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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.

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 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)

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)

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)

To build understanding of, and the ability to use, first-year science and engineering calculus, students were introduced to differential equations and asked to carry out research on differential equation modeling projects. Describes a model for the research paper; appendices provide a copy of the student handout and five examples of student research topics. (MDH)

This paper is designed to provide teachers with more guidance on how to help students become proficient in the recall of basic number facts. Activities and practices are placed in a sequence designed to aid all instructors. The learning of number facts is divided into three stages: (1) the development of basic number facts; (2) establishing number facts; and (3) the memorization of basic number facts. The position adopted is that there is a need for children to have the ability to recall basic number facts readily. This paper confines itself to whole number operations in addition, multiplication, subtraction, and division. Although this material was originally designed for elementary teachers, these materials could be adapted to junior and senior high school use where drill and refreshment in basic number facts is necessary by modifying activities, problem activities, and vocabulary. (MP)

This report presents both a methodology for educational cost index computation and empirical evidence for determining the extent to which Missouri school district expenditures are beyond the control of local decision-makers. The author demonstrates considerable stability in the teachers' salary index from 1974-75 to 1975-76. The report extends previous index computations to cover variables reflecting the underlying causes of regional cost differentials, including administrators' as well as teachers' salaries and district transportation costs. Section 1 summarizes the document. Sections 2-4 provide a review of the study's methodology, an explanation of salary and cost index computation, and a discussion of the data used. The fifth section's analysis of Missouri's educational expenditures includes alternative specifications for determining teacher/administrator salaries and transportation costs, an alternative computation of regional and district cost indexes, and a brief discussion of educational cost index implementation. The report contains nine tables with data on salary and cost variables. Five appendixes include the results of two separate school personnel and school district surveys, a map of Missouri school districts, an updated estimate of the 1974-75 teachers' salary equation, a salary index computation formula, and 20 pages of data with 1975-76 cost indexes for the roughly 1,100 Missouri districts that offer transportation services. (JBM)

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)

This paper discusses the limitations of Classical Test Theory, the purpose of Item Response Theory/Latent Trait Measurement models, and the step-by-step calculations in the Rasch measurement model. The paper explains how Item Response Theory (IRT) transforms person abilities and item difficulties into the same metric for test-independent and sample-independent comparisons. IRT is based on two postulates. First, the performance of an examinee on a test item can be predicted by a set of factors called traits. Second, the relationship between examinee test performance and the set of traits underlying the performance can be defined by an item characteristic curve. There are three models in IRT. The three-parameter model is made up of item discrimination, item difficulty, and guessing parameters. In the one-parameter Rasch model, the guessing and item discrimination parameters are considered negligible. This model is used to analyze differences in test scores that initially are not linear. In this study, a regression analysis was performed to find a correlation between Rasch calibrations and classical measurement calibrations and to plot a scatterplot of the two measures with their regression line. These results challenge the idea that Rasch latent trait measurement is superior to classical measurement because its estimates are item-free and sample-free. High correlations between the two measures indicate that Rasch calibrations are not truly item- or sample-free or that the classical model calibrations are equally item- or sample-free. (Contains 12 tables, 6 figures, and 5 references.) (SLD)

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four of which have solutions, and suggestions for the writing of further problems. (Contains 14 references.) (MM)

Hand-held data collection technology allows for access to real-world data collection--at any other time and almost any place. Is the use of data and its collection desirable to the mathematical learning process? The answer is a resounding yes! Not only can significant mathematical ideas be taught in the process; colleagues are also helped in the sciences. When done correctly, students actively involved in the data collection process take ownership of the data and of the mathematical learning that follow. Ownership, in turn, leads to understanding a key component that may be missing in traditional instruction. Students and teachers must know how to use the software and follow proper data collection techniques. Both of these can be learned with practice in doing data collection. There are marvelous opportunities to collaborate with a science teacher. Data collection is a learned skill, and many times mathematics teachers don't have the "lab" skills that science teachers have because traditionally mathematics has not been thought of as an experimental science. Teachers must also be able to ask good questions to help guide and direct students as they start an activity. If used as a demonstration in class, the teacher must be able to lead students to the desired mathematical outcome--understanding a mathematical concept. (ASK)

Most researchers using analysis of variance (ANOVA) use a fixed-effects model. However, a random- or mixed-effects model may be a more appropriate fit for many research designs. One benefit of the random- and mixed-effects models is that they yield more generalizable results. This paper focuses on the similarities and differences between the various ANOVA models and the factors that should be considered when determining which model to use. An explanation of the "Rules of Thumb" for deriving the correct formulas for computing "F" statistics is also given. (Contains 2 tables and 15 references.) (SLD)

The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core State Standards (CCSS), using mathematical practices, reasoning, and modeling. PARCC assessment is administered in paper-based and computer-based formats; both modes contained constructed response items. This document is designed to help educators understand the scoring of constructed response items.

While functions and relations are important concepts in the teaching of mathematics, research suggests that many students lack an understanding and appreciation of these concepts. The present paper discusses an approach for teaching functions and relations that draws on the use of illustrations from database management. This approach has the advantage of allowing students to undertake projects which will increase their research skills and provides students with an opportunity to become involved in current, up-to-date technology. The paper focuses attention on the relational database model, which is based on ideas inherent in sets, relations, and functions. The paper shows how the abstract mathematical concepts of Cartesian product, relation, function, domain, range, union, intersection, difference, projection, and transitivity enter into this model. A number of concrete examples from database management that can be used in classroom teaching and which can easily be modified to fall within the individual student's repertoire of experience include: career information obtained from The Occupational Outlook Handbook, a beauty salon appointment schedule, missing persons files obtained from the FBI, blood bank information obtained from the Red Cross, and a database in a school counselor's office. (Author/AA)

This publication presents estimates of apprentice and trainee activity in Australia for the December quarter 2011. The figures in this publication are derived from the National Apprentice and Trainee Collection no.71 (March 2012 estimates). The most recent figures in this publication are estimated (those for training activity from the June quarter 2010 to the December quarter 2011). Estimates take into account reporting lags that occur at the time of data collection. Consequently, the figures in this publication may differ from those published in earlier or later reports. Estimated data are presented in this publication on a seasonally adjusted, quarterly and 12-month ending series basis. The 12-month ending series is particularly useful in showing longer-term data trends, but is less useful in identifying turning points. The seasonally adjusted data involve the use of a mathematical model to smooth out fluctuations due to seasonal influences. Seasonally adjusted data are useful to illustrate trends from one quarter to the next, but cannot be further disaggregated. There were 449,000 apprentices and trainees in-training as at 31 December 2011, an increase of 2.5% from the previous year. In the 12 months to 31 December 2011, compared with the previous year: (1) commencements increased by 1.4%, to 318 400; (2) completions increased by 6.9%, to 180 000; and (3) cancellations and withdrawals increased by 5.6%, to 138 600. For seasonally adjusted data, comparing the December quarter 2011 with the September quarter 2011: (1) commencements in trades occupations decreased by 1.3%; (2) commencements in non-trades occupations increased by 1.3%; (3) completions increased by 1.3%; (4) cancellations and withdrawals decreased by 1.1%; and (5) in-training numbers increased slightly. (Contains 19 tables, 3 figures and 5 notes.) [Funding for this paper was provided through the Department of Industry, Innovation, Science, Research and Tertiary Education.]

This publication presents estimates of apprentice and trainee activity in Australia for the September quarter 2010. The figures in this publication are derived from the National Apprentice and Trainee Collection no.66 (December 2010 estimates). The most recent figures in this publication are estimated (those for training activity from the March quarter 2009 to the September quarter 2010). Estimates take into account reporting lags that occur at the time of data collection. Consequently, the figures in this publication may differ from those published in earlier or later reports. Estimated data are presented in this publication on a seasonally adjusted, quarterly and 12-month ending series basis. The 12-month ending series is particularly useful in showing longer-term data trends, but is less useful in identifying turning points. The seasonally adjusted data involve the use of a mathematical model to smooth out fluctuations due to seasonal influences. Seasonally adjusted data are useful to illustrate trends from one quarter to the next, but cannot be further disaggregated. There were 448 800 apprentices and trainees in-training as at 30 September 2010, an increase of 5.1% from the previous year. In the 12 months to 30 September 2010, compared with the previous year: (1) commencements increased by 14.2%, to 305 400; (2) completions increased by 4.5%, to 166 100; and (3) cancellations and withdrawals increased by 2.9%, to 128 600. For seasonally adjusted data, comparing the September quarter 2010 with the June quarter 2010: (1) commencements in trades occupations increased by 1.0%; (2) commencements in non-trades occupations increased by 1.9%; (3) completions increased by 1.0%; (4) cancellations and withdrawals increased by 0.9%; and (5) in-training numbers increased by 0.6%. (Contains 19 tables, 3 figures, and 5 notes.) [For related documents, see "Apprentices and Trainees: September Quarter 2010. Terms and Definitions. Support Document" (ED516825) and "Adjustment Notes for Apprentice and Trainee Estimates. Technical Paper" (ED516872).]

Having low literacy skills could impact everything from reading a newspaper and balancing a checkbook to wise consumer decisions and job advancement. This study estimates adult literacy measures for Cuyahoga County, Ohio and its municipalities. It is also important to have a sense of how many children are at risk for developing literacy problems as adults, and these estimates are also generated. Finally, many efforts are already underway in communities across the county to try to help those who do struggle with literacy issues. The last portion of the research analyzes the distribution of literacy service providers. Appended are: (1) Difficulty Values of Selected Tasks Along the Prose, Document, and Quantitative Literacy Scales; (2) Reference Map for Cleveland Neighborhoods, Inner-Ring Suburbs, and Outer-Ring Suburbs; (3) Mean Literacy Proficiencies by Cleveland Neighborhood and Suburban Municipality, 1990 vs. 2000; (4) Percent at Level 1 Literacy by Cleveland Neighborhood and Suburban Municipality, 1990 vs. 2000; (5) Percent at Level 1 or Level 2 Literacy by Cleveland Neighborhood and Suburban Municipality, 1990 vs. 2000; (6) Census Variables Used to Update Reder's Mathematical Literacy Models; (7) Other Regional Literacy Measurements and Comparisons between Cleveland and Other Ohio Cities (Based on results from Jack Miller's Study); (8) Distribution of Births to Mothers Who Did Not Have a High School Degree, 1998-2002; (9) Percentage of 4th Graders and 9th Graders who Passed the Proficiency Tests; (10) Educational Attainment for the Civilian Youth Population Aged 16-19 by Suburban Municipality and Cleveland Neighborhood, 2000; and (11) Estimated Number of Adults and Children with Possible Literacy Problems. (Contains 17 tables, 23 figures and 45 footnotes.) [This paper was prepared for The Greater Cleveland Literacy Collaborative.]

This paper considers, from a theoretical point of view, two measurement approaches used in measuring success and failure in skills tests in physical education. The first, "fixed length" (FL) testing, entails counting the number of successful performances in a fixed number of trials. The second, "trials-to-criterion" (TTC) testing, involves counting the number of trials required to achieve a specified number of successes. TTC measurement results in high measurement error variance for individuals with low probabilities of success on a single trial. Error variance declines as the probability rises. If there are many more people with low probabilities than there are with high probabilities, which is the case for a positively skewed distribution, the TTC approach will result in less reliable measurement than will the FL approach. Under the latter, error variance is largest for people with a probability of .5. Individuals lower and higher will have smaller error variances. Two generalizations based on these results can be made with regard to skills testing: (1) If the skills test task is one on which most untrained individuals perform poorly, FL testing would be the better choice; and (2) If the test scores tend to be negatively skewed, then TTC testing would be more efficient and reliable for the same total testing time. Two formulas are presented for estimating the reliability of TTC measures. (JM)

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and social activities; (2) how analytic/algebraic combinatorics is similar to analytic/algebraic geometry; (3) basic combinatorial structures with terminology; (4) species of structures; (5) power series associated with any species of structures; (6) similarity of operations between power series and the corresponding species of structures; (7) examples illustrating where the structures are manipulated; and (8) general teaching/learning activities. (KHR)

This technical report provides an updated assessment of the problem of optimizing the periodicity of the Schools and Staffing Survey (SASS). Making use of data from three rounds of SASS data collection (for school years 1987-88, 1990-91, and 1993-94), the report extends and updates the preliminary findings and interim assessments that were previously published in a paper for the American Statistical Association (D. Ghosh et al., 1994) and a technical report for the National Center for Education Statistics (NCES) (D. Ghosh et al., 1995). Part I of the report (Sections 1 through 6) presents the analysis and findings, while Part II provides documentation and numerical results in terms of error projections for selected models, policy variables, cost rations, and periodicities. Basic results are provided for four probable error models. Section 1 provides an overview of the report and characterizes the general task of optimizing the periodicity of the SASS as one of identifying decision rules that will result in the selection of intersurvey time intervals and survey sample sizes that are in some sense "jointly optimal subject to a known, fixed set of cost constraints." While the first three rounds of the SASS were conducted at 3-year intervals, budget constraints meant that the next round was delayed to 5 years later. Section 2 covers the main modeling and analysis features of this study, while section 3 provides a brief review of time series methodology in relation to the periodicity problem. Section 4 sets forth summary conclusions and recommendations, concluding with the suggestion that the NCES should consider adopting an alternating large and small sample design for the SASS with an appropriate full-sample periodicity (such as 6 years) together with a mid-period fractional-sample data collection at the halfway time between full sample data collections. Section 6 provides an extensive bibliography for the whole report. Part II has four sets of detailed appendix tables. Appendix A provides large-sample scenarios for public schools and four states; Appendix B provides an alternating large and small sample design. Appendix C provides similar scenarios for private schools, and Appendix D provides an alternating large and small sample design for private schools. (Contains 2 figures, 8 tables, and 54 references.) (SLD)

Although policy makers have expressed interest in expenditures by private elementary and secondary schools, nationally representative data in this area are not available. In the absence of expenditure data it may nevertheless be possible to derive national estimates of total expenditures by private schools indirectly, by using the information that some associations of private schools collect from their members. Data on expenditures are routinely collected by three major associations of private schools: the National Catholic Education Association, the National Association of Independent Schools, and the Lutheran Church--Missouri Synod. This paper extends an earlier study of their data by examining whether more accurate national expenditure estimates can be derived by linking expenditure data with information on school characteristics collected as part of the National Center for Education Statistics Schools and Staffing Survey (SASS). If an appropriate model relating school characteristics and per-pupil expenditures could be estimated, it might be used to impute per-pupil expenditures for the full sample of private schools. Models incorporating a number of variables were explored, but in spite of the researchers' success in identifying school characteristics related to per-pupil expenditures, these characteristics do not fully explain the large differences in per-pupil expenditures among three sectors of private schools in this study: Lutheran day schools, independent day schools, and boarding schools. It is suggested that the model for Lutheran day schools is likely to provide reasonable estimates of per-pupil expenditures for many religious and nonsectarian private schools, but this assumption cannot be checked with the data available. To obtain improved estimates of the total amount spent by private schools in the United States, it will be necessary to collect data from a national sample of private schools, either through the SASS or a new special-purpose survey. An appendix contains 4 tables reporting results from the models predicting various school characteristics. (Contains 12 tables and 4 references.) (SLD)

Hardware for computer-assisted learning is discussed in three papers. Two papers report on projects using computer graphics, one for teaching structural analysis to university students and the other to teach graph concepts at the secondary level. Guidelines for selecting microcomputers focus on analyzing applications and matching them with available systems. (BBM)

In this paper we describe a teaching approach focusing on modelling in physics, emphasizing scientific reasoning based on empirical data and using the notion of multiple representations of physical phenomena as a framework. We describe modelling activities from a project (PHYS 21) and relate some experiences from implementation of the modelling approach in Norwegian upper secondary physics classrooms. (Contains 7 figures.)

Presents a variety of activities in which 4th grade students investigate prisms and pyramids by building models from folded paper and drinking straws. (Author/NB)

This publication presents teaching strategies to develop understanding of fractions as sensible numbers. Written for the mathematics teacher in grades K-5, it gives suggestions for teacher-led discussions and structured exploratory activities. The activities are conducted with manipulative materials that emphasize the important characteristics and properties of fractions. Sections focus on: the idea that fractions are rational, a developmental sequence for teaching fraction concepts, concrete models for teaching fractions, models for fractions greater than one, models for equivalent fractions, and teaching to improve problem-solving skills. Appended are pages of dot paper, centimeter graph paper, pattern blocks, and a tangram. References are also included. (MNS)

Discusses the parallels between Klein's position at the forefront of a movement to reform mathematics education and that of the National Council of Teachers of Mathematics' (NCTM) Standards. Draws a picture of Klein as an important historical figure who saw equal importance in studying pure mathematics, applying mathematics, and teaching mathematics. (KHR)

Explains that primitive living structures furnish real-world problems that are solvable using mathematics and computer-modeling techniques. (KHR)

Reanalysis of a standard set of data for 16 nations has brought new insights into the leading issues of comparative social mobility. The reanalysis provides considerable support for the Featherman-Jones-Hauser hypothesis, which claims that there is convergence in mobility processes once conditions of occupational supply and demand are controlled. The hypothesis is modified, however, in two respects: First, it is qualified by the suggestion that uniformity in mobility regimes is not limited to highly industrialized societies but may apply equally to less developed societies; and second, it is elaborated through specification of the structure of the shared mobility regime. Properties of mobility shared by the 16 countries considered are: (1) symmetry of exchange between occupational strata; (2) equality of mobility chances off the main diagonal; (3) severe immobility at the two extremes of the occupational hierachy; and (4) considerable mobility in the middle of the hierachy. These findings of basic similarity do not preclude findings of deviation from the common mobility regime, which seem to be at least as much a consequence of political organization as of economic development. The effects of political and economic variables on mobility processes are more complex than commonly supposed because they differ across occupational strata. (Author/CMG)

Guiding principles for using sliding fee scales are presented in this paper in an effort to help states plan new child care initiatives, coordinate or strengthen existing programs, and improve sliding fee scales for current programs. Introductory comments urge states to adopt a single sliding fee scale for all their child care programs. The report then discusses the benefits of good sliding fee scales for children, parents, providers, and states. The Children's Defense Fund (CDF) model for sliding scales is discussed next. This model calls for: (1) fully subsidized care, with no copayment, for families with incomes less than 34% of the state median income (SMI) whenever possible; (2) the gradual increase of copayments from 0% to 8.2% of income for families with incomes between 34% and 75% of SMI with only 1 child in care; (3) the increase of copayments by 25% for families with 2 or more children in care, with copayments gradually rising from 0 to 10.3% of income for families with incomes between 34% and 75% of SMI; (4) gradual increases in the copayment as income rises; and (5) the creation of a sliding scale for families with school-age children in part-time care. Guidelines for determining family size and income, certifying eligibility and copayments, and family income reporting are presented. The final section discusses questions related to fee exemptions for poor families, the income level at which parents should absorb full child care costs, and guidelines for children in protective services. The bulk of the report consists of charts showing family copayments under the CDF model, depending on income, family size, and state of residence. (AC)

Mathematical skills and reasoning and their applications are considered as forming one of the basic and essential areas of knowledge and experience that should be available to all Australian children. This collection of essays explaining problem solving in mathematics as an organizing theme for current and future curriculum development is a means of informing people of the centrality of the theme and of beginning the essential task of teacher development. Essays consider real problem solving and a problem-oriented curriculum approach; how habituated behaviors and memory contribute to the development of heuristic strategies; using developmental efforts to emphasize problem solving; criteria for real-life problems; important variables in increasing school emphasis on mathematical modeling; and selecting content based on adult needs and immediate interests. Finally, a position paper on problem solving is given. (MNS)

In this paper, academic efficiency is operationally defined and a methodology for measuring it at the school level is described. Academic efficiency is defined as the extent to which a school utilizes its time for the academic development of all its students. The measure of academic efficiency must include three elements: time, students, and academic development. The metric used is the student-minute; one student-minute is a minute spent by one student. Assuming that academic engagement is the legitimate proxy of academic efficiency, the index of academic efficiency is the proportion of engaged student-minutes to total student-minutes. To calculate this index, six different types of data must be collected at the school level: total time available in school day, time scheduled for noninstructional activities, total enrollment, average number of students absent per day, average engagement rate, and average proportion of nonacademic instructional time per class. Procedures have been developed at the Mid-Continent Regional Educational Laboratory for sampling engagement rate and non-academic instructional time. (BW)

Many colleges and universities have claimed some degree of financial distress, have sought increased federal, state, and philanthropic assistance, and have agonized over predicted declines in youth demand for higher education. In response to these concerns, numerous cost studies have been conducted but little is known of the relative efficiency of resource use in higher education. This paper estimates empirically the resource use behavior of relatively efficient, historically black four-year colleges and shows that for the variables considered, there are significant economies achievable by adopting the resource use patterns of relatively efficient institutions. Focus is on the theory of production function analysis, previous production function studies in higher education, and its use in black colleges. A five-page bibliography is included. (Author/LBH)

In certain boundary layer or natural convection work, where a similarity transformation is valid, the equations can be reduced to a set of nonlinear ordinary differential equations. They are therefore well-suited to a fast solution on an analog/hybrid computer. This paper illustrates such usage of the analog/hybrid computer by a set of applications of increasing complexity. The examples chosen are the growth of the boundary layer as expressed by the Blasius equation, the steady natural convection plume above a horizontal line heat source, and free convection from horizontal surfaces. The analog computer is effective in both educational and research contexts providing very rapid solutions to such problems. (Author/BB)

This collection of documents promotes simulation as an attractive topic in mathematics instruction that provides game-like activities likely to interest pupils, by illustrating the important ideas of probability and showing how mathematical models can be used in practical problems clearly relevant to everyday life. While computer programs written in BASIC are provided, it is recommended that pupils should perform pencil-and-paper simulations in the early stages in order to fully grasp how they work. Part I of the teaching guide has the following chapters: (1) Introductory Examples; (2) Simulation Using Dice, Coins, and Random Digits; (3) Examples of Simulation; (4) Pupil Material: Suggested Worksheets for Younger Pupils; and (5) Computer Simulation. Part II contains: (6) Program Listings, (7) Theoretical Calculations for Some of the Problems, and (8) Markov Chain Processes. The second part also contains four appendices. (MP)

A description of the development and application of a hierarchical/binary model by which a curriculum may be analyzed to determine alternative instructional sequences given particular instructional objectives and limiting constraints forms the body of this report. The background of the project as part of an effort by the U.S. Navy Recruiting Command to develop training programs for 16 closely related jobs is described; the complexity of the curriculum design process is discussed; the development of an instructional objectives hierarchy is outlined; and the characteristics and uses of binary matrices, transitive relations analysis, and directed graphs (digraphs) in the ranking of instructional objectives are detailed. The method employed to establish an instructional objectives hierarchy during the project is then recounted in step-by-step fashion, drawing on the preceding examination of ranking techniques. A computer algorithm which replicates the design process presented in the report is briefly discussed. Accompanying the text are 13 figures, 4 analytical tables, a 21-item bibliography, and 2 appendices--the first, a detailed computer flowchart for developing a sequence digraph from a set of curriculum objectives and the second, an Applesoft BASIC program listing based upon the flowchart presented in the first appendix. (JL)

Proof-writing is probably one of the most difficult skills for students to master in geometry. This may be due to the fact that students are not being taught the critical thinking skills necessary for proof-writing. The purpose of this paper is to illustrate how the ReQuest method can be used in the geometry classroom to improve students' question generation and proof-writing skills. In the first part of the treatment, a teacher must establish an atmosphere which is conductive to student participation and students will need to master the basic mechanics of questioning by modeling the teacher's questioning. The second step involves teaching students how to develop their own questions by turning sentences into questions and by having students take time asking and answering questions about given information. The last stage, proof-writing, is demonstrated by using the ReQuest method to collect the information necessary to write the proof. Several cautions for using this method are discussed. (YP)

One of the major theoretical and practical developments in testing is latent trait analysis and item response theory. This report provides a guide for practitioners in understanding, evaluating, and using these developments to meet their testing needs. (Author)

The primary objective of this paper is to describe a method of estimating female-male wage ratios. The estimating technique presented is two stage least squares (2SLS), in which equations are estimated for both men and women. After specifying and estimating the wage equations, the male-female wage differential is calculated that would remain if the women in the sample had the same productive, locational, and/or occupational characteristics as the men. The wage differential is then calculated, assuming that the women in the sample have the same structural wage equation as the men. The latter adjustment equates the rate at which men and women transform productivity-enhancing attributes into wages. This adjustment allows the researcher to ascertain what the female wages would be if women were able to convert their productive attributes into wages at the particular rates that men do. Finally, the authors identify explicitly the particular attributes that are most important in closing the wage gap between males and females. (BM)

Describes a classroom project involving the construction of a holiday mobile. Necessary supplies include a lightweight hanger, construction paper, string, scissors, protractors, compasses, and rulers. Concepts involved in the construction of the project include illustrating a chord, radius, diameter, shapes, metric measuring, circumference, area, and concentric circles. (AIM)