Development of Theme-based,Interdisciplinary, Integrated Curriculum: A Theoretical Model

Interest in interdisciplinary, integrated curriculum development continues to increase. However, teachers who have been given primary responsibility for developing these materials are often working with little guidance. A model for developing theme-based, interdisciplinary, integrated curriculum is presented in this article. The model includes two phases, a theme creation phase and an activity refinement phase. Validity criteria from the interdisciplinary curriculum literature are used to assess the power of potential themes. An integration continuum model is used to facilitate refinement of activities included in the theme-based instruction. The curriculum development model is used to clarify the meaning of the terms theme-based, interdisciplinary, and integrated. The model is intended to be used by curriculum developers to facilitate the creation of powerful interdisciplinary lessons.     

Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago.     

Using video representations of teaching in practice-based professional development programs

This article explores how video can be used in practice-based professional development (PD) programs to serve as a focal point for teachers’ collaborative exploration of the central activities of teaching. We argue that by choosing video clips, posing substantive questions, and facilitating productive conversations, professional developers can guide teachers to examine central aspects of learning and instruction. We draw primarily from our experiences developing and studying two mathematics PD programs, the Problem-Solving Cycle (PSC) and Learning and Teaching Geometry (LTG). While both programs feature classroom video in a central role, they illustrate different approaches to practice-based PD. The PSC, an adaptive model of PD, provides a framework within which facilitators tailor activities to suit their local context. By contrast, LTG is a highly specified model of PD, which details in advance particular learning goals, design characteristics, and extensive support materials for facilitators. We propose a continuum of video use in PD from highly adaptive to highly specified and consider the affordances and constraints of different approaches exemplified by the PSC and LTG programs.     

A Survey of Manpower Planning Models and Their Application

Since the late 1950s, much work has been done on developing models of manpower systems which may be used for the purposes of planning. Many organizations have made successful use of such models, but in spite of these successes, manpower planning models are only gradually coming into widespread use. The aim of this paper is to review the models which have been developed, concentrating on their assumptions and applications rather than on mathematical or statistical details. A common theme of successful applications is that good presentation of results and ease of use are more important to users than theoretical sophistication.     

Optimality Regions and Penalty Analysis of the Parameter Space for Machine Replacement Problems

A simple method is presented for developing optimality regions and penalty analysis of the parameter space for machine replacement problems. Optimality regions are regions of the parameter space in which a given economic life is optimal. The optimality regions (penalty analysis) provide a simple, ‘at a glance’, visual means to assess and illustrate the sensitivity of the economic life (cost implications) to errors in the problem parameters. A numerical example is presented in order to illustrate the use of the method in supporting machine replacement decisions.     

Integration of Science and Mathematics: A Theoretical Model

Interest in interdisciplinary, integrated curriculum development continues to increase. However, teachers, who have been given primary responsibility for developing these materials, are often working with little guidance. At present there exists no clear definition of the meaning of integration of mathematics and science. A continuum model of integration is proposed as a useful tool for curriculum developers as they create new integrated mathematics and science curricula or adapt commercially prepared materials. On the continuum, activities range from mathematics or science involving no integration to those activities including balanced mathematics and science concepts. Several examples are given to illustrate the utility of the continuum model for analyzing integrated curricula. The continuum model is intended to be used by curriculum developers to clarify the relationship between the mathematics and science activities and concepts and to guide the modification of lessons.     

Fluctuation analysis for the loss from default

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Numerical results illustrate the accuracy and computational efficiency of the approximation.     

初中学生心理测量的统计分析

本文用相关分析说明了〈中学生素质特点分类培养〉项目研究中所用各种心理诊断量表整体组合运用的合理性 ;用因子分析简化了测试项目的指标体系 ,选定了适当的公共主因子 ,并对公因子给予了合理的解释 ;用聚类分析依据因子得分对学生实施心理素质特点分类 ;根据学生的心理素质特点类型提出了相应的宏观培养策略     

Using a Functional Model to Develop a Mathematical Formula

The unifying theme of models was incorporated into a required Science Capstone course for pre‐service elementary teachers based on national standards in science and mathematics. A model of a teeter‐totter was selectedfor use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing the mathematical relationship for a Class 1 lever, M1D1=M1D1. In this study, 20 student groups (n=72) collected data using the model in an inquiry‐based activity. All groups developed the qualitative relationship, 13 groups developed a correct mathematical formula, 6 groups developed one‐half of the relationship (X = mass × distance), and 1 group attempted to develop a procedural relationship. The pre‐service elementary teachers used a variety of model types in the activity including visual/pictorial, functional/physical and mathematical‐both graphs and formulas. The use of the teeter‐totter model as a visual and functional model of a mathematical formula was a factor in developing the mathematical relationship.     

Optimization challenges in the structured low rank approximation problem

In this paper we illustrate some optimization challenges in the structured low rank approximation (SLRA) problem. SLRA can be described as the problem of finding a low rank approximation of an observed matrix which has the same structure as this matrix (such as Hankel). We demonstrate that the optimization problem arising is typically very difficult: in particular, the objective function is multiextremal even for simple cases. The main theme of the paper is to suggest that the difficulties described in approximating a solution of the SLRA problem open huge possibilities for the application of stochastic methods of global optimization.     

OR in developing countries: A review

The relevance of Operational Research (OR) in developing countries has increasingly engaged the attention of operational researchers in both the industrialised and less developed countries over the last 50 years. With this, there has been a considerable amount of interest in the potential for using OR in developing countries. One sign of this is the emergence of a number of initiatives to promote OR in developing countries and the number of new societies for OR that have emerged from the developing world. This paper is an attempt at providing an overall picture of the state of OR in the developing countries. In particular, it will look at the coverage in terms of countries and methods. It will also highlight the contribution OR is making towards the theme of poverty, the reduction of which is regarded as the key focus of development policy interventions as reflected in the Millennium Development Goals (MDGs).     

Changes of Working Styles in a Computer Algebra Environment – The Case of Functions

This study is an empirical investigation of 11th graders at a German high school (Gymnasium). Working over a 24-hour period in a computer lab, we investigated students' use of quadratic functions with `Derive', and trigonometric functions with `Mathplus' (or `Theorist' for Macintosh). We were particularly interested in the working styles of students while they solved problems and looked for changes in these styles, as compared to traditional paper and pencil activities. While students worked on the computer, their activities (such as inputs from the keyboard, menu choices or mouse movements) were saved by a special program, which ran in the `background'. We are interested in the possibilities of developing a research method based on these `computer protocols'. The study should be seen as an exploratory study for developing hypotheses for further empirical investigations.This revised version was published online in September 2005 with corrections to the Cover Date.     

Effective program planning for multiple projects under limited resources

This work deals with an analytical approach to effective planning based upon the relative economics of projects contained in a program. A mathematical model is formulated to maximize the total return over the planning horizon subject to various annual cash flow and resource constraints. Stochastic mixed-integer programming is applied to determine the optimal sequence of project planning activities. To illustrate the use of the proposed procedure, a numerical example is solved using the mathematical programming software package SCICONIC/VM in a VAX-11/750 computer system.     

CABRI AS A COGNITIVE TOOL FOR THE EVOLUTION OF A SENSE OF PROVING

Cognitive technologies have been described in the literature as reorganisers of thinking processes, especially where problem solving is concerned. This paper aims to analyse the possible use of Cabri-Géomètre as a cognitive tool in the elaboration of mathematical justifications in the context of problem-based mathematics. Some empirical examples are given to illustrate the significance of the specific learning situation. The complexity of learning environments incorporating computer-based activities is stressed as a condition for them to be effective in the introduction of the idea of mathematical justification and its evolution towards a sense of proving.     

Divisibility tests for low-valued primes and their use as generators of simple proofs

This article considers a family of divisibility tests for low-valued primes and their place as activities which develop the use of proof both within school and in teacher training. The way in which these tests can be seen as developing one from another is seen as of value in encouraging students to produce their own proofs.     

An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students’ initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students’ thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students’ conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students’ progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.     

Modelling generator maintenance scheduling costs in deregulated power markets

Generating companies use the maintenance cost function as the sole or main objective for creating the maintenance schedule of power generators. Usually only maintenance activities related costs are considered to derive the cost function. However, in deregulated markets, maintenance related costs alone do not represent the full costs of generators. This paper models various cost components that affect the maintenance activities in deregulated power markets. The costs that we model include direct and indirect maintenance, failures, interruptions, contractual compensation, rescheduling, and market opportunity. The loss of firm’s reputation and selection of loyalty model are also considered using the Analytic Hierarchy Process (AHP) within an opportunity cost model. A case study is used to illustrate the modelling activities. The enhanced model is utilised in generator maintenance scheduling cases. The experimental results demonstrate the importance and impact of market related costs in maintenance schedules.     

Bid and ask prices as non-linear continuous time G-expectations based on distortions

Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly generally measure distortions can be constructed as probability distortions applied to an exponential distribution function on the half line. The valuation methodologies are extended beyond contract valuation to the valuation of economic activities with infinite lives. Explicit computations illustrate the procedures for stock indices and insurance loss processes.     

排队系统中的泰勒展开方法

综述了排队系统中的泰勒展开方法。它由Gong和Hu在1990s首次提出,并在最近几年里有了一些新的发展。首先,通过GI/GI/1队列的简单例子介绍其基本原理;其次,展示如何应用该方法分析相关性队列和离去过程;然后,阐述如何基于该方法发展排队网络近似的高阶矩方法;最后,讨论未来的几个可能研究方向。     

Systems Analysis for Efficient Allocations,Optimal Use of Resources and Appropriate Technology: Some Applications

A systems analytic approach, in which one tries systematically to examine a variety of considerations together rather than in parts, is essential whenever neglect of the interactions of the parts of the system might lead to erroneous conclusions. The O.R. attitude is even more important for developing countries, where the problems are many and solutions are much more severely constrained than in developed countries owing to resource limitation, scarcity of skills, inadequate technological and managerial infrastructure to support sophisticated solutions, and the variety of traditional and ‘modern’ attitudes prevailing in developing societies. To illustrate this, a number of applications carried out by the author in India, covering efficient resource allocation for economic planning, optimal use of resources, such as water and fertilizer, and the choice of techniques of power systems, as well as organizational problems of identification and introduction of appropriate technology in building construction and community bio-gas plants, are briefly described along with comments on the implementation of the results.