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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)

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)

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)

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)

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)

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the modelling cycle. In this paper after discussion about modelling in more details, two modelling cycles will be elaborated in the context of mathematical tasks that are related to everyday life. Main ideas behind different modelling cycles is starting point that would be from real world situation. Then gradually mathematical elements of real world phenomenon identified and mathematics problem will have shaped in a form that could be solved through mathematical problem solving techniques. Furthermore, it would be important phase that call interpretation of mathematics answer and check it in front of real world situation. This paper will be followed by discussion about learning theories that support the idea of modelling. Finally, two educational challenges (Design good modelling tasks and assessing of students performance) in mathematical modelling activity will be discussed. [For the complete proceedings, see ED655360.]

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.

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)

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)

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.]

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)

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)

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)

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)