A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
RALPH BRADLEY KIMBROUGH, JR.
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
I dedicate this study to my wife Nancy N. Kimbrough; my daughter, Rachel L. Kimbrough; and son, Andrew R. Kimbrough. Because of their love and support this dissertation was made possible.
I would like to thank the members of by doctoral committee for their advice and assistance. I would like to thank Dr. David Honeyman for contributing his expertise on educational finance for the school districts. Furthermore, Dr. Honeyman's detailed reading and editing of this dissertation was greatly appreciated. I would like to thank Dr. James Wattenbarger for his contribution of knowledge of the funding methods used by the community colleges. Dr. Wattenbarger's counseling and moral support made this dissertation possible. I would like to thank Dr. Eugene Todd for his assistance .in the areas such as school assessment and evaluation. Dr. Todd was also helpful in contributing literature concerning the problems experienced by the schools in educating disadvantaged students. Dr. Arthur Sandeen was continually helpful in giving advice during doctoral committee meetings. Dr. David Miller was essential in checking and evaluating the statistical results of the multiple regression analysis.
In addition to my committee members, I would like to thank Dr. William Hager, codirector of the Center for Applied Optimization for the Department of Mathematics at the University of Florida. His review of this dissertation and
the models was invaluable to the determination of my conclusion. Dr. William Hager's advice to continue researching the final model for the GED exam was inspiring and fostered my enthusiasm for future research.
I would also like to thank Ms. Patricia McGee and Ms. Barbara Smerage for reviewing this dissertation for editorial errors and making suggestions for its presentation. Their continued assistance was greatly appreciated.
Finally, I would like to thank my family members for their continued support of my completion of this dissertation. I would like to thank my father, Dr. Ralph Kimbrough, Sr., for his advice on dissertation topics and my mother, Gladys Kimbrough, for her support of this endeavor. My wife, Nancy, was very supportive, and her love was a major factor in helping me to complete this dissertation. Finally, my two children must take credit for easing my tension during the more difficult times with their love and affection.
TABLE OF CONTENTS
1 BACKGROUND OF THE STUDY.......................... 1
Definition of Optimization....................... 2
Background of the Problem........................ 2
The Current Status of Adult Education Funding
in Florida..................................... 7
The Florida Education Finance Program (FEFP)..... 8
Community College Program Fund (CCPF)............ 10
Other Funding Methods for Adult Education........ 14
The Purpose of the Study......................... 14
Need for the Study............................... 16
Definition of Terms.............................. 18
Limitations and Delimitations.................... 19
Organization of the Study by Chapters............ 20
2 REVIEW OF THE LITERATURE......................... 21
The Need for Adult Education..................... 21
Adult Education: An International View........... 23
Adult Education in the United States............. 25
State Responsibilities Under the Adult
Education Act.................................. 27
Inequalities of Support in Adult Education....... 29
Benefits of Adult Education...................... 31
Research that Supports the Funding of Adult
Critique of the Studies Performed in Adult
Problems in Determining the Sociological
Benefits of Adult Education.................... 44
The Benefits of Consumer Education............... 45
Arguments Against Funding Adult Education........ 47
Research Findings Not in Favor of Funding
Adult Education................................ 50
Quantitative Methods Used for Evaluating
Educational Programs........................... 52
Chapter Summary.................................. 57
3 PROCEDURES....................................... 60
Procedure of this Study.......................... 60
Population for the Study......................... 67
Research Design.................................. 68
Statement of Variables........................... 71
Collection of Data............................... 78
Analysis of Data................................. 79
Development of Vectors to Determine
Effects and Magnitude of Effects............... 86
4 PRESENTATION OF DATA............................. 88
Analysis of Data................................. 88
Discussion of Administrative and Instructional
Qualitative Reasons for Variable Selection....... 93
Quantitative Reasons for Variable Selection...... 96
Evaluation of the Selection Procedures and
Their Results.................................. 104
Determination of Significance of Variables in
Tests of Partial Correlations of the Model's
Problems of Determining Funding.................. 112
Test of Partial Correlations and Analysis
of Final Model................................. 116
Results of the Solution of Simultaneous
5 CONCLUSIONS AND RECOMMENDATIONS.................. 123
Problems and Limitations of the Study............ 124
Concluding Remarks Concerning the
Mathematical Model............................. 129
Discussion of the Variables of the
Cost Model..................................... 131
Conclusions and Remarks.......................... 133
Suggestions for Further Research................. 134
Final Conclusion................................. 136
A PRESENTATION OF RAW DATA......................... 137
B LISTS OF LOCAL EDUCATION AGENCIES................ 168
C ANALYSIS OF COOK'S D PRINTOUT.................... 172
D LOCAL EDUCATION AGENCIES NOT INCLUDED ON
FEDERAL REPORT................................. 181
BIOGRAPHICAL SKETCH...................................... 189
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
A MATHEMATICAL MODEL FOR THE OPTIMIZATION OF ADULT
Ralph Bradley Kimbrough, Jr.
Chairman: James L. Wattenbarger
Cochair: David S. Honeyman
Major Department: Educational Leadership
The purpose of this study was to develop and analyze a
mathematical model to optimize the funding for adult
education programs in Florida through the simultaneous
solution of linear and nonlinear formulations. Multiple
regression techniques were used to determine the mathematical
model. Forward selection, backward elimination, and stepwise
techniques were used to determine the variables to be
included in the model. For purposes of this study, data
items used in these formulations were evaluated using
statistical techniques to determine their relevancy and
One of the major problems of education is the reality of declining resources. The same forces affecting public education in pre-kindergarten through public elementary and
secondary programs also affect adult education programs. Since most states fund adult education programs with the funding allocated for pre-K through 12th grade, the growing needs for funds, combined with declining resources in kindergarten through 12th grade, will threaten adult education funding and may threaten the very existence of adult education programs. Thus, there is a need to allocate adult education funding in a more efficient and effective manner.
Twelve variables were used in the multiple regression analysis. Of these 12 variables, the variables that had the greatest effect on student success with the GED and the Adult High School Diploma were the state's expenditures on teacher salaries, the costs of other support services, and the costs of materials and supplies. Furthermore, three variables were found to be significant statistically to the increase in cost of adult education. These variables were the percentage of full-time teachers, the percentage of students involved in other educational programs, and percentage of students who resided in correctional facilities. Since the variables which affected success on the GED and the Adult High School Diploma did not coincide with the variables that affected total costs of adult education, a specific solution using simultaneous equations was not meaningful or possible. However, the study did conclude that the use of the formula developed from success on the GED and the Adult High School Diploma may be useful for determining the proper allocation
of funds. Future studies may be helpful in determining mathematical models could be used to determine cost allocations.
CHAPTER 1 BACKGROUND OF THE STUDY
One of the major problems of education is the reality of declining resources. State legislatures across the country are under increasing pressure not to raise taxes. State revenues generated by either income taxes, sales taxes, property taxes, or other personal or intangible property taxes will not be enough to meet the increasing costs of state services, including public education. Thus, the movement toward obtaining more education for less money has now become an important issue in many states. In order to meet the growing needs of public education, state legislatures are forced into the thoughtful allocation of tax dollars for education in the most efficient and cost-effective manner.
The same forces affecting public education in pre-kindergarten through public elementary and secondary programs also affect adult education programs. Since most states fund adult education programs with the funding allocated for kindergarten through 12th grade, the growing needs for funds, combined with declining resources in kindergarten through 12th grade, threaten adult education funding and may threaten
the very existence of adult education programs. Thus, there is a need to allocate adult education funding in a more efficient and effective manner.
Definition of Optimization The definition of optimization used in this study is concentrated on making adult education funding as effective and efficient as possible. According to Webster's Third New International Dictionary, optimize means "to make as perfect, effective, or functional as possible" (p. 1585) Furthermore, the term optimization means "an act of optimizing or the fact of being optimized" (p. 1585) Thus, for this study, the term optimization will mean the act of optimizing adult education funding to make the funding both efficient and effective. In other words, if more monies need to be spent on certain areas, or groups of individuals to make adult education more effective, then the mathematical model will be used to address the needs for additional funding in these areas or groups. Therefore, the model developed herein emphasizes the need for effectiveness and functionality rather than complete efficiency.
Background of the Problem
Florida will be adversely affected by the reality of declining state revenues and a growing and increasingly diverse student population. According to Natale (1992, October),
By 2010, if the demographers are right, one-third of all the children in the United States will live in just four states--California, Florida, Texas, and New York. Those four statesaccording to A Demographic Look at Tomorrow, a report that extrapolates from U.S. Census information--will see significant increases in the number of children in the next 20 years, mostly because of increases in what is now considered minority population. ... In states with increases in the number of youths, the gains are largely attributable to gains in minority populations. And those increases point up another phenomenon of the future as well: Traditional minority populations--blacks, Hispanics, Asians--will become majority populations in some states. In California, Texas, and Florida, more than half of the youth population will be nonwhite well before the year 2010. (p. 24)
Although the growth in minority population in the public schools appears evident, the immediate need to train and teach the parents of these school children is even more critical. According to Edwards and Young (1992, September), "Recent hopes for successfully launching U.S. children into the 21st century have been pinned on reclaiming a part of our past--the involvement of parents as partners in the education of their children. The importance of parent involvement in children's schooling has been a persistent theme in the research and school reform efforts of the last three decades" (pp. 73-74) For example, Bronfenbrenner (1979) in The Ecology of Human Development: Experiments bv Nature and Design and Henderson (1987) in The Evidence Continues to
Grow: Parent Involvement Improves Student Achievement emphasized the importance of parental involvement in improving student performance. Thus the need to educate parents so they can help their children in school is evident.
Edwards and Young (1992, September) concluded, "Studies [Epstein, 1987; Heath & McLaughlin, April, 1987] point to higher student achievement when parents participate in school activities, monitor children's homework, and otherwise support the extension into the home of the work and values of the school" (p. 74).
The immediate need for English as a second language is evident in many counties in Florida. For example, one estimate lists 50 different languages spoken in Seminole County alone. Even more languages are spoken in Dade County. The realization that education of parents may have a direct influence on the success of their children further supports the thesis that more funding is needed for adult education in Florida.
Wood and Honeyman (1992) concurred with Natale (1992) that the changing diversity of Florida's school population will be a major factor in the growing needs for public education in Florida. Although Florida's growth rate recently has slowed, Florida's population continues to climb. According to Wood and Honeyman (1992), "The state [Florida] enjoys the uniqueness of being the fourth largest state in the nation as well as one of the fastest growing states. Florida is projected to be the third most populous state by the year 2000" (p. 170). The financial burden on such a fast-growing state is also being experienced by other states. Natale (1992) wrote, "For schools, the
implications of a student boom are severe. 'It's a terrible time for states to be in a state of terribly rapid growth,1 Hodgkinson  says. 'With the deficit situation the way it is, there is no way for states to pay for [the growth]'" (p. 24).
Without new tax revenues Florida will be forced to reduce the extent of public education. Although funding for Florida's public schools has improved in recent years, the growth in population and language diversity of students may outstrip the availability of needed funds for education. According to Wood and Honeyman (1992), "During the period 1970 to 1973, several studies were conducted on Florida's finance system. Given the changes that were occurring, including growth and development in the southern half of the state, the legislature adopted recommendations to guarantee that students have access to an equal educational program" (p. 165).
This new program was titled the Florida Education Finance Program (FEFP). The standard for computing the state allocation was changed from a formula-based-upon-an-instructional-unit method to a weighted-average-per-pupil calculation based on cost calculations. Weights were determined for 26 student programs. Because adult education was funded in the same way as other public education programs, funding of adult education was governed by the assigned weights of the FEFP. Over the years, the Florida
legislature has changed the formula to reflect changes in population demographics. For example, in 1974 a cost-of-living differential was added. Although the state increased funding in real dollars during this period, funding declined during the 1970s. Wood and Honeyman (1992) wrote,
While approximately $93 million in new money was made available to school districts, rising inflation and rapidly increasing costs in the state resulted in a $78 per pupil increase in constant dollars. Per pupil revenue in constant dollars declined in 1975 as the legislature limited school boards to 8 mills total and included, but never funded, a sparsity adjustment factor. (Johns, 1975) (p. 166)
Further stresses on educational funding were experienced in the state during the 1980s. Because of political pressure to initiate programs to reduce taxes, the legislature lowered the required millage rate from 6.4 mills to 5.15 mills and also lowered the cap on total millage allowed to 6.75 (Wood and Honeyman, 1992, p. 167). Furthermore, the homestead exemption for property taxes was raised to $25,000 in 1980-1981. The legislature attempted to cover these revenue losses with an additional levy of 2 mills for capital outlay expenditures. Wood and Honeyman (1992) stated,
During the period 1981 to 1990, Florida experienced incredible growth and development. To promote educational reform and assist school districts with increasing pressure for special populations, several programs were enacted by the legislature. Program cost factors and weights continued as the heart of the FEFP. By 1989 the number of cost calculations had grown from the original 2 6 (in 1973) to 41. The growth in program classifications was the result of increased need to address special education, special need, and at risk student populations, (p. 167)
Other improvement programs were the Dropout Prevention Act of
1986 (which indirectly affects adult education), PRIME, First
Start, and other programs deemed necessary for preventing the
loss of at-risk kids (Wood and Honeyman, 1992, p. 167).
Unfortunately, these programs did not eliminate the need for
Although the legislature addressed the need for more
programs in pre-K through 12, the area of adult education was
practically ignored. As a matter of fact, stringent
enrollment caps on funding adult education have been in place
since 1986. Without adequate increases in funding, adult
education programs will not be able to meet Florida's future
The Current Status of Adult Education
Funding in Florida
The review of research about the funding of adult
education revealed that a comprehensive formula that
optimizes costs for state and local funding of adult
education has not been researched. Instead, states use a
variety of funding methods already used in pre-K through 12
funding and for the community colleges to determine how funds
are to be allocated for adult education. A majority of
states use the foundation method for funding pre-K through 12
(Thompson, Wood, & Honeyman, 1994). According to the staff
of the National Education Association Search (unpublished
evaluative report, 1987), the methods currently used for
pre-K through 12 education funding may be classified as flat
grants, minimum foundation, full state funding, and capacity equalization programs. Within capacity equalization programs are the percentage equalization (state aid ratio), guaranteed tax base, and guaranteed tax yield formulas. The effects of these funding formulas are varied and may or may not directly influence adult education funding. For instance, because much of the allocation of state funding for adult education may be finalized at the district level, the final funding for adult education may be decided at the local level and based on assessed needs, not on any particular formulas. There are several cases where the school district makes up shortfalls in funding for as much as 50% of the expenditures of the local district (Florida Department of Education, 1992-1993). These shortfalls may reflect a continual lack of adequate
funding of adult education.
The Florida Education Finance Program (FEFP) The current funding system for adult education in Florida's school districts is based upon predetermined weights for funding Adult Basic Education and Secondary Education and for educating the disabled (Florida Department of Education, 1993, May, p. 12). According to the 1993-1994 Florida Education Finance Program: Statistical Report, adult education funding was included in Group 3, which encompasses Adult Job Preparatory Vocational, Adult Supplemental Vocational, and Adult General programs. Because of fiscal priorities, an enrollment cap was established for adult
education. State funding is supplemented by student fees and tuition. According to the statistical report of the staff of the Florida Department of Education (1993, May), "Students who are enrolled in adult general and vocational adult programs who are reported for funding through the Florida Education Finance Programs must be charged tuition fees except those who are exempted by law" (p. 17). State statute (F.S. 239.117) provides a list of those students who are exempted from tuition or fees.
In addition to the current group status of adult education, certain weight factors are used to calculate "weighted FTE." According to the staff of the Florida Department of Education's Division of Public Schools (May 1993), "Multiplying the FTE students for a program by its cost factor produces 'weighted FTE'" (p. 12). Currently, the weight factors for adult education are .721 for Adult Basic Skills, .758 for Adult Secondary Education, and 1.140 for Adult Disabled. By multiplying the program cost factors by the FTE, the state determines the weighted FTE students. This figure of weighted FTE students is then multiplied by the base student allocation (currently $2,501.05 per student) and the district cost factor. The product of these multiplications is then added to legislative-approved adjustments. For instance, the district might obtain additional supplements, such as the declining enrollment
supplements, sparsity supplements, and the hold harmless adjustment.
The present system of funding does not allow for increments based upon the meeting of goals or performance targets. Alamprese and Koloski (1992, March) mentioned the need for adult education programs to be given incentives. Because of the scarcity of resources, recent legislative proposals have centered upon the use of performance-based funding (PBF), which has been defined as paying for production rather than process. In education, competency based programs, such as those in adult and vocational education, were easily adapted to PBF, resulting in payment for student outcomes rather than "seat time." Student outcomes were typically measured as a percentage of program completers and job placements. Enrollments were considered positive student outcomes when recruiting certain populations, such as minorities or the disadvantaged. Although the definition of performance-based funding has been defined rather loosely, the possibility of conforming to such a funding model has been a major topic of discussion in adult education circles.
Community College Program Fund (CCPF) Since 6% to 10% of the funding for adult education is provided by the community colleges, a review of the community college funding program is necessary. The Community College Program Fund (CCPF) is determined by following eight steps,
which become components of the funding formula used to fund the community colleges. These steps are as follows:
Base + Cost to Continue + Enrollment Workload + Operating Cost of New Facilities + Improved Programs + New Programs = Total CCPF Student Fee Revenues = State Funds CCPF.
In order to understand the funding process, one must review the meaning behind each step in the formula. The first step includes the base funding for the community colleges, and subsequent steps are added or subtracted from this base funding. First, the total state general revenue, lottery funds, and calculated student fees are included in the base funding for each college in the current fiscal year. Step two relates to the determination of the cost to continue current programs. The cost to continue current programs is added to the base. According to the The Fact Book 1991-92 (Florida Department of Education, 1992, Fall), "Using the amount of funds expended by each college in each of several expenditure categories, the price level guidelines are applied to these base amounts to determine the additional funds required to maintain the colleges1 existing programs at their present level" (p. 91). Funds are then allocated to cost categories, such as salaries, general expenditures, utility costs, and operating capital outlay expenditures. Each of these sums is multiplied by the price guideline amount, and any additional funding required by each college
is determined. Even though all colleges are subject to the same guidelines, the resulting increases may not be the same because the colleges spend money differently.
Step three relates to the identification of workload changes. According the The Fact Book 1991-92, "The statutes specify that the prior year enrollment shall be the basis of the assigned current enrollment" (p. 91). Last year's enrollment may be a determining factor in funding, even under conditions of high-growth rates. Step four was stated in The Fact Book 1991-92: "When a college adds a new building to its physical plant, additional operating costs are experienced. Based upon the specific college's average cost of operation per square foot, funding is appropriated for each new building's additional space to cover the cost of maintenance and operation" (p. 91). Thus any additional buildings that have been added to campuses will be reflected in increases in base funding.
Step five refers to funding for improving programs. According to The Fact Book 1991-92, "For programs for which the Legislature has previously provided funding, additional funds may be earmarked to improve or expand their delivery. Examples might be funding for the College Level Academic Skills Test, the Gordon Rule, and other such items which have been rolled into the program fund" (p. 91). Therefore, additional funds for program improvement are added to the base. Step six allows for additional funding to be added to
the base for new programs. According to The Fact Book 1991-92,
First time funding for systemwide programs specifically earmarked by the Legislature and which are to be rolled into the CCPF lump sum may be provided. Examples might include funding insurance rate increases or student advisement programs. Each college would receive a share of the total increased funds based on some distribution rationale. This might be FTE, headcount or other factors, (p. 92)
The seventh step is the process of adding the increases and decreases of steps 1 through 6 for each college and therefore determining the new funding base. Thus, each college will have a new total CCPF funding base. The Fact Book 1991-92 states, "Because factors other than FTE may be involved in distributing portions of the increased funding for all issues, it is to be expected that the increase per FTE and the overall percentage increase will probably not be the same for each college" (p. 92).
The final and eighth step is used to adjust the total CCPF funding base of each college for the calculation of student fees. Student fee collections are calculated by multiplying the assigned FTE enrollment by the standard fee rates. Once the student fees have been calculated, these fees are deducted from the total CCPF for each college to determine the state funding portion.
Thus, the state CCPF (Florida Department of Education, 1992, Fall) is clarified as the "lump sum appropriation for each college [that] is allocated to each local Board of Trustees to develop an operating budget for the college"
(p. 92) In conclusion, each board of each college may establish priorities for programs and expenditures to reflect the local needs or to satisfy the intent of the legislature expressed in the proviso language of the appropriations act.
Other Funding Methods for Adult Education
The rest of the funding for adult education originates from federal and state grants. Federal grants make up approximately 3% of the total funding for adult education in Florida. Even though this percentage is small, the need to examine the influence of federal funding is realized in the large number of small organizations funded by federal grants, including Hispanic Unity; Action, Inc.; and others. Because of the success of these organizations, it was necessary to include the funding for these organizations in this study.
The Purpose of the Study
The purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida. Since local districts may spend adult education funds in pre-K through 12 programs or may actually make up deficits in adult education funding, there is no formal method to determine the optimal funding needed in adult education. Therefore, an optimal funding model needs to be developed, subject to the variables affecting adult education and the budgetary constraints, and should be based on current funding (expenditures) for the 1992-1993 school year. An additional aspect of the study was
to determine relationships among the funding amounts estimated by the formula and student performance in the GED and ABE adult education programs in Florida. The research was designed to address the following subproblems:
1. A proposed, conceptually based formula was developed for the total optimal state funding of adult education programs for Florida.
2. The conceptually based formula was based on a production function that described the input-output relationship between selected variables.
3. The formula was used to determine the optimal combination of inputs to maximize output, subject to the budget and other constraints.
4. The formula was used to determine the optimal combination of inputs to maximize output, subject to certain constraints and given increments in the budget constraint.
Currently, the Florida Board of Education has experimented with several simulations of performance-based budgets. Because of the federally mandated requirements for adult education, these simulations include weights based upon the success of recruiting from target populations, status of students recruited, and activities provided by the adult education centers. The simulations do not attempt to look at the needs of the community that the center is attempting to serve. Furthermore, there has not been an attempt to optimize costs incurred in adult education. The methodology of this study included factors that were stated by the adult education administrators during personal interviews.
An alternative funding formula will have to optimize costs and include weights or factors relating to the success
of the center in accomplishing the goals of the adult
education program. For example, as discussed previously, the
problem of the current formula is that there is no measure
concerning how successful the adult education center is in
educating for the GED, ABE, or in educating a special student
in the student's special programs. Such factors as student
status, target populations, and center activities were
included in the different weighted factors.
Need for the Study
The factors associated with estimating costs for adult
learners are uniquely atypical (different) from funding
programs for children and youths in grades K-12. Therefore,
the attendance-based funding methods that are so common among
K-12 funding are not appropriate for adult education funding.
For example, Rose (1990) stated,
The attendance basis for distributing money has been problematical. It can contribute to the deterioration of standards of student performance. Students, particularly mandated students, know that they can sit around doing very little, take long unofficial breaks, and basically not be there except in body, if that is what they choose. As long as they are physically "attending," they will be carried on the books for funding purposes, (p. 127)
Furthermore, many single parents and minimally able students may benefit from attending a sheltered workshop environment without having to contribute to the adult daycare population. Finally, Rose concluded, "Another problem with attendance-based funding is that [it] can lead to discouraging the offering of desperately needed additional help to students,
if this help comes from outside agencies" (p. 127). Rickards (1983, September) would agree with Rose's discussion of adult education funding. According to the ERIC staff, which
The need for the program was determined because it was felt that the existing formula for disbursing adult basic and high school completion funds in Utah and other states (based on class membership and attendance) was burdensome to rural school districts and inappropriate to the needs and preferences of the adult learner. Learning options available for adult students included traditional classes, home study, competency testing, on-the-job training, computer-assisted instruction, audio-tutorial plans, televised instruction, performance-based instruction, and one-to-one tutoring. The program was found to be successful in that some adults benefitted by each approach, and all the approaches were at least as effective as traditional' classroom instruction. The
program was also cost efficient and, although time-consuming to administer, possible to administer on the local level, (pp. 14-15)
As a result of his study, Rickards (1983, September) recommended that Utah change its methods of disbursing funds
for adult basic education and high school education.
Moreover, no study was found in the literature that
approached adult education from a comprehensive and totally
funded process. Finally, the need for the optimization of
school costs was best described by McAfee (1972) :
It is hardly to be questioned that studies confined to the practical applications of models should be energetically pursued to provide, eventually, a firmer basis than now exists for dealing with broad questions of educational policy. Mathematical models, such as was developed in this study, allow decision-makers to form expectations of future consequences, these expectations being based on known empirical relationships and the decision-makers' judgements, (p. 156)
Consequently, there is a need to develop a conceptually analyzed formula for the total funding of adult education programs.
Definition of Terms
The following definitions for Adult Basic Education and Adult Education were obtained from the staff, Florida's Program and Plan for Adult Education, Florida Department of Education (1989-93) .
Adult Basic Education (ABE) is defined as the
Provision of instruction for adults who are functioning at or below the eighth grade level. Such instructional services include reading, hand-writing, arithmetic, spelling, social studies, general (elementary) sciences, health, language arts, and consumer education for grade levels 1-8. Instruction in English-as-a-Second Language/English for Speakers of Other Languages
(ESL/ESOL), adult life stages, aging process and resources and in life coping skills may be included.
Adult Education includes the
Services or instruction below the college level for adults: (a) who are not enrolled in secondary school; (b) who lack sufficient mastery of basic educational skills to enable them to function effectively in society or who do not have a certificate of graduation from a school providing secondary education and who have not achieved an equivalent level of education; (c) who are not currently required to be enrolled in school; and (d) whose lack of mastery of basic skills results in an inability to speak, read, or write the English language which constitutes a substantial impairment of their ability to get or retain employment commensurate with their ability, and thus are in need of programs to help eliminate such inability and raise the level of education of such individuals with a view to making them less likely to become dependent on others (Adult Education Act, 100-297, as amended), (p. 54)
Limitations and Delimitations This study was limited to the adult education programs administered through Florida's 58 county school districts, 11 community colleges, and other institutions, such as public libraries and correctional institutions. Adult education programs housed in other community colleges were also included.
Estimates of transportation and child care were not included as possible additions to the funding of adult education because reliable data were not available for estimating costs. Furthermore, every effort is made by adult education administrators in Florida to locate the adult classes as close as possible to the residential areas of the students.
Although some questions have been raised about the accuracy of information reported about the success variables used in the study, no documentation was found that would support these affirmations. Similar views were also expressed concerning the data reported about public education in areas other than adult education. Since the federal government has rather strict procedures for reporting the results of adult education, it was assumed that the data employed in the study were valid.
This study assumed that all variables are nonnegative. This requirement of nonnegativity refers only to variables. Parameter estimates that demonstrate the effect of the
independent variables on the dependent variable may be negative.
Finally, there are limitations concerning the use of linear and nonlinear programming to optimize the production model. These limitations are discussed later in Chapter 3.
Organization of the Study bv Chapters
This report of the study is organized into five chapters. Chapter 1 is an introduction to the problem consisting of a background of the problem, the current status of. adult education funding, brief reviews of educational funding in Florida, the purpose of and need for the study, definition of terms, and limitations. Chapter 2 is a review of the literature. The procedures used in the study are described in Chapter 3. Chapter 4 consists of a presentation and discussion of the data. The findings, conclusions, and recommendations are given in Chapter 5.
CHAPTER 2 REVIEW OF THE LITERATURE
Relevant literature concerning the need for funding, and the benefits of, adult education in the United States is presented in this chapter. Also included is a review of literature in opposition to adult education programs. This review was conducted through an ERIC search and a review of the literature of the University of Florida libraries. Technological inquiries included computer searches of ProQuest-Dissertation Abstracts; University Microfilms, Inc.; Dissertation and Master's Thesis Reproductions; LUIS (Online Card Catalog for all State of Florida university libraries; ERIC Microfiche; Silver Platter 3.1 of Pcylic; and the General Periodicals Index. Also included was a search through Education Index. The results of correspondence and interviews with state and local officials in adult education were of assistance in the review. The search primarily spanned a 10-year period prior to 1993.
The Need for Adult Education The need for adult education is evident in a recently distributed report by the United States Department of Education. According to Kirsch, Jungeblut, Jenkins, and
Kolstad (1993, September), reporting on Adult Literacy in America: A First Look at the Results of the National Adult Literacy Survey, 21% to 23% or 40 to 44 million adults in the United States demonstrated skills in the lowest prose and quantitative abilities (Level 1: ABE), and 25% to 28% of the respondents, representing about 50 million adults nationwide, demonstrated skills at Level 2. The most shocking detail of the report was that the 90 million Americans who were performing only at Levels 1 and 2 did not realize they were "at risk." Only 21%, or 34 to 40 million adults, demonstrated literacy skills at the highest level of Levels 4 and 5. The need to educate adults not only in basic skills, but in the self-realization of their own abilities is evident in the report.
Beginning with the Smith-Hughes Act of 1917, Congress has demonstrated interest in vocational, adult, and community education programs (Costa, 1988). As a result of national concern, Congress passed the Adult Education Act (AEA) in 1966 (Costa, 1988). This act and subsequent amendments placed emphasis on basic fundamental skills for adults. The nation experienced increased educational needs for immigrants and refugees. The Comprehensive Employment and Training Act (CETA), passed in 1973, and Job Corps emphasized adult education for employment. Thus, the federal government has for many years been interested in the problem of providing for the educational needs of adults. As will be evident in
the following section, adult education is seen as essential
in the development of a global economy and its accompanying
Adult Education: An International View
The literature reveals that concern for the education of
adults is an international concern. Adult education is a
major issue in education in England, Canada, Sweden, and
France (Gordon, Ponticell, & Morgan, 1991). Stock (1992)
gave the following explanation:
In Europe, influenced by distinguished French thinkers and writers, we were beginning to grapple with concepts such as education oermanente and the awesome operational implications for implementation. In the U.K., stimulated by a strong social-anthropological intellectual movement, professional adult educators were encouraged to investigate the concept and reality of "community": the relation of individuals to groups, and of groups to networks; and the montage of networks which constitutes "community." All this resulted in radically different approaches to devising and organizing adult learning programs for constituent communities, as well as to fundamental reconsiderations about the purpose of the whole educational endeavour, (p. 28)
The French and English have recognized the need for
adult education and have also witnessed the social problems
that result when adult education is neglected. Stock (1992)
quoted a Final Report presented by the 1972 UNESCO
International Adult Education Conference in the following
The widening gap between nations, groups and individuals constitutes the greatest moral challenge of our time. To close the gap is more than a question of social justice. In an era of ever-growing interdependence between countries and of increasing human wants, it is an economic imperative and precondition of world peace. This inequality is due
also to the unequal distribution of knowledge. But it cannot be solved simply bv enlarging existing educational facilities. Experience shows that the provision of more education in most communities tends to favour most the already well-educated; the educationally under-privileged have yet to claim their rights. Adult education is no exception to the rule, for those adults who most need education have been largely neglected--they are the forgotten people. (p. 29)
Educational leaders in Canada have also been interested
in adult education programs. The importance placed upon
adult education in Canada can be seen in the following
quotation from Kulich (1992):
Adult learning and adult education have been important to Canada as an immigrant society since the early days. With the increasing complexity of society and of social, economic, political and cultural issues facing the Canadian society and its members, adult learning and adult education become more and more important. Living in the global village of today and having to deal with the rapidly changing conditions, adult learning and education are crucial to the survival of society and individuals alike, (p. 45)
Although adult education has emerged as a great need in many countries around the world, adult educators are still faced with declining public interest and funding. Stock (1992) concluded with the following sobering prediction for the survival of humanity if adult education is ignored: "For unless we learn to change, adapt, negotiate and to re-learn, the ultimate challenge will be the very continuity of a species with any pretensions to humanity" (p. 33), Even though adult educators may have the best of intentions, most writers report little improvement in providing adult education. For example, Stock (1992) stated,
In the best local administrations the growing numbers of specialists in adult literacy, English as a second language, neighbourhood development, rehabilitation of offenders, or health education, were welcomed and incorporated into a holistic service of adult or community education. In the worst cases "private armies" were formed with little or no communication between one another. External analysis of national level policy and practice suggested that the apparently "new" money directed to the special target-group programs was almost exactly commensurate with the cuts in grants to national providing bodies of liberal adult education and the general grants to local education authorities, (pp. 29-30)
As discussed previously, the literature emphasizes an international concern for adult education based on evidence of rapidly changing economic and social conditions.
Adult Education in the United States
Adult education in the United States has not been
financed on a par with most educational programs. A study
done by Kutner, Furey, Webb, and Gadsden (1990, November), to
be reviewed subsequently, indicates that adult education
funding has been relegated to the lowest priority in most
states. However, as stated in the thesis of this study,
adult education may be the most important asset to society.
Yet, Cherem (1990) noted,
The poor stepchild remains in part due to adult education's professional associations, which have diverse interest, and typically, relatively small memberships. Without a coalescing of these associations' interest to common concerns, no sizable group exists to lobby policymakers. Unfavorable national policy and consequent funding formulas also stifle important movement in the field. (p. 23)
However, the United States cannot ignore the changes that are taking place. Cherem (1990) continued by stating the
following three major changes in society that will affect the field of adult education:
1. An exponential growth of information.
2. Changing demographics (i.e., the decrease in the base of taxpayers with children).
3. The emergence of a philosophy of adults 1 continuing development, (p. 24)
Social issues will become so great that the effects on adult
education will be prominent.
The status of adult education in the United States was
best presented in a U. S. Department of Education report
titled Adult Education Programs and Services: A View From
Nine Programs (1990, November). The authors of the report,
Kutner, Furey, Webb, and Gadsden (1990, November), detailed
four major aspects of adult education funding as follows
1. The Adult Education Act represented the manor Federal source of funds that supported adult literacy services in the sites studied. However, other major Federal programs such as JTPA [Job Training Partnership Act], FSA [Family Support Act], and SLIAG [State Legalization Impact Assistance Grants] were also important funding sources. The Family Support Act is expected to become a significant source of funding in future years.
2. Adult Education Act funds did not provide the majority of total funding for any site. For the eight sites that reported financial data--AEA funds represented 37 percent funding for one site, 11-12 percent at two other sites, and about 5 percent in two sites, and about 1 percent for the remaining two sites. One site did not receive AEA funding during the year of the site visit, but had received it in prior years.
3. Seven of the eight sites reported funding from at least one additional source of Federal funding than
Adult Education Act funds. Four sites had SLIAG funding--79 percent of all funds in one site, 54
in another, 20 percent at a third, and an undetermined amount at a fourth. Four sites had JTPA funding, with JTPA representing 11 percent, 8 percent, 6.5 percent, and 2 percent of funding in these sites.
4. States and localities also provided substantial support for adult basic education services. All sites received state funding. At five of the sites, state and local sources provided the majority of funding--ranging from 95 percent to 67 percent in those sites, (pp. ii-iii)
Kutner et al. (1990, November) observed
Nationally, states reported a total of $499.7 million spent on adult education programs in 1987, of which 19 percent ($96.3 million) was Adult Education Act funds and 81 percent ($403.5 million) was from state and local sources. However, two earlier studies have reported that some states may underreport adult education matching funds, providing only the minimum needed to qualify for Adult Education Act funding. (p. iii)
Thus, the funding of adult education by states and local school districts is a minimum requirement for participation in the federal program, which is itself at a low level of
financial support. Insofar as funding is concerned, adult education is indeed a stepchild of the total education
programs in the United States. The problem of inadequate funding is increasing because of federal decreases in financial support.
State Responsibilities Under the Adult Education Act
Kutner et al. (1990, November) wrote that the federal
government has placed a number of administrative duties, reporting requirements, and fiscal responsibilities on the states. Each state is required to (1) develop a state plan
and report it to the Department of Education describing
program needs, activities, and services; (2) allocate adult
education funds to local districts; and (3) evaluate the
effectiveness of all funded programs (p. 2). Kutner et al.
(1990, November) also stated,
The Adult Education Act places a number of fiscal restrictions on the states. States are required to contribute a percentage of the Federal share of expenditures under the program. The Federal share is 90 percent for fiscal year (FY) 1989, 85 percent for FY 1990, 80 percent for FY 1991, and 75 percent for FY 1992 and thereafter. No more than 20 percent of a state's allotment may be used for high school equivalency services. States must spend at least 10 percent for corrections education and education for other institutional adults. States also must spend a minimum of 10 percent for special demonstration projects and teacher training, (p. 2)
Federal funds are distributed to the states based on the proportion of individuals in the state at least 16 years of age who have not graduated from high school and are not enrolled in a secondary school. The decline in the percentage of federal funding, coupled with an aging population, will force many states to reassess their support of adult education. However, as stated above, the need for adult education will remain, regardless of the source of funding.
Many states have supplemented these declining federal funds by supporting adult education programs with funds from local education agencies, institutions of higher education, and other nonprofit agencies or private corporations.
Florida's responsibility toward the Adult Education Act of 1966 is formulated in Florida's Program and Plan for Adult Education (Florida Department of Education, 1989-1993) and The Florida Adult Literacy Plan (Florida Department of Education, 1988). Both reports, submitted and approved by the U.S. Department of Education, list target populations and mention proposals for recruiting and educating these target populations. Unfortunately, Florida's refusal to meet some of the federal requirements has resulted in the loss of some federal funds. Nevertheless, the success rate of GED passing in Florida has increased despite the shortcomings of the state's plan. For instance, the number of persons passing the GED in Florida was 35,546 in fiscal year 1991, 32,722 in fiscal year 1990, 25,280 in fiscal year 1989, and 21,826 in fiscal year 1988 (Florida Department of Education, 1993a). Based on these data, the cap on adult education funding has not affected the general goals of adult education in Florida. However, actual passing rates were not reported; only the total number passing the exam was reported. Thus, changes in the need for adult education have raised new concerns for the inequities of financial support of adult education.
Inequalities of Support in Adult Education
Concern over changes in demographics and student diversity has driven the movement to reassess the needs of adult education. There has been a large shift in the emphasis on adult education from teaching ABE and GED
programs to offering programs for English as a second
language. For instance, concern has been expressed regarding
the ability of current school districts to teach students of
multiple languages and cultures (Ward & Anthony, 1992) .
Thompson, Wood, and Honeyman (1994) expressed the
Of the 47.6 million children in school in 1992, more than 2 million faced severe language barriers, with some of the nation's larger school systems already approaching a majority of minorities. For example, Los Angeles's Limited English Proficient (LEP) students have increased from 15% of total school population in 1980 to nearly 50% in 1992. New York and Chicago also have huge language minorities speaking more than 100 languages, including Apache, Tagalog, Urdu, Cherokee, Greek, and Russian. Border states such as Texas have been especially affected, as in Brownsville where LEP enrollment in elementary grades reached 51% in 1989. LEP growth cannot be accurately estimated because the numbers are so large, but officials speculate that as many as 50% of school districts in some states may not be able to comply with bilingual mandates, (p. 16)
The lack of emphasis on the changing needs of adult
education could have major ramifications in Florida. The
Summary Report: Needs Assessment (Florida Department of
Education, 1993b), dealing with the needs of adult education,
did not emphasize the growing problem of immigration. The
FDOE staff revealed that, of the total targeted population,
Only 2.29% were so restricted in language capability
that they were identified as LEP [Limited English Proficiency] LEP students were represented in the greatest percentages in Home Economics programs at 3.37%, followed by Business at 2.61% and Industrial at 2.57%. Public Service at 0.04% and Agriculture at 0.3 6% served the smallest percentages of LEP students, (p. 11) Because many of Florida's migrant agriculture workers are
from Hispanic backgrounds, the low percentage in agriculture
would lead one to conclude that the state is not recruiting enough individuals with LEP status. These percentages reflect the limited success of the adult education programs in recruiting individuals with limited English proficiency.
Although largely ignored in the literature, some political leaders in Florida are demanding greater emphasis on performance-based funding for adult education programs. Interviews with selected leaders in adult education revealed much opposition to this idea. But, as previously indicated, performance budgeting is primarily absent in the literature.
Benefits of Adult Education
This review of the literature revealed that many writers
concluded that the benefits of adult education more than
outweigh the costs. For many years, writers have promoted
adult education as a potential solution to society's ills.
The ever-present problems of crime, unemployment, and
stagnant economy have been linked to the need for more adult
education. As early as the 1960s and 1970s, adult education
was considered a means to an end to America's growing social
problems. Holtmann (197 0, August 3) offered the following
comment on this point:
There may be a number of reasons for the increase in efficiency of fellow-workers attributable to a comrade's ability to read and write. Workers may have to spend less time in instructing the formerly illiterate in simple machine operations, in correcting his mistakes, etc. In addition, it may simply be impossible to use certain production techniques when some members of the work force are illiterate, (p. 5)
Holtmann continued by concluding that a cost-benefit analysis of adult education should be based primarily on the
assumption that the value of consumption in the society, given a certain distribution of income, is the goal of society. Other social goals of adult literacy education would be to redistribute income among certain racial groups,
certain age groups, or regions. Social goals could include
the stimulation of economic growth, the guarantee of a self-sufficient economy, and correction of the nation's balance-
of-payments problems. Another benefit of adult literacy may
have an indirect effect on the economy. For instance, the
future strength of a nation's economy may be dependent upon
the literacy of the future work force. Holtmann (1970,
August 3) stated, "Another benefit associated with literate parents is the ability they gain in educating their children
There seems little doubt that part of the return from a child's education can be attributed to early investments of
time and energy made in the home" (p. 4). Holtmann also
There are certain types of external benefits that are derived from large numbers of people being literate. For example, the cost of collecting taxes to support government services may be lower for a largely literate population. Along these same lines, some of the benefits associated with literacy may exhibit some of the attributes of public goods. In this case, it will be impossible to determine the individual's willingness to pay for the benefits since by the nature of the goods he cannot be excluded from the benefits if he can read, (p. 5)
Arthur (1989) mentioned that the nonmonetary benefits of adult education may outweigh the costs because many students make several sacrifices in order to complete an adult education program and receive a GED certificate. Arthur added,
The implication of this theory [expectancy theory] for adult education is that those adults who perceive formal education as a means of fulfilling certain needs and who believe that they are able to complete the activity will participate. Those adults who do not share this perception of the value of education, or who lack the will, desire, or confidence to complete the activity, will most likely not participate, (p. 26)
Again, successful participants in adult education must come to realize that the benefits of their participation in adult education more than outweigh the costs.
Research that Supports the Funding of Adult Education Holtmann's conclusions have been supported by several recent studies. According to a report (Utah State Office of Education, 1990, December) of Utah's adult education programs, "For every $1.00 invested [in adult education], our state receives $5.70 in saved, earned or returned income" (p. 1). The total savings were realized through new tax revenues of $4,417,442 and public assistance savings of $3,010,680. When these new revenues and cost savings were combined to make $7,428,122 and compared to a total federal and state expenditure on adult education of $5,179,667, the obvious benefits were realized. These findings were based on the following economic achievements:
1. Obtained a Job
2. Obtained a Better Job or Salary
3. Removed from Public Assistance
4. Unemployed Served
5. Public Assistance Recipients Served
The methods used to obtain the above information were not disclosed in the report.
A longitudinal study of adult education was conducted by the Department of Education for Iowa (State Board of Education, 1992, April). This study used telephone interviews and mailings to question GED graduates about their life status after graduation. Because of the importance of determining the benefits over different periods of time, the surveys were prepared for two, five, or more years after graduation. The findings support the benefits of adult education that were revealed in the Utah study. According to the Iowa study, the graduates' employment rate, job skills, and financial condition appeared to be improved. However, there was only correlated evidence of this improvement; evidence of the exact cause of these improvements did not exist. The study pointed out that "while nineteen percent of the respondents were unemployed and seeking work prior to passing the GED Tests, only nine percent were unemployed and seeking work in 1990" (p. xv). The success of the GED graduates was also reflected in the following statement by the staff: "Job skill level was measured by a five-point
scale on which 1 indicated low job skill level and 5 indicated high job skill level. The mean job skill level increased from 2.8 before passing the GED Tests to 3.5 in 1990" (p. xvi). One of the major benefits of the GED program was that it helped to make participants more independent of public assistance. The staff concluded, "Of the 192 respondents who received welfare prior to passing the GED Tests, 135 (seventy percent) had terminated welfare in 1990. Sixty-five (five percent) of those who did not receive welfare before passing the GED Tests did receive welfare in 1990" (p. xvii). Obviously, the results were mixed when reviewing whether possessing the GED really helped in taking individuals off of welfare. The overall change in those receiving public assistance was positive toward more independence. Furthermore, there were nonmonetary improvements such as improving general quality of life and becoming better parents. The passing of the GED test bolstered the participants' self-esteem and enabled them to help their children in their school work. The staff continued,
Of those in their thirties, the age group which was most likely to have school-age children, a majority of respondents (fifty-four percent) reported that passing the GED Tests helped them to assist their children in school "some" or "very much." In comparison, thirty-one percent of those in their late teens and twenties, who were likely to have pre-school children or no children, responded that earning a GED diploma helped them to assist their children in school "some" or "very much." (p. xxi)
This study reported several limitations. First, there was no control or relevant comparison of the group of adults who had earned traditional high school diplomas and those who had dropped out of high school and had not earned GED diplomas. Because of confidentiality, the researchers could not secure the names and addresses of those who had failed the GED test. Furthermore, the survey was subject to self-reported bias, even though the study's conclusions were based on the assumption that the respondents had answered truthfully. However, even with these qualifications the study has merit in that it further supports the contention that the GED is beneficial for both the recipient and society.
In another study in Wisconsin, the researcher came to the same conclusions that were found in Utah and Iowa. Hayes (1991, December), of the University of Wisconsin-Madison and the principal researcher in this study, noted,
A clear increase in the overall employment rate of the respondents is evident in Table 4. About 66% of respondents were employed full or part-time at the time of the survey in Spring 1991, as compared to 59% at the time of testing in Fall 1989. ... Of the 114 individuals who reported receiving public assistance before earning the GED credential, 34 (29.8%) indicated that they had stopped receiving assistance at the time of the survey, (pp. 18-19)
Other benefits of the GED were stated, such as the enhancement of job advancement, increased skills as parents, and increased self-esteem. As was true for earlier studies, these nonmonetary factors could have influenced indirectly
the respondents' ability to improve the monetary rewards.
Hayes placed the following disclaimer on her findings:
One final caution is relevant when interpreting these responses. The perceptions of these respondents cannot be considered representative of all individuals who participate in GED preparation programs. This sample represents successful GED candidates alone, and it is logical to assume that there is a relationship between positive educational experiences and success on the GED test. While this limitation does not negate the positive perceptions of this study's sample, it does suggest the need to assess perceptions of a wider range of program participants, including program dropouts and individuals who are not successful in passing the GED exam, to gain a more comprehensive student assessment of GED preparation programs in Wisconsin, (p. 33)
Even with these limitations, the author believed that the
surveys reflected the successes and benefits of adult
More recently, a study performed at the University of
Akron found evidence of the benefits of adult education.
Daniels and Hess (1992, March 12-13) reported,
Clients scored higher on all parts of the Ekwall (Silent) following their participation in the PALS program. The higher the client's performance on the SIT the higher the individual's performance on the TABE and Ekwall posttests. PALS clients experienced positive and significant improvements in TABE Vocabulary, Comprehension and Total test scores. [F]acuity revealed that during the course of the PALS program, adult learners (1) began to exhibit greater complexity in ideation; (2) gained greater control over mechanical processes such as punctuation and spelling; (3) expanded their writing repertoire from strictly personal narratives to include letters and creative stories, (pp. 3-4)
In a review of California's adult education programs, Stern (1989, February 9) concluded that the reason for the growing demand for adult education was as follows: "Demand
for high school basic skills instruction is increasing because (1) today's adults place a high value on high school diplomas and (2) high school students are enrolling in adult education programs to meet increased graduation requirements" (p. 41). Although the demand for at least a high school education is important for the work force, the indirect benefits of adult education must be recognized as well. For instance, as has been found in other studies, the researchers in the California study found that adult education contributed to helping students become better parents. California is one of the few states that has developed an evaluation system for English as a Second Language (ESL), Adult Basic Education (ABE), and adult special education classes. The California Adult Student Assessment System (CASAS) program assesses both student and program outcomes. Florida has administered the CASAS to individuals in its literacy programs on a nonrecurring basis (Staff, The Florida Adult Literacy Plan, Florida Department of Education, 1988, p. 12). The core of the CASAS program involves administration of tests to ESL and ABE students to determine whether or not an individual can perform 247 different life skills. Because these life skills are expressed as competency statements, 2 03 are within the general life skills content areas of Consumer Economics, Community Resources, Health, Occupational Knowledge, Government and Law, and Domestic Skills. The balance of the life skills are in the
area of Occupational Skills. Scores on CASAS tests are then
used to evaluate student and program progress.
Mixed reactions have resulted from California's CASAS
evaluation program. According to Stern (1989),
ESL students have gained between 6.1 and 7.3 CASAS scale points per year, while ABE students have gained on the average between 5.7 and 7.0 points per year. ... In 1987-88 some 8,303 ESL and ABE students completed both the CASAS pre- and post-tests in life skills; overall, some 18,3 61 students in 1,312 classrooms completed CASAS pre- and post-tests, (p. 61)
The results of the California study must be qualified. For
instance, Stern wrote,
The accuracy and year to year comparability of this productivity measure [CASAS scores], however, may be suspect since the assumptions have not been tested. Also, the CASAS sample may not be representative of the entire ESL and ABE participant population because (1) half of the students leave the program before taking the post-test (leavers may have different learning rates than completers of both tests) and (2) sample size and sampling and test administration procedures are not uniform across programs (nor is sampling uniformity required by the State Department of Education). (p. 62)
It is possible that the CASAS measures could be made more meaningful by linking analytically the number of hours a student attended the ABE/ESL program with his or her CASAS test score. This would be a burden that any evaluation system would need to overcome.
A Texas study also maintained the need for adult
education. According to the report (Texas State Council on
Vocational Education, 1988, December),
The Texas Strategic Economic Policy Commission reports that when the current dropout dilemma is added to Texas' current near bottom rankings in literacy and SAT scores among the states, "the implications for our state's
economic vitality are clear--a less educated and trained work force, and a greater demand for public service, (pp. 1-2)
The Texas study continued by reviewing the possible benefits
of adult education.
Adult education could be instrumental in the
development of a nation's future economy. Fagerlind and Saha
(1989) expressed it this way:
The cumulative research evidence leaves little doubt that education can be a powerful agent of modernization. Education broadens perspectives and mental horizons, it instills new values and beliefs supportive of modernization programs and goals, and promotes national unity and identity. Furthermore, it provides individual opportunities for upward mobility, develops skills and knowledge important for technological and industrial change, and in general helps overcome immobile ways of thinking and immobile systems of social stratification and differentiation, (p. 110)
These benefits are based on the belief that a direct causal relationship of education on the modernization of individuals exists. These factors are particularly true when community college adult education programs are observed.
In conclusion, the benefits of adult education seem to rest on the needs of society. According to Dubay (1978), the educational needs of adults are often too complex to determine the obligation of the state for instructional programs. He indicated that "[a]s a general guide, however, we may observe that whenever the common welfare of the community requires that the adult population or a notable
section of it be given information of some kind, the
government is bound to provide it" (p. 184).
Critique of the Studies Performed in Adult Education
Most of the research in adult education is based on
surveys and opinion polls. Although the findings have merit,
too often the inadequacies of such studies severely limit the
ability of researchers to extend findings from the samples as
generalizations of the population. Rose (1990), paraphrasing
Smith-Burke (1987), evaluated adult education research in the
following manner: "A further reason for the small voice of
the community of adult education scholars on this topic is
the 'pragmatic orientation' cf the field. Of the 23 6
published articles on adult literacy between 1975 and 1980,
less than a dozen would qualify as research" (p. 24). Beder
(1991) quoted Fingeret (1984) in the following:
The literature in adult literacy education is voluminous, conveying the image of a substantive and useful knowledge base. However, a glance through an extensive bibliography, such as that generated through a thorough ERIC search, leaves the reader immersed in acronyms and discrete, site-specific reports that are difficult to relate to each other or to the planning of
future efforts. In addition, the literature is spread over a range of disciplinary perspectives, confounding
the difficulty of addressing such specific questions as "how do adults read?" (p. ix)
Much of the research in adult education has been based on surveys and expert opinions. Because of the diverse nature of adult education, attempts at evaluating the cost benefits have been lacking. For instance, in the Utah study (Utah State Office of Education, 1990, December) the findings
(i.e., obtained a job, obtained a better job, or removed from public assistance) were all based upon individuals who had attended and successfully completed the adult education programs and had passed the GED elsewhere. Unfortunately, the study does not indicate whether those who did not participate in adult education programs had achieved either less or more success than those who did. For example, the reader is not told of the percentage of individuals who passed the GED test but had not taken any adult education courses. Furthermore, if Utah had experienced a surge of economic growth, the same economic achievements experienced by the adult education participants might also have been experienced by those who had shunned adult education programs. Thus, who is to say whether adult education or passing the GED test contributed any real benefit to the Utah economy or state budget?
Other studies in adult education display similar weaknesses. For instance, the staff of the Iowa study (State Board of Education, 1992, April) admitted that there was no control or relevant comparison of the group of adults who had earned traditional high school diplomas and those who had dropped out of high school and had not earned GED certificates. Thus, the question of whether the GED or high school diploma really made any difference in the success of the individuals in question is not answered. Perhaps possessing a GED certificate was beneficial to the recipient.
However, it really is not known whether those without high school diplomas or GED certificates could have benefitted as well. Finally, the true value of the high school diploma is uncertain.
The Wisconsin study had the same weaknesses as the Iowa study. The researcher (Hayes, 1991, December) based all of her positive assumptions on the following: "[I]t is logical to assume that there is a relationship between positive educational experiences and success on the GED test" (p. 19) Unfortunately, there is little proof as to whether this relationship exists. Finally, Hayes admits that more studies are needed to assess the perceptions or successes of those individuals who dropped out of the program or were not successful in passing the GED test. Steam's (1989, February 9) study of adult education in California fairs no better than the others. However, at least Steam explains why he
did not pursue a study of those who had failed the GED test. California's privacy laws interfered with his ability to investigate the failures of adult education programs.
In summary, the benefits of adult education to those who participate in the courses and are successful are unquestioned. However, determination regarding the benefits to overall society remain unanswered. Because of the lightweight nature of research in adult education, the determination of whether adult education benefits society will be a question for future research. For now, one may
accept the findings with their limitations and assume the
general benefits of adult education.
Problems in Determining the Sociological Benefits of Adult Education
Burket (1992) proposed that several social indicators
would result from a lack of adult education. In his
dissertation, Burket outlined such factors as increased crime
rate, lack of voter registration, and other social ills as
measures of problems resulting from a lack of an educated
populace. According to Burket, "Minimally, it can be
concluded that those with low educational attainment levels
are more likely to be involved in crime, are less likely to
vote or be employed, and are more likely to have low incomes
and experience poverty" (p. 43). However, Drennan (1980) did
not agree that the data .support the social benefits of adult
For example, although few ABE/ESOL staff members ever mention to the recipients-students that a program goal is to get them off welfare, and the program may offer training only in basic skills, a plethora of ABE/ESOL programs use numbers-off-welfare data to judge their success. This is not valid evaluation. Equally invalid are the number registered to vote and voting, the number employed and upgraded on jobs, the number attending PTA meetings, the number reading the newspaper, the number with new library borrowing privileges, and so forth. To judge an educational program mainly on covert criteria is absurd. This is not to say that ABE/ESOL never yields employment or increased citizenship activity or that these results should not be reported. They are important, but they are side effects, (p. 12 5)
The general literature in education has for many years
assumed that society benefits directly from an educated
citizenry. However, the fact remains that no one has
empirically evaluated the benefits of adult education.
The Benefits of Consumer Education
The benefits of consumer education have interested
business and industry. Knapp (1991) noted in his survey
report, "The Benefits of Consumer Education," that consumer
education helps business and industry because it creates more
educated consumers who are better able to make decisions
about the products they are buying. According to an abstract
of Knapp's (1991) survey report, "The responses provide
evidence that modern consumer education teaches more than
getting the best buy. Rather, it is a lifelong process
essential to the economic well-being of society" (ERIC
Document Number ED329772). Knapp further observed that
consumer education offers several benefits to individuals:
(1) encourages critical thinking; (2) imparts life skills that contribute to success in everyday living; (3) promotes self-confidence and independence; (4) fosters broadly accepted values; and (5) improves the quality of life. In addition, consumer education offers several benefits to society: it encourages citizen awareness and promotes a stable society. (ERIC Document Number ED329772)
Additionally, consumer awareness offers several benefits to
the business community.
In his research on the benefits of adult education in
Michigan, Kwon (1990) revealed in a qualitative study the
effect of a microcomputer application training program for
adults. The program contributed economic and noneconomic
benefits to its participants, business organizations, and
society. Finally, a follow-up study by Seppanen (1991, March) of the ABE and GED programs in Washington community colleges showed the following results: 77% of the respondents stated that they had a stronger self-image, 80% stated that they had met their individual goals of improving a basic skill, 50% believed that they had improved a skill that could be applied to their daily work, and 77% of the former students said that their lives had changed for the better since first starting the classes. Marson (1977, July) found, in a one-year cost benefit analysis study of nine full-time vocational technical programs and 3 6 adult education courses, that the benefits of these programs far outweighed the costs. According to Marson"s report (1977, July), the cost-benefit ratio was 2.7 to 1.00 for society and 2.17 to 1.00 for an individual student. Again, although these percentages appear to place adult education in a favorable light, the study is plagued by many of the same limitations of the other studies. Because the study is so dependent upon the honesty of respondents, the study may be biased by the halo effect. In other words, because the respondents were successful, these individuals may have exhibited a positive attitude toward adult education--however unwarranted.
Within recent years some leaders in the Florida legislature have demanded that adult educators justify their programs through outcomes. Marson (1977, July) supported
this concept, which appears to be consistent with the growth
of the accountability movement in the general field of
education. Some political leaders in Florida are demanding
that adult educators adopt performance-based budgeting.
Arguments Against Funding Adult Education
Over the course of history, the view that literacy could
endanger the social structure of society was widely held by
the aristocracy. Donald (1991) attributed to Davis Giddy,
the president of the Royal Society in England during the
1800s, the following statement:
However specious in theory the project might be of giving education to the labouring classes of the poor, it would, in effect, be found to be prejudicial to their morals and happiness; it would teach them to despise their lot in life, instead of making them good servants in agriculture, and other laborious employments to which their rank in society has destined them. [i]t would enable them to read seditious pamphlets, vicious books, and publications against Christianity; it would render them insolent to their superiors; and in a few years, the result would be, that the legislature would find it necessary to direct the strong arm of power against them. (pp. 214-215)
Not surprisingly, because the French Revolution had occurred not long before, the higher classes were dubious of educating the masses. Although this statement appears out of context in our modern world, some adult education administrators stated that some of today's employers exhibit the attitude that if their employees obtain more education, they will leave and go somewhere else. This attitude may seem surprising. Yet, some employers still think very much like Giddy. However, the birth of the public schools in the
United States foretold the movement toward educating the
masses. Costa (1988) stated, "By this time , all
states have [instituted] compulsory school attendance laws;
three states will later repeal theirs (South Carolina in
1955, Mississippi in 1956, Virginia in 1959)" (p. 7). Costa
continued, "By this time , most states have passed laws
encouraging adult education. For example, California
requires illiterates between the ages of 18 to 21 to attend
school and has a literacy test for voters; Connecticut
requires school districts with over 10,000 residents to
maintain evening schools for persons over 14" (p. 9).
Finally, during the 1960s and 1970s there were tremendous
pressures on the states to support adult education programs.
Many of these programs were supported by the Adult Education
Act of 1966. Even with these movements, many experts are
opposed to using public funds to support adult education.
The arguments against funding adult education have
focused upon the economic benefits to society and to business
firms. Because of increased automation and the decreasing
need for workers, there is some question as to the need for
adult education for the training or retraining of workers for
different jobs. Hough (1987) postulated,
[S]ince unemployment is here to stay and therefore labour surpluses will continue in the majority of occupations for the foreseeable future, the government should establish the scale of training activity on the basis of social objectives. [P]erhaps the main problem involved in so doing would be the heavy strain on public expenditure, quite apart from the economic
waste involved in providing training that might not subsequently be put to good use. (p. 114)
Drennan (1980) concurred with Hough:
In a society incapable of supplying enough jobs for everyone interested in working, these factors seem not to have been explored deeply by either adult educators or funders of adult education. In an economic sense the ABE/ESOL graduate who replaces the less-educated worker does not yield social profit; adult education programs often accomplish their goal of rendering graduates employable at the expense of already employed nongraduates. Thus the net gain to society at large is questionable, (p. 99)
Drennan further highlighted the difficulty of demonstrating a
causal relationship between adult instruction and benefits to
the individual in the following:
Even though many adults with limited basic skills who enroll in ABE programs probably are gambling on the purported causal relationship between education and income, economists state that the relationship between adult education and increased income has only the slimmest of documentation nationally. It is difficult to point to data which prove that a decade of remedial adult education programs has lessened the rate of either functional illiteracy among the undereducated adult public or their unemployment--in real numbers or percentages, (p. 99)
Since the beginning of history, the pursuit of adult
literacy has been a subject of constant debate. As
previously discussed, one argument holds that literacy might
have a negative impact on society. For instance, Kaestle
Damon-Moore, Stedman, and Trollinger (1991) wrote,
Although for purposes of public policy, increased literacy is assumed to benefit both individuals and the society as a whole, the association of literacy with progress has been challenged under certain circumstances. Paolo Freire has questioned whether literacy is a good thing for oppressed people if the content and conduct of literacy training are not under their control. From a variety of political viewpoints,
American and British culture critics of the 1950s questioned whether mass culture, including popular reading materials, was debilitating to its consumers, (p. 27)
Kaestle et al. quoted the Princeton historian Lawrence Stone: "[T]hat if you teach a man to read the Bible, he may also read pornography or seditious literature" (p. 27) Obviously, the teaching of literacy in adult education is dependent upon one's viewpoint, the illiterate individual in question, and whose benefit is under consideration.
As to proving the economic benefits of those who would
become employed as a result of adult education, additional
theoretical problems are identified. For instance, when
examining the theories of the human capital approach, the
true value of adult education becomes unclear. Fagerlind and
Saha (1989) further observed that radical critics of
education believe that adult education may create a "docile
and adaptive work force which serves the needs of the power
structure of the economy. For the radical critics, an
education system which does not alter the structure of an
inequitable capitalist society, does not contribute to the
change and development of that society" (p. 49).
Research Findings Not in Favor of Funding Adult Education
As has been stated earlier, most of the research in
adult education has been superficial. However, in one
dissertation study by Huffman (1992), the benefits of funding
vocational education appear mixed. Huffman analyzed the top
10 vocational education programs in Mississippi and compared the amount of funding the programs received with their individual rankings. Huffman reported the following important relationships.
1. The programs that spent less on teacher salaries had better rankings, which suggests that the programs were smaller and perhaps the students had more individualized assistance.
2. The less money spent on teacher travel--the better the ranking. More time with students may significantly increase enrollment, completion, and placement.
3. The less spent on contractual services--the better the ranking.
4. The less spent on supplies and materials--the better the ranking.
5. The intercorrelation did indicate that the less spent on facilities the better the performance.
6. Equipment costs did affect the program performance ranking, but the less spent on equipment--the better the ranking.
7. The enrollment was related to costs and indicated that as enrollments decreased, program costs/FTE increased. (pp. 95-97)
Although these controversies apply to vocational education, the same expenditures may come into question in adult education. Would this mean that if less money were spent on adult education programs, there would be a higher success realized from adult education students? This is a question that is unanswered and may need further study.
Finally, another researcher discovered that the dollar amount spent on adult education courses may not be the issue. The real issue may be how the monies are spent on adult
education. As indicated previously, Rose (1990) found that "students, particularly mandated students, know that they can sit around doing very little, take long unofficial breaks, and basically not be there except in body, if that is what they choose" (p. 127).
Three adult education administrators who were interviewed in preparation for this study had mentioned the above dilemma. According to them, about 50% of the adult education students will never pass ABE Level 2 or reach the grade of 8.9. Thus, for perhaps 50% of the adult education students, the state monies may be wasted. Even worse percentages were revealed when discussing the percentage of those passing the GED or receiving the adult high school diploma and the total population of adult education students. Thus, the jury may still be out on the true value of present adult education programs.
Quantitative Methods Used for Evaluating Educational Programs
Few quantitative studies have been performed on the cost benefits of adult education. Except for Burket1s (1992) and Huffman's (1992) related research in vocational education, few studies have attempted to relate the benefits of adult education with its costs. Such a study should add to the knowledge base in this area.
The use of systems like PPBS (planning-programing budgeting system) was emphasized during the surge of education acts passed by Congress in the 1960s. Because of
the need for efficiency and "getting things done," PPBS became a code word among educators during the 1960s and early 1970s. However, PPBS and related systems were not widely accepted in the field of education, and few of these systems survive today. In the field of vocational education, competency-based and performance-based evaluations have been used since the early 1970s. Many of these programs emphasized placement, so the final goal of employment was tied to the funding of the vocational program. Huffman (1992) wrote,
Several studies highlighted specific factors or outcome variables which should be analyzed in a technical-vocational performance evaluation, such as: enrollment data, job placement, community support, student performance, student aspirations, economic benefit, employer satisfaction, service to special populations, and overall cost-effectiveness, (p. 24)
However, limited literature exists concerning the use of
competency-based or performance-based evaluation or funding
in the field of adult education. One reason for such
omissions is the special nature of adult education. Unlike
vocational education, adult education does not have the goals
of instructing the students in specific skills for specific
jobs. Furthermore, employer expectations of vocational
education graduates range from their possessing the ability
to pass exams for licenses and certifications to their being
able to operate complex machinery. These expectations are
absent in adult education.
In order to review the literature most relevant to adult education, it is important to look at attempts at evaluating either K through 12 programs or programs in higher education, such as those at community colleges and universities. The literature centers upon the evaluation of costs incurred in a program. Most of the literature in adult education has utilized cost-benefit models for evaluation techniques.
For instance, Steele (1971, July) surveyed the possibility of applying cost-benefit techniques to adult education. She concluded that cost-benefit techniques were used in adult education programs that achieved economic outputs and were closely associated with industry. Steele concluded that, while cost-benefit models are useful in education, a more encompassing input-output analysis would be more useful because such a model could deal flexibly with human variables within an educational system. Marson (1977, July) also mentioned the possibility of using a cost-benefit method for evaluating adult education. In Marson's study, two cost-benefit models were tested on nine full-time vocational technical programs and 63 adult education courses, which reflected many different instructional areas in vocational technical education. His findings were that the benefits from vocational education programs and noncredit education courses did outweigh the cost of the courses. Even with these findings, the limitations on cost-benefit analysis
are such that other possible methods of evaluation have been suggested.
Determining the costs to assign to the benefits of adult
education may be difficult. First, if Net Present Value
(NPV) techniques are used, the researcher may have difficulty
in selecting appropriate discount rates. Furthermore, the
measurement and identification of indirect costs and
nonmonetary benefits in an educational organization are
difficult to apply to specific programs. Because many
educational benefits are intangible and are difficult to
quantify, the use of any costing formula would be held
suspect as a means for measuring educational outcomes
(Campen, 1986). Huffman (1992) observed,
Levine in 1981 noted that there were serious "data limitations and ambiguities" in cost-benefit analysis of human service programs. Shugoll and Helms (1982) and Levin (1983) indicated that cost-benefit analysis had significant limitations in measuring educational costs and benefits. Campen (1986) argued that cost-benefit analysis was "procedurally inappropriate" for establishing public policy since it attempted to subrogate the importance of "social ethics; rights, entitlements, and due process; the political process; and environmental values." (p. 46)
Rothenberg (1975) stated that "one of the truly serious
difficulties in conducting cost-benefit studies is the lack
of bases on which to value the flow of public services or the
benefits from public projects" (p. 78).
The concepts of cost-effectiveness and cost-feasibility
have been suggested as possible educational measures.
According to Levin (1983),
Under cost-effectiveness analysis, both the costs and effects of alternatives are taken into account in evaluating programs with similar goals. It is assumed that (1) only programs with similar or identical goals can be compared and (2) a common measure of effectiveness can be used to assess them. These effectiveness data can be combined with costs in order to provide a cost-effectiveness evaluation that will enable the selection of those approaches which provide the maximum effectiveness per level of cost or which require the least cost per level of effectiveness, (p. 18)
However, Levin (1983) reported the following strengths and
weaknesses of the cost-effectiveness model:
The cost-effectiveness approach has a number of strengths. Most important is that it merely requires combining costs data with the effectiveness data that are ordinarily available from an educational evaluation to create a cost-effectiveness comparison. Further, it lends itself well to an evaluation of alternatives that are being considered for accomplishing a particular educational goal. Its one major disadvantage is that one can compare the CE [cost-effectiveness] ratios among alternatives with only one goal. (p. 21)
The same problems that affect the cost-effectiveness
approach also plague the cost-utility approach. Levin (1983) continued,
The major disadvantage is the fact that the results cannot be reproduced on the basis of a standard methodology among different evaluators, since most of the assessments are highly subjective ones that take place in the head of the person doing the evaluation. Another evaluator with the same information and methodology may derive a drastically different result by using a different set of probabilities and utilities, (p. 29)
Finally, Levin (1983) concluded that cost-feasibility analysis "can determine only whether or not alternatives are within the boundaries of consideration" (p. 30). Because of these weaknesses, an evaluation of adult education would be
best suited to an input-output model, which optimizes the outputs of adult education based upon the budgetary-constraints existing at the time of the evaluation. Such a condition would imply that adult education programs can best be evaluated by using the input-output model. According to McAfee (1972),
The review of the literature appears to justify the following generalizations.
1. There is a need for decision-making based upon input-output relationships.
2. The challenge for input-output studies is to determine the proper mix of inputs that will maximize output.
3. In general, input-output studies have not interfaced with cost-effectiveness studies.
4. Serious reservations regarding methodology in input-output studies have been expressed.
5. A mathematical model is appropriate for systematically determining optimal allocation strategies, (p. 29)
Mathematical models have been used to determine funding for
education in K through 12 and other educational programs
(Johns, 1976, Fall). This mathematical model is discussed
more fully in Chapter 3.
Chapter Summary The release of a recently completed national study of adult education needs in the United States revealed that 90 million American citizens were seriously deficient in literacy skills, and many of these persons did not realize their predicament. Moreover, the literature indicated that
in other advanced nations (e.g., Canada, England, Sweden, France), there was an acute need for adult education programs. Some writers expressed concern for the survival of society without attention to adult education needs.
The emphasis for adult education programs was on program outcomes. Although the obvious social benefits of adult education were mentioned, the modern view of adult education was redirected toward cost effectiveness. More and more scrutiny was being placed on the success rate of adult education programs. According to an abstract of Mason's (1988) article, adult educators have not received the recognition for the contributions they have made to local economies; therefore, they should rethink their rationale, reject outmoded beliefs and patterns, and justify their work through program outcomes (ERIC Document number EF378460) Several programs have been reviewed and have been found to be beneficial to society. For instance, as indicated previously, Kwon (1990) remarked in a conference speech that a review of all qualitative data obtained from the Michigan study revealed that the program contributed economic and noneconomic benefits to the participants, the organizations, and society (ED326656).
The benefits of adult education are mostly accepted in the literature. Qualitative measures have been successful at determining the beneficial outcomes of adult education. However, the use of quantitative measures to evaluate adult
education programs has shown mixed results or has not been tried. There is little evidence that performance-based budgeting has been used in any educational programs. A review of the literature reveals no evidence of utilizing performance-based budgeting for funding adult education. Although their opinion was very much in opposition to traditional American thought about the value of an educated citizenry, some persons opposed the education of adults on the basis that helping persons become literate might make them unhappy with life and produce instability in society. But, some writers opposed adult education programs on the basis that they waste taxpayers' money in addition to creating additional problems for the government. Also noted was the opinion that further education of adults might destroy a stable source of unskilled labor and the economic system.
CHAPTER 3 PROCEDURES
The purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida through the simultaneous solution of linear and nonlinear formulations. For purposes of this study, the evaluation of data items used in these formulations must be evaluated using statistical techniques to determine their relevancy and validity. Upon determination of their relevancy, further statistical analysis will help determine the variables that are key contributors of success in adult education.
Procedure of this Study
The procedure used for this study was to formulate production models and use stepwise linear and nonlinear programming techniques to optimize models to reveal the most efficient and cost-effective factors in adult education funding. By simultaneous solution of these models, the process would determine how adult education funding should be allocated to maximize the greatest outputs. Although this study utilized nonlinear models, a review of linear programming explains some of the complexities of nonlinear
programming. According to Sultan (1993), "In linear programming, one studies the best way to allocate limited resources" (p. 1). Dorfman, Samuelson, and Solow (1986) defined linear programming as "the analysis of problems in which a linear function of a number of variables is to be maximized (or minimized) when those variables are subject to a number of restraints in the form of linear inequalities" (p. 8). The present study utilized an input-output model to find the best way to allocate the resources of adult education.
Hillier and Lieberman (1974) pointed out that linear
programming is based on four main assumptions:
proportionality, additivity, divisibility, and that all
parameters of the model are deterministic. They gave the
following example of proportionality:
The assumption is that in this case (1) the measure of effectiveness Z [dependent variable] equals C^X^ [C is
the coefficient of the independent variable X and k is the subscript of the activity for n activities or observations], and (2) the usage of each resource i equals Ai^X^; that is, both quantities are directly
proportional to the level of each activity k conducted by itself (k = l,2,...,n). [A is coefficient of the independent variable X for each activity k for each independent variable X]. (p. 22)
The magnitude of each effect is proportional to the amount of
activity governing the effect in the model.
Hillier and Lieberman stated that "the additivity
assumption requires that, given any activity levels (Xi,
X2,...Xn), the total usage of each resource and the resulting
total measure of effectiveness equal the sum of the corresponding quantities generated by each activity conducted by itself" (p. 23). Of course, this assumption applies only to linear functions and would not always be possible for nonlinear formulations.
Hillier and Lieberman continued, "Therefore, the divisibility assumption is that activity units can be divided into any fractional levels, so that noninteger values for the decision variables are permissible" (p. 23). Finally, all parameters of the model must be deterministic. Although the parameters of nonlinear models sometimes are undeterminable, the necessity for known parameters limited the formulations used in this study. The solution of these parameters was estimated using multiple regression analysis, which is discussed later in this chapter.
Linear programming also entails certain properties that may or may not apply to some nonlinear models. Nonlinear models would be defined as mathematical models that involve nonlinear functions to describe the relationship between the dependent variable and the independent variables. First, this study assumed that all models were standard. According to Sultan (1993), "If we drop the requirement that all the variables be nonnegative in a linear program, then the program falls under the category of problems called nonstandard. Unless explicitly stated otherwise, however, all programs will be standard. That is, all
variables will be > 0" (p. 50). This study assumed that all variables are nonnegative, with the requirement of nonnegativity referring only to variables, estimates that demonstrate the effect of the independent variables on the dependent variable may be negative.
Another assumption concerning most linear models is that they will be canonical. Sultan also stated, "Then we say that the linear program is in canonical form if all of the main constraints are equations, and we can pick out from each main constraint one variable that occurs only in that equation, and which has coefficient 1" (p. 52). Since the
purpose of this study was to maximize outputs in response to restricted resources, a maximization program was adopted. Sultan continued by stating that a "standard maximum linear program is one in which (a) the objective function is to be
maximized, (b) all the main constraints are of the type 'less than or equal to constants,1 and (c) where all the variables are nonnegative" (pp. 149-150). Any maximization program can be made a minimization program by multiplying the models by
ive 1. Sultan defined the minimization program as follows: "A standard minimum program is one where (a) the objective is to be minimized, (b) all the main constraints
are of the form 'greater than or equal to constants,1 and (c) the variables are nonnegative" (p. 150). Hence, this study focused on the maximization of the production model in order to maximize output.
Because the adult education field possesses many goals, this study needed to adopt a model to allow for the simultaneous solution of multiple optimizations. Goal programming could be used in linear programming to attempt to optimize multiple goals. While a company may use linear programming to maximize profits or minimize costs, goal programming allows for several goals to be resolved simultaneously. Sultan (1993) explained, "One great advantage of this technique is that it allows us to treat several objectives at once even though these objectives may be measured in different units, and even though these objectives may be incompatible" (p. 473) The goals of
graduating from different ABE levels or obtaining the GED or
simply transferring to a new educational program may be
included in goal programming. Goal programming allows for
several objective functions or production models, so that all
goals are included in the optimization model. Although goal
programming may be utilized to find solutions to multiple
goals in linear programming, such formulations may fail
because of constraint problems. According to Sultan, "Of
course, there is the question of how we incorporate these
goals into a linear program, since solving linear programs
does not allow for the violation of the constraints" (p.
476). Sultan best describes the problems encountered with
linear programming in the following:
If in a goal we are indifferent as to whether we underachieve or overachieve a target, then the variables
u and v both occur in the objective function. If it is more desirable that we underachieve a target than overachieve a target, then only the overachievement variable associated with that goal occurs in the objective function. If it is more desirable that we overachieve a target than underachieve it, then only the underachievement variable associated with the goal occurs in the objective function. This also illustrates how drastically a solution can change by changing a goal. (pp. 479-480)
McAfee (1972) concurred with Sultan in the following:
"Consequently, it would be vain to hope to maximize the
outcomes of each student in several different areas. In the
utility function [optimization function or formula], only a
few of the outputs would be maximized, at the expense of
other outputs" (p. 51). Thus, any formulation that embraces
the optimization of outputs with the attainment of several
goals would require the complexity of nonlinear programming
models. A study could utilize only linear models; however,
linear programming is plagued with two major limitations that
would not only decrease the magnitude of a study, but could
jeopardize the purpose of the study, which is to determine
how scarce resources should be allocated. According to
Phelps (1992, March),
While Linear Programming appears to address most of the criteria, the remaining few are so critical that they easily become "fatal." Non-linear Optimization addresses these two last criteria: (1) changing returns or nonlinear relationship between the Outcomes and the Effects; and (2) finding an optimal solution without having intersection between competing Effects (some positive and some negative). (p. 32)
Most importantly, the nonlinear programming model allows for a "built-in" balancing effect, so that effects that result in a negative value do not negate potentially positive characteristics of those same effects included as factors in
the optimization model.
Phelps (1992, March) listed the following important
properties of nonlinear modeling:
Non-linear optimization measures the multiple outcomes and the relationship between the outcome and effect in terms of the non-linear and bounded values, (p. 33)
Non-linear optimization easily uses the non-linear function of "cumulative standard normal probability." In many ways, this is the most unique feature of the education production model being presented, (p. 34)
Non-linear optimization allows--indeed requirescost to be included as a constraint and provides the resulting interpretation of "what is the most efficient and effective combination of effects given the given costs
constraint?" (p. 34)
Non-linear optimization allows the relationship between and among effects to be defined as additional constraints, (p. 34)
The properties of the constraints or boundaries of
nonlinear models require further discussion. The constraints
used in nonlinear programming are known as functional
constraints, set constraints, and active constraints.
According to Luenberger (1989),
It is clear that, if it were known a priori which constraints were active at the solution to (1) [minimize f(x) subject to hi(x) = 0 etc.], the solution would be a local minimum point of the problem defined by ignoring the inactive constraints and treating all active constraints as equality constraints. Hence, with respect to local (or relative) solutions, the problem
could be regarded as having equality constraints only, (pp. 296-297)
Thus, for purposes of simplification, an assumption can be made where all constraints are equality constraints.
Nonlinear programming fits nicely with the needs of statewide budgets because of its magnitude. Luenberger
There are many examples of nonlinear programming in industrial operations and business decision making. Many of these are nonlinear versions of the kinds of examples that were discussed in the linear programing part of the book. Nonlinearities can arise in production functions, cost curves, and, in fact, in almost all facets of the problem formulation, (pp. 305-306)
Since nonlinear programming was necessary for this study, alternative techniques for determining the parameters of the production model were required. Furthermore, the very complexity of nonlinear models required the use of computer-based solutions. Nakamura (1993) wrote:
The primary reason why we solve nonlinear equations by using computer methods is that nonlinear equations have no closed-form solution except for very few problems. Analytical solution polynomial equations exist up to the fourth order..., but there are no closed-form solutions for higher orders. Therefore, roots of those nonlinear equations are found by computer methods based on iterative procedures." (p. 65)
The methods by which the production model parameters are estimated will be discussed later.
Population for the Study The population for this study consisted of all districts and adult education centers in Florida. Based on the information obtained from scholars of adult education, it was determined that accurate data on GED and ABE program
performance were indefinite for most of the states; however, all states must report annually to the federal government the results of their adult education programs. The data for this study were taken from Florida's reports to the federal government for the fiscal years of 1991-92 and 1992-93.
Research Design The research design was based upon a data set with 85 observations for fiscal year 1992-1993 and 5 unduplicated observations from fiscal year 1991-1992 on 12 variables for the dependent variable (i.e., number passing the GED or receiving the Adult High School Diploma); 1 cost variable for all 90 observations based on the 85 local education agencies for fiscal year 1992-1993 and 5 unduplicated local education agencies for fiscal year 1991-1992 that offered adult education courses--all representing more than 1,300 data items. Even though the observations are from two different years, the 5 observations from fiscal year 1991-1992 are not duplicated in the 1992-1993 year (i.e., the same students were not included in both years' data). These 5 observations were from organizations such as Action, Inc., the Dozier Schools, Dixie County School District, Glades County School District, and Washington County Council on Aging, Inc. Therefore, inclusion of these local education agencies in the data increased the total number of observations to 90. Stepwise regression was utilized to determine the major factors influencing the success factors. Because of the low
observations to variable ratio (8 to 1), an alpha level of .05 was used to increase the power of the test statistics while using the stepwise method.
The two outputs, the GED and the Adult High School Diploma, were accomplishments verified, using standardized tests. These tests were either statewide or nationally recognized as demonstrating student achievement above a minimum level of educational attainment. Therefore, this study had verifiable evidence of student accomplishment with standardized tests. Although the attainment of the Adult High School Diploma required the completion of different courses than the courses used for preparing for the GED, both the Adult High School Diploma and the GED were considered equivalent. Also, the expenditures for adult education could not be allocated to either the GED students or the students of the Adult High School. Thus, the success on the GED was combined with completion of the Adult High School Diploma to create one success variable. Furthermore, passing rates for the students on either the GED or Adult High School Diploma were not available. Therefore, the dependent variable or success variable encompassed the percentage of the total student population who completed the GED or the Adult High School Diploma. The mathematical model was developed from the use of stepwise regression techniques by using the sum of the GED and Adult High School Diploma as the dependent variable. A second model which was developed from the
stepwise method was then used to determine the coefficients for the budgetary model. The final expenditures of fiscal years 1992-1993 and 1991-1992 for the 90 local education agencies were used as the dependent variable for the second model. Other important constraints were developed and used as constraints on spending. Finally, the first model was maximized by using a solution of simultaneous equations with the second model or budgetary model. Constraints on the maximization of the simultaneous resolution were included in the process of simultaneous equations.
The local education agencies included public school districts, community colleges, correctional institutions, other institutions, local libraries, and other state agencies offering adult education courses. To obtain the most current picture of the relationship between adult education funding and the many variables tested, the latest Adult Education Reports sent to the federal government were used as the source for all data items. These reports encompassed data collected for fiscal years 1991-1992 and 1992-93. Since any regression formulation must be based upon sound research theory, the 12 variables were selected because previous research revealed the importance of these variables in the determination of success in education. Furthermore, the federal government has mandated that these data items be reported annually to the U. S. Department of Education.
Statement of Variables The independent variables associated with the participant inputs for the dependent variable of GED and Adult High School Diploma for adult education were listed by-category .
The variables associated with student factors were as follows:
Xl--Percentage of students (Adult Education students) who were enrolled in other educational programs. This percentage was calculated by dividing the number of students of each local education agency (LEA) who were enrolled in other educational programs by the total number of students at each LEA.
X2--Percentage of students who were female. This percentage was calculated by dividing the number of female students at each LEA by the total number of students at each LEA.
X3--Percentage of students who were handicapped. The percentage was calculated by dividing the number of handicapped students at each LEA by the total number of students at each LEA.
X4--Percentage of students who were eligible legalized aliens. The variable was calculated by dividing the total number of eligible legalized aliens in each LEA by the total number of students at each LEA.
X5Percentage of students who were in correctional institutions. This percentage was calculated by dividing the number of adults in correctional institutions at each LEA by the total number of adults at each LEA.
X6--Percentage of students who were employed. The percentage was calculated by dividing the number of students who were employed for each LEA by the total number of students at each LEA.
X7--Percentage of students who were receiving public assistance. The percentage was calculated by dividing the number of students who were on public assistance and/or homeless at each LEA by the total number of students at each LEA.
The variables associated with school factors were stated as follows:
X8--Percentage of teachers who were part-time. This percentage was calculated by dividing the total number of part-time teachers by the total number of staff members in adult education. The staff in adult education was defined as the part-time teachers, full-time teachers, volunteer teachers, part-time paraprofessionals, full-time paraprofessionals, part-time counselors, and full-time counselors.
X9--Percentage of teachers who were full-time. This percentage was calculated by dividing the total number of full-time teachers by the total number of staff members in
adult education. The staff in adult education was defined as the part-time teachers, full-time teachers, volunteer teachers, part-time paraprofessionals, full-time paraprofessionals, part-time counselors, and full-time counselors.
X10--The ratio of state instructional salary expenditures over total expenditures. This was calculated by dividing the total instructional salary expenditures for each LEA by the total expenditures by LEA. Total expenditures included the expenditures of both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
XI1--The ratio of state support personnel service or contracted services expenditures over total expenditures by LEA. This was calculated by dividing the total cost of other personnel services by the total expenditures by LEA. The total expenditures included the expenditures of both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
X12--The ratio of state expenses of material and supply expenditures over the total expenditures by LEA. This was calculated by dividing the total cost of other expenses by the number at each LEA by the total expenditures by LEA. The total expenditures by LEA included the total expenditures of
both state and federal monies for instructional salaries, contracted services or other personnel services, other expenses, and equipment.
The dependent variables used in the study were as follows:
Yl--Percentage of students who passed the GED or earned an Adult High School Diploma. This variable was calculated by dividing the total number of students who had passed the GED or earned an Adult High School Diploma for each LEA by the total number of students at each LEA.
Y2--The total adult education expenditures per student by LEA divided by 1,000. This was calculated by dividing the total costs (from both state and federal funding) incurred by each LEA and then dividing this number by the number of students of each LEA. The result of this calculation was divided by 1,000 for scaling purposes. Thus, actual coefficients have coefficeints that have moved the decimal three places.
Selection of variables was based upon logic and, in some cases, convenience. Because the focus of this study was on the controllable costs of adult education, only the variables which could be controlled by Florida and which are the generator of expenditures for Florida were chosen. Most of the 12 variables which were used for the model were the only variables which the state could control for cost purposes. Therefore, the 5 observations for fiscal year 1991-1992 and
the 85 observations for fiscal year 1992-1993, which total 90 observations, represented an 8-to-l ratio of observations to the variables. Multiple regression techniques were used to determine the major factors for the optimized model.
Although the number of legalized aliens and students enrolled in other educational programs were not reported on the 1992-1993 Federal Report, these variables had been reported in the 1991-1992 Federal Report. The number of legalized aliens and students enrolled in other educational programs had been reported for the three previous fiscal years of 1988-1989, 1989-1990, and 1990-1991. Therefore, these variables were included in the Adult Education Model.
Teaching in adult education in Florida is mostly done by part-time teachers from the pre-K through 12 program and volunteers. Some of the vital statistics for part-time teachers are listed in Tables 1 and 2. The totals for the volunteer counselors and paraprofessionals were excluded due to lack of data for these categories.
Since the state does not pay volunteers, teaching quality in the volunteer program is questioned. Furthermore, the state has no control over the number of volunteers recruited. Thus, since these volunteers are unpaid and the state cannot predetermine the number of volunteers recruited, the variables involving the number of volunteer counselors and paraprofessionals were ignored in this study.
Vital Statistics on Part-Time Teachers for 1991-1992
Description Number Percentage
Part-time teachers 7,454 60
Full-time teachers 827 7
Part-time paraprofessionals 429 3
Full-time parapro f e s s i ona1s 148 1
Part-time counselors 275 2
Full-time counselors 174 2
Volunteer teachers 3,176 25
TOTAL 12,483 100
Vital Stat ;istics on Part-Time Teachers f or 1992-1993
Description Number Percentage
Part-time teachers 7,671 60
Full-time teachers 886 7
Part-time paraprofessionals 491 4
Full-time paraprofessionals 190 1
Part-time counselors 285 2
Full-time counselors 190 2
Volunteer teachers 2.999 24
TOTAL 12,712 100
The use of so many part-time teachers and para-professionals made the analysis of whether part-time teachers and paraprofessionals were better or worse than full-time teachers impossible. Also, certification is not required for many paraprofessionals. Thus, the quality of assisted teaching of the paraprofessionals was a major question that could not be answered. However, the costs to the state for these paid individuals made their presence significant to the study. Therefore, variables for the costs of these full-time and part-time teachers were used in the study.
As stated previously, forward, backward, and stepwise procedures were used to determine the parameter estimates of the linear equation. After these estimates were determined, two separate linear equations were developed using stepwise regression with two separate dependent variables. The dependent variables that reflected the successes or outputs of the two equations were the total number of individuals who either passed the GED or received the Adult High School Diploma.
After the two production equations were solved simultaneously, a nonlinear formulation was attempted. By using the PROC NONLIN command with SAS, the program used the Newton method of elimination to develop the nonlinear formulation, which best describes the process of adult education funding. The PROC NONLIN does not guarantee that such a developed equation is truly representative. Furthermore, an
examination of the results of the PROC NONLIN procedure should not be used unless the estimated model demonstrates a strong significance with the dependent variable.
As was stated previously, since some of the nonlinear equation calculations demanded nonanalytical solutions, the parameter estimates required the numerical solutions of nonlinear equations. Furthermore, the need to increase the number of variables based on further hypothesized effects required the use of analytical procedures. However, as will be seen in Chapter 4, linear models developed with multiple regression appeared to be the best equations for the purposes of this study.
Collection of Data Data from the Florida Department of Education were used to construct and pre-analyze the proposed formula. Data about funding levels, GED and ABE performance, and related information were collected from directors of adult education programs in Florida, and the annual report, which is submitted to the federal government, was used for analysis of the developed formula. The annual report is not broken down by local education agencies. However, the reports that were produced by the individual local education agencies were summarized, so that specific data concerning each agency were obtained. Therefore, summary reports were used to develop the 90 observations that were discussed in the section titled "Research Design" (see p. 68). The numbers in these reports
were correlated using multiple regression techniques to determine the parameters of the mathematical models. Interviews from adult education administrators and expert faculty of adult education were also used to determine the funding effects and the estimate of the constants in the production function.
Although many of the experts interviewed in this study mentioned that transportation and child care would improve the success rates of adult education centers, these possible additions to adult education funding were not included. Because Florida political leaders have voiced strong opposition to transportation and child-care costs, these factors were not considered feasible as state expenditures. The emphasis was on feasibility of legislative approval of the factors included. Based on current information, it was decided that transportation and child care are not likely to be adopted now, or in the near future, by federal or state politicians. The emphasis in this study was on optimal outputs under existing legislation. Furthermore, because every effort is made to locate the adult classes as close to the residential areas of the pupils as possible, transportation was not considered a factor in the funding of adult education.
Analysis of Data First, the data were analyzed using PROC MEANS and PROC CORR procedures on the SAS system. Because of the low ratio
of observations to variables, the most prominent variables were selected for study. The 5-to-l ratio of observations to variables is a strongly recommended minimum ratio in research using multiple regression. According to Stevens (1992), "Many of the popular rules suggest that sample size be determined as a function of the number of variables being analyzed, ranging anywhere from two subjects per variable to 20 subjects per variable. And indeed, in the previous edition of this text, I suggested 5 subjects per variable as the minimum needed" (p. 384). In discussing stepwise discriminant analysis, Stevens wrote, "The F's to enter and the corresponding significance tests in stepwise discriminant analysis must be interpreted with caution, especially if the subject/variable ratio is small say < 5" (p. 284).
Two major assumptions must be met when using multiple regression analysis to determine a regression model. According to Chatterjee and Price (1991), "The assumptions are (1) the explanatory variables are nonstochastic, that is, the values of the x's are fixed or selected in advance, and (2) the x's are measured without error. These assumptions cannot be validated, so they do not play a major role in the analysis. However, they do influence interpretation of the regression results" (p. 67). Once these assumptions have been accepted, then the researcher can follow certain steps to determine variable selection.
The major procedures usually employed by researchers to develop a mathematical model for testing are the forward selection method, the backward elimination method, and the stepwise method. The forward selection technique was employed first. In the forward selection technique, the F statistics are calculated for each of the independent variables. The results of the forward selection procedure revealed the variables which would give the largest F statistic and R squared. Chatterjee and Price (1991) reported,
The forward selection procedure starts with an equation containing no explanatory variables, only a constant term. The first variable included in the equation is the one which has the highest simple correlation with the dependent variable y. If the regression coefficient of this variable is significantly different from zero it is retained in the equation, and a search for a second variable is made. The variable that enters the equation as the second variable is one which has the highest correlation with y, after y has been adjusted for the effect of the first variable, that is, the variable with the highest simple correlation coefficient with the residuals form step 1. The significance of the regression coefficient of the second variable is then tested. If the regression coefficient is significant, a search for a third variable is made in the same way. The procedure is terminated when the last variable entering the equation has an insignificant regression coefficient or all variables are included in the equation, (p. 23 6)
The backward elimination method is described by Agresti and Finlay (1986) as follows:
The backward elimination procedure works in the reverse direction from the forward selection method. In backward elimination, we begin by placing all of the independent variables under consideration in the model. If they all make significant partial contributions, then that model is the final one. Otherwise, the independent variable having the least absolute partial correlation
with Y, controlling for the other independent variables, is removed from the model. Next, for the model with that variable removed, the partial correlations with Y and each Xi (controlling for the other variables still in the model) are recomputed. If they are all significant, that model is the final model. The process continues until each remaining independent variable makes a significant partial contribution to explaining the variability in Y. (p. 379)
The stepwise procedure was performed in addition to
forward and backward elimination. According to Chatterjee
and Price (1991),
The stepwise method is essentially a forward selection procedure but with the added proviso that at each stage the possibility of deleting a variable, as in backward elimination, is considered. In this procedure a variable that entered in the earlier stages of selection may be eliminated at later stages. The calculations made for inclusion and deletion of variables are the same as FS and BE procedures. Often, different levels of significance are assumed for inclusion and exclusion of the variables from the equation, (p. 237)
In order to select the proper variables needed in the model, the researcher determined the theoretical significance to the model. In other words, common sense, past research, or sometimes just plain guessing was used to determine the variables that should be included in the model.
The summarized results of the backward elimination method listed the variables that were considered by the stepwise method. Although the original ratio of observations to variables was 8 to 1, the true ratio of observations to variables was much higher because the final summary of the backward elimination method included only the variables considered in either the forward selection method or the
stepwise method. Therefore, the final ratio of observations to variables became much higher than 10 to 1.
Even though there is a need to address theoretical considerations and to choose the best method of variables selection, the major purpose of this study was exploratory. Agresti and Finlay (1986) concluded, "In exploratory research, on the other hand, the goal is not to explain relationships among variables so much as it is to find a good set of predictors" (p. 380) Thus, the purpose of this study was to predict the optimized cost of adult education funding in Florida.
According to experts in adult education, the measures of success, for which data were considered most reliable, were graduation rates on the General Education Development (GED) test and completion rate for the Adult High School diploma, as defined by the Florida's Program and Plan for Adult Education (State of Florida, Department of Education, Division of Vocational, Adult, and Community Education, 1989-1993). These success variables were treated as dependent variables in order to determine if changes in adult education funding affected success variables.
The constraint on maximization of outcomes was the funding level of adult education based upon the total expenditures for adult education from all 90 local education agencies for fiscal years 1991-1992 and 1992-1993. The two regression equations were determined using the several
variables stated above. The B coefficients were estimated using multiple regression analysis, and the final optimized formula was determined using both linear and nonlinear programming techniques, as discussed below. The production model (first model) is stated as follows:
Yl = LI (B1)X1 + L2 (Bn)X2 + ... Ln (Bn)Xn.
The above production function was determined from the stepwise regression performed on the first dependent variable
Yl and the 12 independent variables stated previously. This
production function was solved subject to the expenditure
model (second model):
01 > LI (B1)X1 + L2 (B2)Xn + ...Ln (Bn)Xn.
The above constraint was determined by using the coefficients which were calculated using stepwise regression for the variable Y2 and the corresponding 12 independent variables. The variable 01 was the total expenditures for adult education for fiscal year 1992-1993 and the total expenditures for the 5 selected LEAs for fiscal year 1991-1992. This total was then adjusted for possible errors of truncation.
Equation symbols were defined as follows: Yl = The amount of the outcome based upon the performance of a local education agency (passing the GED, receiving the Adult High School Diploma).
01 = The total expenditures for adult education for Florida divided by 1,000. [The division by 1,000 is required to scale the total expenditures in order to prevent truncation errors ($1 = $1000).]
Ln = The unit measure of the effect in a nonlinear function.
Bn = The magnitude of the relationship or the coefficient obtained by using stepwise regression.
Budgetary constraints were based on the funding (expenditures) of each district in Florida. The equation of the funding of budgetary constraints was as follows:
Tn > Xn > Mn.
Tn = The minimum level of the respective effect.
Mn = The maximum level of the respective effect.
Xn = The variable representing the amount of the respective
Since the above equations were generic to the many outcomes of the simulation, a more specific listing of the several outcomes was revealed, and the result of the simultaneous equations was one final production equation. The final equation for the production model was as follows:
Yl: Completion of the GED and Adult High School Diploma. The equation would be as follows:
Yl = Zl Pi +... Zn Ln.
The symbols for the above-stated equations were as follows:
Pn = Vector of student or school factors to the nth local education agency.
Ln = Vector of school factors by the ith local education agency.
Zn = The nonlinear effect of each of the above vectors.
The mathematical model states the outputs of an individual
(nth) LEA equal the profile of the student Pn and the LEA's
contribution to education Ln.
Development of Vectors to Determine Effects and Magnitude of Effects
The variables used in the least-squares equations were
the many data items obtained from Florida's Adult Education
Annual Performance Report, Fiscal Year 1993. These variables
were grouped by their effects of community inputs, school
inputs, student ability inputs, and the endowment position of
the student. Since this study required that nonlinear
programming be used to optimize adult education funding, a
review of the techniques to determine the production model1s
parameters was necessary. The estimations of a model's
parameters were performed using either analytical or
numerical techniques. Much of the research, particularly in
engineering and science, has emphasized numerical techniques.
However, the social sciences have used more analytical
techniques, such as the stepwise regression method. McAfee
(1972) used such stepwise regression techniques in his study-on K through 12 funding. According to Darlington (1990),
The first method is stepwise regression. Standard computer programs for stepwise regression differ from each other more than do standard programs for ordinary regression, so we shall describe the method only in general terms. Both "forward" and "backward" versions exist. (p. 165)
In this study the stepwise regression model was used because of its simplicity. Furthermore, any additional predictions for production function parameters used the stepwise regression method.
The SAS computer program was utilized to determine the
parameters or fitting of the nonlinear relationships of the
production functions. Darlington (1990) stated,
There are some very general methods for fitting curves or curved surfaces to data, as represented, for instance, in SAS PROC NLIN or the STSTAT program NONLIN These are sometimes called nonlinear regression methods However, they are in fact not based on regression methods, so we might better call them general curve-fitting methods. (p. 279)
The estimates of the coefficients of the production function were estimated by using multiple regression analysis. After the production function was determined, the production function was solved with the budgetary constraint; by using mathematical programming. A software program using the SAS statistical package was used to solve simultaneous equations. The results of the simulations are presented in Chapter 4.
CHAPTER 4 PRESENTATION OF THE DATA
As stated previously, the purpose of this study was to develop and analyze a mathematical model to optimize the funding for adult education programs in Florida. The simultaneous solution of linear and nonlinear formulations was attempted to develop the mathematical model. The final mathematical model created by the procedures in this study was formulated using raw data concerning adult education. Because the data used for development of the model were so crucial to its final appearance, an extensive analysis of the data was completed in order to ensure that all statistical assumptions governing the model had been satisfied.
Analysis of Data The SAS statistical program on the University of Florida's main frame was used to analyze the data. The data set was then examined by looking at the listings of these procedures.
The data set included a total of 5 observations for fiscal year 1991-1992. An additional total of 85 observations were noted in the second data set representing fiscal year 1992-1993. As was stated in Chapter 3, the 5
observations in fiscal year 1991-1992 were not duplicated in fiscal year 1992-1993. Therefore, these 5 observations were independent of the 85 observations in the fiscal year of 1992-1993. The total of 90 observations were then available to develop a model from regression analysis. The total list of LEAs used in this study is presented in Appendix B.
Since most researchers adhere to the rule of thumb that no more than 10% of the number of observations for each variable may be missing, the total number of missing data items allowable for this study would approximate nine for the combined observations of fiscal years 1991-1992 and 1992-1993. One of the contributing factors in selecting variables was the presence or absence of data items. However, if the variables were considered important, then, regardless of the "shape" of the data items, these variables were included in the model.
The data base was fairly complete for almost all of the variables. However, some of the local agencies either failed to turn in their report or were delinquent in doing so. As shown in Table 3, for fiscal year 1992-1993, Local Education Agency (LEA) A was missing all items of data for all of the variables except the costs expended for adult education. Because of this omission, the complete records for LEA A for fiscal year 1991-1992 were used in its place. Of the four observations in 1991-1992 (excluding LEA A), LEA D also was void of any data items except for costs data items. Again,
there is no explanation for the absence of data from either
LEA A or LEA D.
Accumulated Missing Items
Total observations in analysis
Observations with missing data:
LEA A (1992-1993)
All data items except costs.
LEA B (1992-1993)
LEA C (1991-1992)
Correctional facilities. Legalized aliens.
Full-time & part-time teachers, counselors, & full-time para-professionals Volunteer teachers
LEA D (1991-1992)
All data items except costs.
LEA E (1991-1992)
Receiving Public Assist. All teaching, counselor, Sc paraprof essionals.
LEA F (1991-1992)
Full-time teachers counselors, para-professionals Volunteer teachers
Total missing items
Other missing data items restricted the researcher's ability to maintain a data base that included all school districts in the study. For example, many of the