Full text of Business Review (Federal Reserve Bank of Philadelphia) : February 1975

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FEDERAL RESERVE BANK

# W hich
'School
'Resources
P elp
Learning
Pfficierjcy^,aqd
Pquity^iri
Philadelphia Public Schools



1975

B U S IN E S S R E V IE W is produced in the Department of Research. Editorial assistance is provided by Robert
Ritchie, Associate Editor. Ronald B. Williams is Art Director and Manager, Graphic Services. The authors will be
glad to receive comments on their articles.
Requests for additional copies should be addressed to Public Information, Federal Reserve Bank of Philadelphia,
Philadelphia, Pennsylvania 19105. Phone: (215) 574-6115.



ABOUT THIS ISSUE . . .
The Department of Research of this Bank has undertaken a lengthy study of the educational "output" of
Philadelphia's public schools. The findings are reported in this issue. The study examines the relationship
between use of school resources and achievement growth of students. A major finding of the study is that, on
the basis of the students analyzed, school resources can have an important impact upon how much students
learn and can help in compensating for the disadvantages of poverty, race, and low ability, when resources
are properly targeted. This finding suggests that the educational achievement of Philadelphia schoolchildren, in some cases, might be increased without necessarily spending more for school resources. That is,
redirecting some educational resources is likely to produce productivity gains.
The involvement of the Federal Reserve Bank of Philadelphia in a study of this nature stems from its
ongoing interest in productivity of the public sector and in urban finance. In the case of education,
productivity gains would reach far beyond the classroom. Boosting learning growth of students now can
mean a more productive work force in future years. In short, the school system would be improving the
quality of human capital.
The study was conducted by economists whose field of expertise is economics, not education. However,
the analytic and measurement techniques of the economics profession are well-suited for studying large
social issues. Moreover, the problems that have appeared in education have revolved around efficiency (or
productivity) and equity, topics of major concern to economists. While a few of the findings may be
controversial to some, neither the economists involved in the study nor the Bank have a particular axe to
grind. The primary intent of this study is to provide an objective analysis of school resource use which could
point the way to improved learning for this City's schoolchildren, to a more efficient use of citizens' tax
dollars, and to providing courts and legislatures with essential information in their quest for equity.
Finally, I wish to express my personal thanks to the School Administration of the School District of
Philadelphia for its exceptional cooperation in making its data and knowledge available to us for this study.
And I wish to thank the School Board for passing the August 14, 1972 resolution which made the study
possible.




David P. Eastburn, President
Federal Reserve Bank of Philadelphia

3

Which School
Resources Help
Learning?
Efficiency and Equity
In Philadelphia
Public Schools
By Anita A. Summers and
Barbara L. Wolfe
these are not rigorously examined. Until plaintiff
and defendant, finance director and school
superintendent, and taxpayer and pupil each
keep the same educational score card— that is,
until they all look at the same range of school
inputs in relation to agreed-upon goals of the
school system— confusion is likely to be the
order of the day.
The Research Department of the Federal Re­
serve Bank of Philadelphia has completed a
study of a sample of Philadelphia public school
students in elementary, junior and senior high
schools. The project uses growth in achievement
as its yardstick in measuring the output of the
educational process, and then examines the im­
pact of variations in a large number of inputs on
that output.
The major finding, in contrast to some wellknown studies, is that school inputs (such as
class size and teacher experience) do help stu­
dents grow in educational achievement and can
compensate for the disadvantages of poverty,
race, and low ability. Moreover, many inputs
have a larger impact on some students' perfor­

Parents of public schoolchildren sue edu­
cators because their children are getting less
education than others. Taxpayers argue that in­
creased school expenditures aren't increasing
education. Government leaders ask whether
compensatory educational funds are compensat­
ing. And almost everyone thinks that educators
aren't being efficient.
This hue and cry over public expenditures for
education, how they are spent and how they are
distributed, is not surprising. Education is big
business in the United States. Public school
spending consumes about 8 percent of the gross
national product; in Philadelphia, for example, it
represents over 30 percent of total governmental
outlays. And education is considered a vital
component of equal opportunity.
Missing from much of the debate is a clear and
workable definition and agreement on what the
public schools are here to do— in other words,
what is the output of the education industry?
Lacking a measure of output, debates in budget
hearings and the courts therefore focus on the
inputs of the educational process, although even




4

FEDERAL RESERVE BANK OF PHILADELPHIA

mance than others. Small classes, for example,
help low achievers, but are of no special benefit
to average and high achievers.1 Further, some
characteristics of staff inputs— extra educational
credits of teachers, for example— do not appear
to boost learning.

sizes, to name just a few. All the while, he is
exposed to various characteristics of school
climate— such as number of disruptive inci­
dents, the racial mixture of the school, and the
relative abilities of his fellow students. He is
tested again at this later stage. How much has he
grown educationally? How much have his read­
ing, writing, and arithmetic skills improved? And
what other school inputs have contributed to his
improved skills (or output)? Especially important,
what factors made him grow more or less com­
pared to other students who came from different
family backgrounds, with different abilities, dif­
ferent sex, and different race? In short, which
school resources help learning, and how can
these resources be allocated to maximize the
learning of various kinds of students? (See Box 1
for a discussion of the economist's rolein analyz­
ing the allocation of educational resources.)

EDUCATIO N : AN ECO NO M IC PERSPECTIVE
Peter Pupil, the raw material of the educa­
tional "production" process, enters the public
school system with a certain set of
socioeconomic inputs or characteristics— for
example, family income and background, race,
sex, and IQ (see Appendix for complete list). He
gets tested on his achievements in reading, writ­
ing, and arithmetic at an early stage. The main
job of the school system, many would agree, is to
transform Peter Pupil into a better-educated prod­
uct by improving his reading, writing, and
arithmetic skills.2 He, therefore, goes through
several years of schooling exposed to many
school inputs— a set of class sizes, experienced
and inexperienced teachers, and different school

is measured by the available standardized test scores: Iowa
Tests of Basic Skills Scores for elementary and junior high
students, and the Cooperative School and College Abilities
Test, California Achievement Test and Comprehensive Test
of Basic Skills for senior high students. Clearly, higher test
scores are not the only things educators try to achieve and
what parents want schools to do for their children. But,
acquiring basic ability in reading, writing, and arithmetic (as
measured by tests that convey what most of the outside world
regards as measures) is surely the most important function of
formal education. Almost everyone would agree that these
test results convey some important information about what
schools are accomplishing.

’Average, high, and low achievers are measured by per­
formance on standardized tests in relation to grade level.
Thus, average achievers perform at or about grade level,
high achievers are above, low achievers below.
2ln this study, the output of the school system is regarded as
growth in achievement over a period of years. Achievement

BOX 1

WHY DO ECONOMISTS LOOK AT EDUCATION?
Economists study how scarce resources are allocated among alternative uses. The analytic
and measurement techniques of economics brought the profession into the analyses of many
large social issues in the 1960s, education among them. Economists are concerned with equity
and efficiency in the allocation process. These issues arise whether they are looking at the
economy as a whole or at a private firm. And education is no exception. Since about 8 percent
of gross national product is allocated to education, both efficiency and equity considerations
have relevance to a large portion of the economy.
First, with respect to equity, a number of problems have appeared. Many disputes involving
educational equity have been brought to the courts. The courts have recognized that no clear
link currently exists between school resources and educational quality. There has been, in the
words of several decisions, no "judicially manageable standard." So, as second best, the courts




5

BUSINESS REVIEW

FEBRUARY 1975

BOX 1 (Continued)
have zeroed in on resource inputs to see if they were equally (not necessarily equitably)
distributed. Also they have looked at whether the financing of education was equitable in
relation to the amount of educational resources. However, the courts have been unable to
come to grips with the issue of whether these resources have bearing on student achievement (a
quality measure). A measurable relationship between student achievement and the volume
and quality of school resources is essential, then. Such a relationship could help to gauge and
enable the attainment of equity goals as they are set by the courts, parents, educators, and state
and Federal government managers of educational funds.
Second, economists typically approach problems with an eye toward maximizing
efficiency— that is, getting the most output from a given set of inputs, or a given amount of
dollars. Noneconomists in the public sector, where survival does not depend upon the
discipline of the marketplace, tend to do this during budgetary crises. Educators, and the public
sector generally, are now experiencing fiscal crunches. Consequently, they are exploring ways
of getting more output for the same or less cost. Improving efficiency in education requires, as a
first step, a d iscipl ined lookat just which school resources, ifany, improve achievement growth
for different types of students. And, along the way, it will also become clear which school
resources are unproductive in improving achievement levels. Then, a simple reallocation of
resources (not necessarily more resources) would yield greater achievement growth— that is
what is meant by being more efficient.
Economists have something to say about efficiency and equity in education because they
look at learning in a way which is analogous to a production process. Educational achieve­
ment, I ike shoes, canned tuna, and clean streets can be regarded as the output of a production
process. In dealing with a process which involves so many immeasurable human elements, of
course, many aspects of the process will not be captured by the production analogy. But, those
which can be captured can be usefully viewed this way.
The process begins with something in a relatively unfinished state— the genetically and
environmentally developed first grader, the leather, the writhing tuna, and the littered streets.
Inputs of labor, capital, and organization are applied and an output results. In education, the
product is a pupil achieving at a certain rate. In order to be efficient at this “ production" task,
educators must arrange the school resources (inputs) available to them in such a fashion that
they generate the largest growth in achievement (output) for different types of students.
When economists examine this production process, they try to isolate the impact of a par­
ticular input on the output. In theory, they hold all other inputs unchanged, and then alter the
amount of the particular input to see what change in output occurs. For example, in education
the output may be regarded as the achievement growth of a student. Now if this student had
more remedial training, with all other school and socioeconomic inputs held constant, would
his achievement growth change? This is the kind of question economists are asking.
In practice, economists do not have the option of shifting inputs about to examine the latter's
impact on output. Hence, they look at past data where such shifts have occurred and try to
determine the impact on output. Several statistical tools or techniques are available to them
(see Appendix for a description of the regression technique used in this study). These cannot
establish that the change in an input caused the change in output. They do, however, identify
a relationship between inputs and output. And it is on the basis of this relationship that policy
conclusions may be reached.




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FEDERAL RESERVE BANK OF PHILADELPHIA

the resources which are less effective— are firm
enough in this study and supported enough by
other studies to warrant confidence.

The findings which follow are addressed to the
question of how student achievement growth
can be increased through school resource allo­
cation. But they should not be regarded as the
answer. Although the data are extensive and the
analysis is careful, the findings are drawn from a
sample of students observed over a few years
(see Box 2 for a description of the student sam­
ple). It is an unfortunate characteristic of social
science investigations, in contrast to the pure
sciences, that replication is difficult, if not im­
possible. If a second, identically constructed
study were done with another group of students,
the results would certainly not be identical.
However, the broad findings— those related to
targeting resources to pupils and those related to

W HICH SO CIO ECO N O M IC INPUTS
AFFECT LEARNING?
An important and repeated finding of many
studies searching for the answers to questions
about educational achievement has been that
the pupil's background— family income and
race, among other things— largely determines
his or her performance in school (see Box 3). This
has exposed schools to the charge of being rela­
tively ineffective tools for changing the
achievement growth of students. A critical ap-

BOX 2

A LOOK AT PUBLIC SCHOOL STUDENTS IN PHILADELPHIA
The exceptional cooperation and data facilities of the Philadelphia School District enabled
us to develop a rich data base. Detailed pupil histories, as of 1970-71 or 1971-72, were
constructed. We looked at 627 students in 103 elementary schools between the end of the third
and the sixth grades, 553 students in 42 schools* between the end of the sixth and the eighth
grades, and 716 students in five senior high schools between the ninth and tweltth grades.
Though the elementary and junior high schools were a random selection from the Philadelphia
school system, the senior high schools were not: They have higher proportions of low-income
and Black students than the average. The students themselves were randomly selected from
their schools.
In many ways, this provided us with a better basis for analysis than other researchers have
been able to obtain: Pupil histories were extremely detailed, following students over time was
possible, the number of schools covered was large, and individual pupils were matched with
the teachers they had and with the characteristics of those teachers.
What do these students look like? The charts on the adjoining pages show this in some detail.
Briefly, though, they are students whose family income averaged less than $10,000 per year,
with over 25 percent of the Black students coming from families with incomes less than $6,000.
Elementary school students, when they reach the sixth grade, register average achievement
scores about 15 months below grade level; eighth graders average almost two years below
grade level; and twelfth graders in the sample (having a higher than average number of
low achievers) have average scores equal to those in the bottom fourth in the nation. Clearly,
the teachers and administration of the School District of Philadelphia, like those in other major
cities, have a particularly monumental task.
*The 42 schools included elementary, junior high and middle schools. All of these schools in the sample have the
seventh and eighth grades.




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FEBRUARY 1975

BUSINESS REVIEW

CHART 1

CHART 2

MOST PUBLIC SCHOOL STUDENTS IN
PHILADELPHIA CAME FROM FAMILIES
EARNING LESS THAN $10,000 A YEAR.

6TH GRADERS AVERAGED BELOW THE
GRADE NORM . . .
Percent of Students

Percent of Students

Gth Grade Scores of Elementary School

Family Income of Philadelphia School
Students
Blacks

Non-Blacks*

6th Grade Iowa Achievement Test Scores
(In Grade Equivalents)*
Source:

Pupil history files, School District of
Philadelphia, 1970-71.

* Raw scores are translated into grade norms.
Thus, if a 6th grade student takes a test in
April of the 6th grade year, the norm for that
student is 6.8.

Source:

Block income estimates were de­
rived from 1970 Census data for
Philadelphia. Block mean housing
values, block mean contract rental
values, tract distribution of block
contract rental values, and tract dis­
tribution of income values were used
to calculate block incomes. A work­
ing paper containing a detailed de­
scription of the method, a full
statement of the computer program,
and a presentation of the block data
is available.
* All pupils other than Black pupils.




8

FEDERAL RESERVE BANK OF PHILADELPHIA

CHART 3

CHART 4

AND SO DID 8TH GRADERS.

THE READING SCORE AVERAGE FOR
12TH GRADERS WAS CONSIDERABLY
BELOW THE 50TH PERCENTILE.

Percent of Students
8th Grade Scores of Junior High School
Sample
30
Grade Level = 8.7 ->
25
• Average = 6.5

Percent of Students
12th Grade Reading Scores of High School

20

15

10

A

I l / / l
1 1, 1 1 i i i i
1 2 3 4 5 6 7 8 9 10 11 12
8th Grade Iowa Achievement Test Scores
(In Grade Equivalents)**
Source: Pupil history files, School District of
Philadelphia, 1970-71.
* Raw scores are translated into grade norms.
Thus, if an 8th grade student takes a test in
April of the 8th grade year, the norm for that
student is 8.8.




(National Percentile)*
District Tapes of Philadelphia School
District, 1971-72.
Raw scores are translated into national
norms. Thus, if a 12th grade student tests
out, in national percentile units, at 50, he or
she would be in the middle of the range for
the nation.

Source:

9

FEBRUARY 1975

BUSINESS REVIEW

BOX 3

WHAT OTHER STUDIES SHOW
James S. Coleman,* a sociologist, in his pathbreaking study, found that (1) throughout the
school years, family background was the most important factor in determining pupil achieve­
ment, (2) the impact on achievement from things schools controlled was barely significant, and
(3) that in school the nature of the student body was more important in affecting achievement
than anything the schools did.
Arthur R. Jensen,** an educational psychologist, found that 80 percent of IQ is genetically
determined and that, therefore, most of the difference in IQs between Blacks and non-Blacks is
a matter of inherited genes. He argues, further, that this means that schools cannot succeed in
bringing achievement levels of Black students up to those of non-Blacks. His findings were met
with a storm of controversy.
Christopher Jencks,*** a sociologist, looked at incomes and occupations in relation to
school and family background characteristics (inputs). He found that the quality of schooling
and the nature of family backgrounds have a very limited effect on one's future income. Luck
plays the most important role of all. The implications drawn are that schools don't make a
difference in one's future occupation or income, though some schools may be more pleasant
places to be in than others.
*)ames S. Coleman et ah, Equality of Educational Opportunity (Washington: Government Printing Office, 1966).
**Arthur R. Jensen, "H ow Much Can We Boost I. Q. and Scholastic Achievement?" Harvard Educational Review,
Winter 1969, pp. 1-123.
***Christopher jencks eta/., Inequality: A Reassessment of the Effect of Family and Schooling in America (New York:
Basic Books, 1972).

praisal of research in this area concluded: “ The
best information we have . . . is that schools do
not now have a tremendous impact on the
achievement that does occur."3

pupil. Thus, in many studies, the only data avail­
able to examine the question of whether or not
more experienced teachers help students to
achieve more were the average experience
levels in schools. The preferable data are the
experience levels of specific teachers con­
fronting specific pupils. Therefore, perhaps
many negative findings on the effectiveness of
school resources emerged because these aver­
ages disguised the true impact. For example, if
experienced teachers help some students (high
income, White, higher ability) achieve and
hinder others, then the net result (if only averages
are looked at) may well show that experience has
no effect. Averaging allows the negative effects
to offset the positive ones.
The methods we have used were selected to
get atthis question of interaction between school

Income and Race Affect School Impact.
Perhaps educational studies have failed to un­
cover the effective accomplishments of schools
because few school inputs consistently benefit
all students. For example, low-income students
may require a different dosage of certain school
resources than high-income students. Many of
these studies have been hampered by the limited
amount of available data specifically tied to the
3Harvey A. Averch et a/., How Effective Is Schooling? A
Critical Review and Synthesis of Research Findings, The
Rand Corporation, R-956-PCSF/RC, March 1972, Santa
Monica, California, P. 160.




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FEDERAL RESERVE BANK OF PHILADELPHIA

input and type of pupil. And a great deal of
interaction was revealed. We find that for many
school resources the effect on some types of
students is very different— and, frequently, in the
opposite direction from the effect on other types
of students. Not only does this finding explain
why many studies have concluded that school
inputs have little impact on achievement, butour
results also point out— most importantly— the d irection of how achievement growth can be in­
creased by targeting school resources.
The evidence from this study suggests that
reallocating school resources so that they are
targeted to those pupils benefiting the most can
increase learning. Low-income, Black, or lowability students are handicapped in terms of ex­
pected achievement growth, but our findings in­
dicate that certain school resources can alter this
expectation. In fact, our study has enabled us to
track down just where being poor, Black, or of
low ability plays a role in absorbing (or not ab­
sorbing) school resources. So much of this in­
teraction has been identified that no un­
explained negative effects of being disadvan­
taged remain.
Sex. A student's sex is related to his or her
achievement at all school levels. Males do more
poorly than females in elementary school. In
junior high school, only low-ability males fall
behind low-ability females. And, in senior high
school, males of average ability or less do better
than females with equivalent ability.
Starting Scores. A pupil's abilities strongly de­
termine his or her growth in achievement at
every level of schooling— that is, if a student
begins school with a higher ability, he or she will
learn more rapidly. But, at each level, the data
show that if a high-achieving Black student and a
high-achieving non-Black student start out with
the same test score in the Philadelphia school
system, the non-Black student will move further
ahead.
Motivation. A student's motivation affects his
or her learning. For all students, at each level of
schooling, more unexcused absences (which are




regarded as reflecting poorer motivation) are as­
sociated with less learning growth. And being in
school more days goes along with more learning
growth. But, high-income students appear to be
the biggest losers from poor attendance. This
finding may mean that when an advantaged stu­
dent misses school it signals a far more serious
negative attitude toward education than when a
disadvantaged student does the same thing.
Residential Moves. Junior high students seem
particularly sensitive to some socioeconomic
characteristics. The results suggest that coming
from a family that moves more frequently has an
adverse effect on the achievement growth of
junior high students. In contrast, frequent family
moves appear to show little or no effect on
elementary or senior high students.
Native Born. Not being born in one of the 50
states (and having parents who were also not
born in them) is associated with lower achieve­
ment for early teen-agers in the Philadelphia
public schools. Most students in this group are
probably of Puerto Rican origin, so language
barriers may be the cause of their difficulties.
Summary. The socioeconomic background of
the pupil clearly plays an important role in what
the student achieves through the school years.
The sex of the student can be a handicap, as can
race, income, and abilities. But, these handicaps
are not “ immutable'' if they can be overcome—
at least in part— through what the schools can
do.
W HICH SCH O O L INPUTS AFFECT
LEARNING?
Socioeconomic factors are not within the im­
mediate control of school administrators and
teachers; class and school size and teachers'
experience are. And, if the spirit is willing,
changes can be made in how these school inputs
are allocated.
Class Size. Thefindings on class sizeshould be
regarded as indications for possible directional
changes, rather than as literal indicators.

BUSINESS REVIEW

FEBRUARY 1975

Elementary students in our sample who are
below grade level gain in classes with less than
28 students, but the rest of the students, can,
without any negative effect on achievement, be
in classes up to 33. For all elementary students,
in the sample, being in classes of 34 or more has
a negative effect, and increasingly so as the size
of the class increases. It is possible that the nega­
tive relationship may arise from a teacher's hos­
tile reaction to a class size larger than mandated
by the union contract, rather than from largeness
itself. In junior high school, classes of 32 or mor.e
showed lower achievement growth for the sam­
ple students, with low-income students ex­
periencing the greatest negative effects from
larger classes. Senior high English classes that
did not exceed 26 had the highest learning rates
(for students of any ability described by the sam­
ple); low-ability students benefited the most
from smaller classes.4
Chart 5 shows the range of class sizes of the
sixth, eighth, and twelfth graders in our sam­
ple. The average class size of each of these levels
approximates the optimal one for the sample.
However, a fair proportion of students are in
larger classes— classes so large that they impede
learning growth.

CHART 5
WHILE AVERAGE CLASS SIZE IN PHILA­
DELPHIA SEEMED TO BE CONSISTENT
WITH LEARNING GROWTH OF N0NDISADVANTAGED STUDENTS, THERE WAS A
WIDE SPREAD IN CLASS SIZES.
Percent of Students
Average Class Size
_

6th Grade

------- 8th Grade

Average Class Size

Size of School. In smaller schools increased
learning at the elementary and senior levels ap­
pears to take place. Black elementary students
seem particularly to benefitfrom being in smaller
schools, and low achievers in smaller senior
high schools. At the junior high level, school size
seems inconsequential overthe range examined.
It seems, however, much more beneficial to be in
an eighth grade that is part of an elementary
school than in one that is not. Chart 6 shows the
wide range of school size in the Philadelphia
School District.

Source:

percent of the teachers had three or less years of
experience, 37 percent had more than three but
less than ten years, and 36 percent had ten or
more years of teaching behind them. These dif­
ferences in teaching experience, according to
our study, have an impact on achievement
growth.
Many studies have found that although
teacher experience is not a very important factor,
it is helpful in the more than three and less than
seven-to-ten years experience span. These
studies, however, did not examine the impact of
teacher experience on students with different
abilities. Yet, it seems reasonable to expect that
the impact of teacher experience on achieve-

Teacher Experience. As Chart 7 indicates, 27
4The September 1, 1972 to August 31, 1976 Agreement
between the Board of Education of the School District of
Philadelphia and the Philadelphia Federation of Teachers
cal Is for a maxi mum class size throughout all levels of school­
ing of 33 by September 1, 1975, and a longer-term goal of 30
in elementary school, and 25 in secondary schools.




Monthly Attendance Reports, Octo­
ber 1970, School District of Phila­
delphia.

12

FEDERAL RESERVE BANK OF PHILADELPHIA

are particularly effective, but those having more
than ten years actually reduce the rate of learning
mathematics. This latter effect arises, perhaps,
because these teachers received pre-Sputnik
training. They were teaching the New Math,
even though they were not originally trained to
teach it.

CHART 6
PHILADELPHIA PUBLIC SCHOOLS VAR­
IED CONSIDERABLY IN NUMBERS OF
PUPILS ENROLLED.
Total Enrollment

Rating of Teachers Colleges. Most teachers in
the Philadelphia School District went to schools
rated lower than, for example, Pennsylvania
State University (which had a rating of 502 on a
scale of 250 to 800).5 Does where a teacher went
to college (or what it implies) affect a student's
learning?

Size of Schools

5The Courman rating, published in The Courman Report
(Phoenix, Arizona: The Continuing Education Institute,
1967), was used. It is.a rating of the undergraduate programs
of nearly all colleges and universities in the United States,
with information drawn from professional societies, com­
mercial publications, foundations, etc., as well as the institu-

CHART 7

Source:

THIRTY-SIX PERCENT OF THE TEACHERS
HAD 10 OR MORE YEARS OF EXPERI­
ENCE.

Monthly Attendance Reports, Octo­
ber 1970, School District of Phila­
delphia.

Percent of Teachers
Teacher Experience
40 ------------------------------------------------------------

ment would vary with the type of student.
In Philadelphia elementary schools, length of
experience has a very different impact on the
high and low achieving pupils in our sample.
High achievers seem to do best with more ex­
perienced teachers. However, these teachers
slow the learning growth of low achievers who
seem to do best with new, relatively inexperi­
enced teachers. Perhaps these teachers have un­
dampened enthusiasm for teaching those who
find it hard to learn.
In junior high, an experienced English teacher
appears to be particularly effective with highability students, but experience of ten or more
years helps all students. The pattern of effective­
ness for mathematics teachers differs somewhat.
Instructors with three to nine years of experience




Source:

13

Philadelphia School District data,
1971-72.

FEBRUARY 1975

BUSINESS REVIEW

educational process. But, in terms of the
achievement objective, and within the range of
expenditures the School District budgets, some
school inputs do notappearto improve learning.

Clearly, in some parts of the school system
teachers from colleges with higher ratings prove
to be more effective teachers. Elementary school
students who study with teachers from colleges
and universities rated 525 or higher achieve at
higher rates. All students do better, especially
those in the low-income category. In junior high,
having attended schools with higher Gourman
ratings seems to matter very I ittle i n the teach i ng
of English or mathematics, but it helps in the
teaching of social science— especially for highability students.

Headstart participation does not improve a
child's achievement growth by the latter half of
elementary school. But such participation does
contribute to the child arriving in the third grade
at an improved level of achievement. This find­
ing is consistent with many Headstart evalua­
tions made around the country.

Summary. In short, some school inputs can
heighten student achievement: Classes over cer­
tain sizes reduce learning; smaller elementary
and senior high schools increase it. Net output
may be increased by targeting teacher experi­
ence and higher-rated college background to the
appropriate students. Moreover, some of these
school inputs can help offset the initial learning
handicaps of race, income, and capability.

The general physical facilities of schools have
I ittle to do with thequality ofa student's learning.
More or less playground space, more or less
crowded science labs, a neworold school build­
ing, or a building rated higheror lower in general
physical condition seem to make little difference
when achievement test scores are the measure of
the student's output.6 If there are benefits from
better facilities, the data do not reflect them.
Some facilities, of course, may be far more im­
portant in imparting specialized knowledge than
they are in imparting the knowledge tested on
the general achievement scores reviewed.
Furthermore, good facilities may be important in
attracting and retaining good teachers.

W HICH SC H O O L INPUTS D O N 'T MAKE A
DIFFERENCE?
Sifting out the school inputs that are less pro­
ductive is almost as important as pinpointing
those that improve learning. Many inputs miss
the goal of increasing learning. This does not
mean, automatically, that expenditures for them
should be reduced to zero. On the one hand,
without some minimum level of expenditures,
negative effects on achievement growth might
result; on the other hand, with much more than
our present level of expenditures, positive effects
might result. Further, the objective of many
school inputs is not limited to the objective de­
fined in this study—growth in achievement
scores. Objectives such as racial attitudes and a
sense of participation in the democratic process
may also be part of the desired outcome of the

The measurable characteristics of school
principals do not appear to be clearly related to
increasing student achievement. There is a wide
range among Philadelphia public school princi­
pals in experience, graduate degrees, and extra
educational credits, but no particular beneficial
impact on student achievement emerges in that
range. Principals receive salary increments on
the basis ofa rating of the "difficulty" of a school.
Not using the measurable characteristics as a
basis for reward is entirely consistent with our
findings that they are not productive in terms of
achievement. Most likely, the characteristics of
school principals which might be effective, such

tions themselves. The areas rated include (1) individual de­
partments, (2) administrations, (3) faculty (including
student/staff ratio and research), (4) student services (includ­
ing financial and honor programs), and (5) general areas such
as facilities and alumni support. The Gourman rating is a
simple average of all of these.




6This finding is confirmed by most of the large studies by
social scientists, including James S. Coleman. Educators have
done little investigation of this, however.

14

FEDERAL RESERVE BANK OF PHILADELPHIA

some may be employed too sparingly to produce
achievement growth. In either case, a careful
reappraisal of school resources that do not seem
to aid learning is appropriate.

as leadership or organizational skills, are not
picked up by these measures.7
Whether teachers have more or less educa­
tion beyond the B.A. or fare better or worse on
the National Teacher Examination (Common)
does not seem to make them more effective
educators. Neither of these factors appears to
result in increased productivity. The absence of
impact on achievement of extra training is con­
sistent with many education studies and with the
large-scale studies by social scientists— yet
teachers who take extra educational work
beyond the B. A. are rewarded with salary in­
creases, unlike principals. Increased use of inservice training in Philadelphia may reflect an
awareness of the need for different training. The
discriminatory powers of the National Teacher
Examination were evaluated by the School Dis­
trict in 1972. The School District concluded that
the examination should not be theonly measure
of a teacher's potentiality; our findings suggest
that it should not be used as any measure.

WHAT ASPECTS OF SCH O O L CLIMATE
AFFECT LEARNING?
School integration is customarily discussed in
terms of "racial balance" but, in the broader
sense, it can apply to balancing income and
abilities as well. It is a common misconception
that the percentage of Black students, the percen­
tage of low-income students, and the percentage
of low achievers are the same group. They do,
indeed, overlap. But they are far from identical,
and lumping them into one category would be
inappropriate and inaccurate— for example,
three-fifths of the students whose family income
was over $7,000 tested below grade level in the
sixth grade.
Therefore, the effects of concentrations of
each of these groups need to be examined sepa­
rately. Attending a school with different concen­
trations of race, income levels, and abilities might
shape a student's learning. In addition, disrup­
tive incidents (assault, fire bombs, drugs, rob­
bery, and use of weapons) might have an impact
on learning. Our findings show that except for
average family income of the school population,
school climate factors greatly influence learning
in Philadelphia public schools.

Whether the race of the teacher does or does
not match the race of the pupil appears to be
unrelated to student learning. Whether a teacher
is Black or non-Black seems to be similarly unre­
lated to achievement growth.
Within the range of expenditures on counsel­
ing and remedial education, no particular bene­
fit in terms of increased learning is discernible.
Both of these are designed to be compensatory—
that is, students having more difficulty receive
more remedial work and guidance counseling.
But, apparently, the amount spent and/or the
techniques used are inadequate for the job.
Low-income and low-achieving students are not
doing better with more remedial resources.
In sum, there are a number of examples where
extra school inputs do not appear to help stu­
dents learn. Some of these resources may relate
to other objectives of the school system. And

Racial Balance. In 1954 the U. S. Supreme
Court, as part of the famous Brown v. Board of
Education decision declaring de jure school
segregation unconstitutional, stated:
Segregation of white and colored children
in public schools has a detrimental effect
upon the colored children. The impact is
greater when it has the sanction of the law;
. . . Segregation with the sanction of law,
therefore, has a tendency to retard the edu­
cational and mental development of Negro
children and to deprive them of some of the
benefits they would receive in a racially
integrated school system . . . [Emphasis
ours.]

7A well-known education study confirms this: See Neal
Gross and Robert E. Herriott, Staff Leadership in Public
Schools: A Sociological Inquiry (New York: )ohn Wiley
and Sons, 1965).




15

BUSINESS REVIEW

FEBRUARY 1975

Does segregation affect achievement? It can­
not be emphasized strongly enough that objec­
tives other than achievement gains may domi­
nate the decision to desegregate schools, but
knowing the impact on achievement (as best it
can be measured) of any desegregation target is
relevant. Busing for desegregation purposes
could create separate effects on achievement,
but these, of course, are not reflected in our
findings.
Many schools in Philadelphia have a high
proportion of Black students, while many others
have a high proportion of non-Blacks. In 197071, 23 percent of the elementary schools, 26
percent of the junior highs, and 18 percent of the
senior highs had less than 10 percent Black stu­
dents. And 40 percent of the elementary schools,
28 percent of the junior highs, and 27 percent of
the senior highs had student populations that
were more than 90 percent Black (see Chart 8).

CHART 8
THERE WERE A SIGNIFICANT NUMBER
OF SCHOOLS IN PHILADELPHIA WITH
EITHER A PREDOMINANTLY BLACK OR
NON-BLACK STUDENT BODY.
Percent of Schools
Percent of Black Students:

In elementary school, when all other school
characteristics are unchanged, Black and nonBlack students appear to have the largest growth
in achievement when they are in schools with a
40 to 60 percent Black student body, rather than
in schools that are more or less racially segre­
gated. The stimulative effect seems to be true
both for Black and non-Black pupils in the sam­
ple. In short, all elementary school students in
the sample benefited in terms of achievement
when they were in schools where the percentage
of Blacks about equaled the percentage of nonBlacks,8

Percent of Black Students
Source:

tive to a number of factors in their surroundings
which don't influence their elementary and
senior high counterparts. For example, they re­
spond, in terms of learning, to whether they have
moved about more or less frequently and
whether they and their parents are native born.
Perhaps the different sensitivity of Black and
non-Black students to the proportion of Blacks in
the school is related to the general psychological
make-up of early teen-agers.
For Black and non-Black students in the junior
high sample there is a very slight positive effect in
attending schools ranging up to half Black. After
50 percent, however, Blacks experience sig­
nificant learning growth as the proportion of
Blacks in the school increases (all other factors
remaining the same). Yet, although non-Blacks

In junior high school, the impact of the racial
balance on Black and non-Blacks varied. In gen­
eral, junior high students seem to be more sensi8Most of the studies on this subject have concentrated on
the impact on Black students being in a segregated versus a
desegregated school. Many studies have shown no differ­
ence in terms of achievement levels. Coleman's study, and a
reworking of his data, show some benefit to Black students of
being in classes with more non-Black students. Our results
confirm these latter findings and, even further, indicate that
non-Black students do better. This finding probably emerges
because it is the change in achievement, rather than just the
level, on which we are focusing.




Enrollment Negro and SpanishSpeaking in the Philadelphia Public
Schools, 1970-71.

16

FEDERAL RESERVE BANK OF PHILADELPHIA

gain in integrated schools up to half Black, they
seem to experience some learning declines
when they attend schools that are more than half
Black.9At a racial balance somewhere around 50
percent, therefore, it appears that Black pupils
will not experience the negative effects of a
non-Black segregated school, and non-Blacks
wi 11not experience the negative effects of attending a Black-segregated school.
Our sample of senior high students includes
data from only five schools. In this sample, 88
percent of the students were Black, and the
proportion of Blacks in the schools ranged from
55 to 99 percent. No strong impact on Black or
non-Black student achievement, one way or the
other, was found. However, the range examined
was so narrow that no decisive conclusions can
legitimately be drawn.

CHART 9
A VERY LARGE PRECENT OF SCHOOLS
HAD A VERY LOW PERCENT OF HIGHACHIEVING STUDENTS.
Percent of Schools
Percent of High-Achieving Students:
11 Sixth Grade

Achievement Mixture. The proportion of
either high achievers or very low achievers in a
school can have an impact on learning. Charts 9
and 10 provide an overview of the variation
among schools of the intellectual strength and
weakness of the Philadelphia student popula­
tion. A very large percentage of elementary and
junior high schools have a very low percentage
of high-achieving students. (As shown in Chart 9,
70 to 75 percent of these schools have less than
10 percent high-achieving students.) And many
schools— 52 percent of the elementary schools
and 43 percent of the junior high schools— have
more than half of the student body achieving at
very low levels (Chart 10). It turns out, according
to our study, that the nature of the mix does seem

10
20
30
40
50
Percent of Students above 84th Percentile
Source:

to make a difference in student achievement
growth.
Elementary school students in the sample who
test at grade level or lower perform distinctly
better when they are with more high-achieving
students. Students performing above their grade
level are not particularly affected. Therefore, it is
the low achievers mixing with high achievers
who seem to benefit most. Variations in the
proportions of low-achieving students also have
little effect on the high achievers, although being
in a student body with more low achievers than
high achievers appears to have a negative effect
on learning for those in the middle. All of this
suggests for elementary schools, that high
achievers go along on their own steam, relatively
unaffected by variations in the percentage of top

9lt might appearfrom these conclusions that Black students
in junior highs should be in segregated schools, since they do
better in schools with more Blacks. However, it is essential to
recognize that the junior high school characterized by more
Black students is also the one with fewer high-achieving and
more low-achieving students. These characteristics also af­
fect learning growth (described in the next section). Some of
the benefits for Black students of being where there are more
Black students, then, may in practice be offset by the disad­
vantages of being where there are more low achievers and
fewer high achievers. (See Anita A. Summers and Barbara L.
Wolfe, "Philadelphia's School Resources and the Disadvan­
taged," Business Review of the Federal Reserve Bank of
Philadelphia, March 1974, pp. 3-16.)




Report of the Spring 1970 Achieve­
ment Test Results, School District
of Philadelphia.

17

BUSINESS REVIEW

FEBRUARY 1975

In senior high schools, the proportion of high
and low achievers referred only to performance
on reading tests, and, further, the schools in the
sample had very few high achievers. Variations
in these proportions showed no impact, but
another meaningful measure— high school
dropouts— did: the greater the proportion of
dropouts in a school, the less learning there is in
the student body. And, particularly hard hit, in
terms of achievement growth, seem to be the
high achievers.
In general, then, peer group abilities influence
student achievement. Therefore, it would seem
that considerations of desegregation should
apply not only to race, but also to student
abilities.

CHART 10
AVERY HIGH PROPORTION OF SCHOOLS
HAD MORE THAN HALF OF THE STU­
DENT BODY ACHIEVING AT VERY LOW
LEVELS.
Percent of Schools
Schools With Over 50 Percent Low Achievers
Elementary School

Source:

Disruption. If a school has fairly serious dis­
ruptions such as stabbings, robberies, and rapes,
what impact does this (and all that disruption
reflects) have on the achievement gains of stu­
dents? In elementary, junior high, and senior
high schools, a greater occurrence of harsh inci­
dents lowers the achievement growth of highachievers significantly, but low achievers are af­
fected much less. School policies which help
reduce the number of serious incidents, then,
will improve the learning of testable skills of
middle- and high-achieving students. However,
since most major incidents of this sort are un­
doubtedly the consequence of a general malaise,
merely stationing police in the corridors (and
thereby reducing the number of incidents) may
not be the policy which contributes to learning.
In general, then, the more heterogeneous a
student body is in terms of race and achieve­
ment, the better a student body will fare in learn­
ing basic skills. Further, a school that is relatively
free of disruption is one where more skills learn­
ing will occur.

Report of the Spring 1970 Achieve­
ment Test Results, School District
of Philadelphia.

and bottom achievers. But the intellectual com­
position of the student body, from top to bottom,
directly affects learning, especially for the low
achievers. In other words, the student body ap­
pears to be better off in terms of learning the
more heterogeneous the composition regarding
abilities.
Junior high students all seem to benefit alike
when they are part of a student body with high
achievers. They do not appear to lose when they
are part of a student body with more low
achievers, however. If, therefore, junior highs
were made more heterogeneous with respect to
ability, some students would gain (where the
proportion of high achievers would increase)
and some would lose (where the proportion of
high achievers would decrease), but low
achievers would appear to be the biggest gain­
ers.




CO N CLU SIO N S
The major finding emerging from this sample
of Philadelphia public school students suggests
that certain school inputs do make a difference in
achievement growth. Many school resources are
effective in im proving learning for all
students— and, many are particularly effective

18

FEDERAL RESERVE BANK OF PHILADELPHIA

achievers into the student body can also push
learning rates up. In short, how school resources
are allocated does have an impact on pupil per­
formance. (See Box 4 for a full summary of the
specific findings of this sample.)
The finding that school resources influence
learning growth has several important policy
implications. First, public school resources can
be used to attain greater equity in educational
opportunity. Some compensation to students
disadvantaged by the incomes of their families,
the pigment of their skins, and/or the number of
their IQs can be achieved by targeting particular
school resources to them. This finding is espe­
cially significant because it varies from the con-

when they are targeted to the type of students
who will benefit most. Students disadvantaged
by socio econo m ic characteristics can be
broughtto learning rates closerto those of advan­
taged students if particular resources— teachers
from higher-rated colleges, for example— are
placed in front of them. High ability students can
be lifted to higher learning rates if some re­
sources are directed specifically to them— such
as experienced elementary school teachers. In
addition, using resources to change school cli­
mates can improve student achievement growth.
For example, reducing the number of disruptive
incidents in schools can boost learning. More
racial integration and mixing more higher
BOX 4

SUMMARY OF FINDINGS
All types of students at all levels of schooling experience larger rates of growth in achieve­
ment if they are attending more, and if unexcused absences and lateness are minimized.
Regarding these attendance features as important signals and effectively reacting to them will
result in increased learning. Reducing the amount of serious disruptions in schools will
increase learning— resources directed to this problem has a direct payoff.
All types of students in elementary school do better if they are taught by teachers who
graduated from higher-rated colleges, if they are in a school with a 40 to 60 percent Black
student body, if they are in classes of 33 or less, and if they are in a school with more
high achievers.
All types of students in junior high school do better if they go to a school which is part of an
elementary school, if they have social studies teachers who graduated from higher-rated
colleges, if they have mathematics teachers who were trained in the post-Sputnik New Math
era, if they are in classes of 31 or less, and, again, if they are in a school with more
high achievers.
All types of students in senior high school do better if they are in smaller schools where
dropouts are less of a problem.
Disadvantaged as well as advantaged students are helped by all these factors, but they can
be helped even further by particular types of resources being targeted to them.
Black students with high IQs would benefit if home and school would allow them to achieve
as much as non-Black students with the same high IQ, especially in the early grades. Later on is
too late— Black and non-Black students with the same third grade achievement levels grow at
the same rate in the higher grades. Black students perform better in smaller elementary schools
and in junior highs with larger Black populations.
Low-income students respond particularly well to elementary school teachers who




19

BUSINESS REVIEW

FEBRUARY 1975

BOX 4 (Continued)
graduated from higher-rated colleges and to junior high classes smaller than 32.
Low achieving students are particularly responsive to certain school inputs. In elementary
school, low achievers do better if they are in classes with less than 28 students, if they have new
teachers, and if they are in schools with more high achievers. In junior high, this group
performs better with new English teachers and with more high achievers in the school. And in
senior high this group responds to English classes that have less than 27 students and to smaller
schools. Presumably, at every level, a redesigned remedial education program— since the
present one does not seem to be helping low achievers— would be helpful.
High achievers do best with experienced elementary school teachers and junior high
English teachers, junior high social studies teachers from higher-rated colleges, more library
books, and with senior high English teachers with higher English exam scores. If they are in an
environment with less disruption and fewer dropouts, and if they move less during their junior
high years, they do better.

elusions of other major education studies which
indicate that school inputs are not effective in
compensating the disadvantaged. It is also sig­
nificant because it means that the courts and
legislatures can get a measurable handle on edu­
cational equity in terms of output— achievement
growth— rather than the traditional approach
which measures equity in terms of inputs— such
as expenditures per pupil. Thus, if achievement
growth is acceptable as a major goal of the edu­
cational system, equity attainment relates to
what the student gets from his or her education,
rather than what the schools put into him or her.
It also suggests that state and Federal compen­
satory funds, now compensating for income and
population density characteristics, would more
appropriately be com pensating for low
achievement.
The second policy implication suggested by
the finding has to do with educational productiv­
ity. Some sch o o l inputs produce greater
achievement growth than others. Thus, shifting
resources toward those inputs could generate a
larger educational output without raising School
District expenditures.
Our study of the School District sample data
for 1968-72 suggests that,on efficiency grounds,
some school resources could be drawn away
from those activities where extra inputs don't



seem to make much difference (such as extra
teacher education, physical facilities above the
minimum, and unproductive class sizes). Fur­
ther, some school resources could be shifted to
those activities which seem to be particularly
productive (making schools more heterogene­
ous with respect to race and ability, and smaller
elementary and senior high schools are exam­
ples). More particularly, school administrators
might do well to put those resources which are
particularly effective for low achievers with that
group (smaller classes in elementary school and
English classes in senior high are examples.)
Making teacher salary scales more reflective
of productivity would also help. Extra education
of teachers does not appear, directly, to produce
achievement results, although it is a characteris­
tic for which teachers are rewarded. There are
other characteristics of teachers which do play
an important role in the learning process. Iden­
tifying and rewarding these would make salaries
more reflective of productivity. For example,
graduating from a higher-rated college seems to
be a "productive" characteristic of teachers (in
terms of achievement growth), though currently
this is not rewarded or even used as a basis for
hiring. In sum, a careful appraisal of the alloca­
tion of school resources and the reward system
might well produce important productivity
20

FEDERAL RESERVE BANK OF PHILADELPHIA

implication, if achievement growth is accepted
as a principal goal, is that taxpayers, parents, and
courts could hold school administrators ac­
countable. Such a result would benefit all con­
cerned. Most important, however, students
might well have a better chance of reaching their
educational potential.

gains.
A third broad policy implication arising from
this study concerns accountability. The concept
of holding a person responsible for seeing that
resource expenditures produce a specified out­
put is an old one in the private sector. For exam­
ple, stockholders hold management account­
able for using resources to generate profits. The
practice has proved more difficult to apply in the
public sector, however, because of the difficulty
of identifying outputs (and relating them to
specific inputs) and because of the absence of a
profit measure. Yet, an important finding of this
study is that in the educational process specific
school resources can be tied to learning. The




21

FEBRUARY 1975

BUSINESS REVIEW

APPENDIX
The data used in this study were obtained from elementary, junior, and senior high schools, pupil his­
tory files, and personnel files. They were in a form that permitted the matching up of school resources,
school climate, and Bureau of Census data to individual pupil data.
The following data classified as socioeconomic, school resources, and school climate were examined
for all three levels.
Socioeconomic
Sex
Race
"Fam ily” income
Density of Census tract
Days present
Unexcused absences
Latenesses
Marital status of parents
IQ*
Residential moves
Pupil born in U.S.
Second-generation
American
Iowa test scores (reflecting initial abilities)

School Resources
Headstart participation*
Size of school
Size of class
Number of pupils per
lab***
Playground footage per
pupil*
Condition of school
Classification of school
Date school built
Capacity utilization
Basic grade organization
Library books per pupil
Number of school
librarians
Number of nonteacher
professionals

Teacher's experience
Teacher's exam score—
common
Teacher's exam score—
subject
Gourman rating, teacher's undergraduate
college
Teacher's credits beyond
B.A.
Teacher's race
Percent of Negro teachers
Percent of teacher vacancies
Principal's experience

Principal's credits beyond M.A.
P rin cip al's additional
degrees
Total expenditure per
pupil
Total Federal funds expenditure per pupil
Counseling expenditure
Remedial education
expenditure
Basic skills expenditure*

School Climate
Percent
Percent
Percent
Percent
Percent
Percent
Percent
Percent
Student

of high achievers in pupil's grade
of low achievers in pupil's grade
of Negro pupils
of high school dropouts**
of Spanish-speaking pupils
of low-income pupils (free lunches)
of high achievers in school****
of low achievers in school****
mobility****

Average income, schoo feeder area, 1970
Average education level, adults 25 + , school feeder
area
Change in feeder area income, 1960-70
Number of disruptive incidents
Average daily attendance
Percent of 1972 graduates planned to continue educa­
tion**
Percent of 1972 graduates unem ployed, Nov.
1972**
Percent of 1972 graduates attending college, Nov.
1972**

*Elementary only.
**High school only.
***Not elementary school.
****Not high school.




22

FEDERAL RESERVE BANK OF PHILADELPHIA

STATISTICAL PROCEDURES

variable, holding all others constant, and growth in
pupil achievement. It also enables us to define the
size or magnitude of each relationship. The amount
of the variation in growth in achievement that is ex­
plained by all the variables in the equation is mea­
sured by the coefficient of multiple determination, the
R2. The R2takes on values between 0 and 1. The closer
R2 is to unity, the greater the explanatory power of
the equation. An R2 of .32 means that the equation
explains 32 percent of the variation— and leaves 68
percent unexplained.

For each level of schooling, equations were
estimated where the change in achievement growth
of each pupil during the period under study (depen­
dent variable) was explained by a set of socio­
economic, school resource, and school climate
factors (independent variables). These equations
essentially state that for any particular student, his
or her achievement outcome is determined by back­
ground factors, amounts and quality of school
resources, and the climate of the school that the pupil
attends.
Generally, we think of many things affecting pupil
achievement. Multiple regression analysis permits the
empirical testing of these relationships. Essentially,
this statistical procedure permits-the sorting out of the
separate effects of different factors entered into each
equation. If, for example, we have an equation with
two explanatory variables, X, = IQ and X2 = percent
of high achievers and the dependent variable Q =
change in student achievement in grade equivalent
form, and the equation is

INTERPRETING THE TABLES
Three tables follow: Table 1 describes the sixth
grade results, Table 2 the eighth grade results, and
Table 3 the twelfth grade results. The tables are
derived from equations which explain achievement
growth.
Output Measure. Table 1 describes the findings
that relate to the achievement growth of elementary
school pupils, as measured on standardized tests.
Tests were taken in the spring of the third grade and
the spring of the sixth grade. The difference between
these two, the growth over the period, is used as the
measure of the pupils' achievement growth. The
results thus refer to change over a three-year period
and are measured in grade equivalent form.
Table 2 describes the findings that relate to the
years sixth through eighth grades. Standardized tests
were taken in the spring of the sixth grade and the
spring of the eighth grade. The difference between
these two, the change over the period, is used as the
measure of achievement growth. The results refer
to growth over a two-year period. They are also ex­
pressed in grade equivalent form.
Table 3 describes the findings of the twelfth grade.
These results are limited to tests on English exams, and
to pupils attending schools in Districts 1, 2, 3, 4 only.
Tests were taken in the ninth and twelfth grades. The
difference between these is used as the measure of
achievement growth. The results, thus, refer to a threeyear period. These are in national percentile form
since the grade equivalents are not available.
Input Measure. In the tables that follow, the lefthand column lists the explanatory variables— the
socioeconomic, school resource, and school climate
variables that affect pupil achievement growth. The
right-hand column describes the findings, giving de­
tailed information on the difference that the unit
variation in the explanatory variable makes on
achievement growth. Wherever this effect is signifi­
cantly different for different types of students, these
differences are described.

Q = 10.04 + . 15Xi + .7X2,
it would be interpreted in the following way: The
coefficient .15 means that, with the percentage of
high achievers fixed, an increase of 1 point on an IQ
test is expected to generate a .15 month increase in
student achievementgrowth. The coefficient .7 means
that, holding IQ constant, a 1 percentage point in­
crease in the percentage of high achievers is expected
to lead to a .7 month increase in student achievement
growth.
A measure is needed to judge the reliability of
these estimates. The formal statistical test for this
looks at the value of the coefficient compared to
the standard error of the coefficient. The standard error
measures the spread or how far, on average, the
likely values of the coefficient are from the estimated
mean value of the coefficient. To be statistically
significant 95 percent of the time, that is, to be
different from zero 95 percent of the time, the value
of the coefficient must be approximately twice the
size of the corresponding estimated standard error.
Strictly speaking, this only applies to one testing of
a hypothesized relationship. Since we engaged in
extensive empirical testing and refining of these rela­
tionships, we do not use these results rigidly, but
use them only as general indicators of statistical
significance.
Thus, multiple regression analyses permit us to
isolate the effects of certain factors and see if there is a
regular relationship between any one explanatory




23

FEBRUARY 1975

BUSINESS REVIEW

TABLE I

SIXTH GRADE RESULTS
Variable
Sex
IQ

Unexcused absences

Latenesses

Sixth grade teacher's college
rating (Gourman)

Sixth grade teacher's
experience

Sixth grade teacher's exam
Library books

Findings: Results expressed in units of three-year growth.*
Over this period, males grew .9 months less than females.
For all pupils who scored between 80 and 100 on the first grade IQ
test, a 10-point higher IQ means 1.3 months more growth. For White
pupils who scored 110 or better on the IQ test, a 10 point higher
IQ means 2.9 months more growth, while for Black pupils who scored
110 or better, a 10-point higher IQ means only .55 months more
growth.
Unexcused absences have a negative effect on achievement. The
negative effect is greater for the more advantaged students, higher
income, and White students. Five additional absences per year for a
student whose family income is $10,000 means a decline in growth
of 2.13 months, while for a student whose family income is $7,000,
the five additional unexcused absences mean a 1.32 months decline
in achievement growth.
Latenesses have a negative effect on achievement growth. The effect
is greatest for low-income pupils. Five more latenesses per year means
2.9 months less growth to a pupil whose family income is $5,000
and 1.2 months less achievement growth for a student whose family
income is $8,000.
Having a teacher who attended a college rated 525 or better compared
to below 525 has a positive effect on low- and middle-income pupils.
In terms of achievement growth this means 8.7 months more growth
to the pupil whose family income is $5,000, 4.2 months to the pupil
whose family income is $10,000.
Teacher's experience has a positive effect on average and
above average students. A student who is at grade level in the
third grade (= 3 .8 ) w ill increase achievem ent growth by .6
months for each three additional years of teacher's experience
(to 11 years). A student scoring 5.0 will increase by 1.3 months
per three additional years experience. Below grade level, down
to 2.0, additional experience has no effect. Below that, it
reduces growth. At a score of 1.5, three years more experience
means .63 months less growth.
As a teacher's score on the National Teacher Exam increases by
50 points, pupil achievement growth declines by .75 months.
As one more book per pupil is added to the library, pupil achieve­
ment growth declines by .5 months.

*Average growth equals two years, three months over the three-year period, end of third grade to end of sixth grade.
The R2 of this equation equals .28 with growth as the dependent variable, .74 with the absolute level of the sixth grade
score as the dependent variable.




24

FEDERAL RESERVE BANK OF PHILADELPHIA

TABLE 1 (Continued)
Class size

School size

Percentage of Black pupils

Percentage of high achievers

Percentage of low achievers

Disruptive incidents

Being in a class of 34 or more reduces achievement growth by 2.1
months. Being in a class of 28 to 33 rather than a class of less than 28
has no effect on students who scored at grade level in third grade, a
negative effect on low achievers, and a positive effect on high
achievers. The negative effect is 1.6 months for a pupil who scored
2.0; the positive effect is 2.4 months for a pupil who scored 5.0.
Larger schools have a negative effect, particularly for Black pupils. An
increase of 300 in enrollment means .6 months less achievement
growth for White pupils, 3.5 months less achievement growth for
Black pupils.
As all pupils go from a less than 20 percent Black school to a 20 to
40 percent Black school, achievement growth increases by 3.3
months. Similarly, going from a less than 20 percent Black school to
a 40 to 60 percent Black school means a 5.6 month increase in
achievement growth or an additional growth of 2.6 months over 20 to
40 percent Black schools. Going from a less than 20 percent Black
school to a 60 percent more Black school means an increase in
achievement growth of 4.3 months or 1.3 months less than a 40 to 60
percent Black school.
Being in a grade with more pupils who scored at the 85th national
percentile or higher has a positive effect on achievement growth
which is strongest for low achievers. A 5-percentage point increase in
the percentage of high-achieving students means an increase in
growth of 1.0 months to a pupil at grade level, 2.0 months to a pupil
below grade level (at 2.0), but no significant effect to a pupil above
grade level (at 5.0).
Being in a grade with more pupils who scored below the 16th
national percentile means .7 months less growth for each 10percentage point increase.
More disruptive incidents in a school have a negative effect on high
achievers. An increase of three in number of incidents means a
decline in growth of 1.4 months to a high-achieving pupil (at 5.0).

TABLE 2

EIGHTH GRADE RESULTS
Variable
Sex

Findings: Results expressed in units of two-year growth.*
Among low-achieving students, males grew 2.0 months less than

*Average growth for pupils in sample equals one year, two months in two years from the end of sixth grade to the end
of eighth grade. The R2 of this equation equals .31 with growth as the dependent variable, .85 with the absolute level
of the eighth grade score as the dependent variable.




25

FEBRUARY 1975

BUSINESS REVIEW

TABLE 2 (Continued)
Second-generation American

Earliest score

Sixth grade score

Unexcused absences

Days present
Residential moves

Eighth grade social studies
teacher's college rating
(Gourman)

Eighth grade social studies
teacher's subject exam
Eighth grade English
teacher's experience




females. For the rest, sex made no difference in achievement growth.
Students who were born in one of the 50 states and whose parents
were born i n one of them grew four months more i n achievement. The
effect is strongest for low-income pupils.
All students benefit from having a higher third grade score, but the
effect of an additional month higher score diminishes as third grade
score goes up. For low achievers (around 1.5), the positive effect is
.4 per additional month higher third grade score. For average
achievers (around 3.0), the positive effect is .25 per additional month
higher score. For high achievers (around 4.5), the positive effect is .12
per additional month higher score.
All students tend to move toward the average over the testing period.
For students below the average (=5.6) in sixth grade testing, the
growth rate is greater by 3.4 months for each 10 months below aver­
age. For students above average in sixth grade testing, growth is less by
3.4 months for each 10 months above the average. This may, in part,
reflect some error in test measurement.
Unexcused absences have a negative effect on those who scored at
5.0 and above on the sixth grade test, and the effect is greater
for higher achievers. Five more unexcused absences per year means
.78 months less growth to a pupil who scored 5.0, 1.69 months less
growth to a pupil who scored at grade level (6.8), and 2.30 months
less growth to a pupil who scored above grade level (at 8.0). The effect
is also more negative as a pupil's income increases.
For all pupils, 10 additional days present means .53 months more
achievement growth.
Residential moves have a negative effect on high achievers and
higher-income pupils. Below grade level at 5.0, each additional move
reduces achievement growth by 1.8 months, at grade level (6.8) it
reduces achievement growth by 3.6 months, while above grade level
(8.0) it reduces achievement growth by 4.8 months.
Having a social studies teacher who attended a college rated 50 points
higher on the Gourman rating, increased achievement growth for
grade level and higher than grade level pupils, .5 months for grade
level, .9 months for above grade level (at 8.0) but had no effect on
below grade level pupils.
For all students, a 10-point increase in their teacher's score on
National Teacher Social Studies Exam meant a .8 months increase in
achievement growth.
The experience of the English teacher does not affect achievement
growth, positively or negatively, through the ninth teaching year.
Having an English teacher with 10 or more years experience, how­
ever, increases achievement growth by 3.8 months, both for the tenth
and eleventh-plus years. The positive effect is strongest for highachieving pupils. For very low-achieving pupils the effect of more
experience is negative.

26

FEDERAL RESERVE BANK OF PHILADELPHIA

TABLE 2 (continued)
Eighth grade math teacher's
experience

Pupil race = race of
eighth grade math teacher
Percentage of Black teachers
Library books

Remedial expenditure
per low achiever
Class size

Eighth grade part of
elementary school
Percentage of Black pupils

Disruptive incidents

One to two years experience of the math teacher has no positive
or negative effect on pupil growth; three to nine years experience
increases achievement growth by .4 months for each year, while ten
or eleven-plus years reduces achievement by 2.1 months for the tenth
and eleventh-plus years.
If the math teacher's race is the same as the pupil's race, student
achievement growth is 2.1 months more.
As the percent of Black teachers increases by 10 points, pupil achieve­
ment growth declines by 1.5 months.
Library books have a positive and increasingly positive effect on
achievement growth of pupils scoring 6.0 and above. At grade level
(6.8) each additional book increases pupil growth by .48 months;
above grade level (at 8.0) the increase is .68 months.
Remedial expenditures have a positive effect on non-low achievers—
.3 months per $10 increase, but essentially no effect on low achievers.
The effect is also only positive for higher-income pupils.
Being in a class size of 32 or more, compared to a class of less than 32
has a negative effect on those with family incomes of $ 10,000 or less.
The negative effect is 2.4 months for a $10,000 income pupil, 4.3
months for a $5,000 income pupil.
Being in an elementary school in the eighth grade increases pupil
achievement growth by 4.3 months.
For non-Black pupils, being in a school with an increasing percentage
of Blacks, up to 50 or 60 percent, may possibly increase their achieve­
ment growth by .5 months per 10-percentage points increase. Above
this percentage Black, the effect may be negative, 1.3 months per
10-percentage points increase. For Black pupils, being in an increas­
ingly Black school, through 50 lo 60 percent may possibly have a very
si ight positive effect; above that, the effect is stronger and positive, 1.4
months per 10-percentage points increase.
More disruptive incidents in a school have a negative effect on high
achievers. An increase of three incidents means a decline in growth of
.36 months for the high achiever.

TABLE 3

TWELFTH GRADE RESULTS
Variable

Findings: Results expressed in terms of change in national percentile rating
of change in national percentile rating on English exams over three-year
period.*

*Average growth equals 2.25 from testing in ninth grade to testing in twelfth grade. The R2of this equation equals
.32 with growth as the dependent variable, .58 with the absolute level of the twelfth grade score as the dependent
variable.




27

FEBRUARY 1975

BUSINESS REVIEW

TABLE 3 (Continued)
Sex

Race

Seventh grade score
Ninth grade score

Unexcused absences

Latenesses

Twelfth grade English
teacher's subject exam

English class size

Percentage of dropouts

Percentage of Black pupils




Among the low achievers, males grew more than females. For those who
scored at the 10th percentile in ninth grade, males grew 2.4 percentage
points more than females. For those who scored at the 20th percentile
in ninth grade, males grew 1.4 percentage points more. Among other
pupils there were no differences by sex.
For high-achieving pupils, the effect of being Black on achievement
growth is negative. For students who scored at grade level in the seventh
grade (7.8), achievement growth is 7 percentile points less if the pupil is
Black and the negative effect increases as the seventh grade achieve­
ment score increases. Pupils who scored one or more years below grade
level are not adversely affected by being Black.
For all students, a one month higher score on the sixth grade test means
a 1-percentage point higher growth in achievement.
All students tend to move toward the average score. For students below
the average, ninth grade SCAT score ( = 23 percent), the growth rate is 1.9
national percentile points greater per 1 point below average. For pupils
above average, the growth rate is 1.9 percentile points less per one point
above average. This may, in part, reflect some error in the test measure­
ment.
Unexcused absences have a negative effect on achievement. Five more
unexcused absences per year means .4 national percentile points less
growth in achievement.
Latenesses have a negative effect on achievement and the effect is
stronger for higher achievers. At the ninth grade average (23 percent),
five more latenesses means .5 percentile points less growth. At 40
percent, five latenesses means 1.1 percentile points less growth.
Below the average score (23 percent), having an English teacher who
scored 10 more points on this teacher's exam has no effect. At the average
score and above, it has a positive effect. At the average (23 percent) the
positive effect is 1.1 percentile points per 10 percentage points on the
English teachers subject exam. Above average (at 40 percent), the positive
effect is 2.8 percentile points per 10 points.
Larger classes have a negative effect on low achievers, no negative or
positive effect on average achievers, and a positive effect on those who
scored at the 50th national percentile or above. For those at the 10th
percentile, the negative effect of having one additional student in a pupil's
English class is .7 percentile points. For those at the 5th percentile, the
negative effect is .92 percentile points. The negative effect is most
pronounced comparing class sizes of above 26 to those below 26.
Being in a school with a higher percentage of dropouts has a negative
effect on achievement growth for most students. It has no negative or
positive effect on very low achievers. At the average (23 percent) the
effect of 5 percent more dropouts is 1.2 percentile points less growth.
Above average (40 percent) the negative effect is about 2.9 percentile
points.
The range in this sample is limited to 55 to 99 percent Black pupils.
As the percentage of Black pupils increases by 5 points, Black pupil
achievement growth increases by .5 points. There is no effect on nonBlack pupils.
28

FEDERAL RESERVE BANK OF PHILADELPHIA

FOR FURTHER INFORMATION . . .
“ Equality of Educational Opportunity Quantified: A Production Function Approach/'
a technical version of this study, was presented by the authors at the winter meetings
of the Econometric Society on December 27, 1974. Copies are available on request
from the authors.
The March 1974 Business Review contains a study, “ Philadelphia School Resources
and the Disadvantaged," in which the authors detail how school resources in Phila­
delphia were distributed to schools in relation to the disadvantaged students. A
more technical version of this study is available in the Philadelphia Fed Research
Papers, “ Intradistrict Distribution of School Resources to the Disadvantaged: Evidence
for the Courts." Copies of these are available on request from the Department of
Research, Federal Reserve Bank of Philadelphia, Philadelphia, PA 19105.
A working paper containing a detailed description of the method used to obtain
block income estimates from 1970 Census data for Philadelphia is available on re­
quest. The paper contains a “ cookbook" description of the procedure and a full
statement of the computer program. Income estimates for each block in Philadelphia
are also available.




29

business review
FEDERAL RESERVE BANK
OF PHILADELPHIA
PHILADELPHIA, PA. 19105