as we know, there is very little indication in the operational research and decision sciences literatures on how to structure this type of model. This paper suggests different ways to structuring portfolio models where projects are divided into areas and evaluated by multiple criteria, and illustrates their use in two action-research projects. Drawing on these experiences it then suggests a general framework for the structuring of such models in practice. Directions for future research are also identified.     

Operational Research and the Universities

University staff may contribute to operational research by developing and refining its special techniques, or by becoming involved in operational research projects; they may investigate practice to guide them in their research, or in the training of operation analysts. The universities are, in many ways, ideally equipped for operational research work, but involvement in long-term consulting activities is not without serious problems of its own.     

Community operational research issues and public art practice: the art director system

The key issues of community operational research, outlined in a paper by Ritchie, have relevance to community projects in general and, we argue, a particular relevance to public art. We illustrate this relevance by describing eight case studies in public art, four in Japan and four in the west, and by considering the projects in a three-way factorial design, make a case for the art director system in the management of public art projects.     

Writing practitioner case studies to help behavioural OR researchers ground their theories: application of the mangle perspective

Behavioural research into the practice of OR needs to be grounded. Case studies written by practitioners can potentially help address this need but currently most do not. The paper explores a way of describing OR projects that place the emphasis on the ‘actors’ who provide the motivating force and the consequences of their actions. The ‘mangle’ perspective focuses on the dynamic intertwining of people, technology and concepts; this can provide the basis for an insightful narrative describing the reality of the project in terms of the planned approach, the problems met and the outcomes. Two examples are given, one of a conventional model building exercise, the second of a ‘soft OR’ intervention: both describe projects conducted by practitioners for commercial purposes. It is concluded that, by using the mangle perspective, the OR case writer can winnow the wheat from the chaff in order to write a succinct informative narrative, a narrative that could be utilized by behavioural OR (BOR) researchers. It is further concluded that BOR researchers should engage with ‘practice theory’ to deepen their understanding of what actually happens in projects.     

Methodological reflections on a three-step-design combining observation,stimulated recall and interview

In this paper a tripartite qualitative design combining abservation, stimulated recall and interview is presented and discussed. This three-step-design makes it possible to get insight into the interaction of internal and external processes when solving mathematical tasks. The data analysis depends on the research question and the methodological approach. In the light of two research projects in mathematics education two different methods of data analysis are presented and methodologically reflected.     

A representation model for the solving-time distribution of a set of design tasks in new product development (NPD)

Given the potential risks of new product development projects (NPD), the characteristics of the design tasks solving-time distributions are critical for their effective management. In OR we need to find what operational characteristics of design tasks may delay projects. Other researchers already identified the technological novelty, the magnitude of the design tasks, the interactions between design tasks in an NPD project, and the balancing between projects among the most important causes of the unpredictability of the design tasks lead times in NPD projects.     

Development of a Community of Science Teachers: Participation in a Collaborative Action Research Project

This article presents a study exploring the beliefs, knowledge, and practices of four middle and secondary science teachers participating in a collaborative curriculum action research project. Using a case study methodology, the views and practices of these teachers were described and analyzed as they investigated novel ideas about scientific inquiry and nature of science, critically examined their practice, and implemented and reflected upon modified curricular practices. Findings indicated that by the end of the study, all participants had enhanced their views of scientific inquiry and nature of science, and the collaborative group evolved as a community of teachers. Wenger's (1998a) community of practice theory provided a useful framework to describe and analyze the experiences of these science teachers. Implications for the professional development of science teachers and the compatibility between a community of practice and collaborative action research projects are presented.     

Uncertainty Modelling in Software Development Projects (With Case Study)

A project scheduling model tailored specifically for software development projects is proposed in this study. The model incorporates uncertainties related to activity durations and network topology. The first type of uncertainty exists due to error-prone coding which might result in elongated task durations caused by validation and debugging sessions. Furthermore, in practice, macro-activities represent groups of sub-tasks in order to simplify the planning and monitoring of the project. Due to the aggregation, it is more difficult to be precise on the duration of a macro-activity.The uncertainty related to the network topology is due to common database design issues or program modules shared among parallel tasks in the project network. These tasks become associated with each other through uncertain Start-to-Start (SS) precedence relationships. On the other hand, SS lags may also be the outcome of technological precedence relationships among pairs of activities. However, the imprecision underlying the work content of a predecessor activity leads to uncertain SS lags.Software development projects are human-intensive projects and hence, the duration of a task depends on the skill of the person assigned to the job as well as his/her learning rate. Thus, a task may be realized by alternative staff members which results in different expected task durations. Hence, a realistic model proposed for software development projects should incorporate staff assignment features under the uncertainties discussed above. In this study, we develop a mathematical model for software development projects and propose heuristic solution methods to be used by the project co-ordinator in preparing the project plan. The heuristic algorithms developed here are tested on real data provided by a consulting firm undertaking software development projects from manufacturing companies in Turkey.     

Decision analysis assessment of a national medical study

To decide whether or not to undertake an expensive national survey to determine the effectiveness of infection control, we devised a quantitative decision model to analyze the costs and probabilities of successful study outcomes. The result allowed us to determine whether the proposed study method and design would provide sufficient statistical power to ensure meaningful conclusions from the research. The model was robust in assessing the adequacy of method accuracy and, within the range of assumptions specified, it suggested that the project should be undertaken. The results helped to secure official approval and funding for this large-scale research project. A novel approach to evaluating sensitivity analysis is included. As constructed, the model is applicable to other projects in applied research and, with some modification, to projects in basic research as well.