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2. Electronic vs. Paper Textbook Presentations of the Various Aspects of Mathematics
- Author
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Usiskin, Zalman
- Abstract
Based in part on our work in adapting existing paper textbooks for secondary schools for a digital format, this paper discusses paper form and the various electronic platforms with regard to the presentation of five aspects of mathematics that have roles in mathematics learning in all the grades kindergarten-12: symbolization, deduction, modeling, algorithms, and representations. In moving to digital platforms, each of these aspects of mathematics presents its own challenges and opportunities for both curriculum and instruction, that is, for the content goals and how they connect with students for learning. A combination of paper and electronic presentations may be an optimal solution but some difficulties with such a complex solution are presented.
- Published
- 2018
- Full Text
- View/download PDF
3. Do Alternative Base Periods Increase Unemployment Insurance Receipt among Low-Educated Unemployed Workers? National Poverty Center Working Paper Series #12-19
- Author
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National Poverty Center, Gould-Werth, Alix, and Shaefer, H. Luke
- Abstract
Unemployment Insurance (UI) is the major social insurance program that protects against lost earnings resulting from involuntary unemployment. Existing literature finds that low-earning unemployed workers experience difficulty accessing UI benefits. The most prominent policy reform designed to increase rates of monetary eligibility, and thus UI receipt, among these unemployed workers is the Alternative Base Period (ABP). In 2009 the American Recovery and Reinvestment Act sought to increase use of the ABP, making ABP adoption a necessary pre-condition for states to receive their share of the $7 billion targeted at UI programs. By June 2012, 40 states and the District of Columbia had adopted the ABP despite the absence of an evaluation of ABP efficacy using nationally representative data. This paper analyzes Current Population Survey data from 1987-2007 to assess the efficacy of the ABP in increasing UI receipt among low-educated unemployed workers. We use a natural-experiment design and logistic regression models to capture the combined behavioral and mechanical effects of the policy change. We find no association between state-level ABP adoption and individual UI receipt for all unemployed workers. However, among part-time unemployed workers with less than a high-school degree, adoption of the ABP is associated with a 3.4 percentage point increase in the probability of UI receipt. (Contains 5 tables, 1 figure and 7 footnotes.)
- Published
- 2012
4. School District Consolidation Study in 10 Michigan Counties: Is District Consolidation Cost Effective? What Is the Alternative to Consolidation? Working Paper #15. Revised
- Author
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Michigan State University, Education Policy Center and Shakrani, Sharif M.
- Abstract
As Duncomb and Yinger (2001) have stated, "School consolidation represents the most dramatic change in education governance and management in the United States in the twentieth century. Over 100,000 school districts have been eliminated through consolidation since 1938, a drop of almost 90 percent (NCES 1999, Table 90). This longstanding trend continues throughout the country, largely because consolidation is widely regarded as a way for school districts to cut costs" (p. 1). The study described in the present paper applies Duncomb and Yinger's methods to Michigan data, looking as possible to financial consequences of consolidation of school districts at the county level. Research data sets for 10 counties in Michigan are used to estimate cost-saving effects of consolidation, as in the Duncombe and Yinger study. It appears that significant savings can be achieved in consolidating school districts at the county level. The coordination of services also produces cost savings for the districts assuming participation in a county level (ISD) coordination of services. These findings are consistent with other research studies in New York and Indiana. However, consolidation studies conducted in Arizona and New Jersey indicated that the fiscal savings hoped for did not materialize to the extent expected. Overall, consolidation seems to make fiscal sense, particularly in rural and small districts. The coordination of services seems more palatable to Michigan communities and also produces significant reduction in cost of services such as transportation and operation. The results of this study should be of interest to state and local elected officials, to state education agency staff, and to public school administrators. The Future of School Districts Consolidation in Michigan is provided in an addendum. (Contains 1 footnote.) [This study was funded by the Booth Newspapers of Michigan.]
- Published
- 2010
5. An Implementation of a Mathematical Programming Approach to Optimal Enrollments. AIR 2001 Annual Forum Paper.
- Author
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DePaolo, Concetta A.
- Abstract
This paper explores the application of a mathematical optimization model to the problem of optimal enrollments. The general model, which can be applied to any institution, seeks to enroll the "best" class of students (as defined by the institution) subject to constraints imposed on the institution (e.g., capacity, quality). Topics explored include how the model was applied to actual data and the results of that application. The presentation touches on how well the model mimics "real life," insights that can be gained from the output, the model's limitations, and the modifications that might be warranted to improve performance. (Contains 17 references.) (Author/SLD)
- Published
- 2001
6. Bus Routing Algorithms: Application to a Rural School District. Working Paper No. 27
- Author
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Ohio Univ., Athens. Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics., Belcher, Johnny, Britt, Deborah, Granade, Sharilyn, Powell, Lori, and Schlessinger, Paula
- Abstract
This paper proposes a mathematical model that delineates a feasible system of bus transportation for this multiple-school district. The model is composed of six elementary school districts which are part of the overall middle school and high school district. This proposal attempts to show Laurel district busing as a representative sample of what needs to be done in all six elementary districts. Final transportation routes from all six districts to the centrally located county Middle and High Schools are included and explained. Both elementary district and entire county algorithms are included. First, the population distribution was analyzed and bus stops were created for the sample Laurel district such that the average number of children per stop is maximized and each child walks no more than a predetermined distance. Next, the bus stops were grouped geographically into regions of roughly equivalent number of students, and the viable routes for each region were determined. Finally, these routes were sequenced by the implementation of the NCL (No Child Left at Bus Stop) algorithm created for the Madison County Schools. The algorithm has been created so that changes can be made to accommodate adjustments in parent and school board decisions.
- Published
- 2005
7. Questioning Assumptions: A Critical Pedagogical Perspective on Mathematics Teaching and Learning in Rural Places. Working Paper No. 18
- Author
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Ohio Univ., Athens. Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics., Hackenberg, Amy J., and Mewborn, Denise S.
- Abstract
In this paper, we address mathematics education in rural contexts from a critical pedagogical perspective. We imagine our audience to be mathematics educators and rural educators who may not have background knowledge of critical pedagogy. We also confess that we are mathematics educators first, with interests in critical pedagogy and rural education. Thus we do not position ourselves as experts and do not intend to proclaim what rural mathematics educators "should" do. To set up our discussion, in this section we characterize (in broad strokes) critical pedagogy, current reform in mathematics education, and issues in rural education.
- Published
- 2004
8. Skiving Addition to the Cutting Stock Problem in the Paper Industry
- Author
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Johnson, M. P., Rennick, C., and Zak, E.
- Published
- 1997
9. Using National Survey of Postsecondary Faculty Data To Form Disciplinary Specific Comparative Productivity Figures for Public Institutions with Significant Graduate and Research Programs. AIR 2000 Annual Forum Paper.
- Author
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Chatman, Steve
- Abstract
This study used the restricted access database of the 1993 National Study of Postsecondary Faculty to examine faculty workload by academic discipline for full-time regularly appointed teaching and research faculty in public Carnegie research I and II and Doctoral I and II institutions (n=2,056). Data are reported for 14 disciplinary areas (agriculture, business, education, engineering, fine arts, health, English, comminations, history, biology, physical science, mathematics, economics, psychology, and sociology) and include teaching load by student level, research funding by source, and scholarly productivity. Chi-square analysis considered whether faculty at different Carnegie class institutions were more or less likely to engage in an activity, and whether there was a difference in magnitude if engaged. In Chi-square analyses significant at the 0.05 level, teaching was associated with Carnegie class in 19 of 120 analyses, obtaining external funding was associated in 3 analyses, and outcomes of publishing was significant in only 1 case. Differences by magnitude were found in 5 instances. There are nine data tables and nine figures. (Contains 12 references.) (CH)
- Published
- 2000
10. Selected Papers in School Finance, 1997-99. NCES 1999-334
- Author
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National Center for Education Statistics (ED), Office of Educational Research and Improvement (ED), Fowler, William J., Fowler, William J., National Center for Education Statistics (ED), and Office of Educational Research and Improvement (ED)
- Abstract
The National Center for Education Statistics (NCES) commissioned the papers in this publication to address advances in measuring education inflation and adjusting for it, as well as to examine the emergence of a new focus on school spending, rather than school district spending, as well as new, private sources of funding for public education, and a review of the status of assessing educational productivity. The first two papers continue the NCES tradition of commissioning papers to address the measurement problems of the education finance research community. The other papers examine the relationship between school district and school spending, and private sources of funding public education, of which surprisingly little is known. The final paper examines the existing attempts to estimate the cost of educational outcomes, and the implications for policymakers and researchers. Following an Introduction and Overview by William J. Fowler, Jr., papers included, in order, are: (1) Adjusting for Differences in the Costs of Educational Inputs (Eric A. Hanushek); (2) An Alternative Measure of Inflation in Teacher Salaries (Dan Goldhaber); (3) School Districts and Spending in the Schools (Amy Ellen Schwartz); (4) New Revenues for Public Schools: Alternatives to Broad-Based Taxes (Michael F. Addonizio); and (5) Modern Education Productivity Research: Emerging Implications for the Financing of Education (David H. Monk and Jennifer King Rice). (Individual papers contain references.)
- Published
- 1999
11. Studying Faculty Flows Using an Interactive Spreadsheet Model. AIR 1997 Annual Forum Paper.
- Author
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Kelly, Wayne
- Abstract
This paper describes a spreadsheet-based faculty flow model developed and implemented at the University of Calgary (Canada) to analyze faculty retirement, turnover, and salary issues. The study examined whether, given expected faculty turnover, the current salary increment system was sustainable in a stable or declining funding environment, and whether further early retirement incentives would be necessary. The model, called the Academic Staff Resource Projection Model, is based on the Markov chain approach to project faculty movement out four years. It was developed using Microsoft's Excel spreadsheet software. Nine alternative policies and assumptions were tested concerning: (1) retirements for ages 55 to 70; (2) resignation rates by years of service; (3) age distribution of newly hired staff; (4) annual attrition of one rank replaced by another rank; (5) overall attrition replacement ratio; (6) adjustments to allow for addition or elimination of academic programs; (7) starting salaries; (8) salary schedule information; and (9) rate of promotion to next rank. Six figures and flow charts illustrate the model and show the spreadsheet file structure and flows. Three appendixes include a policy variables worksheet, a salary schedule, and an age distribution schedule. (Contains 16 references.) (CH)
- Published
- 1997
12. U.S. 2001 PIRLS Nonresponse Bias Analysis. Working Paper No. 2003-21
- Author
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National Center for Education Statistics (ED), Piesse, Andrea, and Rust, Keith
- Abstract
The Progress in International Reading Literacy Study (PIRLS) is a large international comparative study of the reading literacy of young students. The student population for the U.S. 2001 PIRLS (hereafter simply referred to as PIRLS) was the set of all fourth-graders in the United States, corresponding to the grade in which the highest proportion of nine-year-olds are enrolled. The PIRLS school sample consisted of 200 schools (150 public and 50 private) containing a fourth grade, selected with probability proportionate to the school'?s enrollment of fourth-graders. One classroom was sampled from each selected school. PIRLS was conducted in April and May 2001. For the original sample, the unweighted response rate at the school level was 62.5 percent, with 125 out of 200 schools responding. Through the use of replacements, the unweighted response rate was improved to 87 percent, with 174 out of 200 schools responding. However, as the response rate from the original sample was below 85 percent, NCES requested that Westat investigate the potential magnitude of nonresponse bias at the school level. The methodology and results of this investigation are described herein.
- Published
- 2003
13. Faculty Salary Equity: Issues in Regression Model Selection. AIR 1992 Annual Forum Paper.
- Author
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Moore, Nelle
- Abstract
This paper discusses the determination of college faculty salary inequity and identifies the areas in which human judgment must be used in order to conduct a statistical analysis of salary equity. In addition, it provides some informed guidelines for making those judgments. The paper provides a framework for selecting salary equity models, based on four decision elements and the contributions of four fields of study (law, economics, statistics, and institutional research) as the basis for establishing criteria for selecting an appropriate salary equity model. The four decision elements include defining the group to be analyzed, determining the variables to be included, deciding what statistical model should be used, and determining which outcome statistics should be used for interpretation. Contributions from the field of law focus on pay equity, disparate treatment, and comparable worth. The contribution of the field of economics comes from human capital theory. The contribution of statistics is the use of multiple regression analysis in salary equity research and the issues of multicollinearity and statistical significance. The field of institutional research has contributed various studies on methods of indentifying underpaid employees. (Contains 75 references.) (GLR)
- Published
- 1992
14. Statistics for Policymakers or Everything You Wanted To Know about Statistics but Thought You Could Never Understand. Working Paper Series.
- Author
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National Center for Education Statistics (ED), Washington, DC. and Ahmed, Susan
- Abstract
This working paper contains the overheads used in a seminar designed to introduce some basic concepts of statistics to nonstatisticians. The seminar has been presented on several occasions. The first part of the seminar, and the first set of overheads, deals with the essentials of statistics, including: (1) population, sample, and inference; (2) standard errors and confidence intervals; (3) statistical significance; (4) correlation and linear regression; and (5) graphics. The second part of the seminar, and the second group of overheads, concerns basic principles of research design and analysis, including operationalizing terms, types of bias, confounding, and aspects of validity and reliability. (Contains 91 overheads.) (SLD)
- Published
- 1997
15. The Impact of BIB-Spiralling Induced Missing Data Patterns on Goodness-of-Fit Tests in Factor Analysis. Occasional Paper OP93-1.
- Author
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National Center on Adult Literacy, Philadelphia, PA. and Kaplan, David
- Abstract
The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest on forming pairwise available case (PAC) correlation matrices. Developments in statistical theory for missing data show that PAC correlation matrices may not satisfy Wishart distribution assumptions underlying factor analysis, this impacting tests of model fit. A new approach for handling missing data in structural equation modeling advocated by B. Muthen, D. Kaplan, and M. Hollis (1987) is proposed as a possible solution to these problems. The new approach is compared to the standard PAC approach in a Monte Carlo simulation framework. Simulation results show that tests of goodness-of-fit are very sensitive to PAC approaches even when data are MCAR, as is the case for BIB designs. The new approach outperforms the PAC approach for continuous variables and is comparatively much better for dichotomous variables. One table and one figure illustrate the discussion. (SLD)
- Published
- 1993
16. Cost-of-Education Differentials across the States. Working Paper Series.
- Author
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SMB Economic Research, Inc., Washington, DC., MPR Associates, Berkeley, CA., and Barro, Stephen M.
- Abstract
Any interstate comparison that does not take differences in the cost of education into account will give an incorrect impression of the relative levels at which different states support their schools. The lack of cost-adjusted statistics on state expenditures for elementary and secondary education interferes with policy analysis, resource allocation, and decision making in education. An examination of state cost data indicates that there is substantially more interstate variation in per-pupil spending than in the amounts of the main educational resource--instructional staff--that states provide for each pupil. In fact, the main conceptual and technical problems in constructing a cost-of-education index arise from the labor-intensive nature of education and the types of labor on which schools rely. This report evaluates some ways of constructing cost-of-education indices, focusing on existing approaches rather than proposing new ones. Conceptual advantages of econometric supply-demand modeling approach are noted, as are its practical disadvantages. Improvements in databases should make construction of a model-based cost-of-education index much more feasible in the near future. Chapters are: (1) "Introduction: Cost Differentials and Cost-of-Education Indices"; (2) "Conceptual Foundations of Cost-of-Education Indies": (3) "Alternative Index Construction Methods"; (4) "Demonstration and Assessment of Simple Cost Indices and Proxies"; and (5) "Conclusions: Current Capabilities and Promising Options." (Contains 19 tables and 48 references.) (SLD)
- Published
- 1994
17. Generalized Variance Estimate for Schools and Staffing Survey (SASS). Working Paper Series.
- Author
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Synectics for Management Decisions, Inc., Arlington, VA.
- Abstract
The 1987-88 Schools and Staffing Survey (SASS) looked at a national sample of elementary and secondary public and private schools. Components of the SASS, a data collection effort of the National Center for Education Statistics, were surveys of teacher demand and shortage, schools, administrators, and teachers. Approximately 13,000 schools and administrators, 65,000 teachers, and 5,600 local education agencies composed the SASS sample. This study was conducted to develop generalized variance functions that could be used to approximate the sampling error associated with an estimate of interest from the SASS. These generalized variances were designed for the user who does not have half-sample replication software available, but requires an approximation to the sampling error associated with his or her estimates of interest. A generalized variance function is a mathematical model describing the relationship between the variance or relative variance of a survey estimator and its expectation. The method for determining the generalized variance functions was tested in a pilot test, and generalized variance functions were then developed. The first appendix presents summary pilot test results, and the second contains tables of the generalized variance functions for the different survey components. (Contains 9 figures and 15 tables.) (SLD)
- Published
- 1994
18. Schooling, Skills, and the Returns to Government Investment in Education: An Exploration Using Data from Ghana. Living Standards Measurement Study, Working Paper No. 76.
- Author
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World Bank, Washington, DC. and Glewwe, Paul
- Abstract
Investments in schooling are often regarded as essential for economic development, implying that such investments have high rates of return in developing countries. This paper examines the accuracy and usefulness of estimates of rates of return to formal schooling based on the standard human capital model of G. Becker and J. Mincer. Focus is on whether failure to account for differences in ability and school quality across a random sample significantly biases estimates of the private return to schooling derived from estimates of wage equations. This is done using an unusually rich data set from Ghana (over 4,700 households), which includes tests of ability and cognitive skills administered to 389 survey respondents. When years of schooling are used to measure the accumulation of human capital, there are virtually no returns to schooling in the private sector. Replacement of years of schooling by reading and mathematical ability does show positive returns to acquired skills, although these rates may be of little use to governments making schooling investment decisions because of the complexity of such decisions. Many government investments in education are designed to raise rates of return to schooling by raising school quality, but decisions by individuals assume that both rates of return and school quality are exogenous. Thirteen tables present data from the analyses. Four appendices provide supplemental data concerning the calculation of rates of return. (SLD)
- Published
- 1991
19. L-scaling. Working Paper No. 26.
- Author
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Southwest Texas State Univ., San Marcos. Dept. of Finance and Economics. and Blankmeyer, Eric
- Abstract
Given "T" joint observations on "K" variables, it is frequently useful to consider the weighted average or scaled score. L-scaling is introduced as a technique for determining the weights. The technique is so named because of its resemblance to the Leontief matrix of mathematical economics. L-scaling is compared to two widely-used procedures for data reduction, but no attempt is made to survey the voluminous literature on scaling methods. These methods are the first principal component method and the best weight function method. A robust L-scaling technique is described for use when the data matrix is contaminated by outliers. The discussion proceeds in terms of descriptive statistics since the various techniques have sampling properties that are either unknown or intractable. The technique is illustrated with a hypothetical example of 100 observations on three variables drawn from a pseudorandom-number generator. L-scaling is one method a researcher may apply when a sensitivity analysis, which compares the outcomes of several scaling methods, is desired. Four tables illustrate the study. (SLD)
- Published
- 1990
20. Bridging between Real World & Mathematics Ideas through Modelling Task
- Author
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Abolfazl Rafiepour
- Abstract
In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the modelling cycle. In this paper after discussion about modelling in more details, two modelling cycles will be elaborated in the context of mathematical tasks that are related to everyday life. Main ideas behind different modelling cycles is starting point that would be from real world situation. Then gradually mathematical elements of real world phenomenon identified and mathematics problem will have shaped in a form that could be solved through mathematical problem solving techniques. Furthermore, it would be important phase that call interpretation of mathematics answer and check it in front of real world situation. This paper will be followed by discussion about learning theories that support the idea of modelling. Finally, two educational challenges (Design good modelling tasks and assessing of students performance) in mathematical modelling activity will be discussed. [For the complete proceedings, see ED655360.]
- Published
- 2023
21. On the Paper by Leonid A. Gavrilov and Natalia S. Gavrilova entitled “Trends in Human Species-Specific Lifespan and Actuarial Aging Rate” Published in Biochemistry (Moscow), Vol. 87, Nos. 12-13, pp. 1622-1633 (2022)
- Author
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Mikhalsky, Anatoly I.
- Published
- 2023
- Full Text
- View/download PDF
22. Optimal Volume Planning and Scheduling of Paper Production with Smooth Transitions by Product Grades.
- Author
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Voronov, Roman, Shabaev, Anton, and Prokhorov, Ilya
- Subjects
PRODUCTION scheduling ,GREEDY algorithms ,PAPER mills ,CUTTING stock problem ,MATHEMATICAL models ,SIMPLEX algorithm - Abstract
The article deals with the problem of calculating the volume calendar plan of a paper mill. The presented mathematical model and methods make it possible to schedule paper production orders between several paper machines (PM) to even their loading, devise cutting plans for each winder and arrange the order of their implementation. When forming cutting plans, orders are grouped in accordance with such parameters as grammage, roll diameter, core diameter, product type and number of layers. Deadlines and volumes in customer orders are taken into account. The cutting plans for each winder account for the allowable roll width limits and the maximum number of knives. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives' setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm and the local search procedure. We tested the solution approach on real production data from a paper mill in European Russia and obtained the production sequence that better matches deadlines in customer orders compared to the plan devised manually by production planners. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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23. Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405
- Author
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National Bureau of Economic Research, Gelman, Andrew, and Imbens, Guido
- Abstract
It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or other smooth functions.
- Published
- 2014
24. Mathematical modelling of a slow flameless combustion of a two-dimensional paper.
- Author
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Fusi, Lorenzo, Calusi, Benedetta, Giovinetto, Antonio, and Panconi, Leonardo
- Subjects
- *
COMBUSTION , *MATHEMATICAL models , *ADVECTION-diffusion equations , *RAYLEIGH number , *CHEBYSHEV polynomials , *TRANSPORT theory , *AIR flow - Abstract
We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Creating and Publishing an Undergraduate Math Paper
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Hoang, Tram and Lautzenheiser, Roger
- Published
- 2005
26. Teaching Fluid Shifts during Orthostasis Using a Classic Paper by Foux et al.
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Goswami, Nandu, Batzel, Jerry J., Loeppky, Jack A., and Hinghofer-Szalkay, Helmut
- Abstract
Hypovolemic and orthostatic challenge can be simulated in humans by the application of lower body negative pressure (LBNP), because this perturbation leads to peripheral blood pooling and, consequently, central hypovolemia. The classic paper by Foux and colleagues clearly shows the effects of orthostasis simulated by LBNP on fluid shifts and homeostatic mechanisms. The carefully carried out experiments reported in this paper show the interplay between different physiological control systems to ensure blood pressure regulation, failure of which could lead to critical decreases in cerebral blood flow and syncope. Here, a teaching seminar for graduate students is described that is designed in the context of this paper and aimed at allowing students to learn how Foux and colleagues have advanced this field by addressing important aspects of blood regulation. This seminar is also designed to put their research into perspective by including important components of LBNP testing and protocols developed in subsequent research in the field. Learning about comprehensive protocols and carefully controlled studies can reduce confounding variables and allow for an optimal analysis and elucidation of the physiological responses that are being investigated. Finally, in collaboration with researchers in mathematical modeling, in the future, we will incorporate the concepts of applicable mathematical models into our curriculum. (Contains 3 figures and 1 table.)
- Published
- 2011
- Full Text
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27. Mapping Teacher Moves When Facilitating Mathematical Modelling
- Author
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Mathematics Education Research Group of Australasia (MERGA), Brown, Jill P., and Stillman, Gloria A.
- Abstract
This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video and audio-recorded task implementation. The analytical tools developed, with one teacher and one task early in a three-year project were particularly useful in ascertaining what the teacher moves were as we subsequently sought to determine reasons for these.
- Published
- 2023
28. Monte Carlo simulation of the coffee-ring effect on porous papers.
- Author
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Hwang, Youngjin, Kim, Sangkwon, Lee, Chaeyoung, Kwak, Soobin, Lee, Gyeonggyu, and Kim, Junseok
- Subjects
- *
MATHEMATICAL models , *COMPUTER simulation , *MONTE Carlo method - Abstract
In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. Review Paper. An Introduction to Lymphocyte and Viral Dynamics: The Power and Limitations of Mathematical Analysis
- Author
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Asquith, Becca
- Published
- 2003
30. Mining Artificially Generated Data to Estimate Competency
- Author
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Robson, Robby, Ray, Fritz, Hernandez, Mike, Blake-Plock, Shelly, Casey, Cliff, Hoyt, Will, Owens, Kevin, Hoffman, Michael, and Goldberg, Benjamin
- Abstract
The context for this paper is the "Synthetic Training Environment Experiential Learning -- Readiness" (STEEL-R) project [1], which aims to estimate individual and team competence using data collected from synthetic, semi-synthetic, and live scenario-based training exercises. In STEEL-R, the "Generalized Intelligent Framework for Tutoring" (GIFT) orchestrates scenario sessions and reports data as experience API (xAPI)statements. These statements are translated into assertions about individual and team competencies by the "Competency and Skills System" (CaSS). Mathematical models use these assertions to estimate the competency states of trainees. This information is displayed in a dashboard that enables users to explore progression over time and informs decisions concerning advancement to the next training phase and which skills to address. To test, tune, and demo STEEL-R, more data was needed than was available from real-world training exercises. Since the raw data used to estimate competencies are captured in xAPI statements, a component called DATASIM was added. DATASIM simulated training sessions by generating xAPI statements that conformed to a STEEL-R "xAPI Profile." This facilitated testing of STEEL-R and was used to create a demo that highlighted the ability to map data from multiple training systems to a single competency framework and to generate a display that team leaders can use to personalize and optimize training across multiple training modalities. This paper gives an overview of STEEL-R, its architecture, and the features that enabled the use of artificial data. The paper explains how xAPI statements are converted to assertions and how these are used to estimate trainee competency. This is followed by a section on xAPI Profiles and on the xAPI Profile used in STEEL-R. The paper then discusses how artificial data were generated and the challenges of modeling longitudinal development and team in these data. The paper ends with a section on future research. [For the full proceedings, see ED623995.]
- Published
- 2022
31. Understanding Linear Programming Modeling through an Examination of the Early Papers on Model Formulation
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Murphy, Frederic H. and Panchanadam, Venkat
- Published
- 1997
32. Paper Moon: Simulating a Total Solar Eclipse
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Madden, Sean P., Downing, James P., and Comstock, Jocelyne M.
- Abstract
This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.
- Published
- 2006
33. Fiscal Response of School Districts to District Fiscal Capacity and State Aid. Working Papers in Education Finance, Paper No. 15.
- Author
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Education Commission of the States, Denver, CO. Education Finance Center., Adams, E. Kathleen, and Vincent, Phillip E.
- Abstract
Data on 174 Colorado school districts were used to measure districts' responses (as indicated by per-pupil expenditures) to their own fiscal capacity and to state aid that changes over time. Colorado's modified guaranteed tax base (GTB) formula was analyzed and a model constructed that took into account the formula's limits on district spending and its year-to-year changes in a district's state aid based on the district's tax revenues in the preceding year. Such changes comprise an "intertemporal price variable." Data were collected on such variables as district wealth (total and residential assessed value), income, state and federal aid, enrollment size and growth, percentage of minority pupils, and agricultural land prices. Using linear and log-linear correlation equations, researchers analyzed the variables' effects on districts' total and locally-derived expenditures and on the elasticity of these expenditures in relation to changes in other variables' values. Results indicate that Colorado's GTB formula has had significant effects neither on differences across districts in expenditures per student nor on the strong correlation between assessed valuation and expenditures. The results also carry implications for the construction of models of districts' fiscal responses. (RW)
- Published
- 1978
34. Model of School Finance. School Finance Project Working Paper #3. Attachment B.
- Author
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Michigan State Dept. of Education, Lansing. and Phelps, James L.
- Abstract
This paper, one of three related documents, explains a model for school finance in Michigan. First, it analyzes where school districts get their money and how they spend it. Next, it details a financial model that identifies the factors related to staff adequacy levels, estimates the strength of those factors, offers ideas for the components of a policy regarding school funding, and estimates the impact of a possible policy alternative. The paper concludes that the model can be improved in three areas. Salary data can be refined and brought up to date. More factors contributing to staff adequacy levels can be identified. Finally, the model can be observed over time to see if it consistently predicts school district behavior. (Author/LD)
- Published
- 1979
35. Applications of Nonlinear Models. AIR 1984 Annual Forum Paper.
- Author
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Stewart, Ian and Johnson, F. Craig
- Abstract
Some of the conceptual qualitative ideas needed to test nonlinear models empirically and to modify them are described. Relationships among these ideas and computer applications are also examined to elucidate the general process of nonlinear modeling. Two examples are presented along with a discussion of bifurcation, catastrophe, and maximum likelihood estimate methods. The first example concerns administrators' responses to innovation and uses a verbal description of events. The model is developed based on variables such as the amount of voluntary effort committed to the innovative project and the level of funding agreed to by the institution. An equation consistent with the hypotheses is presented. The second example starts with a mathematical model of promotions within an organization and shows how to go beyond the verbal statements. It is concluded that many observed phenomena in institutions are suggestive of nonlinear dynamics models. A number of standard types of dynamic behavior are well understood mathematics (catastrophe, periodicity, stochastic effects) and may be used to construct plausible models. (Author/SW)
- Published
- 1984
36. Discussion on the Papers on `Statistics and Mathematics'
- Published
- 1998
37. Instrumental Variable Estimates of the Labor Market Spillover Effects of Welfare Reform. Upjohn Institute Staff Working Paper.
- Author
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Upjohn (W.E.) Inst. for Employment Research, Kalamazoo, MI. and Bartik, Timothy J.
- Abstract
The labor market spillover effects of welfare reform were estimated by using models that pool time-series and cross-section data from the Current Population Survey on the state-year cell means of wages, employment, and other labor market outcomes for various demographic groups. The labor market outcomes in question are dependent variables that are related to control variables and the state's welfare caseload. A key feature of the analysis is that the endogeneity of caseloads is corrected for with a rich set of instrumental variables. State welfare caseloads are treated as endogenous, and 10 instrumental variables reflecting state welfare reform policies are used. The resultant estimates indicate significant spillover effects of welfare policies. Over the short term, welfare reforms reduce the wages of male high school dropouts, the wages of single mothers, and the employment of male high school dropouts. In the long run, more educated groups gain wage boosts because of welfare reform. Tables detailing the following items are appended: (1) logit estimates; (2) first-stage estimated coefficients for the instrumental variables, single mothers group, corresponding to second-stage equation with ln(Wage) dependent variable; (3) 2SLS coefficient estimates; and (4) simulated effects of welfare reform on various labor market outcomes. (Contains 30 references and 11 tables/figures.) (MN)
- Published
- 2002
38. More on the Demand for Medical Education, with Special Attention to the Effects of Nonprice Rationing. Discussion Paper No. 79-23.
- Author
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Stapleton, David C.
- Abstract
A model in which nonprice rationing has two effects on the number of medical school applicants in the United States is specified and estimated for the 1951-76 period. The results indicate that low acceptance rates discourage many potential applicants and that a fairly large and constant percentage of rejected applicants can be expected to reapply. Four previous applicant studies are examined. The results also indicate that the rapid growth rates of applicants in recent years can largely be attributed to three factors: growth in women applicants, increases in resident salaries; and induced increases in repeat applicants. Medical school tuition, loan availability, and the attractiveness of science careers do not appear to have been important determinants of applicants over the sample period. (Author/SW)
- Published
- 1979
39. The Economic Effects of Immigration: Specification of a Model. Impacts of Immigration in California, Policy Discussion Paper.
- Author
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Urban Inst., Washington, DC. and de Leeuw, Frank
- Abstract
Many of the arguments behind efforts to reform this nations's immigration laws allege that immigrants, especially illegal immigrants, take jobs away from native workers, depress wages, and receive public services valued in excess of their tax contributions. To provide a basis for appraising these economic arguments, this paper presents a model for simulating the economic effects of immigration. The model is a theoretical framework, useful for understanding how the various economic responses triggered by immigration relate to one another. Simulation of the model shows that the effects of an increase in annual flow of immigrants are highly sensitive to the substitutability between labor and capital and among different kinds of labor; to the responsiveness of wage changes to unemployment; to the presence or absence of wage rigidity; and to the skill mix of immigrants. Effects are also sensitive to regional behavior, specifically to the response of interregional migration and interregional trade to wage and price differentials. The report contains an overview of the model, simulation of the model, and an agenda for future work on the model. Included are a list of references and related titles. An appendix lists the variables, the equations with the coefficients used for the reference simulation, and the alterations for each of the other simulations. (LBW)
- Published
- 1985
40. Multiple Alternatives for Educational Evaluation and Decision-Making. Interim Draft. Paper and Report Series No. 72.
- Author
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Northwest Regional Educational Lab., Portland, OR. Research on Evaluation Program. and Wholeben, Brent E.
- Abstract
This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the Modeling Formulation") discusses four stages of modeling development related to acceptance of a modeling formulation for decision-making, contextual assessment, planning for modeling development, and the specific design stage. These chapters use specific real-world problems to illustrate the purpose and application of the model. Part II ("Presentation of a Full Formulation"), also composed of four chapters, provides a detailed description of the multiple alternatives framework as a strategy for purchasing computer equipment. The chapters cover conceptualization, development of the framework, format for execution, and approaches to exploring results. Part III ("Example of a Complete Quantitative Solution") is a single chapter focusing on implementation of the model for determining fiscal rollbacks and program terminations during a crisis. Part IV consists of two chapters focusing on current extensions under research and development and a summary touching on related topics. Three appendixes provide a course outline and syllabus for Multiple Alternatives Analysis instruction and an outline for a field project proposal. (TE)
- Published
- 1982
41. Multiple Alternatives Modeling in Determining Fiscal Roll-Backs during Educational Funding Crises. Interim Draft. Paper and Report Series No. 70.
- Author
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Northwest Regional Educational Lab., Portland, OR. Research on Evaluation Program., Wholeben, Brent E., and Sullivan, John M.
- Abstract
This report provides an extensive discussion of the use of criterion referenced, mathematical modeling procedures to determine which budget reductions minimize reduction in the quality of educational programs. Part I, "Evaluation of Potential Budgeting Roll-backs under Educational Fiscal Crisis," explains the basic design of multiple alternatives analysis and the context for its use. Chapters include (1) philosophical foundation for fiscal modeling, (2) program budgeting for an allocation/deallocation fiscal strategy, (3) traditional modeling via cost analytical design, (4) operations research and the evaluation of feasible alternatives, and (5) simulation modeling within a criterion-impact design. Included also is a background to the field investigation and outline of the technical report. Part II, "Multiple Alternatives Analysis as a Mathematical Decisioning [sic] Model," provides the technical and mathematical details of the analysis, including both construction and validation. Part III, "Field Application of the Rolbak Model," contains an extensive sampling of the use of these procedures in reducing a budget within a local school district, including chapters on (1) construction of the database, (2) initial T-normal transformations, (3) formulation of the rolbak mathematical model, (4) search for regional feasibility as a benchmark, (5) cyclic optimization of the restricted model, (6) cyclic optimization of the relaxed model, and (7) comparison of the restricted and relaxed "decisioning" models. Part IV summarizes the Multiple Alternatives Model and assesses its future. (TE)
- Published
- 1982
42. The Measurement of Equity in School Finance with an Expenditure Disparity Measure. Papers in Education Finance No. 19.
- Author
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Education Commission of the States, Denver, CO., Berne, Robert, and Stiefel, Leanna
- Abstract
This report evaluates alternative approaches to and measures of equity in state school finance plans. It also evaluates the Federal Expenditure Disparity Measure (FEDM). Following an introduction, Part II describes alternative conceptions of equity in education and identifies three components of these conceptions: groups treated, alternative treatments, and criteria for equity. Part III presents numerical models that show how alternative combinations of group, treatment, and criterion can yield different conclusions when applied to a hypothetical school district. In Part IV, the value judgments that underly the alternative conceptions of equity are examined. Since few value judgments are widely held, a number of equity conceptions must be considered valid. Also in Part IV, the value judgments inherent in Per Pupil Expenditure Disparity Measures (PPEDMs) are reviewed and analyzed. In Part V, the theory behind the FEDM and the way the Office of Education applies the FEDM to calculate measures from state data are discussed. In Part VI, recommendations concerning equity measurement in federal regulations and particular procedures used by the Office of Education to measure expenditure disparities are presented. A lengthy appendix considers social welfare theory, social choice theory, equity measures calculations, and the tax price of education. (Author/JM)
- Published
- 1978
43. A Bayesian Method for Evaluating Trainee Proficiency. Technical Paper 323.
- Author
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Army Research Inst. for the Behavioral and Social Sciences, Alexandria, VA., Epstein, Kenneth I., and Steinheiser, Frederick H.
- Abstract
A multiparameter, programmable model was developed to examine the interactive influence of certain parameters on the probability of deciding that an examinee had attained a specified degree of mastery. It was applied within the simulated context of performance testing of military trainees. These parameters included: (1) the number of assumed mastery states--master, nonmaster, and perhaps intermediate (likely to soon achieve mastery); (2) the prior distribution of scores from similar examinee groups; and (3) the number of test trials or items administered. The results of several simulations showed that the degree of confidence that a decisionmaker can have about the testee's mastery is markedly affected by the values for the three parameters, and the effects of their combination. Using the Bayesian model, test length and costs could be reduced--as long as the prior information was accurate and valid for the particular group of examinees. Results of the simulation also showed that a test may be too short to be of decision-making value. (Author/GDC)
- Published
- 1978
44. Criterion-Referenced Testing: A Critical Analysis of Selected Models. Technical Paper 306. Final Report
- Author
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Army Research Inst. for the Behavioral and Social Sciences, Alexandria, VA. and Steinheiser, Frederick H.
- Abstract
Alternative mathematical models for scoring and decision making with criterion referenced tests are described, especially as they concern appropriate test length and methods of establishing statistically valid cutting scores. Several of these approaches are reviewed and compared on formal-analytic and empirical grounds: (1) Block's approach to setting mastery standards, involving student performance and academic requirements; (2) Crehan's classification, comparing scores of students who have and who have not completed training; (3) the probabilistic models of Macready, Dayton, and Emrick, which assume an equal proportion of masters and nonmasters; (4) the binomial distribution model, which allows for partial acquisition of proficiency; (5) the Bayesian model, which considers prior experience; (6) Rasch's one-parameter logistic model, which yields person-free test calibrations and item-free person measurements; and (7) the regression approach of classical test theory, which enables the estimation of true scores to be made from observed scores. Examples of these approaches are given, as well as their advantages, disadvantages, and ambiguities. (GDC)
- Published
- 1978
45. Measuring Stages of Growth: A Psychometric Model of Hierarchical Development. Occasional Paper No. 19.
- Author
-
Australian Council for Educational Research, Hawthorn. and Wilson, Mark
- Abstract
A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the logical construction of the hierarchy which occurs when there is no state between adjacent stages; and (2) rigidity--learning behavior, exhibited by a fixed sequence of progression through stages. Saltus assumes a theory with gappiness expressed through items or tasks, and estimates the rigidity of data, thus testing the hypothesized gappiness. Four experiments tested the Saltus model in elementary school Australian children and with subjects aged 3, 4, 5, 8, 12, and 21 years. Three Piagetian tasks of rule assessment involving proportionality (balance scale, projection of shadows, and a probability task) gave clear evidence of rigidity in the step from the pre-operational stage to the concrete operational stage. The next step, to the formal operational stage, did not show rigidity, although gappiness was evident. The hypothesized existence of a gap to split the concrete operational stage was not supported. The Gagnean data on a subtraction task showed strong rigidity. (Author/GDC)
- Published
- 1985
46. Investigating Item Stability: An Empirical Investigation into the Variability of Item Statistics Under Conditions of Varying Sample Design and Sample Size. Occasional Paper No. 18.
- Author
-
Australian Council for Educational Research, Hawthorn. and Farish, Stephen J.
- Abstract
The stability of Rasch test item difficulty parameters was investigated under varying conditions. Data were taken from a mathematics achievement test administered to over 2,000 Australian students. The experiments included: (1) relative stability of the Rasch, traditional, and z-item difficulty parameters using different sample sizes and designs; (2) effect of different sample types and sizes on the Rasch item fit estimator; (3) effects, on the item fit parameter and the Rasch item difficulty parameter, of removing some less appropriate items from the test; and (4) an examination of Wright's statement that the standard error of the item difficulty parameter is a good estimator of its variance, and that it has an inverse square root relationship to the sample size. Results showed that Rasch and z-item difficulty parameters were similar. Item fit increased as sample size increased. The removal of poorly fitting items improved fit values for the entire test, but worsened them for the remaining items. The Rasch standard error parameter was an appropriate measure of the true error of estimation as calculated from the square root of the sampling variance of the item difficulty index. (Implications for test calibration are concluded, and detailed item analyses are appended.) (GDC)
- Published
- 1984
47. Student Research Papers in Freshman Calculus--Modelling with Differential Equations.
- Author
-
Sherman, Tom
- Abstract
To build understanding of, and the ability to use, first-year science and engineering calculus, students were introduced to differential equations and asked to carry out research on differential equation modeling projects. Describes a model for the research paper; appendices provide a copy of the student handout and five examples of student research topics. (MDH)
- Published
- 1993
48. Two Remarks on the Preceding Paper by L. Egghe.
- Author
-
Rousseau, Ronald
- Abstract
This article offers comments and clarifications of Egghe's paper, which dealt with information production processes (IPP) and the Gini index. Topics addressed include the length of the Lorenz curve as a concentration measure, the discrete duality operator, and a Bradford-Leimkuhler distribution. (10 references) (LRW)
- Published
- 1992
49. Teaching Students to Extend Economic Models Using In-Class Scaffolding Assignments
- Author
-
Lynn Trafton, Tamara
- Abstract
The author discusses how to teach students to extend economic models using in-class scaffolding assignments, supported by discussions and workshops. Methods include discussions of a model's strengths and weaknesses; small group, in-class assignments that provide steps toward model extension; informal presentations of the work resulting from these assignments; and large group, post-presentation discussions in which students critique and build upon each other's work. Students then draw upon what they have learned to take one final step--to write a paper detailing a model extension. Although student model extensions do not reach a professional level of sophistication, students do extend models beyond what they know of them from textbooks and lectures. In doing so, students begin to create knowledge and to participate in economic discourse.
- Published
- 2019
- Full Text
- View/download PDF
50. Mathematical modelling, multi-objective optimization, and compliance reliability of paper-derived eco-composites.
- Author
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Adewale Akinwande, Abayomi, Folorunso, Davies Oludayo, Balogun, Oluwatosin Abiodun, and Romanovski, Valentin
- Subjects
CONSTRUCTION materials ,WASTE paper ,PAPER pulp ,MATHEMATICAL models ,BENDING strength ,SULFATE pulping process ,CEMENT ,PULPING - Abstract
The quest for cost-effective and thermal efficient structural materials onto beating the high cost of construction is gaining more attention among researchers. This study focused on the blending of cement and sand with waste paper pulp into cost-effective structural materials. The composites were prepared in four mix groups with each containing a fixed amount of sand at 5, 10, 15, and 20 wt.% (by weight of pulp). Cement was varied at 10, 20, 30, and 40 wt.% in each group, and curing was done for 28 days. Properties evaluated are compressive, bending, and splitting strengths. It was observed that increasing cement and sand contents enhanced strengths; howbeit, the blend of 30 wt.% cement/15 wt.% sand resulted in a reduction in bending strength even as 30 wt.% cement/20 wt.% sand engendered a decrease in bending and splitting strength. The microstructural features showed that inherent fibers of the pulp were well bonded with hydration products and sand content yielding good performance in the composites. The optimization procedure carried out depicted a combination of 35.27% cement and 20% sand as the optimum composition. Experimental outcomes were modelled for the purpose of prediction of responses. The models were confirmed statistically fit showing how varying cement content affected strength responses at fixed sand proportion. ANOVA affirmed the significant contribution of cement and sand on the strength responses. Compliance reliability was observed to be dependent on the interactive pattern between cement and sand. Going by the standard prescription for the strength properties, cement and sand content of 35.27 and sand 20 wt.% satisfied all strength requirements for low-cost construction having a compliance reliability of 1.31. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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