|
THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234James A. Kadamus Deputy Commissioner Office for Elementary, Middle, Secondary and Continuing Education Room 875 EBA 518.474.5915 |
TO: |
District Superintendents |
FROM: |
James A. Kadamus |
SUBJECT: |
Regents Proposal on State Aid to School Districts for 2004-05 |
SUMMARY: The Regents State Aid proposal for 2004-05 implements a new, multi-year approach to State and local funding of public schools designed to close the student achievement gap. It proposes a Foundation Formula for the distribution of State Aid that assists school districts with the costs of general education instruction, to be phased in over a seven-year period.
This new approach to State Aid has four basic components:
District’s State Aid = [Foundation Cost X Pupil Need Index X Regional Cost Index] - Expected Local Contribution
The Foundation Cost is the cost of providing general education services in New York schools, measured by determining the instructional costs of districts that are performing well.
The Pupil Needs Index recognizes the added costs of providing extra time and extra help for students to succeed in school. It is measured by the number of students eligible for free and reduced price lunch and students living in geographically sparse areas of the State.
The Regional Cost Index is an adjustment that recognizes regional variations in purchasing power around the State. It is measured based on wages of non-school professionals in each region of the State.
The Expected Local Contribution is an amount school districts are expected to spend as their fair share of the total cost of general education. It is measured by multiplying the district tax base by an expected tax rate adjusted by district income per child. The Expected Local Contribution is not a mandated tax rate, but a way of determining a local share in order to calculate State Aid.
Each of these components of the formula is described in more detail in Attachment A. That attachment also provides information on other components of the proposal including: expense-based aids (Building and Transportation),. aid for pupils with disabilities, regional services aid for the Big 5 districts, aid for career and technical education and categorical aids are not included in the Foundation Formula approach (e.g., Universal Pre-K, BOCES Aid, Bilingual Grants/Limited English Proficient Student Aid, Textbook Aid, Library Materials Aid, and other programs).
In the first year of the seven-year period, Exhibit A shows that an $880 million increase is proposed, with $508 million of this increase for Foundation Aid. Exhibit B shows that when the proposal is fully implemented, it will provide $14.35 billion in Foundation Aid, a $5.98 billion increase over comparable funding in 2003-04. Over time, this flow of aid to high need districts will have a significant impact in closing the student achievement gap.
Exhibit C shows that in 2004-05, the first year of the Regents proposal, that 84 percent of the increase in school aid would go to high need school districts to close the achievement gap.
Exhibits D and E show the share of the overall increase in computerized aids for school districts grouped by Need-Resource Capacity category in the first year of the proposal and with full implementation.
Attachment B is a technical supplement in support of the Regents proposal (see page 15). This includes an analysis of the resource and achievement gap, a selected bibliography, definitions of school district need/resource capacity categories used to describe the need status of districts, a list of high need school districts, a list of aids and grants to be consolidated under the Regents proposal, formula components recommended in the Regents proposal, a description of the regional cost adjustment based on professional salaries, a description of the Regents cost study, a summary of aids and grants proposed, and an analysis of proposed aid changes.
Attachments
Regents School Aid
Proposal for 2004-05
Table of
Contents
Attachment A
Introduction
Regents
Goal
Enact a Foundation Formula to Target Aid
to Educational
Need
Transition
Accountability
What's Included in the Foundation
Formula
Other Components
Expense-based aids
Categorical aid programs
Aid for regional shared services
Programs
maintained separately
Attachment B: Technical
Supplement
The Resource and Achievement Gap
Need/Resource
Capacity Category Definitions
High
Need School Districts
Aids and Grants to be Consolidated
Under the Regents Proposal
Other Aids
Formula
Components
Regional
Cost Adjustment Based on Professional Salaries
Regional Cost Index Counties in Labor Force Regions
Estimating
the Additional Cost of Providing an Adequate Education
Summary
of Aids and Grants in the 2004-05 Regents Proposal
Analysis of Aid Changes Under the 2004-05 Regents
Proposal Total
Computerized Aids
Analysis of Aid Changes Under the 2004-05 Regents
Proposal Total
Computerized Aids without
Transportation, Building and Building
Incentive
Selected Bibliography
Introduction (Attachment
A)
Elementary level.
Middle level.
Regents diplomas.
Minority students
Students with disabilities
These successes are happening all over the State, in poorer districts and wealthier districts, and with all groups of students.
Despite these many successes, a troubling resource and achievement gap persists. Students attending schools that have a high percentage of student poverty and limited local resources have a dual problem. First, they tend to have fewer resources. This is especially true in areas where high regional costs mean that a dollar for education buys fewer goods and services than in less costly areas of the State. Second, students attending such high need school districts consistently achieve at lower levels than students at schools with more affluent and less needy peers. These students are more likely to need extra instructional time, tutoring, and assistance from social service agencies, yet are less likely to receive those services. A review of data on school resources and student achievement will be included in a Technical Supplement to this proposal.
If the move to higher standards is to be successful, we must sustain the momentum of improvement exhibited around the State. We must facilitate success by all students regardless of the school they attend, family background, and educational needs. If we have the will to align our State resources to provide the financial support for all students to be successful, the entire State will reap the benefits in greater productivity and reduced costs for assistance. The State must maintain its focus on education and make sure enough resources go to the children who need them most.
The State's system of funding for education should provide adequate resources through a State and local partnership so that all students have the opportunity to achieve the State’s learning standards, including resources for extra time and help for students.
Enact a Foundation Formula to Target Aid to Educational Need
The Regents recommend a new multi-year approach to State Aid to school districts. It would replace a complex system of many formulas that are the result of years of statutory adjustments, and many of which in fact have not been used in State Aid distributions for the past three years. The Foundation Formula is much simpler. It calculates the cost of educating each student to the State’s learning standards. Then this cost is divided between a State contribution and an expected local contribution.
The Foundation Formula is relatively simple:
District State Aid = [Foundation Cost x Pupil Need x Regional
Cost Index] – Expected Local Contribution
Foundation Cost
The Foundation Cost is the cost of providing the average student with an education that meets State learning standards. It is measured by:
§
Determining the instructional costs of districts that are performing well;Pupil Need
A Pupil Need factor recognizes the added costs of providing extra time and help necessary for high-need students to succeed.
q
Pupil Need is determined by combining two measuresThe proportion of K-6 pupils eligible for free and reduced-price lunches, and§
q
The additional cost of providing extra time and help varies with the concentration of needy pupils within the district.Districts with very low concentrations of needy pupils have relatively few additional demands upon them. These districts would get an additional 50 percent of the basic per-pupil cost for each needy pupil.§
The number of pupils served by the district determines the overall amount of services provided. Because districts must staff and plan to serve all children enrolled in the district, the Regents proposal employs a pupil count that is based on the number of pupils enrolled (Average Daily Membership), rather than the more traditional use of average daily attendance.
Regional Cost
Some school districts are in areas of the State where costs are higher. A regional cost adjustment provides comparable purchasing power around the State. The regional cost adjustment should reflect the actual, regional variations in the costs associated with providing an adequate education rather than the cost of additional services that districts elect to provide.
· This Regional Cost Index assesses the labor market for professions that require Masters a bachelor’s degree for entry-level employment degrees.
· Teachers are not included to make the data independent of school districts’ hiring preferences.
· The result is a measure of economic forces beyond the control of school boards which is used to adjust State Aid to recognize unavoidable, regional variations in the cost of education.
Expected Local Contribution
The expected local contribution is the amount school districts are expected to spend as their fair share of the cost of general education. On average, localities would pay slightly less than half of the overall cost of general education services. Lower wealth communities would pay much less. Higher wealth communities would pay more.
The expected local contribution is not mandatory. The Regents acknowledge that local effort in support of schools is a considerable challenge especially for city school districts which are fiscally dependent on their municipalities. Contributing to this phenomenon are the many costs that cities incur to serve large percentages of their population who are economically disadvantaged. For example, New York City, as both a city and a county, must provide public assistance and Medicaid to its residents. Some districts may find they can provide the services needed to succeed at a lower cost to local taxpayers than is anticipated in this proposal.
The expected local contribution is based on two measures:
q
The district tax base is the total taxable property of the district at full value, as determined by the Office of Real Property Services. In order to mitigate the impact of short-term real estate fluctuations, districts may select the more favorable of either the most recent full value assessment or a two-year average.q
The expected local tax rate is based on a statewide standard rate of $15 per thousand. This standard rate is then adjusted to reflect local ability to pay, as measured by district income per child. The lower the income per child, the lower the expected tax rate. This establishes a reasonable level of taxation.Most states use a relatively low tax rate.
The expected rate cannot be too low or expectations will be diminished in districts already above that rate.
Transition
The proposed Foundation Formula
represents a funding system focused on student achievement. This is proposed
following three years in which Operating Aid has been paid based primarily on
estimated 2000-01 data. As in earlier years, equalization will occur based on
district fiscal capacity and pupil need, but pupil need will be recognized to a
greater extent than previously in order to ensure adequate support for programs
and services that provide students with extra time and help to meet State
learning standards. For these two reasons, changes in funding patterns are
expected to occur between 2003-04 and 2004-05. In order to provide school
districts with time to adjust to the new funding system, the Regents propose a
transition adjustment that limits aid increases and losses for a reasonable,
short-term period. Over time, this cap on increases should be eliminated and the
Foundation Formula allowed to operate. An annual limit on loss is continued in
order to allow districts time to accommodate reductions in State Aid.
Accountability
The Regents propose that accountability focus on school districts
with schools that fail to meet adequate yearly progress goals. These schools are
required to develop a plan that shows how the school is allocating resources to
improve student achievement.
What’s Included in the Foundation
Formula?
The proposed
Foundation Formula provides funding for the general instructional program. It
replaces a number of aids and grants, as shown in Table 1.
Table 1. | |
2003-04 Aids and Grants |
Regents Proposal for 2004-05 |
Computerized Aids | |
Comprehensive Operating Aid | |
Operating Aid | |
Tax Effort Aid | |
Tax Equalization Aid | |
Transition Adjustment/Adj. Factor | |
Academic Support Aid | |
Computer Hardware Aid | |
Early Grade Class Size Reduction |
Foundation Grant (Replaces all aids |
Educationally Related Support Services Aid | |
Extraordinary Needs Aid | |
Full Day Kindergarten Conversion Aid | |
Gifted and Talented Aid | |
Minor Maintenance and Repair Aid | |
Operating Growth Aid | |
Operating Standards Aid Operating Reorganization Incentive Aid | |
Small City Aid | |
Summer School Aid | |
Tax Limitation Aid | |
Teacher Support Aid | |
Other Aids and Grants | |
Categorical Reading Programs | |
CVEEB | |
Fort Drum Aid | |
Improving Pupil Performance Grants | |
Learning Technology Grants | |
Magnet Schools Aid | |
Shared Services Savings Incentive | |
Tuition Adjustment Aid | |
Urban-Suburban Transfer Aid |
Other Components
A number of other costs should be aided in the following manner.
Expense-Based Aids
State Support for School
Construction
The
recommendations concerning Building Aid and other State support for school
construction will help overcome barriers to instructional improvement posed by
inadequate school facilities. Early grade class size reduction, pre-kindergarten
programs and science laboratories are examples of instructional programs that
are dependent on the availability and quality of school space. While capital
improvements often take a period of years to implement, their funding can be
spread across the useful life of buildings, and with favorable interest rates,
can be affordable for districts and the State. The recommendations will help
solve severe over-crowding and improve the capacity of school buildings to
support educational programs that are key to closing the student achievement
gap. Recommendations include:
§
Allow school districts to use the Dormitory Authority of the State of New York to finance and manage school construction projects;In addition to the changes noted above, the Regents recommend reducing local costs for school construction through mandate relief. A provision of State Law, known as the Wicks Law, requires municipalities, including school districts, to employ four separate contractors for school construction projects of $50,000 or more. For all but the largest of projects, a general contractor can effectively manage these separate functions.
The Regents recommend the State encourage the reduction of local costs by exempting school districts from the Wicks Law, thereby allowing a single general contractor for school construction projects in excess of $50,000, rather than four separate contractors as currently required. Although estimates vary, this change is expected to result in considerable savings in building costs for school districts.
Transportation Aid
Consolidate
Transportation Aid with Summer Transportation Aid and continue this as a
separate aid.
Aid for Pupils with Disabilities
In its theoretical form, the Foundation Formula could be constructed to address spending for all instruction, both in general and special education. The Regents propose enacting the formula in its first year focused on general education only. This would provide time over the coming year for discussions with the public about raising achievement of students with disabilities in high need school districts and State Aid goals for special education funding. It would also provide time for needed reforms in general education to take hold. Analysis of data on the achievement of pupils with disabilities shows a strong relationship between special and general education programs: students with disabilities achieve significantly better in schools whose general education students also perform well. Understanding the implications of the Foundation Formula for both general and special education may provide new opportunities for closing the achievement gap of students with disabilities. For 2004-05, changes are proposed to Public Excess Cost Aid to help districts with the excess costs of educating students with disabilities by focusing resources on districts with the greatest educational need. In the second year of the proposal, the Regents will consider incorporating aid for students with disabilities (regular Public Excess Cost Aid) in the Foundation Formula.
Categorical Aid Programs
The Regents recommend that categorical aid
programs for Universal Pre-Kindergarten education and Limited English Proficient
students, as well as Bilingual Education Grants, be maintained separately in the
first year of the new funding system. In the future, when pre-kindergarten programs are universally available, the Regents
will consider incorporating aid for pre-kindergarten students in the Foundation
Formula.
Aid for Regional Shared Services
The State should continue to provide State
Aid for regional shared services separately from the Foundation Formula through
BOCES Aid and Special Services Aid for noncomponent school districts including
the Big Five City School Districts. Programs funded include career and technical
education, information technology and professional development. The Regents
recommend that the State:
Provide comparability between Special Services Aid for shared services for noncomponent school districts, including the Big Five City School Districts, and BOCES Aid for shared services among districts in the rest of the State.
Allow access to BOCES services and provide aid for noncomponent districts that share services with at least one other district and pay an administrative surcharge to BOCES.
Require districts to demonstrate maintenance of local effort and receive approval for each service requested by a BOCES District Superintendent appointed to coordinate such requests. The coordinating BOCES should be a BOCES with a Regional Information Center in a region adjacent to the city.
Programs Maintained Separately
A number of aid
programs should be maintained separately. These are for programs that for a
number of reasons are separate from the regular K-12 instructional program.
These include the following aids:
Other Aids and Grants |
BOCES Aid |
Building Aid |
Grants for Overcrowded Schools Building Reorganization Incentive Aid |
Limited English Proficiency Aid |
Private Excess Cost Aid |
Public Excess Cost Aid |
Textbook Aid |
Library Materials Aid |
Computer Software Aid |
Special Services – Career Education |
Special Services – Computer Administration |
Universal Pre-Kindergarten Aid |
Bilingual Education Grants |
BOCES Spec Act, <8,Contract Aid |
Transportation Aid |
Bus Driver Safety Training Grants |
Chargebacks |
Comptroller Audits |
Division for Youth Transportation |
Education of OMH/OMR |
Education of Homeless Youth |
Employment Preparation Education Aid |
Incarcerated Youth |
Native American Building Aid |
Prior Year Adjustments |
Roosevelt |
Special Act Districts Aid |
Teacher Centers |
Teacher-Mentor Intern |
Teachers of Tomorrow |
Technical Supplement (Attachment B)
Resource and Achievement Gap
The relationship between poverty and educational achievement is well established.(2) As student poverty in a school increases, academic performance tends to decline. This is illustrated in Figure 1 in which all New York State school districts are grouped by need-resource capacity category.(3) The figure shows free lunch eligibility and grade 4 English language arts performance for each category. New York City and the large cities (Rochester, Buffalo, Syracuse and Yonkers) have the highest concentrations of children in poverty and among the worst achievement levels. As poverty declines, achievement improves. For this reason, student poverty is considered a legitimate and stable substitute measure for educational need.
These relationships are further illustrated by examining contrasts in student performance, student need and school resources. Table 2 compares the public schools in New York City with those districts that have the highest level of local resources and the lowest levels of student need, known as the low need school districts. A detailed definition of need-resource capacity categories can be found in this Technical Supplement (following the bibliography).
Table 2 | ||
Measure |
New York City School District |
Low Need School Districts |
Proficiency in elementary-level English language arts |
46 |
86 |
Proficiency in middle-level mathematics |
30 |
78 |
Percent of general education students entering ninth grade in 1998 meeting the English graduation requirement |
79 |
98 |
Percent of students earning Regents diplomas |
31 |
73 |
Percent of students eligible for free lunch |
75 |
3 |
Percent of teachers lacking certification in mathematics |
33 |
4 |
In many school districts poverty coexists with another educational need factor, the incidence of limited English proficient (LEP) students. More English proficient students than LEP students achieved the standards in elementary level English language arts by scoring at Level 3 or above (Figure 2). Examining achieve-ment of LEP versus Not LEP students in Regents-level math-ematics (Figure 3) shows that more than a quarteralmost one-sixth of LEP students who met the standard in 2002 scored between 55 and 64.
Examining the number and percentage of limited English proficient students by location reveals an educational need that is particularly concentrated in urban areas (see Table 3). More than 70 percent of New York State’s LEP students attend the New York City school district, where LEP students comprise 13.7 percent of the student body. In urban and suburban high need school districts and the Large City School Districts, LEP students make up approximately 7 and 8 percent of the student body, respectively.
Table 3 | ||
Sector/Location |
Students | |
Number |
Percent | |
High N/RC Districts | ||
New York City |
142,033 |
13.7% |
Large City Districts |
10,052 |
8.0 |
Urban-Suburban |
14,913 |
6.9 |
Rural |
1,286 |
0.7 |
Average N/RC Districts |
16,511 |
1.9 |
Low N/RC Districts |
8,810 |
2.3 |
Total Public |
193,605 |
6.8% |
Note: Includes students who score at or below the 40th percentile on an English language assessment instrument approved by the Commissioner of Education. |
The relationship
between poverty and academic achievement is pervasive. It has been documented by
numerous studies over four decades.(5)
This relationship is a critical policy concern because it affects large numbers
of students. Figure 4 shows that a full 55 percent (approximately 1.6 million
students) of the State’s students are enrolled in high need school
districts.(6)
While not all of these students come from poverty backgrounds, many of them do,
and numerous research studies have illustrated the negative impact of the
concentration of student poverty on the achievement of all students, regardless
of their individual poverty status.(7)
These numbers
suggest that, in order to meet higher learning standards, New York State must be
concerned about: what affects the achievement of students in schools with
concentrations of student poverty; the resources that high need school districts
have require to support their educational program; and the effectiveness with
which school districts use their resources. It suggests that the successful
education of so large a group will have a significant impact on the economic
vitality of the State by producing workers who can function in a competitive,
international market and by reducing the costs of social services and criminal
justice.
That poverty affects student achievement is
well known. What is less well known are the successes of schools in
educating students from poverty backgrounds to high standards. While the
debate on “does money matter?” still exists,(8)
it is now being recast by some as “making money matter” (emphasis
added).(9)
Money matters and how it is used makes a difference as well. Using New
York State school data, we examined the relationship between school district
spending and student achievement as measured by grade 4 English Language Arts
test performance (see Figure 5). Spending data are adjusted in two
ways. First, dollars spent are adjusted by the Regents Regional Cost Index to
reflect comparable purchasing power from one region of the State to another.
Second, spending per pupil is further adjusted by providing an additional
weighting for pupils from poverty back-grounds to reflect the additional
services that such pupils require. The resulting cost and need-adjusted
expenditures per pupil show a trend: the more the school district spends, the
greater the pupil achievement.
Figure 5 shows that a distinct relationship exists between spending, student risk, and academic performance. That is, the emphasis on need and cost is supported by data from New York schools.(10)
Examining the relationship between school spending and student poverty is also illuminating. Poverty is often used as a proxy or substitute measure for educational need. This is because of the high negative correlation between poverty and student achievement and because of the desire to use a measure that is not affected by the varying academic successes of school districts. As a result, poverty rather than achievement may be used as a proxy for educational need in aid formulas, because of the interest in providing incentives for school districts to improve student achievement.
Figure 6 shows that as educational need decreases, need and cost adjusted instructional expenditures per pupil increase. Need and academic performance are virtual mirror images of each other.
While the previous graphs looked at educational risk and the demand placed on school districts, the following charts examine school district fiscal capacity. Fiscal capacity refers to the ability of school districts to raise revenues locally. It is often assessed by a measure that represents an equal mix of property wealth per pupil and income per pupil in the district, known as the Combined Wealth Ratio.(11) The ability of school districts to pay for education varies considerably around the State. Since about half of school revenue comes from local sources, these capacity differences can amount to big differences in educational programs available to students. Figure 7 shows that the balance between fiscal capacity as assessed by property value per pupil versus income per pupil varies as well. Income wealth per pupil exceeds property wealth per pupil in the New York City School District while the opposite is true for high need rural school districts, and average and low need school districts.
We examined revenues raised and tax rates for different groups of school districts. Figure 8 shows the average dollars raised per pupil for each category of school district (tax revenue per pupil displayed by the bars) and tax revenue per $1,000 of actual property value (expressed as tax rate revenue and shown with the line). Low need districts collect more local revenue per pupil while taxing at a comparable rate to the Big Four districts. Overall, the rural high need districts have low tax rates and some of the lowest tax revenues per pupil.
Further analysis of school district local effort shows that districts with higher student poverty and limited fiscal capacity are more likely to have a local effort problem.(12) Contributing to this phenomenon are the many costs that cities incur to serve large percentages of their population who are economically disadvantaged. For example, New York City, as both a city and a county, must provide public assistance and Medicaid to its residents. From those findings, the Regents acknowledge local effort as a significant element in closing the achievement gap.
A major policy focus of the Regents is strengthening teaching. Recent research has documented the considerable impact of teachers on student achievement.(13) In fact, the positive effect of having a quality teacher for three years in a row was equal to the decline in achievement students suffered from economic disadvantage. Examination of New York State data reveals the following. Schools with the largest percentage of minority students have the largest percentage of teachers without appropriate certification (Figure 9). Looking at the percent of uncertified teachers by need-resource capacity category shows that more than one in four teachers teach without appropriate certification in New York City (Figure 10). In school districts outside the Big Five, the rate is one in 25. While having a certificate in the subject area one teaches may not explain why some teachers have a greater impact on student achievement than others, the lack of appropriate certification is found in districts where overall student achievement is among the lowest.
Figure 11 shows that
teacher turnover(14)
has increased in all parts of the State, further contributing to the challenge
of closing the achievement gap. This phenomenon can be attributed in large part
to an aging teacher workforce. Teacher turnover is at the highest levels in New
York City.
We examined teacher
salaries by applying a cost index so as to make salaries comparable a-cross
regions of the State. Figure 12 shows that cost-adjusted teacher salaries are
low in New York City compared to the rest of the State.
Quality career and technical education (CTE) programs provide students with practical, hands-on learning experiences leading to a high school diploma. Often such programs provide practical, hands-on learning experiences that create an alternative way of developing high level reading and computational skills. Approved CTE programs maintain high academic standards, particularly in reading and computational skills, which hold promise for many students who were in the past lost in the traditional program.(15)
Existing aid forumulas result in a higher level of reimbursement to BOCES programs than to those operated by the Big Five city school districts. Conversely, the local share that the Big Five city school districts must exert to support CTE programs is greater (see Figure 13). With the considerable need for such programs in the Big Five, a similar level of reimbursement is important to provide a fiscal incentive for these programs.
In New York State, 43
percent of the pupils enrolled in special education are in the large city school
districts where support services in general education are limited, greater
numbers of teachers are uncertified, and the lack of resources makes it more
difficult to provide quality instruction and early intervention. This means a
greater likelihood that these students will have less access to a rigorous
general education curriculum, which results in lower performance on State
assessments and less likelihood of meeting graduation requirements. As a result,
their ability to access postsecondary education and employment may be affected.
The use of special education classes that are separate from general education
programs further limits the academic options for students with disabilities.
Figure 14 shows that high need school districts use the special class model to
educate students with disabilities considerably more often than other
districts.
Figure 15 shows the average age(16) of school buildings by need-resource capacity category of school districts. The chart shows that the average age of school buildings in our largest cities is more than 55 years and in urban and suburban high need school districts it is about 48 years.
Legislative changes enacted in the late 1990’s provided a variety of incentives for school construction. These changes include the following:
A regional cost index (1997) was enacted (1997) to meet the school construction needs in the cities;
For projects approved by the voters on or after July 1, 1998, a 10 percent increase in the Building Aid formula was enacted (1998) on top of existing provisions which allowed a choice of the best aid ratio (State share) going back to 1981-82; (1998); and
For projects approved by the voters on or after July 1, 2000,
the protection afforded by the aid ratio choice was reduced (2000) by giving
districts the choice of i) the current year Building Aid ratio, or ii) the best
aid ratio from the 1981-82 through 1999-2000 aid years less 10 percent.
Figure 16 shows the impact of aid changes on school construction by school district need-resource capacity category during the period 1998 to 2001. School construction (as measured by the average annual percent of building replacement value) was greatest in the high need/resource capacity rural school districts, followed by construction in average and low need/resource capacity districts. These State Aid incentives had the least impact on construction in the Big Five cities, and high need/resource capacity urban and suburban school districts. In the case of New York’s five largest cities, school district fiscal dependence on their municipalities may have limited a positive response to these incentives.
Figure 16 also shows the leveraging effect of these State Aid incentives; that is, the additional capital construction that the same local effort purchases. This potential for increased construction with the same local effort was greatest for the high need-resource capacity rural districts, which responded with a high level of school construction. Despite relatively large increases in their ability to leverage local effort, the urban school districts did not respond with a level of school construction comparable to that of high need rural, average need or low need school districts.
The ability of school districts to meet student needs is affected by the cost of doing business in the region in which the district is located. Table 4 shows that costs are about 50 percent higher in the New York City-Long Island region than in the North Country. New York State legislative commissions and blue-ribbon panels have noted this phenomenon(17) and recommended that State Aid be adjusted to compensate for these cost differences. The State Aid dollar should purchase the same amount of goods and services around the State.(18)
Table 4 | ||
Labor Force Region |
Index Value |
Purchasing Power of $1,000 by Region |
Capital Distict |
1.168 |
$856 |
Southern Tier |
1.0612 |
$942 |
Western New York |
1.0801 |
$925 |
Hudson Valley |
1.35960 |
$735 |
Long Island/NYC |
1.4967 |
$668 |
Finger Lakes |
1.181 |
$847 |
Central New York |
1.1323 |
$883 |
Mohawk Valley |
1.016 |
$984 |
North Country |
1.000 |
$1,000 |
In conclusion, the additional needs of schools educating concentrations of students from poverty backgrounds are well supported. Yet school districts with concentrated poverty tend to spend less. They have limited capacity to raise revenues locally, raise fewer local revenues per pupil, lack certified teachers, have greater teacher turnover, and, in the case of New York City, have lower cost-adjusted teacher salaries. Aid formulas are less beneficial for the State’s largest cities in supporting career and technical education as an alternative path to a high school diploma and in not recognizing regional cost differences in aid provided for school operation.
NEED/RESOURCE CAPACITY CATEGORY DEFINITIONS
The need/resource capacity index, a measure of a district's
ability to meet the needs of its students with local resources, is the ratio of
the estimated poverty percentage(19) (expressed in standard score form) to the Combined
Wealth Ratio(20)
(expressed in standard score form). A district with both estimated poverty and
Combined Wealth Ratio equal to the State average would have a need/resource
capacity index of 1.0. Need/Resource Capacity (N/RC) categories are determined
from this index using the definitions in the table below.
Need/Resource |
Definition |
High N/RC Districts |
|
New York City |
New York City |
Large City Districts |
Buffalo, Rochester, Syracuse, Yonkers |
Urban-Suburban |
All districts at or above the 70th percentile (1.18855) which meet one
of the following conditions: 1) at least 100 students per square mile; or
|
Rural |
All districts at or above the 70th percentile (1.18855) which meet one of two conditions: 1) fewer than 50 students per square mile; or 2) fewer than 100 students per square mile and an enrollment of less than 2,500. |
Average N/RC Districts |
All districts between the 20th (0.7706693) and 70th (1.18855) percentile on the index. |
Low N/RC Districts |
All districts below the 20th percentile (0.7706693) on the index. |
High Need School Districts
Used to Assess the Impact of
the
Regents 2004-05 Proposal on State Aid to School Districts
Albany County
Aids and Grants to be Consolidated Under the Regents
Proposal
on State Aid to School Districts
for School Year
2004-05
Aids and Grants Replaced by the | |
2003-04 Aids and Grants |
Regents Proposal for 2004-05 |
Computerized Aids | |
Comprehensive Operating Aid | |
Operating Aid | |
Tax Effort Aid | |
Tax Equalization Aid | |
Transition Adjustment/Adj. Factor | |
Academic Support Aid | |
Computer Hardware Aid |
Grant (Replaces all aids to the left) |
Early Grade Class Size Reduction | |
Educationally Related Support Services Aid | |
Extraordinary Needs Aid | |
Full Day Kindergarten Conversion Aid | |
Gifted and Talented Aid | |
Minor Maintenance and Repair Aid | |
Operating Growth Aid | |
Operating Standards Aid | |
Operating Reorganization Incentive Aid | |
Small City Aid | |
Summer School Aid | |
Tax Limitation Aid | |
Teacher Support Aid | |
Other Aids and Grants | |
Categorical Reading Programs | |
CVEEB | |
Fort Drum Aid | |
Improving Pupil Performance Grants | |
Learning Technology Grants | |
Magnet Schools Aid | |
Shared Services Savings Incentive | |
Tuition Adjustment Aid | |
Urban-Suburban Transfer Aid |
Other Aids
Other Aids and Grants |
BOCES Aid |
Building Aid |
Grants for Overcrowded Schools |
Building Reorganization Incentive Aid |
Limited English Proficiency Aid |
Private Excess Cost Aid |
Public Excess Cost Aid |
Textbook Aid |
Library Materials Aid |
Computer Software Aid |
Special Services – Career Education |
Special Services – Computer Administration |
Universal Pre-Kindergarten Aid |
Bilingual Education Grants |
BOCES Spec Act, <8,Contract Aid |
Transportation Aid |
Bus Driver Safety Training Grants |
Chargebacks |
Comptroller Audits |
Division for Youth Transportation |
Education of OMH/OMR |
Education of Homeless Youth |
Employment Preparation Education Aid |
Incarcerated Youth |
Native American Building Aid |
Prior Year Adjustments |
Roosevelt |
Special Act Districts Aid |
Teacher Centers |
Teacher-Mentor Intern |
Teachers of Tomorrow |
2004-05 Regents Proposal
Formula
Components
Foundation
Aid
Foundation: Foundation Operating Aid is the
greater of $500 or Formula Foundation Aid multiplied by Selected Total Aidable
Pupil Units (TAPU). The Foundation Aid is the product of $4,504, the Regional
Cost Index (see explanation following) and a Pupil Need Index, less the Expected
Local Contribution. The Pupil Needs Index, which ranges from 1.0 to 2.0, is the
sum of 1.0 plus the product of the Extraordinary Needs percent (changed to
exclude a Limited English Proficiency count) multiplied by the concentration
factor. The concentration factor (maximum of 1.0) is 0.5 + (0.5 x [(EN percent -
10 percent)/70 percent]). The Expected Local Contribution is the product of
0.015 multiplied by the Alternate Pupil Wealth Ratio multiplied by the Selected
Actual Value (AV) per 2002-03 TWPU. Selected AV is the lesser of the 2001 AV or
the average of 2000 AV and 2001 AV. Selected TAPU, Total Wealth Pupil Units
(TWPU), and TAPU for Expense have been changed to be based on average daily
membership (instead of average daily attendance), eliminate the 0.25 additional
weightings for Pupils with Special Educational Needs and secondary pupils and
continue the 0.12 weighting for summer school pupils (in TAPU). Aid for New York
City is on a citywide basis.
The following aids and grants are eliminated, as are several grants and aids that do not appear on the computerized aid estimates, including aid for CVEEBs, Learning Technology Grants, the Shared Services Savings Incentive, Tuition Adjustment Aid and Urban-Suburban Transfer Aid:
Comprehensive Operating
Operating Aid
Tax Effort
Tax
Equalization
Tax Limitation
Gifted & Talented
Minor Maintenance and
Repair
Operating Standards
Extraordinary Needs
Summer School
Early
Grade Class Size Reduction
Educationally Related Support Services
Computer
Hardware
Operating Growth
Operating Reorganization Incentive
Full Day
Kindergarten Conversion
Teacher Support
Academic Support
Small
Cities
Improving Pupil Performance
Categorical Reading
Magnet
Schools
Fort Drum
Transition Adjustment: The base includes the
2003-04 aids listed above which appear in the computerized aid estimates. For
those districts for whom the new formula is less beneficial, districts are
guaranteed between 85 percent and 95 percent of the 2003-04 consolidated base
aids. The save-harmless percent is: 0.85 + (0.10 x [(Need/Resource Index -
0.002)/(1.500 - 0.002)]). The Need/Resource Index is the district’s
Extraordinary Needs Ratio (i.e., district Extraordinary Needs percent divided by
the State average of 50.4 percent) divided by its CWR. District Foundation Aid
is capped at a need-adjusted 5 percent over 2003-04 aids. The cap is: 0.05 x
(Need/Resource Index, but not less than 1.0) with a minimum of 0.05 and a
maximum of 0.15.
Support for Students with Disabilities
Excess Cost - Public: A district’s 2002-03 Approved
Operating Expense/TAPU for Expense is limited to a $2,000 to $8,800 range. The
aid equals the allowed expense times the Aid Ratio (1 - (.51 * CWR), with a .25
minimum). Pupils are aided by district of attendance. A 1.30 weighting (down
from 1.65) is provided for pupils who require special services or programs for
60 percent or more of the school day consistent with an Individualized Education
Program (IEP). High Cost expense must exceed the lesser of $10,000 or four times
district AOE/TAPU for Expense. Declassification Aid is included based on 50
percent of the basic Public Excess Cost Aid per pupil. No district receives less
than 95 percent of its 2003-04 aid per pupil however this cannot exceed 150
percent of formula aid. Excess cost aid for students in integrated settings is
the product of excess cost aid per pupil multiplied by 70 percent (up from 50
percent) of the attendance of pupils who receive special education services or
programs by qualified personnel, consistent with an IEP, for 60 percent or more
of the school day in a general education classroom with non-disabled
students.
Excess Cost - Private: Aid is for public school students attending private schools for students with disabilities. Net tuition expense is multiplied by the Aid Ratio (1 - (.15 * CWR), with a .5 minimum).
BOCES/Career and Technical Education
BOCES:
BOCES Aid is included for administrative, shared services, rental and capital
expenses. Save-harmless is continued. Approved expense for BOCES Administrative
and Shared Services Aids is based on a salary limit of $30,000. Aid is based on
approved 2003-04 administrative and service expenses and the higher of the
millage ratio or the Current AV/2002-03 TWPU Aid Ratio: (1 - (.51 * Pupil Wealth
Ratio)) with a .36 minimum and .90 maximum. The millage ratio factor remains 8
mills. Rent and Capital Aids are based on 2004-05 expenses multiplied by the
Current AV/2002-03 TWPU Aid Ratio with a .00 minimum and a .90 maximum. Payable
aid is the sum of these aids.
Special Services Computer Administration: Computer Administration Aid equals the Current AV/2002-03 TWPU Aid Ratio (1 - (.51 * Pupil Wealth Ratio)) with a .30 minimum multiplied by approved expenses not to exceed the maximum of $62.30 multiplied by the Fall 2003 public school enrollment with half-day kindergarten weighted at 1.0.
Special Services Career Education: Career Education Aid equals the Current AV/2002-03 TWPU Aid Ratio (1 - (.51 * Pupil Wealth Ratio)) with a .36 minimum multiplied by $3,720, multiplied by the 2003-04 Career Education pupils including the pupils in business and marketing sequences weighted at 0.16.
Instructional Materials Aids
Textbook: Aid is based on
2003-04 approved textbook expenses up to the product of $57.30 multiplied by the
2003-04 resident public and nonpublic enrollment.
Computer Software: Aid is based on 2003-04 approved computer software expenses up to the product of $14.98 multiplied by the 2003-04 public and nonpublic enrollment.
Library Materials: Aid is based on 2003-04 approved library materials expenses up to the product of $6.00 multiplied by the 2003-04 public and nonpublic enrollment.
Expensed-Based Aids
Building: Aid is equal to the product
of the estimated approved building expenses multiplied by the highest of the
1981-82 through the 2001-02 AV/RWADA Aid Ratios or the Current AV/TWPU Aid
Ratio. For projects approved by voters on or after July 1, 2000, expenses are
multiplied by the higher of the Building Aid Ratio used for 1999-00 aid less .10
or the Current AV/TWPU Aid Ratio. Up to 10 percent of additional building aid is
provided for projects approved by voters on or after July 1, 1998. Building
expenses include certain capital outlay expenses, lease expenses, and an assumed
debt service payment based on the useful life of the project and an average
interest rate. Aid is not estimated for those prospective and deferred projects
that had not fully met all eligibility requirements as of the November
15th database.
Building Reorganization Incentive: Building Reorganization Incentive Aid on capital outlay, lease and debt service is subjected to the same requirements as regular Building Aid. Aid is provided for reorganization projects which have been approved by voters within five years of district consolidation and where the project is contained in the five year capital reorganization plan.
Transportation: Aid is based upon estimated approved transportation operating expense plus capital expenses as reported to the Commissioner by November 15, 2003 (except in cases of emergency) multiplied by the selected Transportation Aid Ratio with a .9 maximum and a .065 minimum. The selected Aid Ratio is the highest of 1.263 multiplied by the State Sharing Ratio or 1.01 - (.46 * Pupil Wealth Ratio) or 1.01 – (.46 * Enrollment Wealth Ratio), plus a sparsity adjustment. The sparsity adjustment is the positive result of 25 minus the district’s 2002-03 enrollment per square mile, divided by 58. The State Sharing Ratio is the greater of: 1.33 – (1.085 * Combined Wealth Ratio) or .915 – (0.56 * Combined Wealth Ratio) or 0.53 – (0.238 * Combined Wealth Ratio), with a maximum of 1.00.
Summer School Transportation: Transportation Aid for summer school programs is based on estimated approved transportation operating expense plus capital expenses as reported to the Commissioner by November 15, 2003 (except in cases of emergency) multiplied by the selected Transportation Aid Ratio with a .9 maximum and a .065 minimum. Aid is no longer prorated to remain within a $5.0 million appropriation. This proposal combines summer school and regular transportation aid. Aid is shown separately in a subsequent table for the purpose of comparison to the base year.
Other State Aids
Grants for Overcrowded
Schools: A $31 million grant is proposed for New York City.
Limited English Proficiency: Aid is based on the 2003-04 LEP pupils multiplied by Foundation Operating Aid per pupil multiplied by 0.131.
Universal Pre-Kindergarten: The grant per pupil for unserved four-year olds is based on $260 plus the product of $4,000 multiplied by an adjusted State Sharing Ratio. For those districts that applied for a grant in 2003-04, the grant per pupil is save-harmlessed to the 2000-01 level. New York City's unserved count is phased-in at 66 percent; rest of State pupils are phased-in at the product of the unserved four-year olds multiplied by the October 2002 free and reduced price lunch percent. If the resulting count is at least 19.0, it is multiplied by 0.6320 to prorate the State total to $215 million.
Regional Cost
Adjustment
Based on Professional Salaries
A regional cost index was generated using an approach first developed by education finance researchers in the state of Oregon. Their method recognized that school districts are often the dominant purchasers of college-educated labor in a community. As such, they exercise unusual market influence over the price they pay for such services – a phenomenon that may distort the usual "free-market" model. For this reason, teacher salaries were specifically excluded from the construction of the index, and selected professional salaries used as a proxy for the purpose of determining regional cost differentials.
The index includes 63 titles for which employment at the entry level typically requires a bachelor’s degree, and excludes teachers and categories that tend to be restricted to federal and state government. The wage data are provided by the Bureau of Labor Statistics and are drawn from the 2001 Occupational Employment Statistics (OES) Survey. The OES survey is an establishment survey and according to U.S. Department of Labor analysts, "wages and earnings tend to be more accurately reported in establishment surveys as they are based upon administrative records rather than recall by respondents."(21) Additionally, the survey is administered on a three-year cycle where each year one third of the establishments are surveyed and wage data are aggregated using a technique known as wage updating. Thus, the approximations of wages become increasingly accurate and are most precise in the third year. The RCI calculations are based on the third and most accurate data-year in the cycle. The triennial nature of the data means that the RCI need only be updated in those years in which the most accurate data in the cycle are available.(22)
Method of Calculation
The index was calculated as the weighted median annual wage for a given labor force region divided by the weighted median annual wage for New York State ($65,189). The index was truncated to three decimal places then divided by the North Country value of .731. Index values range from 1.000 for the North Country to 1.496 for the Long Island/New York City Region. The accompanying table lists the counties included in each labor force region. The weighted median wage for New York State and for each labor force region was calculated as follows:
Weighted Median Hourly Wage
= The sum of: (Title Weight * Median Annual Wage) for all 63 titles making up the index.A separate index was created for each labor force region based on a subset of 46 of the 63 titles. These 46 occupations represent those titles for which there were no missing data in any of the labor force regions. This index was then used to estimate the median annual wage of titles with missing data in any given labor force region. This was done by multiplying the statewide median annual wage for the title with missing data by the 46-title index for the specific labor force region for which the salary data was missing.
For the purpose of index construction, the New York City and Long Island labor force regions were treated as a single labor force region. The New York City/Long Island weighted median wage was calculated as follows:
NYC/LI Weighted Median Wage
= The sum of (Title Weight * NYC/LI Median Annual Wage) for all 63
titles making up the index
1. Title Weight =
same as above.
2, NYC/LI Median Annual Wage =
for each title:
[(# of emp LI * LI median annual wage)+(# of emp NYC * NYC
median annual wage)]
(# of employees in LI + # of employees in
NYC)
Regional Cost
Index
Counties in Labor Force Regions
Capital
District
Albany
Columbia
Greene
Rensselaer
Saratoga
Schenectady
Warren
Washington
Central
New York
Cayuga
Cortland
Onondaga
Oswego
Finger
Lakes
Genesee
Livingston
Monroe
Ontario
Orleans
Seneca
Wayne
Wyoming
Yates
Hudson
Valley
Dutchess
Orange
Putnam
Rockland
Sullivan
Ulster
Westchester
Estimating the
Additional Cost of Providing an Adequate Education
One of the traditional principles in school finance which has
guided Regents Proposal development in past years has been a wealth and need
equalization principle. This principle was designed to drive greater amounts of
aid per pupil to school districts with limited fiscal capacity and high
concentrations of pupils in need. In recent years, however, the focus of school
finance, particularly in New York State, has begun to shift from equity to the
provision of an adequate education.(23)
By the term adequate education is meant the greater equalization of academic
outcomes (not resource inputs) so that all children are provided the opportunity
to receive an education, which will subsequently allow them to lead meaningful
and productive adult lives.
Purpose
The
purpose of this report is to describe the methodology that was used to estimate
the likely additional expenditures needed by districts with lower academic
performance to achieve educational outcomes that demonstrate that an adequate
education is being provided.
Methodology
Three General Approaches.
The literature identifies three basic empirical methods for identifying the cost
of providing an adequate education.(24)
These methods include:
1) Econometric analyses that use sophisticated statistical techniques to estimate the resource costs associated with different levels of school district performance.
Other strategies are designed to determine the instructional and other costs associated with districts that have already achieved acceptable or adequate performance levels. These approaches are typically of two types:
2) Expenditure per pupil analyses use strategies based upon the gross instructional (and related) expenses of school districts whose achievement meets accepted levels of performance and
3) Professional judgement models employ strategies in which the key instructional components needed to achieve a desired achievement standard are identified by panels of experts, and then costed out. This latter method relies heavily upon the use of professional judgment as to what practices or resources are needed in order to achieve a desired level of academic success and is often referred to as the professional judgement model.
The Econometric Approach: Econometric approaches designed to estimate the cost of achieving a specified academic performance standard are complex, and require the use of two-stage least squares estimation methods. Ultimately, researchers estimate the direct effects or impacts of district characteristics, enrollment characteristics, wealth characteristics, and desired performance requirements on cost per pupil.
Once researchers have estimated these effects statististically, it is possible to insert the actual values of these variables for a given district into a prediction equation – while setting the performance level variable at a desired value – in order to estimate overall cost per pupil. The bottom line is this: when one statistically controls for district-level size and wealth characteristics, the higher the performance expected in the model, the higher the projected costs.
Unfortunately, the results of these more complex correlational
approaches lack transparency, being very difficult to explain to lay people. As
Guthrie and Rothstein have noted, "…when courts demand or legislatures determine
that an adequate education be funded, they will require a calculation of this
adequacy that seems intuitively reasonable, that is understandable to reasonably
well-educated policymakers, and that can be explained to constituents."(25) The comments of both Guthrie and Rothstein make clear
their view that such an "ease-of-understanding" standard is not likely to be met
by some of these more complex statistical approaches. In addition, many of the
variables incorporated in these regression models are not particularly intuitive
and do not relate specifically to instructional cost components; consequently,
the results are often viewed as a "black box". That is, while total costs at the
school district level can be estimated by such econometric studies, how these
total costs should be distributed by the state to the district or within the
district to its various school buildings is beyond the scope of such
studies.
The Academic Success Approach: Empirical estimates of the
cost of an adequate education typically begin by investigating districts that
are already achieving a desired state of academic performance. The most
straightforward application of the empirical method starts with an examination
of the spending patterns among all such districts to determine the average
expenditure per pupil of the successfully performing districts. Since districts
that perform at high levels often enjoy a very substantial wealth base, and
therefore also spend at very high per pupils levels, concerns about technical
efficiency are characteristic of this method.
A traditional response to the efficiency concern is to constrain the selection of districts to be analyzed. For example, the districts for which the average expenditure per pupil of successful school districts that would be established could be restricted to the lowest spending 50 percent of such adequately performing districts.
A common variation of this approach is to empirically identify the staffing patterns of academically successful school districts. For example, pupil-teacher ratios, class sizes, number of guidance counselors are some of the patterns that could be examined in a study of this type. Based upon the judgements of SED analysts, normatively appropriate staffing patterns could then be identified and their associated costs calculated. As with the expenditure per pupil approach, it is possible to introduce efficiency into the calculation of cost by limiting the districts analyzed to those who appear to achieve adequate levels of performance at modest cost.
The Professional Judgement Approach: An important variant or extension of the Academic Success Approach relies more heavily on the use of consensus methods and professional judgment to identify the key instructional components to be costed out. Professional judgement methods consist of developing a consensus among professionals as to the appropriate staffing patterns and instructional components needed to achieve academic success. These components are then costed out based upon empirical data in order to estimate overall district-level costs. While this approach benefits politically from significant "buy-in" of the various expert-groups, such a method can be very time-consuming and would require at least one to two years to implement.
Three Critical Methodological Questions
For this study, each of the approaches described above was evaluated. However, in developing an estimate of the expenditures needed to ensure that all districts can provide the opportunity for an adequate education to all students, it was believed that the approach most transparent to the general public would be one based upon demonstrated academic success. The associated expenditures per pupil identified in these successful districts could be modified to reflect regional cost and the educational need of pupils. In short, the study would estimate the expenditures per pupil needed to achieve a specified academic outcome based on the spending patterns of districts actually achieving the specified level of academic performance.
As the methodology was developed, researchers answered three questions involving very specific operational definitions of major concepts. The questions were:
How should academic performance be measured?
How should pupil
need be addressed? and,
Should there be a regional cost
adjustment?
Measurement of Academic Performance
A critical methodological issue addressed by the study concerned the measurement of academic performance. New York State is presently implementing a series of tests designed to measure academic performance at various grade levels. Examples of such examinations include:
·
English Language Arts and Mathematics (fourth grade)Fourth Grade Tests. Fourth grade test results can be grouped into four categories or performance levels. These performance categories are:
·
Level 1---Does not meet the standards;High School Regents Examinations. Several important issues had to be addressed in using the results of high school examinations as components in the operational definition of an adequate education. First, results on Regents exams are given as a numerical score only. Scores are not automatically translated into levels of performance. Based on a review of the School District Report Card and the Annual Report to the Governor and Legislature on the Educational Status of the State’s Schools the classification system shown below for high school Regents exams was developed by this study. The researchers concluded that these classifications best approximated the four-level scoring system that exists for elementary and middle school students.
The classifications are:
·
Level 1 = a score of 0 to 54Data on Regents High School examinations were collected for five tests. The tests were:
·
Mathematics A;A potential problem with using single-year test results, of course, is that academic outcomes in any one-year may be atypical and more reflective of a one-time phenomena rather than a typical example of academic outcomes over a multi-year period. This traditional critique was addressed for this study by using a three-year average of test results. Test results used in the study were from the 1999-00, 2000-01 and 2001-02 school years.
Ultimately, to make a cost estimate, adequate education needs to be defined in quantitative terms. In establishing its definition, the study had two basic choices. It could use either test scores or the percent of test takers achieving a specified educational result. Use of either measure would be valid. However, since the Court of Appeals in the Campaign for Fiscal Equity court ruling indicated that every child should be provided with an adequate education, it would appear that a threshold measure which captures the percent of test takers achieving a specified standard would be the most appropriate measure to use.
Upon reaching this decision, the study addressed three questions:
1. What level of achievement should be reached?
2. What
percent of students should attain the specified outcome? And,
3. What tests
should be used?
If students in a district are receiving an adequate education, it would seem that the vast majority of its students should be capable of achieving the Regents standards. This means, on whatever tests one uses for defining academic outcomes, the vast preponderance of students should be scoring at the equivalent of level 3 or level 4. So for this study, it was believed that if a district had on average 80 percent of its students scoring at level 3 or higher on the specified tests, the district would be considered as providing an adequate education.
Finally, the study had to determine which specific examinations would be used in developing the cost estimate. It was decided:
To use both fourth grade tests in the definition of an adequate education. This decision was made primarily because only the central high districts do not have a fourth grade. Only one district was lacking fourth grade data. Thus almost every district would have fourth grade data, which would be a strong indicator of whether students had or had not acquired a sufficiently strong educational foundation to insure that high school graduation requirements were likely to be met; and,
To use the test results of the five high school examinations previously listed, since passing of these or similar tests is required for high school graduation.
Missing Data. An important issue from a methodological perspective was how to treat a district if it were missing data. Missing data could occur because of several factors. These factors include:
Grade configuration of a district. A K-6 district would not have eighth grade or high school results. Conversely, a central high school district would not have any fourth grade results. In a sense, the district wasn’t missing data as much as the data were non-existent for the district. Grade configuration was a major factor in missing data. For example, of the five districts without any data for either the fourth grade tests, four were central high schools.
Data were truly missing. No test data exists for one district. Other data may be missing due to administrative error or because a particular test was not given in a district for one or more years.
Based on these circumstances, the following decisions were made:
If absolutely no test data existed for a district on any of the tests used, it would not be included in the study. Kiryas Joel was the only district not included in the study for this reason.
If a district had some test data, the determination concerning provision of an adequate education would be based on existing data.
Operational Definition of an Adequate Education
Based on all of the considerations described above, an adequate education was operationally defined as a district:
With a simple, unweighted average of 80 percent of its test takers scoring at Level 3 or above on seven examinations (Fourth Grade English Language Arts, Fourth Grade Mathematics, high school Mathematics A, Global History, U.S. History, English and Earth Science) in 1999-00, 2000-01 and 2001-02. The reader will note that, given this operational definition, a district could have less than 80 percent of its test takers with a score below Level 3 on one or more of the individual tests and could still be found as providing an adequate education.
Although this definition does not meet the Regents goal that all students achieve the standards, it does identify districts where the opportunity to achieve exists. Thus this operational definition can be viewed as a reasonable compromise.
Student Need
If student need is believed to be an important issue in understanding academic performance two methodological questions concerning the quantification of need must be addressed. The questions are:
·
What type(s) of students best reflect student need?What Pupil Count Should be Used to Measure Need? An assortment of measures could be used to estimate student need. Each of the possible counts possess strengths and weaknesses. A common measure used to identify student need among the 50 states is the percent of students eligible for a free and reduced price lunch. Indeed, in New York State, the K-6 percent of students eligible for a free or reduced price lunch is one of the pupil counts used to allocate a supplement to Operating Aid to help districts meet the needs of at risk students, known as Extraordinary Needs Aid. For these reasons, the study concluded student need could best be measured by the percent of K-6 pupils eligible for a free and reduced price lunch.
The count of K-6 students eligible for a free or reduced price lunch, however, may be subject to wide variation in some districts. For this reason, average counts reflecting three school years were used. Such an average would minimize the possibility of grossly misidentifying a district’s poverty rate due to a unique circumstance. K-12 districts that did not provide a school lunch program in 1999-00, 2000-01 and 2001-02 were given a K-6 free and reduced percent of zero. Central high school districts were given the average count of their component school districts.
What Should Be the Additional Weighting for Need? To incorporate "need" into a student count requires the development of an additional weighting. In school finance, the term additional weighting is usually associated with the quantification of the extra costs associated with providing a specified service. These extra costs are then translated into an additional weighting. For example, secondary students (grades 7-12) in New York State are provided an additional weighting of 0.25. This means a secondary pupil in certain student counts used in state aid formulas has a calculated value of 1.25 (1.0 + 0.25).
The additional weighting selected is critical in determining the cost of an adequate education. This immediately raises the question of what is the appropriate additional weighting for need. In seeking guidance for a suitable need weighting, we have two sources - existing practice and the research literature.
The legislation of other states concerning the additional weighting of poverty or at-risk pupils is another source to consider in determining the appropriate additional weighting for such students. Carey described the practices of states as of the 2001-02 school year4 and found that the funding level for poverty-based education aid varied widely among the states. In his view this was often more a reflection of available resources than of the actual costs of educating such students.
Since the 2001-02 school year, several states have taken legislative action concerning poverty or at-risk pupils. Maximum additional weightings enacted for poverty or at-risk pupils have ranged from 0.25 to 1.0. In New Hampshire and Wyoming the concept of a variable additional weighting for need based on the concentration of poverty pupils has been introduced.
Although a wide range exists in the research literature in terms of the appropriate additional weighting for student need, most of the literature suggests an additional weighting of at least 1.0. Indeed, in September 2003 the State Education Department released a study on educational need, expenditures per pupil and educational achievement in which student need was given an additional weighting of 1.0.
For these reasons it was decided that pupils would be given an additional weighting of 1.0 for poverty (based on 1999-00, 2000-01 and 2001-02 K-6 students eligible for free and reduced price lunch).
Cost Adjustment
In recent years, the Board of Regents in its State Aid
proposal has also endorsed the concept of adjusting State Aid to reflect the
variation in regional cost found to exist in New York State. It has done so due
to the dramatically different costs associated with educating students in
various geographic regions of the State.
To properly reflect these differing educational costs, it was decided to incorporate regional cost into the cost estimates. The cost indices used in calculating the estimate are the Regional Cost Indices (RCI)7 calculated for the 2004-05 State Aid Proposal of the Board of Regents. The RCIs were calculated based upon labor force regions as these have been defined by the New York State Department of Labor. The RCIs calculated for these labor force regions have been normed to a "North Country standard" and are described in Table 1 below:
Table 1: Regional Cost Indices for Labor Force regions in New York State:
North Country 1.000
Mohawk Valley 1.016
Southern Tier 1.061
Western
NY 1.080
Central NY 1.132
Capital District 1.168
Finger Lakes
1.181
Hudson Valley 1.359
Long Island/New York City
1.496
Expenditures Per Need-Adjusted Pupil
The final approach was to develop an "expenditure per need
adjusted pupil" model, which compared the expenditure pattern of districts with
acceptable academic performance to districts with educational performance below
the stated standard. Expenditures were defined as general education
instructional expenditures8 (including an estimated amount for fringe
benefits) as adjusted by the Regents Regional Cost Index calculated in 2003. The
pupil count was the same count used for general education instruction as defined
in statute for the Fiscal Supplement to the School Report Card.9 This
count was then adjusted to reflect student need by weighting the free and
reduced price lunch count at 1.0.
A graph of this prototype is shown in Figure 1. Under this approach, the first step was to identify districts providing an adequate education. As noted earlier, such districts were defined as districts in which an average of 80 percent of the students taking the seven previously identified examinations had a score that was at Level 3 or above. Districts in which on average 80 percent of the students tested did not score at levels 3 or 4 were identified as districts which may need to increase instructional expenditures in order to improve academic performance.
The next step in the methodology was to calculate the mean need and cost-adjusted instructional expenditure per pupil for all districts classified as providing an adequate education. These districts were then ranked from high to low on need and cost-adjusted instructional expenditures per pupil. At this point an efficiency measure was introduced. The mean expenditure per pupil was calculated for the lower half of these districts, based on per-pupil expenditures.
Thus, the procedures followed by the study to estimate the amount of additional instructional expenditures required to achieve adequacy can be figuratively expressed as shown in Figure 1.
Figure 1: Estimating the Increase in Instructional
Expenditures
Needed So That the Opportunity for an adequate Education
is
Provided by All Districts
Identify High Performing Districts |
|
Identification of Other Districts | |
Convert Expenditures into Cost Adjusted $ | |
Adjust Pupil Count to Reflect Need | |
Determine Expenditure/Pupil
Patterns of High Performing Districts 9; 9; 9; 9; 9; 9; | |
Apply Any Efficiency Criteria | |
"Spending Per Pupil Gap" Analysis | |
Determine
Dollar Increase Needed in Cost and Need Adjusted Dollars (Per Pupil Need x Need | |
Convert
Adjusted Dollars Needed into Actual Dollars (Cost and Need Adjusted Dollars |
SUMMARY OF AIDS AND GRANTS AS
REQUESTED IN | |||||||
2003-04 |
2004-05 |
Change |
|||||
School Year |
School Year |
Amount |
Percent |
||||
Aid Category |
(---------------Amounts in Millions---------------) |
||||||
I. Foundation Aid |
|||||||
Operating Aid/Foundation Aid |
$6,840.63 |
$13,209.50 |
$6,368.87 |
93.10 |
|||
Gifted & Talented |
0.00 |
0.00 |
0.00 |
NA |
|||
Operating Standards |
0.00 |
0.00 |
0.00 |
NA |
|||
Academic Support |
0.00 |
0.00 |
0.00 |
NA |
|||
Tax Effort |
0.00 |
0.00 |
0.00 |
NA |
|||
Tax Equalization |
0.00 |
0.00 |
0.00 |
NA |
|||
Tax Limitation |
29.93 |
0.00 |
-29.93 |
-100.00 |
|||
Extraordinary Needs |
703.12 |
0.00 |
-703.12 |
-100.00 |
|||
Summer School |
36.18 |
0.00 |
-36.18 |
-100.00 |
|||
Early Grade Class Size Reduction |
138.31 |
0.00 |
-138.31 |
-100.00 |
|||
Minor Maintenance & Repair |
49.97 |
0.00 |
-49.97 |
-100.00 |
|||
Educationally Related Support Services |
71.08 |
0.00 |
-71.08 |
-100.00 |
|||
Computer Hardware |
28.10 |
0.00 |
-28.10 |
-100.00 |
|||
Operating Growth |
29.93 |
0.00 |
-29.93 |
-100.00 |
|||
Operating Reorganization Incentive |
17.53 |
0.00 |
-17.53 |
-100.00 |
|||
Full Day Kindergarten Conversion |
7.57 |
0.00 |
-7.57 |
-100.00 |
|||
Teacher Support |
67.48 |
0.00 |
-67.48 |
-100.00 |
|||
Small Cities |
81.88 |
0.00 |
-81.88 |
-100.00 |
|||
Improving Pupil Performance (IPP) |
66.35 |
0.00 |
-66.35 |
-100.00 |
|||
Categorical Reading |
63.95 |
0.00 |
-63.95 |
-100.00 |
|||
Magnet Schools |
135.80 |
0.00 |
-135.80 |
-100.00 |
|||
Fort Drum |
2.63 |
0.00 |
-2.63 |
-100.00 |
|||
Plus: Cap on Losses |
0.00 |
382.74 |
382.74 |
NA |
|||
Less: Cap on Increases |
0.00 |
-4,714.42 |
-4,714.42 |
NA |
|||
Sum |
8,370.43 |
8,877.82 |
507.39 |
6.06 |
|||
II. Support for Students with Disabilities |
|||||||
Public Excess Cost Aid |
2,198.81 |
2,162.49 |
-36.31 |
-1.65 |
|||
Private Excess Cost Aid |
187.42 |
204.49 |
17.07 |
9.11 |
|||
Sum |
2,386.22 |
2,366.98 |
-19.24 |
-0.81 |
|||
III. BOCES/Career and Technical Education Aid |
|||||||
BOCES |
505.05 |
519.87 |
14.83 |
2.94 |
|||
Special Services Computer Administration |
38.35 |
41.12 |
2.77 |
7.23 |
|||
Special Services Career Education |
94.02 |
119.78 |
25.76 |
27.40 |
|||
Sum |
637.42 |
680.78 |
43.36 |
6.80 |
|||
IV. Instructional Materials Aid |
|||||||
Computer Software |
45.88 |
46.40 |
0.51 |
1.12 |
|||
Library Materials |
19.26 |
19.58 |
0.32 |
1.67 |
|||
Textbook |
189.01 |
188.65 |
-0.36 |
-0.19 |
|||
Sum |
254.16 |
254.63 |
0.47 |
0.19 |
|||
V. Expense-Based Aids |
|||||||
Building Aid |
1,194.60 |
1,348.45 |
153.85 |
12.88 |
|||
Building Reorganization Incentive |
12.73 |
0.94 |
-11.80 |
-92.65 |
|||
Capital Outlay/Transition Grant Adjustment |
11.44 |
0.00 |
-11.44 |
-100.00 |
|||
Transportation |
1,071.94 |
1,227.21 |
155.26 |
14.48 |
|||
Summer Transportation |
5.00 |
10.81 |
5.81 |
116.22 |
|||
Sum |
2,295.71 |
2,587.40 |
291.69 |
12.71 |
|||
VI. Other State Aids |
|||||||
Overcrowded Schools |
0.00 |
31.00 |
31.00 |
NA |
|||
Limited English Proficiency |
77.41 |
119.84 |
42.43 |
54.81 |
|||
Universal Prekindergarten |
201.94 |
214.97 |
13.03 |
6.45 |
|||
Sum |
279.35 |
365.81 |
86.46 |
30.95 |
|||
Calculated Aids Subtotal |
14,223.29 |
15,133.42 |
910.13 |
6.40 |
|||
VII. All Other Aids |
|||||||
Bilingual Education |
11.20 |
11.20 |
0.00 |
0.00 |
|||
Education of OMH/OMR Pupils |
25.00 |
26.00 |
1.00 |
4.00 |
|||
Homeless |
5.38 |
5.68 |
0.30 |
5.58 |
|||
DFY Transportation |
0.23 |
0.23 |
0.00 |
0.00 |
|||
Employment Preparation Edn. (EPE) |
84.00 |
84.00 |
0.00 |
0.00 |
|||
Incarcerated Youth |
14.00 |
14.50 |
0.50 |
3.57 |
|||
BOCES Spec Act, <8, contract |
0.68 |
0.68 |
0.00 |
0.00 |
|||
Bus Driver Safety Training Grants |
0.40 |
0.40 |
0.00 |
0.00 |
|||
Less: Local Contribution due for certain students |
-18.00 |
-18.00 |
0.00 |
0.00 |
|||
Comptroller Audits |
0.25 |
0.25 |
0.00 |
0.00 |
|||
Native American Building |
2.00 |
2.00 |
0.00 |
0.00 |
|||
Roosevelt |
6.00 |
6.00 |
0.00 |
0.00 |
|||
Special Act Districts |
2.20 |
2.20 |
0.00 |
0.00 |
|||
Mentor Teacher |
4.00 |
4.00 |
0.00 |
0.00 |
|||
Teacher Centers |
30.00 |
30.00 |
0.00 |
0.00 |
|||
Teachers for Tomorrow |
20.00 |
20.00 |
0.00 |
0.00 |
|||
County Vocational Ed. Extension Boards (CVEEB) |
0.92 |
0.00 |
-0.92 |
-100.00 |
|||
Learning Technology Grants |
3.29 |
0.00 |
-3.29 |
-100.00 |
|||
Shared Services Savings Incentive |
0.20 |
0.00 |
-0.20 |
-100.00 |
|||
Tuition Adjustment Aid |
1.18 |
0.00 |
-1.18 |
-100.00 |
|||
Urban-Suburban Transfer |
1.13 |
0.00 |
-1.13 |
-100.00 |
|||
Prior Year Adjustments |
90.00 |
65.00 |
-25.00 |
-27.78 |
|||
Sum |
284.04 |
254.13 |
-29.91 |
-10.53 |
|||
Combined Total |
$14,507.33 |
$15,387.54 |
$880.22 |
6.07 |
FOOTNOTES
(1) New York State Board of Regents (June
2003). 2003 Chapter 655 Report: Annual Report
to the Governor and the
Legislature on the Educational Status of the State’s Schools.
(2) See the annual Chapter 655 reports (for example, New York State Board of Regents, July 2003), Arnot and Rowse, 1987, Evans, Oates and Schwab, 1992, Jencks and Phillips, 1998, and others.
(3) Need-resource capacity categories group school districts into six categories based on their student poverty in relation to their ability to raise revenues locally. A detailed definition of need-resource capacity categories can be found in this Technical Supplement.
(4) New York State Board of Regents (June 2003). 2003 Chapter 655 Report: Annual Report to the Governor and the Legislature on the Educational Status of the State’s Schools.
(4a) Kevin
Carey. State Poverty-Based Education Programs: A Survey of Current Programs and
Options for Improvement. Center on Budget and Policy Priorities. 2002. http://www.cbpp.org/
(5) See annual
reports of the Chapter 655 Report (for example, New York State Board of Regents,
July 2003), Arnot and Rowse,
1987, Evans, Oates and Schwab, 1992, and Jencks and Phillips, 1998.
(6) New York State Board of Regents, June 2003, p.88.
(7) See Arnot and Rowse, 1987; Evans, Oates and Schwab, 1992; Henderson, Mieszkowski and Sauvageau, 1978; Link and Mulligan, 1991; Rumberger and Willms, 1992; Shavit and Williams, 1985; Summers and Wolfe, 1977; Willms, 1986.
(7a) Based upon professional wage data provided by the Department of Labor.
(8) See for example Hanushek, E. (1966), and Ladd, H. F. and J.S. Hansen (2002).
(8a) Instructional
expenditures include teacher salaries, other instructional salaries, BOCES,
tuition, equipment and other expenditures.
(9) Ladd, H.F. and J.S. Hansen (2002).
(9a) Average daily membership plus resident students attending other districts plus resident students attending charter schools plus incarcerated youth, as applicable.
(10) See Glasheen, R. , 2002.
(11) A measure of school district income and property, the State average Combined Wealth Ratio is 1.0. State averages for 2000-01 Operating Aid were $98,300 income per pupil and $244,900 actual value per pupil.
(12) See New York State Board of Regents (September 2002).
(13) Rivkin, Hanushek and Kain (2000).
(14) Teacher turnover is a measure of the teachers employed in a district in Year 1 who don’t come back in Year 2. It is calculated as: the number of teachers employed by a district in year one but not in year two, divided by the number of teachers employed in year one. Note that if a district employed 75 teachers in year one, and everybody came back for year two, the district hired an additional 10 more teachers, the turnover rate would be zero for that district because everybody came back.
(15)See for example Berryman, Flaxman and Inger, 1999; Grubb, David, Lurn, Plihal and Morgan, 1991; and Grubb and Stasz, 1991.
(16) Age is calculated as a weighted average based on the construction date of different parts of the building. For example, a building first constructed in 1951 and renovated with a new wing of equal size in 2001 would have an average age of 25 years ((50 years + zero years) / 2 = 25 years average age).
(17) See Fleischmann, 1972; Rubin, 1982; and Salerno, 1988.
(18) (Reference is made to the need to cost adjust operating aids, which constitute the largest share of the aid pie. Other aids already include cost adjustments, namely Building Aid, Transportation Aid, Excess Cost Aids, etc.
(19) Estimated Poverty Percentage: A weighted average of the 2000-01 and 2001-02 kindergarten through grade 6 free-and-reduced-price-lunch percentage and the 2000 Census poverty percentage. (An average was used to mitigate errors in each measure.) The result is a measure that approximates the percentage of children eligible for free- or reduced-price lunches.
(20) Combined Wealth Ratio: The ratio of district wealth per pupil to State average wealth per pupil, used for 2000-01 aid.
(21) “Interarea Comparisons of Compensation and Prices,” Report on the American Workforce,1997, p. 73.
(22) For a detailed discussion of regional cost and the construction of the Regents Cost Index see, Recognizing High Cost Factors in the Financing of Public Education: A Discussion Paper and Update Prepared for the New York State Board of Regents SA (D) 1.1 (Sept., 2000) and the technical supplement entitled Recognizing High Cost Factors in the Financing of Public Education: The Calculation of a Regional Cost Index (Nov., 2000). Copies can be obtained by contacting the Fiscal Analysis and Research Unit at (518) 474-5213 or visiting their web site at http://www.oms.nysed.gov/faru/articles.html.
(23) The shift from equity to adequacy in school
finance is a shift that has been driven by an emerging consensus around high
minimum outcomes as the orienting goal of both policy and finance. This has been
well described by William H. Clune. The Shift From Equity to Adequacy in School
Finance. June 1993. See also the Report on Funding Equity and Adequacy, The
State Aid Work Group (July, 1999), SA (D) 1.1. and Attachment.
(24) An excellent discussion of these three approaches is provided
by James W. Guthrie and Richard Rothstein, “Enabling ‘Adequacy’ to Achieve
Reality,” in Helen F. Ladd, Rosemary Chalk, and Janet S. Hansen (eds), 1999,
Equity and Adequacy in Education Finance, National Academy Press.
(25) Guthrie and Rothstein, “Enabling ‘Adequacy’ to Achieve Reality,’ pp. 223.
Selected Bibliography
Berryman, S.E., Flaxman, E. and Inger, M. (1999), "Integrating Academic and Vocational Education: An Equitable Way to Prepare Middle Level Students For The Future." Eric Clearinghouse on Urban Education: Digest 83.
Evans, William N., Wallace E. Oates, and Robert M. Schwab (1992), "Measuring Peer Group Effects: A Study Of Teenage Behavior," Journal of Political Economy 100(5), pp. 991-996.
Fleischmann, Manly (Chairman) (1972). "Report of the New York State Commission on the Quality, Cost and Financing of Elementary and Secondary Education," Volumes 1, 2 and 3.
Glasheen, R. "Towards an Understanding of the Relationships Among Student Need, Expenditures and Academic Performance." New York State Education Department Report to the Board of Regents, September 2002.
Glasheen, R. "An Exploratory Study of the Relationships Among Student Need, Expenditures and Academic Performance." New York State Education Department Report to the Board of Regents, September 2003.
Grubb, W.W., Davis, G., Lurn, J., Plihal, J., and Morgan, C. (1991), "The cunning hand, the cultured mind: Models for integrating academic and vocational education." Berkeley: University of California, Berkeley, National Center for Research in Vocational Education.
Grubb, W.W; & Stasz, C. (1991) Assessing the integration of academic vocational education. Berkeley: University of California, Berkeley, National Center for Research in Vocational Education.
Hanushek, E. (1966), "School Resources and Student Performance" in G. Burtless, ed. Does Money Matter? The Brookings Institution: Washington, D.C. pp. 43-73.
Hanushek, E. (1998), "The Evidence on Class Size" Working Paper, pp. 1-40.
Henderson, Vernon, Peter Mieszkowski and Yve Sauvageau (1978), Peer Group Effects and Educational Production Functions, Journal of Public Economics 10, pp. 97-106.
Jencks, C. and M. Phillips (1998), "The Black-White Test Score Gap," Chapter 1 in C. Jencks and M. Phillips, eds., The Black-White Test Score Gap, The Brookings Institution: Washington D.C., pp. 1-25.
Ladd, Helen F. and Janet S. Hansen (2002). Making Money Matter: Financing America’s Schools. In Developments in School Finance, 1999-2000. Fiscal Proceedings from the Annual State Data Conference July 1999 and July 2000. National Center for Education Statistics.
Link, Charles and James Mulligan (1991), Classmates’ Effects on Black Student Achievement in Public School Classrooms, Economics of Education Review 10, pp. 297-310.
Mosteller, F. (Summer/Fall 1995), "The Tennessee Study of Class Size in the Early School Grades," The Future of Children, 5, pp. 113-127.
New York State Board of Regents (September 2002). Local Effort. Report to the Regents Subcommittee on State Aid.
New York State Board of Regents (June 2003). 2003 Chapter 655 Report: Annual Report to the Governor and the Legislature on the Educational Status of the State’s Schools.
Rivkin, S. G., E.A. Hanushek, and J.F. Kain (2000). Teachers, schools, and academic achievement. National Bureau of Economic Research, Working Paper No. 6691 (revised).
Rubin, Max J. (Chairman) (February 1982). New York State Special Task Force on Equity and Excellence in Education, Volumes 1, 2 and 3.
Rumberger, Russell and J. Douglas Willms (1992). The Impact of Racial and Ethnic Segregation on the Achievement Gap in California High Schools. Educational Evaluation and Policy Analysis 14(4), pp. 377-396.
Salerno, Frederic V. (Chairman) (December 1988). Funding for Fairness. A Report of the New York State Temporary State Commission on the Distribution of State Aid to Local School Districts, Volumes 1 and 2.
Shavit, Yehuda and Robert A. Williams (1985), Ability Grouping and Contextual Determinants of Educational Expectations in Israel, American Sociological Review 50, pp. 62-73.
Summers, Anita and Roberta Wolfe (1977), Do Schools Make a Difference? American Economic Review 67, pp. 639-652.
Willms, J. Douglas (1986), Social Class Segregation and its Relationship to Pupils’ Examination Results in Scotland, American Sociological Review 51, pp. 224-241.