2011. Vol.2, No.8, 859-868
Copyright © 2011 SciRes. DOI:10.4236/psych.2011.28131
School Size as a Factor in the Academic Achievement of
Elementary School Students
Kerry Reimer Jones1, Anthony Nnajiofor Ezeife2
1Windsor-Essex District School Board, Ontario, Canada;
2Faculty of Education, University of Windsor, Windsor, Ontario, Canada.
Received August 31st, 2011; revised September 29th, 2011; accepted October 31st, 2011.
This study empirically assessed the relationship between school size and academic achievement of elementary
school students in Ontario, Canada. Utilizing data from the Ontario provincial standardized test, the Educational
Quality and Accountability Office (EQAO), the results of 541 schools from ten school boards, were studied. A
One-way Analysis of Variance (ANOVA) indicated that overall, there was no statistically significant correlation
between school size and student achievement. However, there were significant correlations with respect to levels
of performance in both Grades three and six in some curricular areas. Also, further analysis at each independent
achievement level revealed that the mean percentage of students achieving at stipulated provincial standards in
Grade three writing and in Grade six reading, writing and mathematics were highest in large-sized schools
(schools with more than 420 students). Results further indicated that the mean percentage of students performing
above provincial standards in Grade six reading and writing was also highest in large schools. Students in me-
dium-sized schools (between 246 and 420 students) also had the highest mean percent age of students performing
above provincial standards in Grade three writing and in Grade six mathematics. The limitations and implica-
tions of the results are di s cu s s ed , and relevant suggestions made.
Keywords: School, Siz e, Achievement, Elementary, Students
Optimal school size has long been an issue of contention at
both the elementary and secondary levels. Throughout the last
century, the organizational tendency in education has fluctuated
between a push for small or large schools. Advocates for each
perspective have fought relentlessly for referendum in school
boards across North America. Such debates are further exacer-
bated by emotional, financial and political investments. Clari-
fication from the research literature does not provide an ade-
quate resolution to the issue of optimal school size, as empirical
validation exists for each side of the argument.
Over the last five years, the trend in educational reform has
favoured smaller schools (Mulrine, 2002). For example, the
Annenberg Foundation had pledged $500 million to reform
urban schools in Chicago (Ready, 2004). The Bill and Melinda
Gates Foundation had also contributed $51.2 million for the
creation of 67 small theme-based schools in New York (Ready,
2004). In Ontario, Canada, the location of this study, the debate
over the physical constitution of schools that effectively pro-
mote positive academic growth continues. This debate has been
intensified with the specific physical makeup of Ontario
schools and the deliberate composition of the public funding
formula. According to People for Education (PFE) (2006) al-
most half of the elementary schools in Ontario would be con-
sidered small in size, having less than three hundred students. A
similar situation exists in Ontario high schools, with thirty-three
percent having an enrolment of less than six hundred students.
The existing funding formula is based on larger school enrol-
ments, with sixty percent of elementary schools and fifty-five
percent of high schools below the formula limitations that
would permit for a full-time principal (People For Education,
2006). In order to staff their schools, school boards have been
making cuts in other areas. Small schools have faced a steady
decrease in the amount of full-time principals, librarians, spe-
cialized teachers and guidance counselors. Intensifying the
debate is a current government-mandated reduction of class
sizes in junior kindergarten through to the third grade, with an
implementation of a hard cap of twenty students per class.
Research has shown that communities hold schools account-
able for students’ academic achievement (Lee, & Loeb, 2000).
Knowledge concerning whether the size of a school impacts
academic success is invaluable in informing community deci-
sions to consolidate or maintain small schools and establish
effective funding formulas. The purpose of this study was to
determine whether there is a relationship between school size
and student academic achievement, and if there is, to investi-
gate the nature of the relationship.
Literature Review
Historical Overview
Historically, there is little agreement over what constitutes
the most effective school size. From the evolution of the one-
room schoolhouse to the mega-schools of today, debates on
whether to consolidate or maintain small schools had been rag-
ing for a long time (Howley, 1995). In a book about rural edu-
cation, Cubberley (1922) traced the school consolidation trend
back to a Massachusetts law in 1867, which marked the loss of
independent self-control over individual schools and the com-
mencement of local town management. Prior to this law, most
schools were small in size and many were considered rural in
nature. The introduction of town management resulted in the
effective consolidation of country schools. The consolidation
trend continued throughout the 1920s, as schools grew larger as
a consequence of the increasing immigrant populations in major
cities. The large influx of new students caused districts to con-
solidate administration, instruction and curriculum (Abbott,
Joireman, & Stroh, 2002).
Additionally, the President of Harvard University, Conant
(1959), further solidified North American consolidation efforts
with the publication of the book, The American High school
Today, which claimed that larger schools were the solution to
narrowing the learning gap and winning the space race. The
Harvard educator believed that small schools did not allow for a
beneficial diversified curriculum and reasoned that larger high
schools offered more comprehensive instructional programs of
greater quality at lower costs.
Having reviewed nearly 120 studies conducted between
1924-1972 pertaining to school size and its relationship to
school effectiveness, Stemnock (1974) found that the studies
generally served as justifications for larger schools. The re-
search studies tended to focus on the relationship among input
variables, including the curriculum, teacher credentials and
teaching styles. The few studies which related school size spe-
cifically to academic achievement were found to be void of any
recommendations in reference to optimal school size.
Throughout the literature, consolidation advocates have also
relied heavily on expenditure theories as justification for the
abolition of small schools (McGuffey, & Brown, 1979). They
have maintained that the reduced per pupil expenditures feasi-
ble in larger schools, translated into greater student achieve-
ment. This relationship was achieved through the calculated
investment of monetary savings into various methods of school
improvement. Fiscally this argument was very appealing to
educational policy makers, and in an era of economic pressure,
the trend to consolidate continued.
The association between reduced expenditure and achieve-
ment previously reported (McGuffey, & Brown, 1979) was not
found in subsequent replication studies in the 1980s (Burrup,
Brimley, & Garfield, 1988; Monk, 1987). Consequently, the
enthusiasm to consolidate began to fade, as the effectiveness of
large schools was questioned (Guthrie, & Reed, 1986). Sergio-
vanni (1995) argued that school size was associated with valu-
able process variables that large schools disabled or suppressed,
and urged educational decision-makers to go beyond simple per
student cost and consider the ratio of productivity to cost. Ad-
ditional research concluded that per student expenditure was
positively related to student achievement and that a ten percent
increase in per pupil expenditures was related to an increase in
student achievement of one standard deviation over 12 years of
schooling (Greenwald, Hedges, & Laine, 1996).
Contempor ar y Advocation for Small Sch ool s
Researchers (Greenwald, Hedges, & Laine, 1996) performed
a meta-analysis of studies from the 1960s and found student
achievement in small schools to be superior to that in large
schools. Using the American National Educational Longitudi-
nal Study data set, Lee, Smith and Croninger (1997) similarly
found that larger high schools had a negative influence on aca-
demic achievement particularly in mathematics and science. In
a study of the reading and mathematics proficiency scores from
every high school in North Dakota, Hylden (2005) found that
schools with over 500 students had the poorest performance
At the elementary level, research on third graders in 1,021
New York schools found that increasing school size had a nega-
tive effect on academic achievement (Wendling, & Cohen,
1981). In a large urban Missouri school district, Alspaugh and
Gao (2003) studied the results of the Stanford 9 Normal Curve
Equivalent (NCE) scores among fifth grade students. Control-
ling for socioeconomic status (SES), Alspaugh found a decline
in achievement levels as enrolment increased, particularly in
inner city and suburban schools. Similar findings of a positive
relationship between academic achievement and small schools
had been replicated in many other studies (Eberts, Kehoe, &
Stone, 1982; Fowler, & Walberg, 1991; Miller, Ellsworth, &
Howell, 1986; Wasley et al., 2000).
Other Variables in the Size and Achievement
Some researchers have cautioned that school size and aca-
demic achievement should not be correlated in isolation, and
have concluded that other variables, particularly socioeconomic
status (SES), must be considered in this relationship. Having
dubbed this association the Matthew Principle (Howley, 1995),
after the biblical reference to the phenomenon of the rich get-
ting richer and the poor getting poorer, Howley found that the
relationship between school size and academic achievement
was completely dependent on the socioeconomic status of the
community in West Virginia. Results indicated that small
school size mitigated the negative effects of poverty on aca-
demic achievement.
Extending the work of the Matthew Project, research in Mon-
tana, Georgia, Texas and Ohio, also found that smaller school
size cut the variance in achievement associated with SES by 20
to 70 percent (Howley, Strange, & Bickel, 2000). The percent-
age was usually 30 to 50 percent, depending on the grade level.
The relationship was notably weakest in Montana, where there
was a large percentage of small schools. In a report on their
findings, Howley, Strange, and Bickel (2000) concluded that
the correlation between poverty and lower academic achieve-
ment in the four States of interest was ten times stronger in
large schools than in small ones. Research further indicated that
larger schools served the same function for affluent communi-
ties. An exact replication study in Washington reached the same
conclusion (Abbott, Joireman & Stroh, 2002). Other researchers
also found that as school size increased, achievement levels for
schools with economically deprived students decreased (Bickel,
Howley, Williams & Glascock, 2001; Caldas, 1993; Franklin &
Crone, 1992).
Another variable that was correlated with school size and
academic achievement was grade level. In a study of students
in California, Friedkin and Necochea (1988) looked at the 3rd,
6th, 8th and 12th grades. They concluded that large schools
were associated with greater achievement for the 12th grade
students, but small schools were associated with greater
achievement for students in the 3rd, 6th and 8th grades. In a
similar study, the Texas Education Agency (1999) found that
students in the elementary and middle school grades were more
adversely affected by school size than at the high school level.
The Agency concluded that any potential benefits of large
school size may be negated until students had acquired founda-
tional academic skills, such as reading and arithmetic, and had
become capable o f inde pendent learning.
Canadian researchers have also studied the relationship be-
tween academic achievement and school size (Lytton, & Pyryt,
1998; Ma, & Klinger, 2000). Lytton and Pyryt used data col-
lected through the completion of the Alberta Achievement Test
by almost all the elementary schools in the Calgary Board of
Education in 1996. Controlling for the variable of socioeco-
nomic status, the researchers found no relationship between
school size and achievement. In a similar study in New Bruns-
wick, Ma and Klinger (2000) used the New Brunswick School
Climate Study of 1996 to accumulate data, which evaluated
student achievement in mathematics, science, reading and writ-
ing. The researchers focused on the entire grade six population
in the English school system. Using a hierarchical linear model,
they found no association between achievement and school
Optimal School Size
Taking cognizance of the reported benefits of small schools,
many researchers sought to numerically clarify what constituted
an optimal school size. Long ago, large school advocate, Co-
nant (1959), urged schools to have a graduating class of 100,
which is notably small by today’s standards. Other high school
researchers reported that there was no reason for a high school
to have more than 400 students (Haller, & Monk, 1988). Ser-
giovanni (1995) recommended no more than 300 students at-
tending a school, at either the high or elementary school level.
Meier (1996) had concluded that schools with enrolments of
300 to 400 students were optimal for seven reasons, namely,
governance, respect, simplicity, safety, parent involvement,
accountability and belonging. Lee and Smith (1997) concluded
that a curvilinear relationship existed because they found that
high school achievement increased as enrolment levels rose to
600, stayed steady up to 900, and then decreased as enrolment
size further rose. They recommended an optimal high school
enrolment of 600 to 900 students. Research conducted primar-
ily at the elementary level concluded that the optimal upper
limit of enrolment in an effective school would be 300 students
(Goodlad, 1984).
In summary, there has been vigorous debate over the optimal
size of efficient schools. Research has provided little clarity on
whether there is a relationship between school size and aca-
demic achievement. Some research has shown a correlation
between the two variables, while others have concluded that the
relationship is totally dependent on other sociological and eco-
nomic factors, and still others have found that there is no rela-
tionship at all. Researchers who have concluded that there is a
correlation between school size and academic achievement do
not concur on what the optimal size of a school should be.
There is also no conclusive clarification of what impact, if any,
the innate characteristics of small and large schools have in the
achievement and size relationship. With the foregoing as an
impetus, this study set out to explore the issue further, focusing
on the Province of Ontario, Canada, where the EQAO (Educa-
tion Quality and Accountability Office)—a standardized achieve-
ment test—is routinely administered, and used to assess the
academic achievement of elementary school students.
The target population for the study was the Grade three and
Grade six students in Ontario school boards that participated in
the EQAO assessment in May of 2003. A sample of ten Eng-
lish-Language public school boards was selected from the
population. Sampling of the Ontario school boards was done
strategically, resulting in a clustered sample. School board se-
lection was based on the following criteria: the geographical
location of the board, the existence of both rural and urban
areas within each school board district and an assortment of
different-sized schools within the board. With regard to geo-
graphical location, school boards were strategically selected so
that they spanned across the entire province. Eight of the ten
school boards were located in the Southern area of the province,
and two were located in the Northern area. The ten school
boards included in the clustered sample were: Algoma District
School Board (DSB), Bluewater DSB, Durham DSB, Grand
Erie DSB, Greater Essex County DSB, Kawartha Pine Ridge
DSB, Lakehead DSB, Limestone DSB, Ottawa-Carleton DSB,
and Peel DSB. In total, 48,482 third and sixth Grade students
who attended the 541 schools within the ten selected school
boards, and participated in the 2002/2003 EQAO assessment
were subjects in this study.
Within the sample, some individual school results were sup-
pressed by the Education Quality and Accountability Office.
Suppression occurred when the schools had fewer than fifteen
students at the Grade three or Grade six level who were eligible
to participate in the assessment. All suppressions were made in
the interest of protecting personal information, so that individ-
ual results could not be inferred from the data. As a result of the
EQAO suppression practices, the data for 15 schools were not
available for inclusion in this study. Schools that did not have
both Grade three and Grade six classes were also omitted from
this study. This purposeful exclusion was done to maintain a
more homogeneous sample because the researchers did not
want any variables resulting from the specialization of educa-
tional experiences within primary and junior schools to skew
the results.
Description of EQAO
The study relied on data emanating from the Education Qual-
ity and Accountability Office (EQAO) assessments in the se-
lected schools. The EQAO assessment measures the variable of
academic achievement. EQAO was established based on the
recommendation of the Ontario Royal Commission of Learning
in 1995 (EQAO, 2005). The Commission concluded that prov-
ince-wide assessments would meet the societal demands for
greater quality and accountability in the publicly funded school
system. The purpose of the EQAO assessment is to provide
“accurate, objective and clear information about student
achievement that teachers and parents can use to improve
learning for all students” (EQAO, 2003a, p.1). Included in the
EQAO Assessment package was the Administration Guide for
the Grade 3 and Grade 6 Assessments of Reading, Writing and
Mathematics and the Teachers Daily Plans (EQAO, 2003b).
Both books contained all the policies, procedures and instruc-
tions needed to administer the assessment in the most fair and
consistent manner possible. These instructions included the
sequence of the activities for each day, information about which
resources were permitted, introductory activities, time allot-
ments and the exact wording that the teacher should use when
introducing each segment of the assessment. Strict adherence
to these procedures was mandatory so as to ensure the reliabil-
ity of the results across the province.
The 2002/2003 EQAO assessment for Grades three and six
came in individualized student packages that consisted of a
reading magazine, a reading answer booklet, a writing booklet,
a mathematics booklet and a multiple choice booklet. All of the
student booklets at a particular Grade level were identical, with
the exception of the multiple-choice booklets. There were four
versions of the multiple-choice booklets within each class. The
only difference in the versions was the sequencing of the ques-
tions within the booklet. Each reading magazine comprised of
two selections—a fictional story and an information article.
Students answered questions based on these readings in the
accompanying reading answer booklets. The writing compo-
nent of the EQAO assessment comprised of two assignments.
At the Grade three level the students were to write a fictional
adventure story and a journal entry. At the Grade six level the
students were to write a fictional adventure story and a letter of
The format of the mathematics component was also similar
in both the Grade three and Grade six versions of the EQAO
assessment. The mathematics booklets were broken into three
sections, entitled Investigations 1, 2 and 3. They consisted re-
spectively of 7 questions, 7 questions and 6 questions in the
third Grade assessment and 7 questions, 6 questions and 7
questions in the sixth Grade assessment. The questions inte-
grated many of the mathematical expectations outlined in The
Ontario Curriculum for Mathematics for the respective Grades,
covering all five strands of Data Management and Probability,
Number Sense and Numeration, Geometry and Spatial Sense,
Measurement, and Patternin g and Algebra.
The EQAO assessment is administered yearly to pupils in
Grades three and six in Ontario. EQAO ensured validity of the
2002/2003 assessment by basing all of the reading, writing and
mathematics tasks on the appropriate grade expectations out-
lined in The Ontario Curriculum, Grades 1 - 8 (Ontario Minis-
try of Education, 2006). The 2002/2003 assessment was ad-
ministered over a period of five days. Testing occurred for no
more than two hours and thirty minutes per day. At the end of
the five-day period, all the student packages were returned to
the Education Quality and Accountability Office for evaluation.
Many steps were taken to ensure examiner reliability. EQAO
ensured that the work of every person chosen to evaluate the
assessment was of consistently high quality through a careful
selection process, comprehensive training and monitoring.
Training consisted of two full days prior to the evaluation of the
assessment, as well as ongoing training throughout the marking
period. The ongoing training included the completion of train-
ing booklets, orientation papers, paired marking, marker readi-
ness exercises and group marking.
Some booklet-related steps were also taken to ensure reli-
ability of the assessment. Every student was assigned a barcode,
to remain anonymous to the evaluator. Booklets were scram-
bled to ensure that individual schools and school boards could
not be identified during the evaluation process. Each booklet
was evaluated by multiple markers. The blind reinsertion of
student papers was also done to check the consistency of mark-
ers’ scoring. EQAO also conducted a generalizability study of
the 2002/2003 assessment. This study allowed for EQAO to
report on the consistency of the examiners and assessment
items and estimate an overall generalizability coefficient.
Design and Procedures
The design of this quantitative study is correlational. The
data for achievement and school size utilized in the study is a
matter of public record. The Grades three and six 2002/2003
EQAO assessment results for each school in the stratified sam-
ple were obtained from the official EQAO Web site. EQAO
reported the findings from the assessments in two ways: Meth-
ods 1 and 2. Method 1 reported leveled data in percentage for-
mat from all eligible students in the grade, including those that
were exempt and students who did not provide enough data on
the assessment to score. Method 2 is an alternative view of the
results. It did not include the results of those that were exempt,
or those students who did not provide enough data to score, in
the final formulation of the percentages.
This study utilized the results that were reported only in
Method 1. This decision was based on the researchers’ percep-
tion that the results for Method 1 provided a more accurate and
complete description of actual student achievement because
these results included all eligible Grades three and six students,
not just those who participated and achieved at specific levels.
The view of the researchers is similarly reflected in the media
presentation of the EQAO results. Newspaper reports present
the assessment scores only in Method 1 form. The main focus
of the study was on the percentage of students in the third and
sixth Grades who achieved a level three or higher on the 2002/
2003 EQAO assessment in each school in the selected school
boards. The achievement of level three or higher indicated that
the student was performing at or above the provincial standard
for that grade. The percentages of those who achieved at levels
one and two, those who performed below the level one standard,
and those who did not include enough information to score,
were also obtained for analysis.
Included in the EQAO assessment results was the number of
students who participated in the assessment in May 2003, in
both the third and sixth Grades, for each selected school. These
data were used to categorize each selected school as a small,
medium, or large school. For the purposes of this study, small
schools were defined as having less than 245 students, while
the enrolment figure for medium-sized schools was between
246 and 420, and large schools had more than 420 students.
Data Analysis
The EQAO results, represented in percentage form, were ar-
ranged in a Microsoft Excel spreadsheet table for each school.
Each school table was divided into a Grade three and a Grade
six section, and sub-divided by subject; reading, writing, and
mathematics. The results were further sorted into six achieve-
ment categories—Not Enough Information to Score (NEIS),
Not Enough Information to Score a Level One (NE1), followed
by Level One, Level Two, Level Three, and Level Four. In
addition, the researchers classified each school according to
size, that is, small, medium, or large. All of the EQAO results
were then aggregated because if a student had achieved a Level
4, then he/she had also logically achieved Levels 1, 2 and 3.
Using the Statistical Package for the Social Sciences, (SPSS),
a one-way analysis of variance (ANOVA) was conducted to
evaluate the relationship between school size and student aca-
demic achievement. The independent variable was school size
and the dependent variable was student academic achievement.
Variations both within and between each of the groups were
analyzed statistically, yielding F-values. The significance level
for this procedure was established at the .05 level.
This study tested the null hypothesis that there would be no
statistically significant correlation between school size and
academic achievement under the seven categories:
In Grades three and six;
At the Not Enough Information to Score level in Grades
three and six;
At the Not Enough Information to Score a Level One
level in Grades three and six;
At Level One in Grades three and six;
At Level Two in Grades three and six;
At Level Three in Grades three and six;
At Level Four in Grades three and six.
Summary of Results and Findings
A one-way analysis of variance was performed and results
indicated that there was no statistically significant correlation
between school size and academic achievement in Grades three
and six. Table 1 summarizes the results.
An ANOVA was performed and results indicated no statisti-
cally significant correlation between school size and academic
achievement at the Not Enough Information to Score level and
at the Not Enough Information to Score a Level One level in
Grades three and six. Tables 2 and 3 summarize the results.
Results shown in Tables 4 and 5 indicated no statistically
significant correlation between school size and academic
achievement at Level One and at Level Two in Grades three
and six.
Result s sho wn in T abl e 6 i ndic ated no statistically significant
correlation between school size and academic achievement at
Level Three in Grade three in the areas of reading and math, so
a fail-to-reject decision was reached. Results indicated that
there was a statistically significant correlation between school
size and academic achievement at Level Three in Grade three in
the area of writing, so the null hypothesis for this comparison
was rejected at the .05 level of significance. Results also indi-
cated that there was a statistically significant correlation be-
tween school size and academic achievement at Level Three in
Grade six in the areas of reading, writing and math, so the null
hypothesis for this comparison was rejected at the .05 level.
Results shown in Table 7 indicated there was no statistically
significant difference between school size and academic
achievement at Level Four in Grade three in the areas of read-
ing and math, so a fail-to-reject decision was reached. Results
Table 1.
Correlation between school s ize and academic ac hievement.
Sum of
Squares df Mean
Square F Sig.
AA Between Groups .000 2 .000 .0001.000
Within Groups 9467.5003243 2.919
Total 9467.5003245
3 reading Between Groups 36.888 2 18.444 .060.942
Within Groups 999168.896 3243 308.100
Total 999205.784 3245
3 writing Between Groups 27.064 2 13.532 .034.966
Within Groups 1280284.672 3243 394.784
Total 1280311.736 3245
3 math Betwee n Groups 16.393 2 8.197 .023.977
Within Groups 1159602.596 3243 357.571
Total 1159618.990 3245
6 reading Between Groups 22.644 2 11.322 .035.966
Within Groups 1056323.515 3243 325.724
Total 1056346.159 3245
6 writing Between Groups 15.787 2 7.894 .024.977
Within Groups 1084003.002 3243 334.259
Total 1084018.789 3245
6 math Betwee n Groups 23.444 2 11.722 .041.960
Within Groups 925000.503 3243 285.230
Total 925023.947 3245
Table 2.
Correlation between school size and academic achievement at the not
enough information to sco re le v e l.
Sum of
Squares df Mean
Square F Sig.
3 readingBetween Groups60.882 2 30.441 .365.694
Within Groups 44881.403 538 83.423
Total 44942.285 540
3 writingBetween Groups18.535 2 9.267 .408.665
Within Groups 12222.911 538 22.719
Total 12241.445 540
3 mathBetween Groups144.282 2 72.141 .944.390
Within Groups 41107.400 538 76.408
Total 41251.682 540
6 readingBetween Groups81.173 2 40.587 .947.388
Within Groups 23049.374 538 42.843
Total 23130.547 540
6 writingBetween Groups72.497 2 36.249 1.615.200
Within Groups 12075.384 538 22.445
Total 12147.882 540
6 mathBetween Groups7.639 2 3.820 .068.934
Within Groups 30326.176 538 56.368
Total 30333.815 540
Table 3.
Correlation between school size and academic achievement at the not
enough information t o score a level one level.
Sum of
Squares df Mean
Square F Sig.
3 readingBetween Groups.153 2 .076 1.438.238
Within Groups 28.535 538 .053
Total 28.688 540
3 writingBetween Groups.615 2 .307 1.141.320
Within Groups 144.968 538 .269
Total 145.582 540
3 mathBetween Groups.029 2 .015 .214.808
Within Groups 36.658 538 .068
Total 36.688 540
6 readingBetween Groups.048 2 .024 .382.683
Within Groups 33.479 538 .062
Total 33.527 540
6 writingBetween Groups.052 2 .026 .707.493
Within Groups 19.881 538 .037
Total 19.933 540
6 mathBetween Groups.021 2 .011 1.148.318
Within Groups 4.962 538 .009
Total 4.983 540
indicated that there was a statistically significant correlation
between school size and academic achievement at Level Four
in Grade three in the area of writing, so the null hypothesis for
this comparison was rejected at the .05 level. Results also indi-
cated that there was a statistically significant correlation between
school size and academic achievement at Le ve l Four i n Gra de six
in the areas of reading, writing and math, so the null hypothesis
for this comparison was rejected at the .05 level.
Table 4.
Correlation between school size and academic achievement at level one
in grades three and six.
Sum of
Squares df Mean
Square F Sig.
3 reading Between G ro ups 34 7.3502 173.675 1.253.287
Within Groups 74580.514 538 138.625
Total 74927.863 540
3 writing Between Groups 206.5272 103.263 1.568.209
Within Groups 35431.473 538 65.858
Total 35638.000 540
3 math Between Groups 264.4522 132.226 1.071.343
Within Groups 66422.868 538 123.463
Total 66687.320 540
6 reading Between G ro ups 8.572 2 4.286 .051.951
Within Groups 45455.646 538 84.490
Total 45464.218 540
6 writing Between Groups 10.0432 5.021 .078.925
Within Groups 34675.772 538 64.453
Total 34685.815 540
6 math Between Groups 102.3332 51.166 .562.570
Within Groups 48960.421 538 91.005
Total 49062.754 540
Table 5.
Correlation between school size and academic achievement at level two
in grades three and six.
Sum of
Squares df Mean
Square F Sig.
3 reading Between Groups 747.761 2 373.880 1.631.197
Within Groups 123360.246 538 229.294
Total 124108.007 540
3 writing Between G r oups 442.804 2 221.402 2.76 4.064
Within Groups 43097.011538 80.106
Total 43539.815540
3 math Between G roups 777.335 2 388.667 1.892.152
Within Groups 110510.015 538 205.409
Total 111287.349 540
6 reading Between Groups 618.479 2 309.239 2.008.135
Within Groups 82858.608538 154.012
Total 83477.087540
6 writing Between G r oups 281.333 2 140.666 1.49 5.225
Within Groups 50611.407538 94.073
Total 50892.739540
6 math Between G roups 706.352 2 353.176 1.754.174
Within Groups 108324.510 538 201.347
Total 109030.861 540
Table 6.
Correlation between school size and academic achievement at level
three in grades three an d s i x .
Sum of
Squares df Mean
Square F Sig.
3 readingBetween Groups1324.853 2 662.427 2.001.136
Within Groups178060.906538 330.968
Total 179385.760540
3 writingBetween Groups4886.709 2 2443.355 9.483.000
Within Groups138617.605538 257.654
Total 143504.314540
3 mathBetw een Groups1904.918 2 952.459 2.021.134
Within Groups253529.803538 471.245
Total 255434.721540
6 readingBetween Groups3996.820 2 1998.410 6.695.001
Within Groups160597.979538 298.509
Total 164594.799540
6 writingBetween Groups6327.488 2 3163.744 13.083.000
Within Groups130100.675538 241.823
Total 136428.163540
6 mathBetw een Groups3774.297 2 1887.148 4.714.009
Within Groups215388.653538 400.351
Total 219162.950540
Table 7.
Correlation between school size and academic achievement at level
four in grades three and six.
Sum of
Squares df Mean
Square F Sig.
3 readingBetween Groups132.070 2 66.035 1.761.173
Within Groups 20168.507 538 37.488
Total 20300.577 540
3 writingBetween Groups703.032 2 351. 516 10.892.000
Within Groups 17362.388 538 32.272
Total 18065.420 540
3 mathBetween Groups531.877 2 265.939 1.852.158
Within Groups 77236.093 538 143.562
Total 77767.970 540
6 readingBetween Groups633.355 2 316.677 5.711.004
Within Groups 29834.578 538 55.455
Total 30467.933 540
6 writingBetween Groups831.653 2 415. 827 9.245.000
Within Groups 24199.023 538 44.980
Total 25030.677 540
6 mathBetween Groups713.910 2 356.955 2.578.077
Within Groups 74491.646 538 138.460
Total 75205.556 540
To further investigate the statistical significance of the results
where the null hypothesis was rejected, the mean percentage
number of students who performed at the various levels for
each school size was examined. Table 8 summarizes the results.
Results indicate that the mean percentage number of students
who performed at Level 3 was highest in large schools in Grade
three writing and in Grade six reading, writing and mathematics.
The respective mean percentage number of students who per-
formed at Level 3 was lowest in small schools.
Results also indicate that the mean percentage number of
students who performed at Level 4 was highest in large schools
in Grade six reading and writing. The mean percentage number
of students who performed at Level 4 was highest in medium
schools in Grade three writing and in Grade six math. All the
respective mean percentage numbers of students who per-
formed at Level 4 was lowest in small schools.
Implications of the Findings
The results indicated that overall, there was no statistically
significant correlation between school size and academic
achievement in Grades three and six. This finding reflects simi-
lar conclusions reached by many North American researchers,
who had previously determined that a size and achievement
relationship did not exist (Barker, & Gump, 1964; Borland, &
Howsen, 2003; Caldas, 1993; Edington, & Gardner, 1984;
Fowler, 1995; Haller, Monk, & Tien, 1993; Howley, 1996;
Huang & Howley, 1993; McGuire, 1989; Smith & DeYoung,
1988; Stockard, & Mayberry, 1992).
The main result of the study echoes the findings of some
other Canadian studies which also failed to find statistical evi-
dence of a relationship between school size and academic
achievement (Lytton, & Pyryt, 1998; Ma, & Klinger, 2000).
Like these previous studies, carried out in the Canadian prov-
inces of Alberta and New Brunswick respectively, the re-
searchers focused on elementary schools in Ontario, and used
standardized provincial assessments as a means of determining
student academic achievement. This study makes a valuable
contribution to the growing body of research in Canada, by
offering a look at the size and achievement situation in Ontario.
Replication of the study in other Canadian provinces, and pos-
sibly in different countries in other parts of the world, could be
beneficial in helping educators and government officials make
decisions regarding the creation or maintenance of schools, and
the appropriate allocation of funding.
Results further indicated that there was no statistically sig-
nificant correlation between school size and academic achieve-
ment at the Not Enough Information to Score level or at the Not
Enough Information to Score a Level One level in Grades three
and six. In addition, data analysis revealed no statistical evi-
Table 8.
Mean percentage number of students who performed at the various
levels for each school size.
Grade Academic Achievement Subject School Size
Small MediumLarge
3 Level 3 Writing 47.65 53.6 54.41
6 Reading 49.82 54.77 56.5
Writing 45.45 51.43 54.12
Math 47.25 52.7 52.75
3 Level 4 Writing 4.89 7.38 6.77
6 Reading 6.68 8.5 9.48
Writing 7.41 8.83 10.9
Math 9.95 12.48 11.74
dence of a relationship at Level One or at Level Two in either
Grade. It should be noted that unlike many of the studies re-
ported in the literature which found evidence of a size and
achievement relationship (for example, Abbott, Joireman, &
Stroh, 2002), this study did not control for the variable of so-
cioeconomic status. Howley (1995) had cautioned that size and
achievement should not be studied in isolation, without the
consideration of the influential variable of socioeconomic status.
Roeder (2002) had also insisted that poverty was the biggest
factor in the achievement and size relationship. Having not
directly controlled for the socioeconomic variable may have
affected the results of this study. Future replication studies are
needed to determine if other variables, particularly socioeco-
nomic status, have an impact on the results.
Data analysis also found that there was no statistically sig-
nificant correlation between school size and academic achieve-
ment at Level Three in Grade three in the areas of reading and
math. There was however, a statistically significant correlation
at the .05 level of significance between school size and aca-
demic achievement in the area of writing. These results agree
with the finding of some researchers that when a relationship
between size and achievement is found it is limited in scope
(for example, Slate, & Jones, 2005). Unlike Okpala (2000),
who found a relationship in reading alone at a fourth grade
level, this study found a correlation only in writing. This find-
ing was also obtained in the Grade three results at Level Four,
where writing was the only area in which a statistically signifi-
cant correlation was observed.
In reviewing the EQAO assessment package to determine
what made the writing section unique from that of reading and
mathematics, the researchers found one noteworthy difference.
Writing was the only section of the assessment that did not
contain a multiple-choice component. The student was ulti-
mately assessed entirely on individual output, without the pos-
sibility of increasing his/her achievement score solely on the
basis of possible successful guesswork. It could, therefore, be
concluded that the writing section was the most valid part of the
The most significant results were observed at Levels Three
and Four in Grade six. There was a statistically significant cor-
relation between school size and academic achievement in all
areas of the assessment; reading, writing and mathematics. The
finding of a consistent correlation at the higher of the two
Grade levels was not surprising after the literature review. In
previous studies, higher grades were more likely to reveal a
statistically significant correlation between student achievement
and school size (Howley, 1989). Howley had concluded that
school size played a greater role in achievement as students
Reflecting on the immense fundamental differences between
Grades three and six, it is not surprising to find disparity in the
results. Third graders are still learning the basic components of
reading, writing and mathematics. The Grade three curriculum
is focused on the mastery of an essential foundation of knowl-
edge, often seen as the basic building blocks of learning. In
contrast, sixth graders are expected to have already built such a
foundation, and are more focused on utilizing higher level
thinking skills to manipulate new knowledge. Education past
the primary level becomes more individualized and specialized,
allowing students in the junior division to have more freedom
and control over their educational experience.
Developmental differences, both physical and psychological,
may also account for the different assessment outcomes in
Grades three and six. Students in the two respective Grades,
with an approximate three-year chronological age gap, have
undoubtedly unique capabilities and characteristics. For exam-
ple, according to the renowned developmental psychologist,
Jean Piaget, third graders would be in the Concrete Operational
stage, during which they learn to think logically in concrete
situations. Conversely, sixth graders would more likely be in
the Formal Operational stage, where they are able to think
logically in abstract situations and are more interested in the
world of ideas (Wood, Wood, Green Wood & Desmarais, 2005).
In addition, unlike their third Grade counterparts, the EQAO
assessment is not a new experience for sixth graders. The older
students have had the advantage of previously participating in
the EQAO assessment when they were in Grade three. This
previous experience of what to expect regarding the assessment,
both in terms of procedures and format, could be considered
In conjunction with the definitions used in this study, me-
dium schools consisted of between 246 and 420 students, and
large schools consisted of an enrolment of more than 420 stu-
dents. When comparing these parameters with those of previous
studies, the difference is notable. Throughout the literature,
researchers who had found a relationship between school size
and academic achievement, particularly those who found a
correlation between small schools and higher achievement lev-
els, had recommended an optimal enrolment of around 300
students (Goodlad, 1983; Meier, 1996; Sergiovanni, 1995).
This specific level of enrolment coincides with this study’s
definition of a medium-sized school. Upon closer inspection,
the finding that students who attended schools of this size
achieved highest in Grade three writing and Grade six math at
Level 4, is not surprising. It seems, therefore, that it is not the
findings that are contradictory, but rather the conflict lies with
the school size parameters as defined by individual researchers.
These results, and the review of the literature, have also
raised some questions concerning the current initiatives pro-
moting small schools. With such disparity in the findings, the
investment of large amounts of money in small school projects
becomes a questionable venture. Does the scientific evidence
actually support the establishment of such expensive initiatives?
Certainly the results of this study, as well as many others, indi-
cate that not enough is currently known about the size and
achievement relationship to make critical decisions for educa-
tional reform. Howley (1995) had cautioned that some small
school advocates were misrepresenting or misinterpreting re-
search findings as a means of furthering their own agenda. With
such ambiguity in the literature, advocation for schools of a
specific size, based primarily on the achievement and size rela-
tionship, should be cautioned. With activist groups, like the
People for Education, campaigning for the maintenance of
small schools throughout Ontario, it is clear that more research
is needed so that fully informed decisions can be made.
This study relied on data provided by a province-wide as-
sessment given to students in the third and sixth grades
throughout Ontario, as a measurement of student academic
achievement. Despite strict guidelines provided for the admini-
stration of the assessment and mandated adherence to the poli-
cies, procedures, and instructions given, there may have been
deliberate or unintended effects of individual administrators on
the students.
The EQAO assessment is considered to be valid because it is
based on The Ontario Curriculum, Grades 1 - 8. In practice,
however, the content validity of the test is questionable. Edu-
cators throughout Ontario are encouraged to adopt a construc-
tivist philosophy to teaching. Constructivism is based on the
tenet of creating educational experiences in which the students
can construct their own meaning. It is a learn-by-doing ap-
proach. The questions in the EQAO assessment do not reflect
this philosophy. This contrast between how the students learn,
and ultimately how they are assessed, is obvious in mathemat-
ics. The routine use of manipulatives in learning math is a
standard practice in Ontario classrooms. Students construc-
tively use the manipulatives to facilitate the learning of math.
However, on the 2002/03 EQAO assessment, there was only
one question which demanded the use of manipulatives. If
standard classroom teaching practices are not reflected in the
assessment, the content validity must be questioned.
Additionally, the EQAO assessment, like all tests, can only
be considered a snapshot of an individual student’s academic
achievement level. There are many variables that could affect a
student’s performance during the five days of the assessment
which would limit the reliability of the results. These variables
could include i l ln e s s , fati g u e , and environmental factors.
Canada prides itself on being a multicultural country. The
student communities within many Ontario schools reflect the
wide diversity of the Canadian population. There needs to be
more research into whether the EQAO assessment accurately
reflects the interests of all Ontario students and their various
cultural backgrounds.
The researchers also could not control for full participation in
the EQAO assessment within each school. All third grade and
sixth grade students were mandated by the Ontario provincial
government to participate in the 2002/2003 assessment. Ex-
emptions from the assessment were only granted students who
were in the Individual Education Plan, or English as a Second
Language students who were in the early stages of English
Language acquisition. Some parents disagreed with the admini-
stration of the assessment and withheld their children from
school during the testing period. Therefore, the EQAO test
scores may not have been accurate reflections of all academic
achievement levels within a given class.
The suppression of some of the individual school assessment
results by the Education Quality and Accountability Office also
limits the conclusions drawn from this study. With the mandate
for suppression being an enrolment of fewer than 15 students in
the class, this directly affected the small school achievement
results. Classes with such a small enrolment would have been
included in the small school category, if the results had been
Suggestions and Recommendations
Based on the findings of the study, the researchers make the
following recommendations:
1) Additional studies are needed to investigate the relation-
ship between school size and academic achievement at the ele-
mentary school level;
2) Replication studies, in which the socioeconomic status
variable is controlled, are needed to provide more information
on the size and achievement relationship. Future research stud-
ies should focus specifically on smaller schools with the goal of
finding more information within this variable, including opti-
mal enrollment and if extreme smallness could be considered
3) School board officials, educators, government officials,
and policy makers who are in the position to make decisions
regarding the sizes of schools in their districts should be fully
informed with regard to the entire body of research on the rela-
tionship between school size and academic achievement;
4) The Education Quality and Accountability Office should
consider developing a rotational schedule, in which a limited
number of proctors would administer the EQAO assessment
throughout the province, in the hope of improving the reliabil-
ity of the assessment;
5) Future research by the Education Quality and Account-
ability Office should be done to ensure that there is no cultural
bias in the assessment, and that the interests of the entire On-
tario student body are reflected in the test;
6) The Education Quality and Accountability Office should
ensure that the EQAO assessment accurately reflects standard
classroom practices and expectations in Ontario schools so as to
increase the content v ali dity of the assessment ;
In conclusion, this study indicates that the relationship be-
tween school size and academic achievement is limited. Evi-
dence of a relationship is more likely to be found at the higher
grade levels, as shown in both the literature and in the study.
These results should be read with caution, with particular atten-
tion paid to how a researcher defines school sizes. Additional
studies in which other variables that may influence the size and
achievement relationship are also needed. Finally, until the
literature becomes less ambiguous, advocation for elementary
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