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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.
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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
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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
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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
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Ohio Univ., Athens. Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics., Hackenberg, Amy J., and Mewborn, Denise S.
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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. 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.
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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
9. Selected Papers in School Finance, 1997-99. NCES 1999-334
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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)
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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
10. U.S. 2001 PIRLS Nonresponse Bias Analysis. Working Paper No. 2003-21
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National Center for Education Statistics (ED), Piesse, Andrea, and Rust, Keith
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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.
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- 2003
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. Faculty Salary Equity: Issues in Regression Model Selection. AIR 1992 Annual Forum Paper.
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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
13. Statistics for Policymakers or Everything You Wanted To Know about Statistics but Thought You Could Never Understand. Working Paper Series.
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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
14. The Impact of BIB-Spiralling Induced Missing Data Patterns on Goodness-of-Fit Tests in Factor Analysis. Occasional Paper OP93-1.
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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
15. Cost-of-Education Differentials across the States. Working Paper Series.
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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
16. Generalized Variance Estimate for Schools and Staffing Survey (SASS). Working Paper Series.
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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
17. Schooling, Skills, and the Returns to Government Investment in Education: An Exploration Using Data from Ghana. Living Standards Measurement Study, Working Paper No. 76.
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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
18. L-scaling. Working Paper No. 26.
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Southwest Texas State Univ., San Marcos. Dept. of Finance and Economics. and Blankmeyer, Eric
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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
19. Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405
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National Bureau of Economic Research, Gelman, Andrew, and Imbens, Guido
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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
20. Mapping Teacher Moves When Facilitating Mathematical Modelling
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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
21. Mining Artificially Generated Data to Estimate Competency
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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
22. 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
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23. Paper Moon: Simulating a Total Solar Eclipse
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Madden, Sean P., Downing, James P., and Comstock, Jocelyne M.
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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
24. Remedial Mathematics: Diagnostic and Prescriptive Approaches. Papers from the First National Conference on Remedial Mathematics.
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ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., Higgins, Jon L., and Heddens, James W.
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The papers in this publication were developed from speeches and reactions presented at the first National Conference on Remedial Mathematics held at Kent State University in 1974. Papers focus on identifying and describing the remedial mathematics student, classroom diagnosis, clinical diagnosis, the diagnostic process, and promising procedures and directions in remediation. In addition to reactions to each paper, a conference summary is included. (MS)
- Published
- 1976
25. Classroom Observation Data: Is It Valid? Is It Generalizable? A Compendium of Methodological Papers.
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Texas Univ., Austin. Research and Development Center for Teacher Education. and Borich, Gary
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The issues discussed in these four papers concern the validity and generalizability of classroom observation instruments. These issues have been studied and are reported here in an attempt to better define the limits to which classroom observation instruments can be used in researching relationships between teacher behavior and student outcome. The premise undergirding these investigations is that before consistent and positive process-product relationships can be found, investigators must be cognizant of the sources of variance which affect the validity and generalizability of their process measures and which, in turn, affect the credibility of their research findings. The four papers are: "Convergent and Discriminant Validity of Five Classroom Observation Systems: Testing the Model" by G. Borich, D. Malitz, C.L. Kugle, and M. Pascone; "Generalizability of Teacher Behaviors Across Classroom Observation Systems" by D. Calkins, G. Borich, M. Pascone, and C.L. Kugle; "Measuring Classroom Interactions: How Many Occasions Are Required to Measure Them Reliably?" and "Generalizability of Teacher Process Behaviors During Reading Instruction" both by O. Erlich and G. Borich. (RC)
- Published
- 1977
26. An Introduction to Modelling through a Microbial Interaction Application
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Fabiana Zama
- Abstract
This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms.
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- 2024
- Full Text
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27. What Does Mathematical Modelling Have to Offer Mathematics Education? Insights from Students' Perspectives on Mathematical Modelling
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Kerri Spooner
- Abstract
The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience.
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- 2024
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28. Mathematical Modelling Using Scenarios, Case Studies and Projects in Early Undergraduate Classes
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G. R. Fulford
- Abstract
Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a "Classroom Note": modelling the dynastic cycles in Chinese history.
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- 2024
- Full Text
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29. Real-Time AI-Driven Assessment & Scaffolding That Improves Students' Mathematical Modeling during Science Inquiry
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Adair, Amy, Segan, Ellie, Gobert, Janice, and Sao Pedro, Michael
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Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative performance-based assessments designed to elicit fine-grained data about students' competencies on these practices can be leveraged to develop embedded AI scaffolds to support students' learning. In this paper, we present the design and initial classroom test of virtual labs that automatically assess fine-grained sub-components of students' mathematical modeling competencies based on their actions within the learning environment. We describe how we leveraged underlying machine-learned and knowledge-engineered algorithms to trigger scaffolds, delivered proactively by a pedagogical agent, that address students' individual difficulties as they work. Results show that the students who received automated scaffolds for a given practice on their first virtual lab improved on that practice for the next virtual lab on the same science topic in a different scenario (a near-transfer task). These findings suggest that real-time automated scaffolds based on fine-grained assessment can foster students' mathematical modeling competencies related to the NGSS.
- Published
- 2023
30. Assessing Students' Competencies with Mathematical Models in Virtual Science Inquiry Investigations
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Adair, Amy, Sao Pedro, Michael, Gobert, Janice, and Owens, Jessica A.
- Abstract
Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating" mathematical models in science inquiry contexts aligned with the NGSS (2013). Results show that model development and evaluation competencies are correlated, but students who demonstrate proficiency with model development often struggle with evaluation. Nuanced data illustrate how components of modeling competencies differ and how they may be related.
- Published
- 2023
31. Instrumental Variable Estimates of the Labor Market Spillover Effects of Welfare Reform. Upjohn Institute Staff Working Paper.
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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
32. 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
33. Theoretical Labor Supply Models and Real World Complications. Institute for Research on Poverty. Discussion Papers.
- Author
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Wisconsin Univ., Madison. Inst. for Research on Poverty. and Dickinson, Jonathan
- Abstract
This paper discusses discrepancies between the observable labor market and the idealized world which is assumed in theory. The proposed solutions are focused on the development of an empirical model applicable to data on prime-age males from the Michigan Panel Study of Income Dynamics, but the author notes that many of these issues are relevant for the construction of models for other groups. The discussion covers five basic areas: (1) The potential limitations of the simple labor supply model, based only on income-leisure tradeoffs, are discussed. (2) Sources of randomness in observed labor supply behavior and its consequences for the stimulation of systematic labor supply responses are considered, and the intertemporal variation are discussed. (3) The model is extended to accommodate earnings opportunities other than a simple constant wage rate, with increasing marginal income tax rates and overtime premiums being the major factors considered. (4) Demand-related factors that prevent workers from achieving marginal equilibrium at their marginal wage rates are explored, and criteria are suggested for the selection of a sample of workers who are less seriously affected by these problems. (5) The treatment of time lost due to unemployment and illness is discussed in the context of a model developed by Samuel Rea, which is also applied to time spent commuting to work. (Author/HD)
- Published
- 1975
34. STRATOP: A Model for Designing Effective Product and Communication Strategies. Paper No. 470.
- Author
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Purdue Univ., Lafayette, IN. Herman C. Krannert Graduate School of Industrial Administration. and Pessemier, Edgar A.
- Abstract
The STRATOP algorithm was developed to help planners and proponents find and test effectively designed choice objects and communication strategies. Choice objects can range from complex social, scientific, military, or educational alternatives to simple economic alternatives between assortments of branded convenience goods. Two classes of measured input data are used, one cognitive and the other affective. In addition, data on brand choice are needed to fit the parameters of the choice model. The STRATOP technique and the assorted preliminary analytical methods used modest amounts of standard data and yield very extensive findings, explicitly tailored to the needs of strategists and designers. Further experience is being accomulated with the expectation that the methods will find application in a number of areas involving significant social and economic choices among competing alternatives. (Author/JG)
- Published
- 1974
35. Some Thoughts on the Cost Effectiveness of Graduate Education Subsidies. ISP Discussion Papers No. 245-74.
- Author
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Wisconsin Univ., Madison. Inst. for Research on Poverty. and Bishop, John H.
- Abstract
A mathematical model of the Ph.D. scientist labor market demonstrates that subsidies of graduate training can be more cost effective than higher wages if the supply of doctorates is substantially more responsive to $1000 of early subsidy than to higher future wages with a present discounted value of $1000. Whether this is true is an unsettled empirical matter. There are three reasons for targeting subsidies at Ph.D. scientists: (1) As a condition of taking a job they demand freedom to do basic research and publish their results. (2) Because of their special knowledge and loyalty to professional values, hiring scientists and engineers contains an extra risk that trade secrets will be stolen or that one of them will be a "whistle blower." (3) From the firm's point of view these factors reduce the scientist's productivity. They do not from society's point of view, so an externality is created by the employment of scientists. (Author/LBH)
- Published
- 1974
36. Income, Ability, and the Demand for Higher Education. Discussion Paper No. 293-75.
- Author
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Wisconsin Univ., Madison. Inst. for Research on Poverty. and Bishop, John
- Abstract
This paper develops and estimates a model of college attendance that focuses on the influences of public policy and of economic environment. The Policy instruments examined are tuition, admissions requirements, college locations, breadth of curriculum, draft deferments, and class integration of neighborhoods. The aspects of the economic environment examined are the opportunity cost of the students' study time and the size of the anticipated earnings payoff to college graduates. The first five sections of the paper develop a theory of college attendance and then apply it to the choice and definition of variables and the seletion of functional form for the estimating equation. Section 1 examines the college entrance decision when unlimited borrowing is possible. Section 2 handles a more realistic situation. Section 3 applies this theory to the selection of the college. Section 4 examines how planning for college influences model specification and the selection of variables. Section 5 derives the functional form for estimation and describes how the estimated parameters will be used to test the hypotheses discussed in sections 1 and 2. Section 6 describes the data and section 7 presents the results. Section 8 analyzes the effectiveness of public subsidies of undergraduate education by calculating the subsidy cost of an extra student from each of the 20 ability-by-income strata and discusses the policy implication of the results. (Author/KE)
- Published
- 1975
37. 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
38. 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
39. The Structure of Inequality and the Process of Attainment. Discussion Paper 364-76.
- Author
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Wisconsin Univ., Madison. Inst. for Research on Poverty. and Sorensen, Aage B.
- Abstract
This paper proposes a model for the process of attaining occupational status and income, where change in attainment is generated by the creation of vacant positions in social structure. The distribution of attainments, or the structure of inequality, is assumed fixed and described by a simple exponential or geometric distribution function, depending on whether attainment levels are assumed discrete or continuous. Persons leaving the labor force create chains of vacancies in this structure that present mobility opportunities for persons entering the labor force. The implications of the model for the attainment process derived from these considerations for status attainment research and stochastic models for job-mobility are discussed. (Author/JM)
- Published
- 1976
40. Forecasting--A Systematic Modeling Methodology. Paper No. 489.
- Author
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Purdue Univ., Lafayette, IN. Herman C. Krannert Graduate School of Industrial Administration., Mabert, Vincent A., and Radcliffe, Robert C.
- Abstract
In an attempt to bridge the gap between academic understanding and practical business use, the Box-Jenkins technique of time series analysis for forecasting future events is presented with a minimum of mathematical notation. The method is presented in three stages: a discussion of traditional forecasting techniques, focusing on traditional techniques that relate to the Box-Jenkins model; a presentation of the key characteristics of the Box-Jenkins model; and a detailed demonstration of the method's steps. A discussion of the technical requirements needed to use the model, its cost versus that of other forecasting methods, and the potential areas of its application conclude the paper. The mathematical rationale is appended. (Author/DW)
- Published
- 1974
41. The General Equilibrium Impact of Alternative Antipoverty Strategies: Income Maintenance, Training and Job Creation. Discussion Papers 386-77.
- Author
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Wisconsin Univ., Madison. Inst. for Research on Poverty. and Bishop, John H.
- Abstract
This paper attempts to provide a general equilibrium framework for comparing the merits of alternative methods of raising the income of the employable poor. The strategy is to specify a complete and interacting set of factor markets, parameterize alternative program types in a manner convenient to this specification, and then solve the system of equations that characterize this economy for the comparative static response to the initiation of a small version of each program type. Within the income maintenance category the rankings implicit in impact effect analysis recur when general equilibrium effects are considered. Wage subsidies are more transfer-efficient than the negative income tax, or earning supplements. The size of policy multipliers are, however, quite sensitive to elasticities of substitution in production. The general equilibrium impact of targeted employment and training programs is quite different from the impact effect. Expanding the employment of the skilled lowers the income of the less skilled, especially when elasticities of substitution and occupational choice are low. In general, equilibrium effects of transferring workers from the low to the high skilled work force imply that education and training are by far the most effective means of aiding the low skilled. (Author/AM)
- Published
- 1977
42. 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
43. 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
44. A Disposition to Attend to Relationships: A Key Shift in the Development of Multiplicative Thinking. Key Shifts in Thinking in the Development of Mathematical Reasoning. [Symposium]
- Author
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Mathematics Education Research Group of Australasia (MERGA) and Siemon, Dianne
- Abstract
This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment Framework for multiplicative thinking, it has been difficult to move students through Zone 4 at the same rate. A closer examination of item responses at this level reveal that a disposition to notice and work with relationships between quantities may explain this phenomenon.
- Published
- 2022
45. A Typology for Instructional Enablers of Mathematical Modelling
- Author
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Mathematics Education Research Group of Australasia (MERGA), Geiger, Vince, Galbraith, Peter, Niss, Mogens, and Holland-Twining, Ben
- Abstract
Competency with mathematical modelling is increasingly important for career and informed and engaged participation in personal, civic and work life. In this paper we report on an aspect of a three-year longitudinal study that aimed to identify and describe enablers of mathematical modelling. Teacher interview data has been drawn upon to exemplify key features of a typology for instructional enablers of mathematical modelling. Findings highlight the importance of the didactical contract and socio-mathematical norms in promoting students' mathematical modelling competency, as well as teachers' anticipatory capabilities.
- Published
- 2022
46. Promoting Covariational Reasoning with the Aid of Digital Technology = Promoviendo el razonamiento covariacional con apoyo de la Tecnología digital
- Author
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Pérez Martínez, Helen Mariel, Cuevas-Vallejo, Carlos A., Islas Ortiz, Erasmo, and Orozco-Santiago, José
- Abstract
In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning Trajectory supported by digital technology and elements of Cuevas-Pluvinage didactics. The activities were evaluated according to the levels of covariation proposed by Carlson and colleagues, categorizing students' achievements and difficulties for each level of understanding. The results show that the activities favor students' progress by moving from the context situation to the different representations, establishing the relationship between the variables, and identifying their functional dependence. [For the complete proceedings, see ED630210.]
- Published
- 2022
47. Leveraging Equity and Civic Empathy through Community-Based Mathematical Modeling
- Author
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Aguirre, Julia M., Suh, Jennifer, Tate, Holly, Carlson, Mary Alice, Fulton, Elizabeth, and Turner, Erin E.
- Abstract
This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy, and elevating justice. We illustrate how these goals work together to advance equity and cultivate civic empathy through classroom vignettes of community-based modeling lessons. Through this theoretical synthesis, implications for community-based mathematical modeling instruction will be discussed. [For the complete proceedings, see ED630210.]
- Published
- 2022
48. Research on the Evaluation of Teachers' Teaching Quality Based on [delta]S Equation
- Author
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Hongnan Wan
- Abstract
The teaching quality evaluation of college teachers is an important indicator of school evaluation, performance assessment and teacher promotion. However, the existing evaluation methods are only limited to the formal evaluation of teaching behavior, and have not achieved objective, reasonable and scientific evaluation results. The purpose of this paper is to propose a [delta]S equation of the state of the teaching system from the point of view of the teaching system's operation process. On this basis, a Markov process evaluation method for teachers' teaching quality is established. The research results show that the application of the [delta]S equation of the teaching system to the evaluation of teaching behavior and teaching effect has its own characteristics, and the key lies in the reasonable selection of the [delta]S equation and the the combination of Markov analysis can effectively achieve the evaluation goal of teachers' teaching quality. [For the full proceedings, see ED638044.]
- Published
- 2022
49. Teaching Students to Extend Economic Models Using In-Class Scaffolding Assignments
- Author
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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. Tentative Outlines of a Mathematics Curriculum for Grades 7, 8, and 9. SMSG Working Paper.
- Author
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Stanford Univ., CA. School Mathematics Study Group.
- Abstract
This document is the report of a curriculum writing session. Using the recommendations and suggestions of the planning conference (SE 012 733), the writers produced detailed outlines for the grade seven through nine curriculum. The purpose and rationale of each unit are stated, and the separate sections outlined. Sample exercises are included for most units. The aims of making mathematics more relevant to real world problems, and of avoiding excessive abstraction and rigor, are continually stressed. Also included are three general reports on geometry, real analysis, and mathematical models; several position papers on specific topics; and a comparison of the new syllabus with the "first round" curriculum. (MM)
- Published
- 1966
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