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2. 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
3. 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
4. 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
5. 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
6. 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
7. 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.]
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- 2022
8. Remedial Mathematics: Diagnostic and Prescriptive Approaches. Papers from the First National Conference on Remedial Mathematics.
- Author
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ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., Higgins, Jon L., and Heddens, James W.
- Abstract
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
9. Classroom Observation Data: Is It Valid? Is It Generalizable? A Compendium of Methodological Papers.
- Author
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Texas Univ., Austin. Research and Development Center for Teacher Education. and Borich, Gary
- Abstract
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
10. 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
- Abstract
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.
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- 2023
11. Assessing Students' Competencies with Mathematical Models in Virtual Science Inquiry Investigations
- Author
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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
12. 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
13. 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
14. 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)
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- 1974
15. 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)
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- 1974
16. 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
17. 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]
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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
18. A Typology for Instructional Enablers of Mathematical Modelling
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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
19. Promoting Covariational Reasoning with the Aid of Digital Technology = Promoviendo el razonamiento covariacional con apoyo de la Tecnología digital
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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
20. Leveraging Equity and Civic Empathy through Community-Based Mathematical Modeling
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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.]
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- 2022
21. Research on the Evaluation of Teachers' Teaching Quality Based on [delta]S Equation
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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
22. Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group = Actes De La Rencontre Annuelle 2011 Du Groupe Canadien D'étude en Didactique Des Mathématiques (35th, St. John's, Newfoundland, Canada, June 10-14, 2011)
- Author
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Canadian Mathematics Education Study Group (CMESG), Liljedahl, Peter, Oesterle, Susan, and Allan, Darien
- Abstract
This submission contains the Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Memorial University of Newfoundland in St. John's, Newfoundland. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) Pattern Composition: Beyond the Basics (Chris K. Palmer); (2) The Pair-Dialogue Approach in Mathematics Teacher Education (Pessia Tsamir and Dina Tirosh); (3) Mathematics Teaching and Climate Change (Richard Barwell, Stewart Craven, and David Lidstone); (4) Meaningful Procedural Knowledge in Mathematics Learning (Wes Maciejewski, Joyce Mgombelo, and Annie Savard); (5) Emergent Methods for Mathematics Education Research: Using Data to Develop Theory / Méthodes émergentes pour les recherches en didactique des mathématiques : Partir des données pour développer des théories (Olive Chapman, Souleymane Barry, and P. Janelle McFeetors); (6) Using Simulation to Develop Students' Mathematical Competencies--Post Secondary and Teacher Education (Eric Muller, Jean-Philippe Villeneuve, and Philippe Etchecopar); (7) Making Art, Doing Mathematics / Créer de l'art; faire des maths (Eva Knoll and Tara Taylor); (8) Selecting Tasks for Prospective Teachers in Mathematics Education (Marie-Pier Morin, Christian Bernèche, and Ralph Mason); (9) How to Prepare a Public Lecture? First Questions, Then Execution??? (Yvan Saint-Aubin); (10) Warm Hands Taking Cold Mathematics (David Wagner); (11) Opportunities to Learn IN and THROUGH Professional Development: An Analysis of Curriculum Materials (Jenny Sealy Badee); (12) Challenging Our Beliefs and Practices in Secondary Mathematics Education (Lorraine Baron); (13) Pattern Rules, Patterns and Graphs: Analyzing Grade 6 Students' Learning of Linear Functions Through the Processes of Webbing, Situated Abstractions, and Convergent Conceptual Change (Ruth Beatty); (14) Learning Mathematics for the Workplace: An Activity Theory Study of Pipe Trades Training (Lionel Lacroix); (15) Transforming Mathematics Education for Mi'kmaw Students through Mawikinutimatimk (Lisa Lunney Borden); (16) Coming to Know Mathematics: Views of Two Teacher Mathematicians (Veda Abu-Bakare); (17) What Does 'Better' University Mathematics Instruction Look Like? (Mary Beisiegel and Asia Matthews); (18) Exploring Variability in a Dynamic Computer-Based Environment (George Ekol); (19) Virtual Mathematics Marathon: A Mathematical Game For All Children (Margo Kondratieva and Viktor Freiman); (20) Early Childhood Mathematics Education (Donna Kotsopolous and Joanne Lee); (21) The Challenges of Mathematics In-Service (Susan Oesterle); (22) High School Mathematics Students' Trajectories: Tracking or Differentiating for Success? (Ralph T. Mason and P. Janelle McFeetors). Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Appendixes contain: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, tables, and figures. [For the 2010 proceedings, see ED529564.]
- Published
- 2012
23. Fuzzy Linguistic Variables in Mathematical Activities in Kindergarten
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Jankovic, Branka and Magzan, Maša
- Abstract
In this paper, the application of fuzzy logic in mathematical education is viewed from the perspective of pre- school education. The aim of the paper is to give a brief overview of examples from the literature related to fuzzy logic and to point out the presence of fuzzy linguistic variables in the everyday life of a preschool child, as well as the importance of developing and respecting the approximate reasoning of preschool children. Although crisp mathematics requires crisp arguments that characterize our cognitive development, preschoolers start from common argumentation and use vague words. Fuzzy logic is an excellent tool for supporting such approximate reasoning which allows preschoolers to model real-life situations using vague words.
- Published
- 2020
24. Modeling in Mathematics and History as Teaching and Learning Approaches to Pandemics
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Papadopoulou, Maria, Argyri, Panagiota, and Smyrnaiou, Zacharoula
- Abstract
The integration of innovative interdisciplinary approaches to the ?-12 Curriculum aims to deepen students' knowledge and help them develop transversal skills. Applying an interdisciplinary lens, with a focus on pandemics, can help shape attitudes by means of inculcating the values of responsible global citizenship, and a high sense of personal and social responsibility. In the midst of the current lock-down due to Covid-19, a teaching approach to pandemics is presented, as an interdisciplinary connection between history and mathematics, based on the methodology of modeling in mathematics and the humanities. The main research questions posed: a) can modeling, as analyzed in the scientific literature, be used to interpret pandemics, e.g. in the case of the 'plague of Athens' (430 B.C.), as analyzed in the primary sources? b) Can the mathematical tools of statistical analysis be used to understand prevention measures through the centuries? Taking a longue durée perspective on history, students were asked to work on additional cases of pandemics across time and space, mobilizing both their mathematical and historical knowledge: process numerical data from primary sources, study maps, combine and compare elements of the past and the present using mathematical epidemiological models and real numerical data to study and predict the spread of infectious diseases. This paper presents the assessment of the effectiveness of this approach, conducted by means of closed and open questionnaires, administered in two phases (pre- and post-teaching) to a sample of 40 students aged 16-17 years. The results highlight statistics as a key tool for understanding real-world situations, and record the strengthening of students' knowledge in history, the raising of their critical thinking skills, as well as their enhanced ability to tackle real-world problems and understand responsible decision-making processes. Finally, the paper suggests that such good practices can prepare students for the complexity of globalized knowledge. [For the full proceedings, see ED626375.]
- Published
- 2020
25. Quantitative Reasoning and Covariational Reasoning as the Basis for Mathematical Structure for Real-World Situations
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Kularajan, Sindura Subanemy and Czocher, Jennifer A.
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In this paper we address the question, how do quantitative reasoning and covariational reasoning present as students build structural conceptions of real-world situations. We use data from an exploratory teaching experiment with an undergraduate STEM major to illustrate the explanatory roles quantitative reasoning and covariational reasoning play in, (a) coordinating more than two interdependent quantities, (b) conceiving of real-world situations in more than one way, (c) constructing networks of quantitative relationships, and (d) creating a mathematical expression. We make the case that looking at mathematical model construction through the lens of quantitative reasoning and covariational reasoning may provide insights into students' mathematical decisions as they structure complex real-world scenarios. [For the complete proceedings, see ED630060.]
- Published
- 2021
26. Basic Mathematical Modelling Competencies for Non-STEM Higher Education
- Author
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Marchisio, Marina, Roman, Fabio, and Sacchet, Matteo
- Abstract
The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in facing a problem belong to the study programs of secondary schools, and should thus be familiar also to students without a specific background in Mathematics. Difficulties can arise in various phases of modelling: in the comprehension of the problem, in the translation into mathematical formulas, in the resolution process or even in the interpretation of the results. In this paper, we give an analysis of an online test taken by 75 non-STEM students. The 10 questions of the test focused on specific items in mathematical modelling. During the test, students had to write down the reason why they chose a specific answer. The test allowed us to find and categorize the common errors students make and the phase in which it happens, suggesting actions in order to prevent them. Results show percentages of errors and discuss students' arguments. [For the full proceedings, see ED621892.]
- Published
- 2021
27. Mathematical Knowledge and Skills of University Students When Solving a MEA = Conocimientos y Habilidades Matemáticas de Estudiantes Universitarios al Realizar una MEA
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Rodríguez-González, Iván I., Vargas-Alejo, Verónica, and Montero-Moguel, Luis E.
- Abstract
In this paper we present the results of an investigation related to the developing of mathematical knowledge and skills by first semester university students when solving a Model Eliciting Activity [MEA] which involves quadratic function knowledge. This was a qualitative research. The theoretical framework was Models and Modeling Perspective [MMP]. The results show that the students used their mathematical knowledge and skills related to linear and quadratic functions to describe the situation; they moved from a quantitative cycle of understanding (associated with linear and quadratic behaviors), to an algebraic cycle of understanding (associated with quadratic behaviors). [For the complete proceedings, see ED629884.]
- Published
- 2020
28. How Mathematical Modeling Enables Learning?
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Kandasamy, Sindura Subanemy and Czocher, Jennifer
- Abstract
In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict as it arises during validation of a model; and (2) viewing model validation as a reflection on activity-effect relationship. We explain why we chose to look deeply into model validation specifically, present examples for each lens, and consider implications. [For the complete proceedings, see ED629884.]
- Published
- 2020
29. Lower Secondary Students Using Mathematical Modeling for Managing Water Consumption: The Case of Asma
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Rafiepour, Abolfazl and Abdolahpour, Kazem
- Abstract
The main purpose of the current study is modifying students' daily drinking water and managing waste water through modelling activities as context and modelling cycle as tool. In this study, 12 students (13-14 years old) from the lower secondary school were participated. These students were participated in two sessions (60 minutes) each week for three months. Three modelling activities had been designed for this study. These modelling activities were related to the amount of water consumption. Classroom activities were video recorded and used as data in this study. In some cases, interviews conducted and used as complementary data. Tension which happened during the implementation of these two activities analyzed with activity system as a theoretical framework. The results of this study show that students were able to manage and modify their daily water consumption through doing modelling activities. Results of this study also show that power of mathematics could help students to solve their real-world problems and help them to have better life. [For the full proceedings, see ED630948.]
- Published
- 2022
30. Potential of an MEA to Advance Business Students' Modeling Skills
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Montero-Moguel, Luis E., Vargas-Alejo, Verónica, Lima, Cynthia, and Carmona-Domínguez, Guadalupe
- Abstract
The development of modeling skills in mathematics is essential for individuals to understand, describe, control, and predict phenomena around them. This article describes the results of an investigation to find out how an activity -- based on a Models and Modeling Perspective -- stimulates the mathematics modeling skills of undergraduate students who are in the first quarter of a business degree. As a result, it was shown that the MEA [model-eliciting activity] enabled students to exhibit, develop, and refine different modeling skills, such as: identification of variables, assumptions based on the real-life context, identification of patterns, and construction of mathematical representations. [For the complete proceedings, see ED630210.]
- Published
- 2022
31. Justifications Students Use when Writing an Equation during a Modeling Task
- Author
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Roan, Elizabeth and Czocher, Jennifer
- Abstract
Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -, ·, ÷) provided insight into how participants expressed real-world relationships among entities with arithmetic relationships among values. We extend the findings from K-12 literature (e.g., using multiplication to instantiate a rate) to STEM undergraduates and found evidence of new ways of justifying the usage of arithmetic operations (e.g., using multiplication to instantiate an amount). [For the complete proceedings, see ED630210.]
- Published
- 2022
32. STEM Undergraduates' Structural Conception of Rate of Change
- Author
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Kularajan, Sindura Subanemy and Czocher, Jennifer A.
- Abstract
Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they constructed mathematical models for real-world scenarios. [For the complete proceedings, see ED630210.]
- Published
- 2022
33. Development of a Mathematics Discipline-Specific Language Scale
- Author
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Gibbons, Alanna and Lyublinskaya, Irina
- Abstract
Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the MDL of elementary school teachers. The final instrument developed through iterative analysis included 20 items on a 4-point Likert-like scale distributed between three distinct MDL categories: technical, symbolic, and visual. Instrument validity was confirmed using Confirmatory Factor Analysis with the set of 211 video recordings and corresponding lesson plans of mathematics lessons taught by pre-service elementary school teachers enrolled in a graduate special education program. [For the complete proceedings, see ED630210.]
- Published
- 2022
34. Using a Randomized Experiment to Compare the Performance of Two Adaptive Assessment Engines
- Author
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Matayoshi, Jeffrey, Uzun, Hasan, and Cosyn, Eric
- Abstract
Knowledge space theory (KST) is a mathematical framework for modeling and assessing student knowledge. While KST has successfully served as the foundation of several learning systems, recent advancements in machine learning provide an opportunity to improve on purely KST-based approaches to assessing student knowledge. As such, in this work we compare the performance of an existing KST-based adaptive assessment to that of a newly developed version--with this new version combining the predictive power of a neural network model with the strengths of existing KST-based approaches. Using a cluster randomized experiment containing data from approximately 140,000 assessments, we show that the new neural network assessment engine improves on the performance of the existing KST version, both on standard classification metrics, as well as on measures more specific to the student learning experience. [For the full proceedings, see ED623995.]
- Published
- 2022
35. Abstracts of contributed papers
- Published
- 1994
36. The history of NATO TNF policy: The role of studies, analysis and exercises conference proceedings. Volume 2: Papers and presentations
- Author
-
Rinne, R
- Published
- 1994
37. Modelling End-of-Session Actions in Educational Systems
- Author
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Hansen, Christian, Hansen, Casper, Alstrup, Stephen, and Lioma, Christina
- Abstract
In this paper we consider the problem of modelling when students end their session in an online mathematics educational system. Being able to model this accurately will help us optimize the way content is presented and consumed. This is done by modelling the probability of an action being the last in a session, which we denote as the End-of-Session probability. We use log data from a system where students can learn mathematics through various kinds of learning materials, as well as multiple types of exercises, such that a student session can consist of many different activities. We model the End-of-Session probability by a deep recurrent neural network in order to utilize the long term temporal aspect, which we experimentally show is central for this task. Using a large scale dataset of more than 70 million student actions, we obtain an AUC of 0.81 on an unseen collection of students. Through a detailed error analysis, we observe that our model is robust across different session structures and across varying session lengths. [For the full proceedings, see ED599096.]
- Published
- 2019
38. Tendencias en Modelación Matemática en Latinoamérica = Latin American Trends in Mathematical Modeling
- Author
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Solares Rojas, Armando, Preciado Babb, Armando Paulino, Peña, Fredy, Ortiz, Andrea, Rosas, Marisol Sandova, Velasco, Remedios Soriano, Vázquez, Vicente Carrión, and Fuentes, Mauricio Farrugia
- Abstract
Throughout the years, Mathematical Modeling has gained international attention, not only in research but also in the development of curricula and its applications in the classroom. However, systematic literary surveys are scarce. In this paper, we present some findings from a survey of 485 international publications related to different aspects of mathematical modeling. While the number of Latin-American publications is rather small compared to the number of international publications, the vitality of the currently discussed themes in this region and their innovative perspectives testify to the international relevance of this developed work on mathematical modeling. [This paper is provided in both Spanish and English. For the complete proceedings, see ED606531.]
- Published
- 2018
39. Telecommunications Policy Research Conference. Competition in the Local Loop Section. Papers.
- Author
-
Telecommunications Policy Research Conference, Inc., Washington, DC.
- Abstract
Four papers consider competition, new technology and economics of local telephone companies in a deregulated environment: (1) "An Engineering and Policy Analysis of Fiber Introduction into the Residential Subscriber Loop" (Marvin Sirbu, Frank Ferrante, and David Reed); (2) "Competition in the Local Loop: Pricing Carrier Access" (Steve G. Parsons); (3) Default Capacity Tariffs: Smoothing the Transitional Regulatory Asymmetrics in the Telecommunications Marketplace" (Dennis Weisman) (abstract only); and (4) "The Economics of Bypass in a Simple Model of the Telephone Network" (Glenn A. Woroch). The first paper is supplemented by 14 figures and 46 references, and the fourth paper includes a stylized model and six references. (EW)
- Published
- 1987
40. Telecommunications Policy Research Conference. Standards and Standardization Section. Papers.
- Author
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Telecommunications Policy Research Conference, Inc., Washington, DC.
- Abstract
These three papers consider various models and mechanisms for the achievement of industrial standardization. The first, "Duopoly Compatibility Standards with Partial Cooperation and Standards Leadership" (Sanford V. Berg, University of Florida) presents a model of duopolists producing differentiated substitutes, and considers the equilibrium outcomes for two products under Cournot rivalry, multiproduct monopoly, second-best standards-specification, and welfare maximization. The text is supplemented with two tables. The second paper, "The Economics of Gateway Technologies and Network Evolution: Lessons from Electricity Supply History" (Paul A. David and Julie Ann Bunn, Stanford University), examines the historical development of the technology of electric light and power systems, with particular attention to the role which the induced invention of a compatibility-creating technical device (the rotary converter) played in the industry's technological and organizational development. The text is extensively footnoted, and 71 references are provided. The third paper, "Coordination through Committees and Markets" (Joseph Farrell, University of California at Berkeley, and Garth Saloner, Massachusetts Institute of Technology), discusses two common mechanisms--standardization committees and "market leadership"--for achieving coordination, with particular reference to the choice of compatibility standards. The text is supplemented with figures, and is extensively footnoted. A list of 25 references is also provided. (Author/EW)
- Published
- 1987
41. The Coastal Ocean Prediction Systems program: Understanding and managing our coastal ocean. Volume 2: Overview and invited papers
- Published
- 1990
42. The Use of Computation Diagrams and Nomographs in Higher Education. AIR 1983 Annual Forum Paper.
- Author
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Brandenburg, Richard K. and Simpson, William A.
- Abstract
The way that graphs can be used to make calculations that are commonly used by institutional researchers is described using specific examples, and the technique of constructing computational graphs (and nomographs) is outlined. It is shown that once a calculation involving several variables has been represented by a computation diagram or a nomograph, the user can often obtain solutions more quickly than is possible by computer. Two situations in higher education that warrant the use of diagrams and nomographs are as follows: whenever a routine calculation must be performed repeatedly, using different input values; and where a relatively simple analytical model is needed to calculate responses to "what if" questions posed in the form of values assigned to input variables. It is claimed that these devices equal the performance of a microcomputer, are more convenient to undertake, and can be used by all participants in a planning session. A mathematical model relating departmental workloads, student numbers, and faculty strength is developed. Diagrams include the following: a three-variable graph and a four-variable computational diagram for analyzing a technical/professional program. Seven reference texts on nomography and two on computation diagrams are identified. (SW)
- Published
- 1983
43. The Use of Multiple Regression and Trend Analysis to Understand Enrollment Fluctuations. AIR Forum 1979 Paper.
- Author
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Campbell, S. Duke and Greenberg, Barry
- Abstract
The development of a predictive equation capable of explaining a significant percentage of enrollment variability at Florida International University is described. A model utilizing trend analysis and a multiple regression approach to enrollment forecasting was adapted to investigate enrollment dynamics at the university. Four independent variables were used in a stepwise linear regression analysis to explain variance in the total university full-time-equivalent enrollment. Three of the four variables used are presently employed in business forecasting models to account for changes caused by trends, seasonal variations, and cyclical variations. The fourth variable was introduced to account for the opening and operation of a new campus. The model accounts for 99.6 percent of the variation observed in total university enrollments for the past 20 quarters and provides estimates of the enrollment within one percent of the enrollments actually observed. The model also has the potential for making reasonably accurate and reliable short-range enrollment forecasts. The model demonstrated that changes in economic conditions in the county, reflected by changing unemployment rates, correlate significantly and positively with changes in total university enrollment. Total university enrollment did not change from its second to its sixth year of operation except for those changes that could be accounted for by changes in unemployment in the county. The opening and operation of the new campus increased total university enrollment by about six percent. (SC)
- Published
- 1979
44. Departmental Enrollment Projection Model. AIR Forum 1979 Paper.
- Author
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Toporovsky, R. H.
- Abstract
The Departmental Enrollment Projection Model (DEPM), which is based on the assumption that enrollments are essentially influenced by economic and social forces, is described. Under the model's approach, the department, rather than the institution as a whole, is seen as the focal point of both the enrollment projection and, by implication, the planning strategies. The pool of students individual departments are now concerned with is that of potential students, in the relevant higher-education region, contemplating formal training. Quality of education, placement prospects, and relative tuition are factors which can now be directly related to enrollment and controlled in the attainment of institutional and departmental goals. Labor market and education market factors form the economic foundations of the model. The current version of the DEPM has been developed as a recursive system of four behavioral, one trend, and one policy or control equations for each program or department of instruction. Restrictively, each department's direct enrollments are assumed to be independent from the other departments. Equations used in the model are presented and discussed. The data concepts and sources of information used in the model are summarized. The effect of specification, exogenous variables, and policy variations are also described. (SC)
- Published
- 1979
45. Estimating Errors in Student Enrollment Forecasting. AIR Forum 1979 Paper.
- Author
-
Marshall, K. T. and Oliver, R. M.
- Abstract
The use of data on longitudinal student attendance patterns to determine variances, and hence confidence bounds, on student enrollment forecasts, in addition to finding the forecasts themselves, is demonstrated. The formulation of the enrollment model based on longitudinal student attendance patterns is described step by step, presenting the equations used in the model and some sample data obtained through application of the model. Applications of various equations are demonstrated. The model is analyzed assuming that the new admissions each period follow a Poisson distribution. The enrollment permits the development of statements about the approximate behavior of the conditional distribution of the total number of students in attendance at a given time. It is assumed that entering cohorts contain large numbers of students. Equations relative to this function are presented and discussed. Sample data on the forecasts and confidence intervals for each semester enrollment are presented. The model provides a measure of the error that could be present for each forecast. (SC)
- Published
- 1979
46. The Search for Better Predictors of Incomes of High School and College Graduates. AIR Forum 1979 Paper.
- Author
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Witmer, David R.
- Abstract
A search for better predictors of incomes of high school and college graduates is described. The accuracy of the prediction, implicit in the work of John R. Walsh of Harvard University, that the income differences in a given year are good indicators of income differences in future years, was tested by applying standard statistical procedures to data describing the annual incomes of men 25 years old and older during the period 1956 to 1975. Addition of the gross national product in the year prior to the previous equation yields much improved results. Application of Richard B. Freeman's three-equation recursive adjustment model indicates that the starting salaries of college graduates are not good correlates of income differences. Several sets of data from the American Council on Education "Fact Book on Higher Education" were then entered into a series of multiple correlation and regression studies. Studies of the 184 independent variables identified four that, taken together, yield significantly better predictions of future income differences. These factors were: (1) male population 22 years old, 13 years prior; (2) male college graduates at the B.A. and first-professional degree level/male population 29 years old, 11 years prior; (3) male college graduates at the B.A. and first-professional degree level, 14 years prior; and (4) male college graduates at the B.A. and first-professional degree level/male population 29 years old, 14 years prior. However, no theory to explain the connections among these variables is apparent. (SC)
- Published
- 1979
47. Bayesian Decision Theory in Enrollment Forecasting. AIR Forum 1979 Paper.
- Author
-
Lind, Douglas A.
- Abstract
The use of subjective probability as a theoretical model for enrollment forecasting is proposed, and the results of an application of subjective probability to enrollment forecasting at the University of Toledo are reported. Subjective probability can be used as an enrollment forecasting technique for both headcount and full-time equivalent using the following steps: (1) assume the various subpopulations are normally distributed; (2) determine the mean and standard deviations of these subpopulations; (3) sum the means and variances of the subpopulations to obtain the mean and variance of the university forecast; and (4) perform a linear transformation on the headcount distribution to obtain the full-time equivalent distribution. Major advantages of this method are: it allows the study of homogeneous subpopulations; it allows comparisons with other methods, since the variability is known; and it allows probability statements regarding various headcount and full-time equivalent outcomes. Application of the subjective probability method to enrollment forecasting at the University of Toledo resulted in a difference of 0.4 percent between the actual and the forecasted headcount enrollment and a difference of 0.3 percent between actual and forecasted full-time equivalent enrollment. In comparison with the conventional forecasting techniques also employed in the test study, the forecasting errors using the subjective probability were the smallest. (SC)
- Published
- 1979
48. Replicating Freeman's Recursive Adjustment Model of Demand for Higher Education. AIR Forum 1979 Paper.
- Author
-
Wish, John R. and Hamilton, William D.
- Abstract
The viability of Freeman's Recursive Adjustment Model as a management tool for explaining and predicting enrollments and the job market is examined using macro and micro cases. To establish a relationship between college attendance and the college job market, Freeman employed a 3-equation model to analyze the causative supply and demand determinants. Freeman's equations and published and unpublished data are used to ascertain the goodness of fit for the entire United States, the entire state of Oregon, the University of Oregon, and two major departments at the University of Oregon (business and psychology). Freeman's model is presented, its application is discussed, and the method utilized to test Freeman's model is described. The study results suggest that Freeman's model for explaining college enrollments and graduate job market could be effectively employed by university administrators and institutional researchers to help analyze the major determinants in college attendance. The model might be more valid for the larger macro entities, such as national, state, or university, than it is for the smaller micro entities. The study results indicate that the degree of fit for the model on the micro level will vary considerably from university department to university department and on the general availability of the required data. (SC)
- Published
- 1979
49. Estimation of the Reliability of a Test Consistency of More Than Three Congeneric Parts. Iowa Testing Programs Occasional Papers, Number 28.
- Author
-
Mayekawa, Shin-ichi and Haebara, Tomokazu
- Abstract
A least squares approach to estimating the reliability of a measure consisting of more than three content homogeneous or congeneric parts is proposed. The advantages of this method over a more indirect approach in which certain parts of a measure are combined to use Kristof's or Feldt's coefficients are examined. One hundred four-part tests were created by randomly assigning certain items from a 48-item mathematics achievement test to each of the four parts. Data on 400 examinees who took the test were divided into five subsets. Seven estimates of reliability were computed for 100 random splits for each subset of data. Some of the main results included: (1) there is a consistent order in the magnitudes of the means of the coefficients, regardless of sample size; (2) values of the average of the Kristof coefficients are greater than unity when sample size is small; (3) the proposed coefficient has smaller standard deviation and range than the Kristof coefficient; and (4) the Feldt coefficient tends to have smaller standard deviation and range than the proposed coefficient, and depends on the assumption that the error variance of a part is proportional to its length. (Author/RL)
- Published
- 1980
50. Comparative Efficiencies in Projecting Faculty Rank Distribution. AIR Forum 1980 Paper.
- Author
-
Greenhill, Craig J.
- Abstract
Comparative applications of simple and complex faculty flow models are examined to determine (1) their relative demands for data and calculations, (2) the divergence of their projections, especially when modelling a no-growth faculty, and (3) an estimate of the error incurred (i.e., the cost to analysis) when a simple model is used. The results support the view that academic personnel policy changes have delayed effects and are nonlinear. It is suggested that simple models may mislead analysts by being insensitive, for example, to backlogs of term appointees who expect promotion. Similarly, it may be that no model is needed at all if one is only looking for estimates on a two-year horizon. (Author/SW)
- Published
- 1980
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