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of Achievement
in Country and Town Schools
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By Norman Frost
Submitted in Partial Fulfillment of the Requirements of the
Degree of Doctor of Philosophy in the Faculty
of Philosophy, Columbia University
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A Comparative Study of Achievement
in Country and Town Schools
By Norman Frost
Submitted in Partial Fulfillment of the Requirements of the
Degree of Doctor of Philosophy in the Faculty
of Philosophy, Columbia University
New York
1921
COPYRIGHT, 1921, BY NORMAN FROST
Rolumbia Unce to
M'QUIDDY PRINTING CO.
NASHVILLE
ACKNOWLEDGMENTS
T
HIS study has been made possible by the help of a number of peo-
ple. Thanks are extended to the school officials who have fur-
nished data or permitted tests to be given in the schools in their charge.
Indebtedness is acknowledged to the many members of the faculty of
Teachers College, Columbia University, who have assisted by con-
structive criticism. Special thanks are due Dr. N. L. Engelhardt, Dr.
G. D. Strayer and Dr. E. L. Thorndike for advice, suggestion and
encouragement.
N. F.
408988
CONTENTS
I. Previous Objective Studies of Achievement in Country
Schools
7
II. Purpose and Scope of the Present Study
: 15
III.
Achievement Measured by the Trabue Language Scales
18
IV. Achievement Measured by the Courtis Standard Research
Tests in Arithmetic Series B
33
V. Achievement Measured by the Thorndike Silent Reading
Scale Alpha 2
56
VI. Summary and Conclusions
61
Appendix
68
A COMPARATIVE STUDY OF ACHIEVEMENT
IN COUNTRY AND TOWN SCHOOLS
CHAPTER I
PREVIOUS OBJECTIVE STUDIES OF ACHIEVEMENT IN
COUNTRY SCHOOLS
An accurate comparison of school systems in objective terms is
necessary for the proper solution of problems in regard to the organi-
zation and administration of schools. Such a comparison is made
possible by the use of standardized tests in the systems to be compared,
and has been made with great profit in many city school systems. To
a much more limited extent the same kind of comparisons have been
made among rural schools.
The Ohio Survey Commission Report, 1914, on pages 133 and 134,
reports the median score on the Hillegas scale of 97 eighth grade
composition papers from Delaware (city) as 521.6, and the sim-
ilar median of 118 eighth grade composition papers from Dela-
ware (county) is reported as 387.6. On pages 135ff. of the same
report results of handwriting scores by the Ayres Scale are given.
These results are from 1,397 pupils in 176 rural schools in 21 coun-
ties in Ohio; from 214 pupils in the three upper grades of the rural
schools of Delaware County ; from 312 pupils in the three upper grades
in the city schools of Delaware; and from a small city in Iowa, based on
results obtained by I. King and H. Johnson, whose study was originally
published in the Journal of Educational Psychology (III: 514-520).
Tables are given which show, among other things, that in the small
Iowa city 98 per cent of the eighth grade papers were scored over 50
on the Ayres Scale; that 77.8 per cent of the like papers from the Ohio
rural schools made like scores ; 73.5 per cent from the Delaware County
(rural); and 91.3 per cent from the city of Delaware. In conclusion
it is stated that "the handwriting in both Delaware city and Iowa city
is on the whole better than in the rural schools
and that
"there is greater uniformity in the city schools."
Results of work with the Courtis Standard Research Tests in
Arithmetic Series B and Starch's Arithmetical Scale A are reported
on pages 33ff. of A Study of Rural Schools in Travis County, Bul-
letin of the University of Texas, December, 1916. Tables are given
showing grade results of the Courtis tests, and the discussion is sum-
1.
len
7
8
Study of Achievement in Country and Town Schools
marized in this statement: "In every instance the number of examples
attempted and the number of examples worked correctly were lower
in this group of country schools than for the corresponding grades in
Boston and Detroit, and among the 11,800 pupils tested in Iowa.
Sometimes this difference was as great as 50 per cent, the average dif-
ference being approximately 25.5 per cent.” Concerning the results of
the Starch test the following statement is made: “As a test for the
reasoning ability of these pupils on arithmetical problems, Starch's
Arithmetical Scale A was used. The results from the fourth to the
eighth grade were duly tabulated. Each grade scored below the scale
standard established for it. The fourth grade was 11 per cent below
standard; the fifth grade 19 per cent; the sixth grade 5 per cent; the
seventh grade 6 per cent; and the eighth grade 8 per cent."
In 1916 the State Board of Education in Connecticut made a num-
ber of studies of the schools in certain of the towns (townships) of
that state. The tests used were not standardized, but they were uni-
form for all of these investigations. The subjects covered were arith-
metic, reading, language, history, geography and spelling. Compara-
tive tables for different towns in the state are given in these reports,
which were published separately as bulletins of the Connecticut State
Board of Education. The following quotations give an idea of the
character of the findings: "The accomplishment of the pupils as shown
by the tests given is only from fair to poor. Especially is this true
in view of the retardation in the schools.” (Educational Enquiry,
Trumbull, p. 29.) "While the results in this fundamental test are not
satisfactory, they nevertheless compare favorably with the work of
pupils in the towns of Seymour, Westbrook and Bloomfield.” (Edu-.
cational Enquiry, New Hartford, p. 24.) “It would appear from the
above that the children cannot add with facility and accuracy, although
some progress is being made from grade to grade." (Educational
Enquiry, Seymour, p. 23.) "It is obvious that most pupils in these
towns are unable to interpret and solve correctly simple problems."
(Educational Enquiry, Westbrook, p. 25.)
In an unpublished survey of the Haldane school, Cold Springs, N. Y.,
made in 1917, a table on page 30 gives a comparison of median achieve-
ments in English composition by grades (Hillegas Scale, Nassau
County Extension), which includes grade medians for the schools of
Mobile County, Ala., and for the city of Mobile. In every grade re-s
ported the median for the city schools is higher than that for the
country schools.
Previous Objective Studies
9
The Survey and Report of The Virginia Public Schools Education
Commission, published in 1919, gives comparative results for country
and city schools for the following tests: Thorndike Reading Scale A2,
Virginia Reading Test Sigma 8, Virginia General Examination Exer-
cise 1, Ayres Spelling Scale, Starch Scale for Measuring Handwriting,
Woody Arithmetic Scale Series B, Courtis Standard Research Test
in Arithmetic Series B, and the Nassau County Supplement to the
Hillegas Scale for Measuring English Composition. About sixteen
thousand different children were examined with from six to forty dif-
ferent tests. Of these sixteen thousand children about five thousand
were in grades three to seven of rural white schools. The general
character of the results is indicated by the following quotations from
the report : "In summary it may be said that the condition of reading
in the Virginia city schools is fairly satisfactory. Such deficiencies
as do exist will be easily adjusted when once attention is called to them.
In the rural schools, however, there is a deficiency that should be met
by vigorous remedial measures." (p. 121.) In regard to handwriting
the report has this to say: “The scores for rural schools having four
or more rooms compare favorably with those for city schools, and the
progress is regular from grade to grade. The average progress is
four-tenths of a scale step per year, which is less than it should be by
Starch Standards. The one-room country school shows the poorest
record.” (p. 122.) In regard to spelling it says: “The most notable
deficiencies are in the one-room school (all grades) and in the seventh
grade for every group tested. In three cases the deficiency is a year
or more of progress as measured on the Ayres Scale.” (p. 123.)
Concerning arithmetic the report states that "The average seventh
grade score for Virginia city children at the end of the year is 15.9,
which is the sixth grade Woody Standard for the beginning of the
year, and it is 15.1, or less than the sixth grade Woody Standard for
the seventh grade in the best graded rural schools. For the one-room
rural schools it is only 13.5.” (p. 124.) “What is true of addition
is generally true of the results in subtraction, multiplication and divi-
sion.” (p. 125.)
(p. 125.) In general conclusion in regard to the results in
rural schools the report says: “The inferiority of the small rural school
is apparent from the figures given. In reality that inferiority is even
greater since in all non-city schools children are on the average about
a year older than city children and in the one-room schools children
are on the average about a year and a half older than city children in
each of the upper grades of the elementary schools. In arithmetic the
10
Study of Achievement in Country and Town Schools
inferiority of the one-room school is perhaps most marked, children
in such schools being on the average one grade behind children in the
larger non-city schools." (p. 129.)
E. H. Taylor, in an article, "A Comparison of the Arithmetical
Abilities of Rural and City School Children," published in the Journal
of Educational Psychology (V: 461-466, October, 1914), reports the
results of Courtis arithmetic tests given by himself and the county
superintendent to most of the children in a county in Illinois. Tests
were given to 309 children in 28 schools. Results are tabulated and
compared by grades with scores of 7,008 children, published by Courtis
in Elementary School Teacher (XII: 133f). The comparison shows
that the rural schools are consistently below the others; grades 3 and
4 of the rural schools are approximately a grade below, grades 5 and 6
are almost two grades below, grade 7 is more than one grade but less
than two grades below, and grade 8 is at least two grades below.
Richard Zeidler reports in Elementary School Journal (XVI: 542-
555) tests of efficiency in the rural and village schools of Santa
Clara County, California. Courtis arithmetic tests were given by the
writer to 587 children in grades 5 to 8 inclusive. Results are compared
with a group of 20 small Western cities, with Salt Lake City, and with
Butte. The writer concludes that "From these tables it will be noted
that rural and village schools in Santa Clara County, in every subject
and in every grade, fall below the median scores for the cities. This
inferiority ranges as high as 600 per cent, as is shown in division in
the fifth grade of Santa Clara County compared with the fifth grade
division in Salt Lake City, Utah. It must be admitted, however, that
Salt Lake City has an enviable record.”
It will be seen that
rural and village schools of Santa Clara County fall, on the average,
fully two grades below Salt Lake City, and one grade below the twenty
small cities."
The same author reports tests in silent reading in the rural
schools of Santa Clara County, California, in Elementary School
Journal (XVII: 55-62). Starch Reading Tests were given by the
writer in 26 rural schools. Eight of these schools were one-teacher
schools, 7 were two-teacher, 7 were three-teacher, and 4 had more
than three teachers. The results are tabulated in detail, and compared
with results from San José. Mr. Zeidler says: "In comparing the
median number of words read per second in the rural schools with
the medians for the San José schools, it will be seen that the rural
schools compare very favorably with the city schools. The fifth grade
4
Previous Objective Studies
11
falls 2/10 below, while the seventh and eighth grades score higher
than the city schools of that community. But if we make a compari-
son of both the rural schools of Santa Clara County and the city
schools of San José with the standardized scores, we find that both fall
below, with the single exception of the seventh grade in the rural
schools, which surpasses the standards by 1/10.” “In the reproduction
of the thought, the rural school children fall below the children of the
city of San José. There is a marked difference in the third grade,
where the median for the rural schools is 7.5 as against 12.5 in the
city.”
Charles L. Harlan is the author of "A Comparison of the Writing,
Spelling and Arithmetic Abilities of Country and City Children," pub-
lished in Educational Administration and Supervision (II: 560-573).
Tests were given to 359 pupils in 21 rural schools in a "typical” county
in Pennsylvania. Handwriting was scored on the Ayres Scale and
compared with Freeman's average based on a study of handwriting
in 56 cities. No material difference appears between the results in
Mr. Harlan's study and the averages obtained by Freeman, either in
the quality or the speed of writing. Three hundred and thirty-seven
pupils were tested in spelling, words being used from the Ayres list.
Results are tabulated, and Mr. Harlan concludes: "A comparison of
the above averages shows an advantage of from seven to fourteen
words per one hundred in favor of the city pupils. The country
averages are uniformly lower than the city averages. This is no mere
statistical accident. The pupils of the rural schools do not spell as
well on written tests as do the children of the city schools.” Courtis
Arithmetic Tests Series B were given to 255 pupils. The comparison
is with the Courtis Standards. “In summarizing, one may say that in
the fundamental operations of arithmetic the pupils of the rural
schools rank approximately two grades below the pupils of the city
schools.” “The improvement in arithmetic from grade to grade is
less for country children than for city children.”
M. E. Haggerty, in Studies in Arithmetic, Indiana University
Studies, No. 32 (September, 1916), reports results from 5 counties
in Indiana. Results are tabulated, and it is concluded that “These bome
data point to the conclusion that the district schools are more efficient
in procuring achievement in the function measured than the graded.
(p. 68.) This is the only study found that reports an actual advan-
tage in favor of the rural school. Mr. Paul Mort is directly responsi-
ble for the data collected. It is not definitely stated how the material
12
Study of Achievement in Country and Town Schools
given in this study was gathered, but it is to be inferred from the ex-
tent of the study that the testing was done by the teachers.
In A Report on the Use of Some Standard Tests, Wisconsin State
Department of Public Instruction Studies in Educational Measure-
ments in Wisconsin, Bulletin No. 1, W. W. Theisen reports results
for 36,564 children in Wisconsin, of whom 15,825 were in rural schools.
He summarizes on page 22 as follows: "Judged by the Ayres stand-
ards, rural children in Wisconsin do not spell well. They average not
less than 10 points below the standard in every grade. However,
when compared with other classes of Wisconsin schools, as will be
seen from Table 1, they are not conspicuously poorer nor better spell-
ers than the pupils in the cities and villages.
The same author in the same report gives results of penmanship
scored according to the Thorndike Handwriting Scale from 141 rural
schools in 28 counties. He summarizes (p. 85): "Rural schools on the
whole make the best showing of Wisconsin schools in writing. Their
quality is not inferior to that of other classes of schools, and their
speed is more nearly in accord with desirable standards in most grades."
The Sixty-Ninth Report of the Public Schools of the State of Mis-
souri (June 30, 1918) reports a series of investigations as to rural
school conditions in that state. Courtis Standard Reading Test No. 2
was given to 6,056 pupils in 547 schools. in 82 counties. Among the
findings it is stated (p. 74) that “A second observation based on the
table is that in all three phases of reading ability the rural school chil-
dren in these grades (2-8) are below the standard set by Courtis."
The Kansas City Scale for Measuring Handwriting was used for
scoring papers of about 8,000 pupils in 86 counties in the same state.
The results are reported in detail by grades, and it is concluded (pp.
80-81) that "The quality or form of handwriting of the rural school
pupils is far below the accepted standards, grade for grade. The
speed is above the accepted standards, except in the seventh and eighth
grades."
Results are also reported from 6,445 pupils in grades 4 to 8 inclu-
sive and from 87 counties for the use of Courtis Standard Research
Tests in Arithmetic, Series B. (pp. 81-85.) It is concluded that
"On the whole the rural school children in Missouri are not up to the
ability of the city pupils as shown by the Courtis general tabulations.
This is particularly true of the sixth, seventh and eighth grades. In
the eighth grade it was pointed out that the Missouri rural school pu-
pils were below in every particular."
Previous Objective Studies
13
In the same report (pp. 85-87) results are given for a spelling test
based on the Ayres' Spelling Scale given to 8,326 pupils in 611 schools
in 86 counties. In conclusion it is stated (p. 87) that “The rural
school pupils in Missouri are below the standard attainment for the
city school pupils in 84 of the larger cities of the United States, and
the writer of the report of which this section is a summary says also
that the rural school pupils are below the attainment of the ten town
schools in the state studied by him."
In 1918, in Report on Spelling and Penmanship in Country Schools,
Louisiana State Department of Education, Bulletin No. 1, June,
1918, John M. Foote reported the results of spelling test from the Ayres
list given to 4,584 pupils in rural schools in Louisiana. He concludes
(p. 11) that: “While it may be that the superiority of the large type of
school as compared with the small type is decisively reflected in the
instruction in some of the subjects taught, it must be concluded that
in so far as spelling ability in the rural schools is concerned no such
decisive difference exists. The results show clearly that there is a
difference in favor of the large school, but the assumption that the
classroom results are very much better is not warranted.”
The same author in the same bulletin reports handwriting results
according to the Ayres Scale for 4,073 pupils in 114 rural schools,
and concludes (p. 24) that "It will be seen by reference to the table
and diagram that there is comparatively little difference in both qual-
ity and speed between the five groups. It will be noted that the dif-
ference in quality is less than in speed. The situation is similar to that
found in spelling. The evidence therefore points to the conclusion
that the pupils in the large schools are slightly superior, but that no
great difference prevails.”
The same author, in Silent Reading in Rural and Village Schools,
Louisiana State Department of Education, Bulletin No. 9, July, 1919,
reports results from work with Monroe's Standardized Silent Reading
Tests with 4,315 pupils in 96 schools located in 15 parishes. He con-
cludes (p. 8) that "A comparison of the three groups A, B, and C
reveals a distinct difference in favor of the larger school. With the
exception of the fourth grade the scores of group B are better than
those of group C. Group A scores are higher in every instance than
groups B and C. This superiority of the large type of school is in
agreement with results reported for Santa Clara County, California.”
Still later, in A Study of Arithmetic in Rapides Parish, Louisiana
State Department of Education, Bulletin No. 11, September, 1919, Mr.
14
Study of Achievement in Country and Town Schools
Foote reports results for the use of the Courtis Arithmetic Test Series
B in the schools of Rapides Parish, Louisiana. In this study schools
are grouped in four classes, those in the city of Alexandria in group
A, eight high schools in group B, eight graded schools in group C, and
twenty-eight one- and two-teacher schools in group D. Mr. Foote
concludes (p. 12) that “Superior results are obtained in the large type
of schools.” (p. 13.) “Group A and D vary in speed by 1.0 year
and in accuracy by 2.0 years. It is therefore evident that the large
schools as represented by groups A and B obtain results that are dis-
tinctly superior to those obtained by groups C and D."
George A. Grim, in "Spelling in Northampton County," University
of Pennsylvania Bulletin, Vol. XX, No. 1, October, 1919, Sixth An-
nual Schoolmen's Week Proceedings, reports spelling results for the
rural and urban sections of Northampton County. The results are
reported for grades 2 to 8 inclusive, and in five of the seven grades
reported the urban schools surpass the rural. The differences re-
ported are not great in any case.
Cyrus D. Mead, in The Spelling Ability of the Plumas County Chil-
dren, California State Board of Education, Supplement of California
Blue Bulletin, December, 1919, reports on the spelling ability of the
pupils of Plumas County, California, as shown by a test from the
Ayres list. He concludes (p. 5) that “The pupils of this county are
just about of the average ability of city children over the
country.”
The above references include all the data easily available dealing in
an objective way with the comparative results of instruction in rural
and in urban schools. The difficulty of collecting data in rural schools,
where distance is great and classes small, makes the time element in
collecting any large number of cases very great and seems to have pre-
vented the collection of extensive material. The studies reported in-
clude 2 studies of composition work; both of these favor the urbán
school. There are 6 studies of handwriting reported, and of these 3
favor the urban school, 2 show negligible differences, and 1 favors the
rural school. Nine studies of arithmetic are reported, and 8 of these
favor the urban school, while 1 favors the rural school. Four studies
of reading are reported, and all of them favor the urban school.
Seven studies of spelling are reported, 3 of which favor the urban
school and 4 of which find negligible differences. In all 28 studies are
reported, of which 20 find the results better in urban schools, 6 find
negligible differences, and 2 find results superior in the rural schools.
1
CHAPTER II
PURPOSE AND SCOPE OF THE PRESENT STUDY .
THE studies of results of instruction in rural schools reported in
Chapter I are in objective terms, and seem to indicate a situation that
is quite generally inferior to that in cities and towns. All of the com-
parisons are made, however, upon a grade basis, which assumes that
the third grade, or the eighth grade, or any other grade should be the
same in one system as in another. That grades are not in fact equal
is shown by results. Under the present diversity of conditions it is
entirely possible that grades should not be equal.
Particularly is this true in country schools as contrasted with city
schools. The shorter terms, poorer attendance, and inherent difficul-
ties involved in the small school make it probable that grading in these
schools should be different from that in city schools. For example,
in Madison County, Kentucky, the school year for the smaller schools
is only six months. This means that a boy or girl entering school at the
age of six and progressing normally would at the age of fourteen com-
plete the eighth grade, having attended school a total of 48 months, A
child entering one of the larger schools of the country, such as that in
Richmond, would have nine months' schooling each year, and would,
if he progressed normally, complete the eighth grade with a total of 72
months in school; that is, with 24 months' more schooling than the
country child received.
Again, in some of the states the school system is organized on the
basis of seven grades in the elementary school, so that a direct compar-
ison of a fifth grade in a seven grade system with a fifth grade in an
eight grade system is impossible.
Further, the use of grade standards must assume that tests are given
at the same time in the school year. This would be
This would be necessary either
to compare the system tested with another system or with the work
in the same system in other years, since the standard for any grade
must be different at the beginning and at the close of the school year.
It is not always convenient, or even possible, to give tests in any partic-
ular part of the school term. There will be material gain in the ease
of using standard tests if it can be made possible to give them at any
convenient time and to obtain results comparable with those from other
places and given at other times.
15
16
Study of Achievement in Country and Town Schools
Then, too, in any system of schools some pupils are likely to fail of
promotion each year. This causes retardation, and is much more se-
rious in some systems than in others. Any consideration of the effi-
ciency of a school system must account for this factor. Grade stand-
ards do not do so.
It is for such reasons as these that the Nassau County Survey, pub-
lished as a bulletin of the University of the State of New York (De-
cember, 1917), in reporting the measurements of the achievements of
pupils, carefully refrains from making any comparison of the urban
and rural schools, and makes the following statement (p. 146): "The
classification of school districts by the approximate size of the schools
has not been continued in this chapter, because of the possible injus-
tice which might thereby be done to the small schools, in which the
exact classification of pupils into eight grades is not always possible.
There might have been possible a more accurate comparison of the
results from large and from small districts, if the results had been
tabulated by age rather than by school grade. A comparison of the
ability children have in a rural school by the time they are 'twelve
years old with the ability of children of the same age in a large village
school might possibly be more significant than a comparison of the
ability between children of the ‘sixth grade' in the two types of schools.
For several reasons, however, we have not been able to make such
comparisons between the achievements of pupils of the same ages in
districts of various sizes."
To really measure school efficiency it is necessary to show the prog-
ress, not only of those who are promoted, but of all the children; and
to do this in terms of some unit common to all schools, city or country,
seven grade or eight grade system, and long or short school term.
There will be added convenience if such a unit can be so devised as
to be usable at any time during the school year.
The chronological age of school children is such a unit. If the prog-
ress made by children can be shown, say between the ages of 7 and 12,
a measure that is definite, universal, and approximately equal at any
time during the school year is obtained, provided only that children of
both ages are tested at the same time. The question is whether such
progress can be shown.
This study undertakes:
First, to show that the difference in performance in school subjects
of children of different ages can be obtained;
Purpose and Scope of Present Study
17
Second, to show that this difference is a measure of school efficiency ke
which may be used to measure schools or school systems;
Third, to apply this measure to a system of country schools;
Fourth, to compare the results in this country system of schools with
the results in certain city school systems.
The country school system to which this measure is applied is that
of Madison County, Kentucky. This county lies a little east of the
central portion of the state, and includes both blue-grass and mountain
land. In the 1910 census it ranks 20th in the land area among the
counties of the state, 5th in the value of all farm property, and 12th
in the value of all farm crops. Corn and tobacco are easily the lead-
ing crops. The county is one of the wealthier and larger counties of
the state. There are two normal schools, the Eastern Kentucky State
Normal at Richmond and a normal department in connection with
Berea College at Berea. The number of public white schools is 68,
six of which have three or more teachers and a term of nine months.
The rest of the schools have only one or two teachers and a six-month
school year. A county supervisor of schools is employed to assist the
county superintendent. There is no reason to suppose that the schools
of this county are particularly worse than those of surrounding counties.
For the purposes of this study three tests were selected: Trabue
Completion-Test Language Scale B, Courtis Standard Research Tests
in Arithmetic Series B, and Thorndike Silent Reading Scale Alpha 2.
These tests were given in grades 3 to 8 inclusive of all the public
schools for white children in the county during November and Decem-
ber, 1919.1 The results are tabulated separately for the schools hav-
ing a six-month term and for those having a nine-month term.
In order that the results in Madison County may be compared with
results in other places, data are included as follows: From Louisville,
Kentucky, data for each of the three tests used; from Paterson, New
Jersey, and St. Paul, Minnesota, data for the Trabue Language Scale;
from Louisiana, Arkansas City and Salina, Kansas, and Hibbing,
Minnesota, data for the Courtis Standard Research Tests in Arithme-
tic Series B; from Hamilton Township, New Jersey, and Amsterdam,
New York, data for Thorndike Silent Reading Scale Alpha 2.
In order to show clearly the method followed, the results of the
Trabue Completion-Test Language Scale B are worked through in de-
tail in the next chapter.
* Five of the one-teacher schools were not in session when visited, and no re-
sults from them are given.
CHAPTER III
ACHIEVEMENT MEASURED BY THE TRABUE LANGUAGE SCALE
TABLE I shows the age-grade distribution of scores made in the
Trabue Language Scale B by pupils in the Madison County schools
having a term of 6 months. The table reads as follows: There are
8 pupils 7 years of age in the third grade, 1 of whom made a score of
3, 2 a score of 4, 2 a score of 5, 3 a score of 6, etc. In this table and
throughout the study the age used is that of the last birthday at the
time the test was given. A child is considered as 10 years old who is
as much as 10 years old and less than 11 years old.
It is evident from the total number of cases occurring for the re-
spective ages that the distributions are incomplete for most ages; prob-
ably for all. There should be at least as many 8-year-old children, for
example, as there are 9-year-olds. This incompleteness for the younger
ages represents children in the first and second grades, which were not
tested, or children who have not yet entered school. Since these chil-
dren have not yet been promoted to the third or higher grades, it is
evidently the opinion of the teachers that they could not do so well as
the children who are in the third or higher grades. It follows that the
distributions for children of the younger ages are lacking in the num-
ber of cases for the lower scores. The distributions for the older
children, on the other hand, may be considered as lacking in the num-
ber of cases for the higher scores, since the older children not appear-
ing in the table are those who have either completed the eighth grade
before reaching the age indicated, or who have for some reason stopped
attending school.
If the difference in performance in school subjects of groups of
children of different ages is to be a valid measure of the efficiency of
a school system, it is evident that the age-groups in the respective sys-
tems must be comparable. That is to say, either these groups must
include all children of the age indicated, or the selection must be shown
to be by random sampling only, or the selection must be shown to be
influenced only by known causes acting equally and in the same direc-
tion, or it must be possible to so correct the age groups given as to
meet substantially the above conditions.
The age-groups presented in Table I do not meet the first of these
18
TABLE I: Age-GRADE DISTRIBUTION OF TRABUE LANGUAGE SCALE B SCORES IN
THE 6-MONTH WHITE
WHITE SCHOOLS OF MADISON
MADISON COUNTY, Ky. (NOVEMBER AND
DECEMBER, 1919)
SCORES
Age Grade
Total
0 1
2 | 3
4
5
6
7
8
9 10 11 12
13
14
15
16
17
18
7
1 2
3
4
5
2
1
1
3.
1
1
1
Ngico
-
.
1
.
-
{
1
1
Total
8
3
4
5
6
1
1
1 53
1 3 2
1 3 1
2
1
5
10
7
1
16
27
22
5
2
1
4
4
1
1
1
-
-
.
.
1
1
-
-
-
1
1
3
3
4
7
1
1
1
1
Total
9
7
6
6
1
1
1
-
3
4
5
26
12
1
1
1
6
2
1
1
181
9
7
4
2
3
3
2
2
3
7
54
40
33
20
3
!
1
.
ابن هر
-
1
2
1
1
1
1
-
1
-
12
1) 13
5) 20
12
7
3
2
-
1
1
-
1
Total
10
9
1
1
1
1
1
-
3
1
5
3
2
1
2
3
5
1
2
4
2
3
4
5
6
7
8
8
3
2
2
9
6
4
1
1
1
3
5
1
د امير دي د لمر
1
2
2
3
4
2
1
93
30
31
32
11
1
2
-
1
1
1
1
-
-
.
!
1
1
1
-
.
.
-
-
-
1
1
1
4
1
9
17
7
11
2
4
1
Total
11
1
-
3
3
1
1
3
1
11 10 6
3
3 1
2 3
2
22
5
10
3
1
2
1
3
9
1
4
3
-
1
-
-
3
4
5
6
7
8
HN
armaci
1
5
2
1
1
4
1
1
2
ܙ ܙ ܙ ܙ ܙ ܟܬ ܝܚ
107
19
28
34
16
5
2
-
-
2
-
!
!
-
1
1
2
1
-
.
1
1
1
1
-
-
1
Total
8
13
8
8
2
1
3
2
1
1
4
1
1
51.
1
12
1
8
1
1
2
1
-
-
6191
1 3
9
2 8
1 1
-
-
1
61 101
2
4 3
3 5
3
1
1
1
-
1
1
1
)
3
4
5
6
7
8
1
ܙ
. -
-
1
NONO
1
5
1
2
4
2
1
4
4
7
2
ܙ ܕܬ ܢܙ ܟܬ
104
10
25
31
27
16
7
1
med II 1
-
.
-
1
1
1
1
-
-
-
-
-
1
1
-
1
3
-
-
1
2
1
2
4
17
7
8
18
6
3
3
-
-
Total
13
4
1
1
--
-
-
.
1
3
1
-
-
1
-
!
1
1
1
1
1
1
1
21| 101 11
1
2 2 1
7 6 4
3
2
1
2
1 1
1
2
4
5
NNAI
3
4
5
6
7
8
-
2
2
1
116
6
16
27
23
12
16
NONNI
-
1
I
1
2
2
3
1
1
2
5
2
.
-
1
2
4
1
-
-
-
-
1
1
2
4
14
9
10
12
13
7
6
7
8
2
1
-
1
1
Total
14
21 3
1
1
1
}
1
-
-
-
1
2
. -
-
-
-
1
1
1
ܒܚܕܢܚܙ ܟܬ ܚܙ
1
2
2
1
3
4
5
6
7
8
1
2
1
-
I
5
2
1
2
2
1
ܙ ܟܨ ܒܝ ܟܬ ܟܬ
100
3
11
18
15
13
22
3
3
.
2
1
OsNWNI
1
1
2
5
1
1
1
1
2
1
1
-
1
-
1
1
.
3
1
1
2
5
12
10
5
10
3
131
9
3
.
Total
15
5
1
1
.
.
-
-
-
.
-
1
1
1
1
1
1
82
2
3
2
3
6
17
1
3
4
5
6
7
8
--
-
1
1
4
1
1
1
3
2
1
1
2
1
3
3
1
-
-
2
1
2
2
7
3
5
3
4
3
1
33
-
--
-
-
.
Total
16
1
-
-
1
-
-
i
-
1
2
2
1
4
5
6
7
8
1
2
1
3
1
3
4
9
16
1
1
4
4
Total
1)
1
2
1
41
3
4
7
1
4
28
19
20
Study of Achievement in Country and Town Schools
conditions, in that they do not include all the children of the ages
indicated. Take, for example, the group of 12-year-old children, the
largest group presented. This shows 10 children in the third grade,
25 in the fourth, 31 in the fifth, 27 in the sixth, 16 in the seventh, and
7 in the eighth. Since the distribution of 12-year-old children through-
out the grades is not rectilinear, as is shown by the part of the distri-
bution given, it seems unlikely that if a full distribution were available
it would stop at the lower end with 10 children in the third grade or
at the upper end with 7 children in the eighth grade. It seems likely
that there would be some 12-year-old children in grades below the
third and in grades above the eighth. This opinion in the latter in-
stance is substantiated by the fact that some 10- and 11-year-old chil-
dren are in the eighth grade this year. If they progress normally,
they will complete the work of the elementary school this year, and
will not be enrolled in the school next year. The same thing is likely
to have happened last year, so that there are now some children who
are 12 years old and have completed the work that the school offered
and are therefore not in school. Also, there are 13-, 14-, and even 15-
year-old children in the third grade. There is every reason to sup-
pose that there are 12-year-old children in grades lower than the third.
In addition to the above considerations, it is known that there were
some children absent from school on the day the tests were given.
As regards the second possibility mentioned for comparable groups:
Is the selection by random sampling only? In so far as the selection
is due to absence from school on the day the test was given, the se-
lection may be considered random as to ability in the test concerned.
The chief causes of absence mentioned by the teachers were work, bad
weather, illness, and indifference on the part of the parents. The
work for which the children were kept at home during the time these
tests were being given (November and December) was usually work-
ing tobacco or killing hogs. While it is likely that more of the older
children than of the younger ones were kept at home for work, still
some of the younger ones were kept at home for this purpose. The
discrepancy in absences between the older and younger children in re-
gard to absence for work is reversed and probably neutralized by the
discrepancy in absences due to bad weather and roads. The absences
due to illness of the children and to indifference on the part of the
parents may be assumed to be about the same for children of all ages.
On the other hand, the selection due to the inclusion of only those
children in grade 3 to 8 inclusive is not random. The older children
Achievement Measured by Trabue Language Scale
21
in grades 1 and 2, that is, those who are not included in the distribu-
tion given, are in those grades because, in the opinions of the teachers,
they are not so able as the children of the higher grades, or because
they have for some reason become so retarded in their school work as
to make them distinct from other children. In other words, these
children are, in the opinions of the teachers, of less ability in school
work than those of corresponding age who have been promoted to the
higher grades. This means that the distributions given in Table I
do not include the children who have the lower degrees of ability in
school work. In the same way the younger children who have com-
pleted the eighth grade and are therefore not included in the table are,
in the opinions of the teachers, the children having the higher degrees
of ability in school work. All of which goes to show that the selec-
tion of cases for the age-groups as they are presented is not random.
The next consideration is whether the selection of age-groups, in
such respects as it is not random, is due to the same causes acting
equally and in the same direction, for all the schools to be measured,
and in each of the age-groups. As is shown above, there is decided
selection due to the failure to include children in grades 1 and 2, and
those who have completed the eighth grade. This number of children
is determined by the rate of progress of children through the grades.
This rate of progress is unequal even for different schools within the
same system, as has been shown repeatedly by studies widely sepa-
rated both in time and locality. A good and recent example is fur-
nished by the age-grade tables on page 90 of An Educational Study of
Alabama, United States Bureau of Education Bulletin, 1919, No. 41.
The possibility still remains of correcting the tables presented. In
order to correct an incomplete distribution such as that presented it
is necessary to have a reasonably large part of the complete distribu-
tion. In the data presented the most nearly complete distributions are
those for the ages 10, 11, 12 and 13. The distribution of 12-year-
olds is the largest given, which indicates that it is most nearly complete.
Taking this distribution as a sample, how may it be corrected ?
Unfortunately the form of this distribution is not exactly that of
the normal frequency curve. This is shown by that portion of the
distribution which is given. It might also be inferred from the fact
that in most school systems it is easier for a child to become retarded
than it is for a child to make two grades in one year. This natu-
1
Strayer and Thorndike, Educational Administration, p. 38.
22
Study of Achievement in Country and Town Schools
rally causes a skewed distribution. To correct a skewed distribution for
truncation by the development of mathematical formula is a lengthy
and complicated process, and one that is liable to serious error. Fur-
ther, since the degree of skewedness and of truncation may both vary
for every distribution to be studied, such correction is obviously too
tedious and cumbersome a method to be used in a measure of school
efficiency that is to be easily available for busy school men.
If an age-grade table of all the children in all the grades were avail-
able, it might serve as a basis for calculating the number of children in
grades 1 and 2. It does not furnish a ready basis for finding the num-
ber who have completed the eighth grade. Also, for Madison County
schools no such table is available..
The problem resolves itself into an attempt to find the number of 12-
year-old children who are in either the first or second grade, or who
have completed the eighth grade. The 13-year-old children in the
third grade this year probably were in the second grade last year when
they were 12 years old. The probability is that last year the number
of 12-year-old children in the second grade who were not promoted
to the third grade was about equal to the number of 13-year-old chil-
dren in the third grade who were not promoted to the fourth grade.
Inasmuch as there has been no particular change in the school popu-
lation of Madison County during the last few years, and in view of
the above probabilities, the number of 13-year-old children in the
third grade may be considered a fairly reliable indication of the num-
ber of 12-year-old children in the second grade.2 Reference to Table
I shows this number to be 6. Similarly, the 14-year-old children in
the third grade may be considered a measure of the 12-year-olds in
the first grade. This number is 3.
In much the same way it may be supposed that the number of 11-
1 To get a census showing the ages of children in the first and second grades
of the Madison County public schools it would be necessary to visit each school,
and in the case of children who do not know their age, to visit the home.
2 In order to test the validity of this assumption a study was made of the
age-grade tables for rural children and for children in places having a popula-
tion of less than 2,000 given on page 90 of An Educational Study of Alabama,
United States Bureau of Education Bulletin, 1919, No. 41, and the age-grade
table for pupils in non-city schools given on page 309 of the Survey and Report
of the Virginia Public Schools Education Commission. The actual number of
10-, 11-, 12- and 13-year-old children in grades 1 and 2 was compared with the
number of such children estimated to be in these grades on the basis of the
above assumption. The difference between the actual number of such children
and the estimated number was reduced to a percentage basis showing the per
cent of error in each estimate. Twenty-four estimates were made, and the
median per cent of error, direction of error being taken into account, was -41/2.
Achievement Measured by Trabue Language Scale
23
year-old children in the eighth grade this year is the same as the num-
ber of 11-year-old children in the eighth grade last year. These should
be added to the 12-year-old distribution this year. Reference to Table
I shows this number to be 2. In the same way the number of children
who are 12 years old this year and who completed the eighth grade
two years ago is estimated as 2.
Using these estimates, the following distribution of 12-year-old chil-
dren is obtained: 3 in grade 1, Language Scale scores unknown; 116
in grades 3 to 8 inclusive, distributed according to Language Scale
scores; 2 who completed grade 8 last year, Language Scale scores un-
known; and 2 who completed grade 8 two years ago, Language Scale
scores unknown.
Estimating corrections for the 10-, 11- and 13-year-old distributions
on the same basis as for the 12-year-olds, gives Table II. In this
table the figures in the columns under the captions X1, X2, X9, X10,
and X11 are the estimated number of children of the respective ages
in grades 1, 2, 9, 10 and 11 respectively.
These corrections make the distributions for the ages 10, 11, 12 and
13 reasonably complete. There is still some elimination of children in
the grades to be accounted for, and there is the possibility that some
of the children of these ages may not have entered school. These
considerations are probably not so serious, however, as the fact that
the scores of the children represented by estimated additions to the
distributions are unknown. It is known, however, that the children
in the lower grades are likely to have made very low scores, while,
on the contrary, the children who have completed the eighth grade
would probably have made relatively high scores. Allowing these
cases to remain undistributed at the respective ends of the distribution,
the medians, Q's and P.E.'s of Table II are obtained.
The distributions of scores in this table show a great amount of
overlapping for the different ages. Twenty per cent of the children
in the 10-year-old group have scores superior to those of 50 per cent
of the 13-year-old children. This overlapping is in accord with the
results obtained with grade distributions.
* An attempt was made to estimate the necessary additions for these distribu-
tions on the basis of an age-grade table showing a form of distribution similar
to that in Madison County. The age-grade table for the Alabama schools in
places of less than 2,000 population was used. No estimate of children who
had completed the eighth grade seemed feasible on this basis, and the medians
calculated on the basis of the distributions corrected in this way showed co-
efficients of unreliability greater in every instance than those of the medians cal-
culated on the basis of the above corrections.
1
24 Study of Achievement in Country and Town Schools
tween progress at different ages. The improvement the 11-year-old
As in the overlapping of grade distributions, so in this overlap-
ping with age distributions, the unreliability of the individual measures
gives an indication of greater overlapping than really exists.1 In this
case there is an added element tending to exaggerate the amount of
overlapping in the undistributed scores at both ends of the age distri-
butions. These scores tend to increase the inter-quartile range, and
consequently the Q.
TABLE II
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF TRABUE LANGUAGE SCALE B SCORES
IN THE 6-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
Age
X1 X210 | 1 | 2 4 5 6 7
ele
Another notable feature of this table is the great discrepancy be-
SCORES
Total
3
8
9
10 11 12 13 14 15 16 17 18 X9
X10 X11
1
-
-
-
I
11 10
8
1
3
1
-
-
w
10
11
12
13
101 19
6 10
3 6
2 3
3
5
2
4
4
4
2
2
-
6 22 9 17 9 7 11 2
6 19 6 10 8) 13 8 8
4 21 101 11 17 7 8 18
31 14 9 101 12 13 6
4
2
6
7
1
1
2
8
2
3
1
136
122
129
116
2
2
7
-
1
-
ܙ ܕܬ ܟܬ
1
NA
N
2
1
2
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P. E.
centile
centile
10
11
12
13
6.63
7.50
9.02
9.75
.37
.34
.30
.35
9.00
10.73
12.04
13.00
2.00
4.68
6.48
6.92
3.50
3.02
2.78
3.03
M11-M10= .87
M12-M11=1.52
M13—M12= .73
M13-M10=3.12
.311
.283
.305
.316
children show over the 10-year-olds is .87 of a step; that of the 12-
year-olds over the 11-year-olds is 1.52; and that of the 13-year-olds
over the 12-year-olds is .73 of a step. The progress in language ability
as measured by this test is almost as great from ages 11 to 12 as the
combined progress from ages 10 to 11 and from ages 12 to 13.
The total progress for the three-year period from 10 to 13 inclusive
is 3.12 with a P.E. of .316.2 Since these schools were in session for
6 months each year, the total school time for the three years is 18
months. This makes the average progress per month for the period
.173 of a step
The results of the Trabue Language Scale B test in the white schools
of Madison County having a 9-month school term are handled in the
1 Thorndike, E. L.: Mental and Social Measurements, p. 93. Kelley, T. L.:
“The Measurement of Overlapping,” Journal of Educational Psychology, X:
458ff. (December, 1919).
2 Thorndike: Mental and Social Measurements, p. 194.
Achievement Measured by Trabue Language Scale
25
same way as are those from the schools having a 6-month school term.
Table III gives the facts for these schools.
From this table it seems that the overlapping of language perform-
ance of children of different ages is about as great in the 9-month
schools as in the 6-month schools. Some of the 10-year-old children
have scores above the median score of the 13-year-olds. The same
causes are operating to make this overlapping appear greater than it
really is.
TABLE III
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF TRABUE LANGUAGE SCALE B SCORES
IN THE 9-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1 X2
0
1
2
3
4 5 6
7
8
9 10 11 12 13 14 15 16 17 18 X9 X10 X11
1
-
1
10
11
12
13
91 17 2
2 97
3 2 5
4 3 7
ܪܬ ܘܬ ܘܬ
1
1
8
3
6
71 18
4] 14
3 8
1 2
71 17 8) 12 8 8 3 1 2
6 16 58 5 7 4 3 2
4 8 14 12 12 12 15 10 11
4 41 10 9
7 9) 11 11
1
1
7
2
1
1
1
KI
132
101
139
101
1
1
10
1
1
1
-
Median
P. E, true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.32
10
11
12
13
7.42
8. 15
11.12
12.21
.31
10.33
10.84
13. 81
14.97
4.37
5.31
8.09
9.02
2.98
2. 76
2.86
2.97
M11-M10= .73
M12-M11=2.97
M13-M12=1.09
M13-M10=4.79
.290
.284
.295
.304
.30
.36
NOTE.-In these and succeeding tables X1 is the estimated number in grade 1,
scores unknown. X2, X9, X10 and X11 represent the corresponding facts for
grades 2, 9, 10 and 11 respectively. M10 is the median for 10-year-old children,
age last birthday at the time the test was given. M11, M12 and M13 are the
medians for the ages 11, 12 and 13 respectively.
Also, the progress between the different ages is unequal, as in the
case of the children in the 6-month schools. The improvement between
ages 10 and 11 is .73 of a step; between ages 11 and 12 it is 2.97 steps; L
and between ages 12 and 13 it is 1.09 steps. The total improvement for
the three-year period from ages 10 to 13 inclusive is 4.79 steps, with a
P.E. of .304. Since there are 9 months of school each year, the total
school time represented is 27 months. The average monthly improve-
ment, therefore, is .177 of a step. The corresponding improvement
for the 6-month schools is .173 of a step.
This comparison would be valid and significant if it could be as-temi
sumed that the quality measured, ability to complete correctly sen-
tences in which certain words are missing, was improved only by school
26
Study of Achievement in Country and Town Schools
work. Such, however, is not known to be the case. It is entirely
possible that this quality improves by a natural development as the age
and experience of the subject increases. It is possible, and even prob-
able, that this ability to complete sentences is improved both by natural
development and by school work. The conclusion from the above
comparison, therefore, is that schooling and natural development ac-
complish an improvement of this ability of 4.79 steps between the
ages of 10 and 13 inclusive for the children in places in Madison
County having a 9-month school term, and of 3.12 steps in places in
the same county having a 6-month school term.
TABLE IV
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF TRABUE LANGUAGE SCALE B SCORES
IN CERTAIN WHITE SCHOOLS OF LOUISVILLE, Ky.
SCORES
Age
Total
X1 X2 X3 0 1] 2
3
4
5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X9
1
.
-
-
10
11.
12
13
4 12 36
1 4 12 2
1 4
1
1
4
2
2
2
1
8
5
2
3
2 18
113
3 21
1 10
4 32 17 43 17 29 6 14
6 39 9 55 11 67 13 26
31 19 12 43 19 77 16 70
5 22 8 53 131 65 27 46
1 3
1 17
41 27
61 20
-
-
247
292
332
316
6
4
7
-
4
1
1
26
-
1
Median
P. E. true
-obtained
mediad
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
11.32
12.90
14.46
14.61
.24
.14
. 13
. 14
13.48
14.37
16.37
16.58
7.37
10.36
12.34
12.50
3. 11
2.00
2.01
2.04
M11-M10=1.58
M12-M11=1.56
M13-M12= .15
M13-M10=3.29
. 174
. 120
. 120
. 174
Table IV gives the facts in regard to the Trabue Language Scale B
test for certain of the white schools of Louisville. The papers on
which this table is based were given, collected and scored by the
Psychological Laboratory of the Louisville Board of Education.
The total improvement in ability to complete sentences in these
schools for the three-year period from ages 10 to 13 inclusive is 3.29.
The P.E. of this gain is .174, a little over 5 per cent of the gain. The
probable deviation of the true measure of this gain from the measure
obtained is only about half as great as in the Madison County schools,
either those having a 9-month school term or those having a 6-month
term. The total gain made is a little greater than in the case of the
Madison County 6-month schools and is not quite so great as in the
case of the Madison County 9-month schools. The median ability of
the respective age-groups, on the other hand, is materially higher than
4.
Achievement Measured by Trabue Language Scale
27
is the case in any of the Madison County schools. The median for the
Louisville 10-year-old children is higher than for any of the age groups
of the 6-month schools, and is higher than all except the 13-year-old
group for the 9-month schools. The median ability of the Louisville
13-year-old group is 14.61; that for the Madison County 9-month
schools of corresponding age is 12.21, and for the 6-month schools is
9.75. The 13-year-old children in Louisville have an ability to com-
plete sentences that is 50 per cent greater than the like ability of chil-
dren of the same age in the 6-month schools of Madison County.
The progress made each year in the Louisville schools is unequal,
as is the case in the Madison County schools. In Louisville the prog-
ress from 10 to 11 is 1.58; from 11 to 12 it is 1.56; and from 12 to 13
it is .15.
TABLE V
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF TRABUE LANGUAGE SCALE B SCORES
IN PATERSON, N. J.
SCORES
Age
Total
X1
0 1
2
3 4
56
7
89
10 11 12 13 14 15 16
17
18
19 X9 X 10
5
2
-
-
"
27
1
-
1
10
11
12
13
5
6
5
1
4 23 18 31 201 341 23 15 13 4 2
4 11 10 17 16 34 27) 29 18 11 4
2 8 8 151 161 391 19 32 25 18 9
2 6 2 14 13 25 20 29 26 17 16
1
7
9
12
2
3
9
1
1
1
3
1
2
3
1
209
200
224
246
8
42
2
8
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
9.03
11.30
11.78
13.30
.12
.16
16
.24
10.01
12.82
13.80
16.87
7.02
9.06
9.87
10.82
1.49
1.88
1.96
3.02
M11-M10=2.27
M12-M11= .48
M13--M12=1.52
M13–M10=4.27
. 128
. 141
. 180
. 170
Table V gives the facts in regard to the Trabue Language Scale B
for schools in Paterson, New Jersey. The data from which this table
is compiled were collected by the department of school administration
of Teachers College, Columbia University.
The total gain in ability to complete sentences in the Paterson schools
is 4.27. This gain is greater than in the case of any other schools pre-
sented in this study. The P.E. of this gain is .170, which is about the
same as that for the like measure in Louisville. Since the gain in this
case is greater, the proportion of the probable error to the gain is a
little less; in Paterson 4 per cent as against a little more than 5 per
cent in Louisville. The median ability of the 13-year-old children in
the Paterson schools is 13.30 as against 14.61 in the Louisville schools.
+
28
Study of Achievement in Country and Town Schools
CHART I
PROGRESS IN TRABUE LANGUAGE COMPLETION TEST SCORES BETWEEN AGE
GROUPS IN THE PUBLIC SCHOOLS OF MADISON COUNTY, Ky.; LOUIS-
VILLE, Ky.; PATERSON, N. J.; AND ST. PAUL, MINN.
SCORES
161
C
15-11
1
14
LOUISVILLE
13
12
ST. PAUL
11 -
PATERSON
10
MADISON COUNTY
9-MONTH SCHOOLS
9.
8
MADISON COUNTY
6-MONTH
SCHOOLS
74
6
5.
4
3
2
!
0
AGES 10
Il
12
13
Achievement Measured by Trabue Language Scale
29
This median ability of the 13-year-old children in Paterson, however,
is greater than is the like measure for the 6-month or the 9-month
schools of Madison County.
The yearly gains are again unequal. From 10 to 11 the gain is
2.27; from 11 to 12 it is .48; and from 12 to 13 it is 1.52.
Table VI gives the facts in regard to the Trabue Language Scale B
in St. Paul, Minnesota. This table is based upon data printed in the
St. Paul Survey.
TABLE VI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF TRABUE LANGUAGE SCALE B SCORES IN
St. Paul, MINN. BASED ON TABLES PUBLISHED IN THE St. Paul SURVEY
SCORES
Age
Total
0 1
2
3
4 5 | 6
7
8
9
10
11
12 13
14
15
16
17
18
19
X9
3
4
1
2
10
11
12
13
15
2
1
2
4) 19
1 8
1 3
1 5
9
6
4
1
30
24
13
10
24
8
13
11
56
39
42
21
33
25
21
16
63
53
55
41
41 52
30 53
39 77
394 61
26
35
45
54
24
50
50
66
12
8
30
40
4
11
20
29
1
3
4
14
417
359
422
38 453
-
4
7
1
-
Median
P.E. true
-obtained
median
75 per-
25 per
Q
P.E.
centile
centile
. 13
10
11
12
13
10.32
11.41
12. 24
13.34
14
11
12.28
13.55
14.05
15.29
7.96
9.03
10.13
11.13
2.25
2.26
1.96
2.08
M11-M10=1.18
M12-M11= .83
M13-M12=1.10
M13–M10=3.11
. 120
. 106
.098
. 106
0
. 12
The total gain in ability to complete sentences in this case is 3.11.
This gain is less than in any of the other systems studied. The median
ability of the 13-year-old children, on the other hand, is 13.34, which
is higher than the like ability of the same age-group in any of the other
systems studied except Louisville. The P.E. of the gain in these
schools is .106, which is less than 4 per cent of the gain made. The
reliability of the measure in St. Paul seems a little greater than in any
of the other systems considered. The progress from age to age is un-
equal. From ages 10 to 11 it is 1.18; from ages 11 to 12 it is .83; and
from ages 12 to 13 it is 1.10.
Chart I shows the progress for the different systems both relatively
and absolutely. It is significant that while the progress in the Madison
County schools having a 9-month school term is relatively a little
greater than the progress in the city schools presented, the total result
is less. In other words, although the children gain as much or a little
more in ability to complete sentences between the ages of 10 and 13,
they have less of this ability when they began and less when they get
30
Study of Achievement in Country and Town Schools
through. This would seem to indicate either later entrance in school
or poorer work with the lower grades, possibly both.
The following table summarizes the total gain in ability to complete
sentences, as measured by the Trabue Language Scale B, between the
ages of 10 and 13, for the respective school systems considered. It
also shows the P.E. of this total gain, and the number of cases on
which this measure of gain is based.
TOTAL
GAIN
P.E. OF
TOTAL
GAIN
TOTAL
FREQUENCIES
SCHOOL SYSTEMS
10 to 13
10 and 13
Madison County, 6-month schools.
Madison County, 9-month schools ---
Louisville
Paterson
St. Paul.
3.12
4.79
3.29
4.27
3.11
.316
.304
.174
.170
.106
252
233
563
455
870
It should be noted that the reliability of the gains given, as indicated
by a relatively small P.E., is much greater in the city schools than in
the Madison County schools. This is due in part to the greater num-
ber of cases. That it is not wholly due to this cause is indicated by
the fact that the reliability is greater for the Madison County 9-month
schools than for the 6-month schools, though the number of cases is
slightly less. It is possible that this greater reliability is due in part
to a more uniform type of work in the city and town school systems
than in the country schools.
It is also to be noted that the combination of elimination, natural
development and schooling over a three-year period increased the ability
to complete sentences -4.79 steps in places in Madison County having
a 9-month school term, 4.27 steps in Paterson, 3.29 steps in Louisville,
3.12 steps in places in Madison County having a 6-month school term,
and 3.11 steps in St. Paul. If it may be assumed that the amount of
this increase due to natural development is the same in all these places,
the efficiency of the schools in training and eliminating children be-
tween the ages of 10 and 13 in such ability in language as is measured
by the Trabue Language Scales would rank in the above order.
This ranking does not agree with that obtained by ranking in order
of the median ability of the 13-year-old children. Ranking in this
way, Louisville comes first with a median of 14.61, St. Paul second
with 13.34, Paterson third with 13.30, Madison County 9-month schools
fourth with 12.21, and Madison County 6-month schools last with 9.75.
Achievement Measured by Trabue Language Scale
31
This discrepancy may be due to a difference in the work with chil-
dren under 10, to a greater irregularity of attendance of the younger
children in some systems than in others, to a difference in the amount
of gain due to natural development because of different environment,
to a difference in care in scoring papers, to a difference in intellectual
level of the communities, or to a combination of these causes.
The following table shows the yearly gains in each of the systems
of schools studied :
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
1
Madison County, 6-month schools..
Madison County, 9-month schools.
Louisville
Paterson.
St. Paul
.87
.73
1.58
2.27
1.18
1.52
2.97
1.56
.48
.83
.73
1.09
.15
1.52
1.10
1
1
-
-
-
-
1
-
-
Total.
6.63
7.36
4.59
This table seems to indicate that the greatest gain is made from
ages 11 to 12, but that material gain may be made during any of the
yearly periods from ages 10 to 13 inclusive.
CONCLUSIONS
1. The difference in performance as measured by the Trabue Lan-
guage Scale B of school children of different ages can be obtained.
2. Since this test measures a quality not proved to be solely, or even
largely, determined by school training, this difference is not a reliable
measure of school efficiency.
3. This difference does measure the improvement of children in the
respective systems as to the function measured, such improvement be-
ing due to school training and other influences.
4. The children in the Madison County 6-month schools show less
improvement during the three-year period from 10 to 13 inclusive than
do the children in any of the other systems except St. Paul.
5. The 13-year-old children in the Madison County 6-month schools
show less ability in the function measured than do the children of like
age in any of the other systems studied.
6. The children in the Madison County 9-month schools show rea-
sonable improvement during the three-year period from 10 to 13 in-
32
Study of Achievement in Country and Town Schools
4
clusive, but the ability of the 13-year-old children to complete sen-
tences is less than the like ability of 13-year-old children in any of the
systems studied except the 6-month schools in the same county.
CHAPTER IV
ACHIEVEMENT AS MEASURED BY THE COURTIS STANDARD
RESEARCH TESTS IN ARITHMETIC SERIES B
At the same time that the Trabue Language Scale B was given in
the schools of Madison County, the Courtis Standard Research Test
in Arithmetic Series B was used.
The problems involved in finding the difference in performance of
different age-groups are practically the same as in the work with the
Trabue Language Scale B. Distributions for the respective age-
groups are completed on the same assumptions, and the same age-
groups are used throughout. The number of examples correctly com-
pleted has been used as the score.
The work in addition, subtraction, multiplication and division is
presented in sections 1, 2, 3 and 4 respectively of this chapter.
SECTION 1. ADDITION
Table VII gives the data in addition for the children 10 to 13 years
of age inclusive in the Madison County schools having a 6-month term.
A new problem is presented in this table in that the medians of the
TABLE VII
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
ADDITION RIGHTS IN THE 6-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1
X2
2
0
1
2
3
4
5
6
7
8
9
X9
X10
X11
1
10
11
12
13
11
5
3
2
19
11
5
3
65
54
62
45
25
20
19
16
9
12
19
13
7
10
5
8
6
6
7
11
4
8
5
1
2
4
2
4
13
2
144
126
140
123
ANI
2
Median
P.E. true
-obtained
median
75 per-
25 per-
Q
P. E.
centile
centile
10
11
12
13
.64
.87
1.00
1.71
.07
. 11
. 12
.21
1.52
2.37
2.48
4.47
.09
.28
.43
.57
.71
1.04
1.20
1.90
M11-M10= .23
M12-M11= .13
M13—M12= .71
M13–M10=1.07
.072
.092
. 147
. 136
10- and 11-year-old groups fall in the 0 to 1 interval, and that the 25
percentiles of all age-groups fall in the same interval. It may be
33
34
Study of Achievement in Country and Town Schools
questioned whether the children in grades 1 and 2, grouped under
the captions X1 and X2, should be considered as having a score of 0,
or whether an attempt should be made to distribute their scores. Tab-
ulation of the pupils' test papers shows that there are 147 children in
grade 3, and that 127 of these grade 3 children made a score of 0.
Since 127 out of 147 children made a score of O and since it may be
safely assumed that children in grades 1 and 2 would not do so well
as children in grade 3, the score of these first and second grade chil-
dren has been considered as 0. Scores given under the caption 0 have
been considered as distributed evenly between 0 and 1.
The large number of scores in the 0 to 1 interval as well as the
scores considered as O indicate that the ability in addition required to
do any of the examples in the Courtis Standard Research Tests in
Arithmetic Series B is so great as to preclude measurement of many
of the individuals tested further than to show that their ability is less
than the lowest ability measured by this test. The great number of 0
cases also reduces Q.
TABLE VIII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC Tests
ADDITION RIGHTS IN THE 9-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky,
SCORES
Age
Total
X1
X2
0
1
2
3
4
516171819
10
11
X9
X10
1
X11
1
1!
-
-
.
10
11
12
13
9
1
3
4
16
9
1
3
23 14
21 13
21 19
7 15
19
12
15
11
11
7
24
11
16
10
17
17
6
7
6
8
5
9
13
5
5
2
6
3
NNN
1
3
1
1
127
94
131
98
1
1
8
1
1
1
1
1
Median
P. E. true
-obtained
median
75 per-
25 per-
LQ
P.E.
centile
centile
.26
10
11
12
13
2.07
2.25
3.27
3.81
.21
.26
. 19
.25
4.20
4.75
4.89
5.68
.64
1.97
2.05
1.74
1.99
M11--M10= .18
M12-M11=1.02
M13-M12= .54
M13-M10=1.74
. 206
.194
. 186
.198
1.40
1.70
The total gain in ability to add for the three-year period from ages
10 to 13, as measured by the difference in the median scores of the
10-year-old and the 13-year-old children who took the test, is 1.07,
with a P.E. of .136. This P.E. is slightly over 12 per cent of the total
gain indicated.
The improvement in ability to add from year to year, as measured
by the difference between the median scores of the respective age-
groups, is uneven, as it is in the case of language. From ages 10 to
11 the improvement is .23; from ages 11 to 12 it is .13; and from ages
Achievement Measured by Courtis Arithmetic Tests
35
12 to 13 it is .71. The improvement from ages 12 to 13 is practically
twice as great as the combined improvement from ages 10 to 11 and
from ages 11 to 12. Apparently the first real teaching of such ability
to add as is measured by the Courtis Standard Research Tests in Arith-
metic Series B in these schools is to children between the ages of 12
and 13.
Table VIII presents the facts in regard to addition in the 9-month
schools of Madison County. The same statistical method is used as
that used with the data from the 6-month schools.
The total improvement in ability to add in these schools for the
three-year period from ages 10 to 13 inclusive is 1.74. The P.E. of this
improvement is .198, or slightly under 12 per cent of the total gain.
The accuracy of the measurement for the 6-month schools is indi-
cated by a P.E. showing slightly over 12 per cent of the total gain;
just about the same degree of reliability.
The improvement by years varies for these schools as it does for
TABLE IX
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
ADDITION RIGHTS IN LOUISVILLE, Ky. (WHITE SCHOOLS)
SCORES
Age
Total
X1 X2 X30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 X9
1
1
-
1
-
-
1
8
5
-
-
-
1
16
8
5
3
1
-
-
10
11
12
13
-
43 12 16 19 38|332728|14 18 101 5 6 1 1
16101121 28 31 35 29 28 27 21 10 10 4 2
8 6 10/22 23 25 34 26 28 3728|13|131 6 9
5 8 9 19 18 25 2926 30 24 25 18 13 13 9
3
4
1
1
1
1
1
NN 1
289
304
304
25 | 306
1
2
4
-
-
1
1
1
.
1
1
Median
75 per-
25 per-
P. E. true
obtained
P.E.
centile
centile
10
11
12
13
3. 77
5. 62
6.73
7.46
. 21
. 18
. 18
.27
6. 26
8. 22
9.14
12.80
. 43
3.17
4.08
5.08
2.91
2.52
2,53
3.86
M11-M10=1.85
M12-M11=1.11
M13-M12= .73
M13-M10=3.69
. 170
.155
. 202
.213
the 6-month schools. From ages 10 to 11 it is .18; from ages 11 to 12
it is 1.02; and from ages 12 to 13 it is .54. The greatest gain occurs
between the ages of 11 and 12. This occurs a year earlier than the
greatest gain in the case of the 6-month schools.
The median achievement for children of each age is materially higher
than is the case in the 6-month schools. For the 13-year-old children
this median achievement is 3.81 in the 9-month schools as against
1.71 in the 6-month schools; a difference of 2.10 in favor of the schools
having the longer term.
36
Study of Achievement in Country and Town Schools
For the purposes of comparison, data are presented in Tables IX
to XIII inclusive from certain other school systems.
Table IX, for Louisville, Kentucky, is based on data in the Psycho-
logical Laboratory of the Louisville Board of Education, and is for cer-
tain of the white schools of the city. The tests were given under the
direction of the Psychological Laboratory during the school year prior
to June, 1918.
Table X, for Louisiana, is based on tests given by the parish super-
visors in thirteen Louisiana parishes.' The schools tested were white
schools selected by the supervisors as neither the best nor the worst
in their respective parishes. They range in size from one teacher to
TABLE X
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
ADDITION RIGHTS IN CERTAIN WHITE SCHOOLS IN LOUISIANA
SCORES
Age
Total
X1 X2 X30 1 2
x10 x ,
34
5
6
7
8
9
10
11
12
13
14
15 X9 X10 X11
-
-
-
10
11
12
13
24
13
7
43
24
13
7
58 48 31 24 23 12 10 6 4
431 471 381 27 28 201 161 10 8
24 451 371 51 41 30 18 11 11
13 50 35 421 31 28 16 16 8
-
-
1 - 1
2 1
6
6 5
1
1
1
1
1
1
287
280
299
277
1
1
17
1
1
1
1
Median
P. E, true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.38
.09
10
11
12
13
1.34
2.46
2.79
. 13
12
. 15
2.46
3.64
4.20
5.10
0.00
0.00
.68
.98
1.23
1.83
1.76
2,06
M11-M10= .96
M12-M11=1, 12
M13-M12= .33
M13-M10=2.41
.094
. 106
114
. 102
TABLE XI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC Tests
ADDITION RIGHTS IN ARKANSAS CITY
SCORES
Age
Total
X1
X2
X3
1
2
3
4
5
6
7
8
9
10
X9
15
8
10
11
12
13
54
15
8
3
65
54
15
8
54
49
63
34
46
33
54
32
19
35
37
36
29
17
33
39
14
29
34
37
8
10
22
32
6
4
8
12
2
3
6
4
312
259
294
254
2
8
6
-లు
3
5
4
1
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
.40
1. 10
2.10
3. 33
. 03
.11
. 12
0.00
0.00
1.00
3.01
4.22
5.01
.50
1.50
1.73
1.68
M11-M10= .70
M12-M11=1.00
M13-M12=1.23
M13–M10=2.93
072
098
. 106
.75
. 13
1.64
.082
sixteen teachers. In some cases only a limited number of the pupils
were tested in each grade. When this was done, the teacher was asked
Achievement Measured by Courtis Arithmetic Tests
37
to select pupils neither the brightest nor the dullest. This manifestly
gives a selection that is not accurately representative of the Louisiana
schools; it seems likely that the selection tends to be above rather than
below the median situation, and the range is less in proportion as the
teachers and supervisors have succeeded in avoiding the extreme cases.
Tables XI and XII, for Arkansas City and for Salina, are based on
tabulations made from papers collected by the Bureau of Educational
Measurements and Standards of the State Normal School at Emporia,
TABLE XII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
ADDITION RIGHTS IN SALINA, KAN.
SCORES
Age
Total
X1 X2 X30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 X9 X10
-
-
.
-
1
-
-
-
-
1
16
4
2
-
-
2
10
11
12
13
.
i
7
1
20
16
4
2
43 46 43 44 14 26 20 15 14 31 1
20 15 49 42 36 36/37 11 8 12 8
1
16 14 24 38 48 57 43 29 6 8 6 9 1 4
4 13 13 30127140/32 10 16 17 11 101 5! 4
335
296
311
274
2
5
1
2
2
-
-
-
Median
P.E. true
-obtained
median
25 per-
Q
P.E.
75 per-
centile
centile
10
11
12
13
1.98
3.06
4.16
5.25
. 12
13
. 12
3.89
5.10
5.70
7.25
.10
1.34
2.46
3.24
1.89
1.34
1.62
2.00
M11-M10=1.08
M12-M11=1.10
M13–M12=1.09
M13–M10=3.27
. 120
.114
. 114
120
. 15
TABLE XIII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
ADDITION RIGHTS IN HIBBING, MINN.
SCORES
Age
Total
X2 X30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 X9 X10
16
-
-
--
.
1
1
10
11
12
13
34 34 27 31 32 24 19 12 12 71 3 2 1
1623 30 20 32 25 20 12 17 12 9 9 8
11 16 25 16 14 19 24 17 19 16 13 4
3 4 8 15 10 13 9 16 18 11 11 10
1
3
7
2
1
4
3
1
3
3
3
لمر میرا یہ
257
244
222
179
2
NNI
2
-
- -
-
-
4
33
2
1
1
4
---
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.16
.21
10
11
12
13
2.56
4.00
6.41
8.63
4.78
7.22
9.34,
15. 12
.41
1.73
3. 21
5.36
2.18
2.74
3.06
4.88
M11-M10=1.44
M12-M11=2.41
M13-M12=2.22
M13-M10=6.07
. 164
. 206
.322
. 25
. 45
. 297
38
Study of Achievement in Country and Town Schools
Kansas. The tests were given and scored by the teachers during the
two years prior to June, 1917.
Table XIII, for Hibbing, Minnesota, is based on papers collected by
the Department of Research of the Hibbing schools. The tests were
given by the teachers and scored by clerks in the fall of 1919.
In the following summary the total improvement in ability to add
for the three-year period from ages 10 to 13 inclusive is given for each
system of schools reported, and also the median ability of each 13-year-
old group. This median for the 13-year-old group may be considered
in a way as a measure of the result obtained in any system with chil-
dren up to the age of 13.
TOTAL GAIN
MEDIANS
SCHOOL SYSTEMS
10 to 13
inclusive
13-year-old
children
Hibbing
Louisville
Salina...
Arkansas City-
Louisiana.
Madison County, 9-month schools.-
Madison County, 6-month schools.-
6.07
3.69
3.27
2.93
2.41
1.74
1.07
8.63
7.46
5.25
3.33
2.79
3.81
1.71
-
-
1
-
1
-
-
-
-
It is significant that the ranking in order of median ability of 13-
year-old children so nearly coincides with ranking in order of total
improvement for the three-year period from 10 to 13 inclusive. The
only difference is that the order of Louisiana schools and the Madison
County 9-month schools is inverted in the two rankings. The ability
to add is a mechanical ability, taught definitely in the schools, and very
little affected by the process of natural development which was so
potent a factor in the case of language ability as measured by the Tra-
bue Language Scale.
Differences in method of giving the tests and in detail of procedure
in different places affect the medians of the 13-year-old groups of chil-
dren. These elements of error may be of determining size in cases
where the tests are given by interested parties, such as teachers. When
the difference between medians for groups of children of different
ages is taken as a measure, the sources of error referred to above
neutralize each other, since it may be assumed that the errors will be
as great for one group of children as for another group, the tests be-
ing given at the same time in the same system and with the same
Achievement Measured by Courtis Arithmetic Tests
39
general directions or lack of directions. The ranking in order of the
total gain in ability to add over the three-year period from ages 10 to
13 inclusive is therefore the more significant ranking.
The following summary shows the yearly gain in each of the sys-
tems of schools studied :
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
1
Hibbing-
Louisville
Salina.com
Arkansas City
Louisiana..
Madison County, 9-month schools.
Madison County, 6-month schools.
1.44
1.85
1.08
.70
.96
.18
.23
2.41
1.11
1.10
1.00
1.12
1.02
.13
2.22
.73
1.19
1.23
.33
.54
.71
-
-
-
-
1
Total..
6.44
7.89
6.95
-
The extreme variation in the amount of yearly gain is significant
in that it shows so great a lack of uniformity in the time of teaching
so fundamental a process as that of column addition. The totals in-
dicate that as a rule greater progress is made in teaching this process
between the ages of 11 and 12; that the period from ages 12 to 13 is
next; and that the least gain is made from ages 10 to 11.
CONCLUSIONS
1. Such difference in performance in addition as is measured by
the Courtis Standard Research Tests can be obtained for school chil-
dren of different ages.
2. Since this test measures an ability trained in the schools and not
greatly dependent on natural development, this difference in perform-
ance is a valid measure of school efficiency in teaching this process.
3. Material gain in ability to add may be made with children dur-
ing any of the age periods, 10 to 11, 11 to 12, or 12 to 13.
4. The difference in ability of children of different age-groups is a
valid measure, even though there may have been some irregularity in
the giving of the tests.
5. That all the school systems investigated are doing better work in
the teaching of addition than are the schools of Madison County.
40
Study of Achievement in Country and Town Schools
ser som
6. That the schools in Madison County having a 6-month school
term are doing poorer work than the schools having a 9-month term.
That is to say, the one- and two-teacher schools are doing poorer work
than the larger schools.
SECTION 2. SUBTRACTION
The data presented in subtraction are tabulated from the same sets
of
papers
used for addition. The subtraction tests were given under
the same conditions as those in addition, by the same people, and were
corrected and collected in the same way. The statistical procedure
has been the same in tabulating and calculating.
Table XIV gives the facts in regard to subtraction in the Madison
County 6-month schools.
TABLE XIV
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN THE 6-MONTH WHITE SCHOOLS
OF MADISON COUNTY, Ky.
SCORES
Age
Tota
X1 X2
0
1
2
3
4
5
6
7
8
9
10
11
12
X9
X10 X11
1
3
1
-
-
10
11
12
13
10
6
3
2
19
10
6
3
76
69
61
48
13
11
13
12
7
6
13
11
5
6
10
8
8
8
8
8
2
3
7
5
NA 1
NI
3
4
2
141
125
137
123
2
4
11
1
2
ANI
1
2
Median
P. E, true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.54
.08
. 48
10
11
12
13
.05
.08
. 17
.25
.67
.97
1.70
1.05
1.79
3.67
5.05
.058
. 111
.22
.41
.53
M11-M10= .13
M12-M11= .30
M13-M12= .73
M13—M10=1.16
.78
1.63
2.26
. 188
. 162
In these schools the median ability in subtraction for children 10,
11 and 12 years of age is between 0 and 1, and the 25 percentile for
each of the age-groups presented falls within the same interval. Ap-
parently most of the children in these schools under 14 years of age
possess an ability in subtraction that is so slight that it cannot be
measured by this test.
The total gain in ability to subtract for the three-year period from ages
10 to 13 inclusive, as measured by the difference between the median
scores of the 10-year-old children and the 13-year-old children, is 1.16.
The P.E. of this measure of gain from the true measure is .162, almost
14 per cent of the total gain. The probable actual deviation from the
difference obtained is reasonably small, but the very small difference
Achievement Measured by Courtis Arithmetic Tests
41
obtained makes this probable deviation quite large proportionately.
The same thing is true in the case of addition.
The improvement from year to year increases consistently. From
ages 10 to 11 it is.13; from ages 11 to 12 it is .20; and from ages 12 to
13 it is .73.
Table XV gives the facts in regard to subtraction in the Madison
County 9-month schools.
The median ability in subtraction of each of the age-groups is above
1. The 25 percentiles of the 10- and 11-year-old groups fall in the
0 to 1 interval.
TABLE XV
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN THE 9-MONTH WHITE SCHOOLS
OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1 X2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14 X9 X10 X11
6
2
3
6
10
11
12
13
9
2
3
4
17
9
2
3
38
26
25
3
12
12
8
8
6
6
16
11
17
6
10
7
11
9
13
9
7
5
14
9
5
6
10
6
1
1
9
4
-
4
3
4
1
6
13
1
124
98
130
103
1
1
8
1
1
10
1
1
1
Median
P. E. true
-obtained
median
75 per-
25 per-
P.E.
centile
centile
. 26
10
11
12
13
1.66
2.00
4.50
5.27
.33
.31
35
4.88
5.83
7.05
8.42
.17
.51
1.31
2.59
2.35
2.66
2.87
2.91
M11-M10= .34
M12-M11=2.50
M13--M12= .77
M13-M10=3.61
270
.280
.289
.279
The total gain for the three-year period from ages 10 to 13 inclusive
is 3.61, as against a gain for a similar period of years in the 6-month
schools of 1.16. The P.E. of the gain in the 9-month schools (3.61)
is .279; a little less than 8 per cent of the total gain. The probable
actual deviation of the true from the obtained difference in the case
of the 9-month schools is greater than in the case of the 6-month
schools, .279 as against .162, but in proportion to the respective gains
it is less.
The progress from year to year is uneven.
year to year is uneven. From ages 10 to 11 it is
.34; from ages 11 to 12 it is 2.50; and from ages 12 to 13 it is .77.
By far the largest gain occurs between the ages 11 and 12.
Tables XVI to XX inclusive present comparative data from other
school systems, as was done for addition. In the following summary
the total improvement in ability to subtract for the three-year period
from ages 10 to 13 inclusive is given for each of the systems of schools
42
Study of Achievement in Country and Town Schools
TABLE XVI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN CERTAIN WHITE SCHOOLS OF LOUISVILLE, Ky.
SCORDS
Age
Total
X1
X2 X3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 X9
-
1
10
5
-
-
-
-
1
10
11
12
13
181 45 5 15 22 29/34 27/2714 18 11 4 4 2 1 - 1 1
10 18 9 11 12 18 22 27 32 27/34 31 21 10 12 31 5 1 1
5 10 2 6 15 12 20 28 31 37 34 23 26 19 11 11 10 9 3
5 3 1 1 2 15 26120 36 29 31 21 30 16 11 13 5 7
1
2
2
1
5
3
1
1
1
2
2
NNI
286
313
324
310
-
NI
26
1
-
Median
P.E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
. 23
.19
10
11
12
13
4.02
6.76
7.89
9.54
6.42
9.31
10.76
12.78
.10
3.73
5.39
7.12
3.16
2,79
2.68
2.83
M11-M10=2.74
M12--M11=1.13
M13-M12=1.65
M13—M10=5.52
184
. 162
. 162
.184
. 18
.20
TABLE XVII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN CERTAIN SCHOOLS IN LOUISIANA
SCORES
Age
Total
X1 X2 X3
0
3
4 5
6
7
8
9
10
11
12
13
14
15
X9 X101 X11
Χιο
1
1
-
-
24
14
7
2
-
10
11
12
13
1
46
24
14
7
521 52 21 381 13 15 100 10 1 3 1
46 46 35) 30 22 21 19 12 6 4 5
24 42 23 28 361 35) 29 20 81 11 9
14 36 18 29 29 34 21 25 13 12 12
-
1
8
5
1
6
3
297
289
304
277
1
1
1
16
1
1
1
1
1
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
.31
1.41
3.38
4.16
. 13
. 14
3.75
3.98
5.65
6.79
0.00
0.00
.73
1.68
1.87
1.99
2.41
2.55
M11-M10=1.10
M12-M11=1.97
M13–M12= .78
M13-M12=3.85
120
. 134
. 156
. 144
.17
.19
TABLE XVIII
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN ARKANSAS CITY
SCORES
Age
Total
X1 X2 X3
0 1
2
3
4
56
7
8
9
10 11 12
13
14 X9
3
10
11
12
13
18
8
4
1
52
18
8
4
60 37
52 33
18 29
8 21
31
31
22
10
25
22
31
18
25
24
26
25
23
16
45
31
16
18
25
20
7
7
25
37
8
17
19
26
1
1
7
11
16
2
2
7
2
5
3
3
305
257
283
254
2
4
25
2
Median
P. E, true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.11
. 16
10
11
12
13
.60
1.56
4.07
5.45
3.23
4.29
6.17
7.59
0.00
0.00
1.53
3.06
1.61
2.14
2.32
2.26
M11-M10= .96
M12-M11=2.51
M13–M12=1.38
M13-M10=4.85
. 122
. 141
148
.17
.
. 17
. 130
Achievement Measured by Courtis Arithmetic Tests
43
TABLE XIX
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN SALINA, KAN.
SCORES
Age
Total
X1 X2 X3 0 1 2 3 4 5 6 7 8 9 10/11 12 13 14 15 16 17 18 19 20 21 22 X9 X10
-
-
1
10
11
12
13
15
4
3
1
19
15
4
3
46 1721 33 30 41 35 31 23 20 6 4
19|11|19|13|14|40|32|36)23 30 18 8 7 4 2
15 3 5 10 27 36 27 45 28 33 27 19 11 8 3
4 5 3 4 8 17 31 45 37 28 20 24 13 6 7 1
341
295
309
266
1
3
3
1
1
2
1
2
1
2
.
0
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
3.65
5.39
6.54
7.35
19
.19
. 16
5.96
7.79
8.87
9.72
.30
2.44
4.28
5.72
2.83
2.62
2.29
2.00
M11-M10=1.74
M12-M11=1.15
M13—M12= .81
M13–M10=3.70
.162
. 148
. 134
. 150
. 15
TABLE XX
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
SUBTRACTION RIGHTS IN HIBBING, MINN.
SCORES
Age
Total
X2 X3 o 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 x9 x1
16
-
I
1
2
1
10
11
12
13
35 33 9 10 12 14 22 20 16 16 15 4 9 6
16 2016/11 9/25 15 20 16 22 18/19 12 6
31 6 6 13 11 12 22 19 18|18|1925 11
2 2 4 4 101 9 31 9 16 13 10 19 15
5 3
7 4
7 13
5
2
6
6
3
4
7
1
2
2
4
1
3
2
248
238
227
179
1
.
-
-
-
-
1
1
4
32
4
I
-
-
1
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.30
10
11
12
13
4.64
6.80
9.19
11.34
25
23
7.93
10.02
11.93
15.87-
.33
3.72
6.26
8.10
3.80
3.15
2.83
3.88
M11-M10=2.16
M12--M11=2.39
M13-M12=2.15
M13–M10=6.70
.240
.212
.260
.284
.36
reported, and also the median ability of each 13-year-old group. As
in addition, so in subtraction, this median for the 13-year-old group
may be considered in a way as a measure of the result obtained in
any system with children up to the age of 13.
TOTAL GAIN MEDIANS
SCHOOL SYSTEMS
10 to 13 13-year-old
inclusive children
Hibbing
Louisville.
Arkansas City--
Louisiana -
Salina...
Madison County, 9-month schools.--
Madison County, 6-month schools.
- -
6.70
5.52
4.85
3.85
3.70
3.61
1.16
11.34
9.54
5.45
4.16
7.35
5.27
1.70
1
-
-
-
44
Study of Achievement in Country and Town Schools
The ranking in order of total gain made for the three-year period
from ages 10 to 13 inclusive corresponds quite well with the ranking
in order of medians for the 13-year-old children. This correspond-
ence is not so close as was the case with addition; there are four dis-
placements in the ranking. As was the case with addition, the rank-
ing in order of total gain for the three-year period is the more sig-
nificant, since the use of a difference as a measure tends to neutralize
errors in the giving and scoring of the test.
It is interesting to note that the rank in gain in ability to subtract is
not the same as that in ability to add. Arkansas City and Louisiana
both come ahead of Salina in subtraction, and not in addition. This
difference between the rank of these systems for the two processes
would seem to indicate that subtraction needs to be taught; that im-
provement in addition does not necessarily carry with it exactly pro-
portionate ability to subtract.
The following summary shows the gain for each yearly age-period
in the systems studied :
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
-
1
Hibbing
Louisville
Arkansas City
Louisiana...
Salina
Madison County, 9-month schools.-
Madison County, 6-month schools...
-
2.21
2.74
.96
1.10
1.74
.34
.13
2.34
1.13
2.51
1.97
1.15
2.50
.30
-
-
2.15
1.65
1.38
.78
.81
.77
.73
-
Total.com
9.22
11.90
8.27
The variations are as great in the amount of yearly gain as they
were shown to be in addition. As in addition, so in subtraction, the
greatest yearly gain seems to be between the ages of 11 and 12. In
subtraction the next greatest gain seems to be between the ages of 10
and 11, while in the case of addition the second greatest gain was be-
tween the ages of 12 and 13. The smallest gain is made between the
ages of 12 and 13.
CONCLUSIONS
1. The conclusions reached in regard to addition (p. 39) hold in the
case of subtraction.
Achievement Measured by Courtis Arithmetic Tests
45
2. Improvement in addition does not necessarily carry with it pro-
portionate ability to subtract.
SECTION 3. MULTIPLICATION
The data presented in multiplication are from the same sources as
those for addition and subtraction, and the method of treatment has
been the same throughout.
Table XXI gives the facts in regard to multiplication in the Madison
County 6-month schools.
TABLE XXI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
MULTIPLICATION RIGHTS IN THE 6-MONTH WHITE SCHOOLS
OF MADISON COUNTY, Ky.
SCORES
Age
Total
Xi X2
0
1 2 3 4
3 5
6
7
8
9
10
11
12
13
14
15
X9 X10 X11
1
-
10
11
12
-
-
9
8
4
2
19 82 16 3 5
91 751 11 11 8
61 62 12 16 12
41 57 15 8 9
4
2
9
5
1
2
3
3
4
140
124
136
124
1
2
4
10
1
1
ANI
13
4
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.04
.08
.05
.21
10
11
12
13
.51
.62
.93
.98
.93
1.27
3.16
3.77
.42
.53
1.39
1.67
M11-M10=.11
M12 M11=.31
M13-M12=.05
M13–M10=.47
.036
.094
142
.14
.38
. 18
.43
. 111
The median of each of the age-groups given falls below 1, and even
the 75 percentile of the 10-year-old group falls between 0 and 1. It
seems that most of the children in these schools below the age of 14
have an ability in multiplication that is less than can be measured by
the Courtis Standard Research Tests in Arithmetic Series B.
The total gain in ability to multiply during the three-year period, ages
10 to 13 inclusive, is only .47. The P.E. of this statement of gain is
.111, something over 25 per cent of the gain itself. The gain noted is
very slight. Apparently these 6-month schools in Madison County are
failing to teach most of the pupils under 14 how to multiply.
The improvement from year to year necessarily is very slight, since
the total improvement is so small. From ages 10 to 11 the improve-
ment is .11; from ages 11 to 12 it is .31; and from ages 12 to 13 it is
.05. The greatest gain in any one-year period is .31 from ages 11 to 12.
The results of instruction in multiplication in these schools are very
meager.
46
Study of Achievement in Country and Town Schools
TABLE XXII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
MULTIPLICATION RIGHTS IN THE 9-MONTH WHITE SCHOOLS
OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1
X2
0
1
2
3
4
5
6
7
8
9
10
11
X9
X10
X11
-
!
3
10
11
12
13
9
1
3
4
16
9
1
3
37
31
32
13
4
10
14
10
12
7
14
11
14
7
23
11
10
12
16
9
12
11
10
12
6
4
9
11
2
NI
120
96
131
101
2
1
1
8
-
3
5
1
1
1
2
.
-
-
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
.21
.94
1.70
3.06
3.86
. 13
.45
11
12
13
. 26
3.85
4.58
4.56
6.25
1.86
2.06
1.84
2.36
M11-M10= .76
M12/M11=1.36
M13–M12= .80
M13-M10=2.92
. 206
200
.216
.222
.87
.20
. 29
1.52
Table XXII gives the facts in regard to multiplication in the 9-
month schools of Madison County.
The median ability in multiplication in these schools for 10-year-old
children is .94; a little less than 1. The 25 percentile of the 10-, 11-
and 12-year-old groups is less than 1 in each case. The situation
here presented is materially better than that in the 6-month schools.
The total gain in ability to multiply for the three-year period from ages
10 to 13 inclusive is 2.92. The contrast between this gain and that in
the 6-month schools (.47) is marked. The P.E. of this gain of 2.92
is .222, a little over 7 per cent of the gain. The probable actual de-
viation of the true from the obtained measure is greater in the case of
the 9-month schools than in the case of the 6-month schools, but in
proportion to the gain made it is much less.
The improvement in ability to multiply from ages 10 to 11 is .76;
from ages 11 to 12 it is 1.36; and from ages 12 to 13 it is .80. The
gain during any one of the year periods is much greater than the gain
for the entire three-year period in the 6-month schools. The great-
est gain is from ages 11 to 12, as is the case in the 6-month schools.
Tables XXIII to XXVII inclusive give comparative data in regard
to multiplication from other school systems. In the following sum-
mary the total improvement in ability to multiply during the three-year
period from ages 10 to 13 inclusive is given for each of the school sys-
tems studied, and also the median ability for the respective groups of
13-year-old children. The schools are listed in the order of amount of
improvement made.
Achievement Measured by Courtis Arithmetic Tests
47
TABLE XXIII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
MULTIPLICATION RIGHTS IN CERTAIN WHITE SCHOOLS IN LOUISVILLE, Ky.
SCORES
Age
Total
X1
X1 X2
X3 0 1 2 3 4 5
6
7
8
9
10 11
12
13
14 | 15
16 | 17
1
-
10
11
12
13
101 16 43 7 15 23 34 32 30
5 10 181 10 81 11 17 37 41
5 10 2 9 11 18 31 34
5 3 3 9 18 22 32
26
36
38
43
21
35
35
40
12
32
41
38
5
21
34
34
7
14
15
18
3
3
17
13
7
9
13
5
6
8
1
2
2
284
309
320
305
2
1
4
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
3.82
5.98
7.05
7.43
.21
.14
. 15
.14
6.11
8.17
9.17
9.46
28
4.00
4.80
5.50
2.91
2.08
2.18
1.98
M11-M10=2.16
M12-M11=1.07
M13-M12= .38
M13–M10=3.61
158
. 127
. 120
152
TABLE XXIV
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
MULTIPLICATION RIGHTS IN CERTAIN WHITE SCHOOLS IN LOUISIANA
SCORES
Age
Total
X1 X2 X3
x34
0
1
2
3
4
5
6
7
8
9
101
11
12 X9 X10
X11
-
10
11
12
13
24
13
7
42
24
13
7
61
43
24
13
69
63
74
50
24
31
36
33
21
30
28
35
21
26
34
25
12
16
34
27
8
11
21
23
4
9
12
17
2
7
5
16
4
6
3
1
3
2
1
1
1
1
1
17
289
280
300*
275
-
1
1
3
1
Median
P. E. true
--obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.23
10
11
12
13
.080
. 106
.95
.06
. 12
. 13
.17
1.85
3.23
4. 26
5.70
0.00
0.00
.41
.97
.92
1.61
1.92
2.86
M11-M10= .72
M12--M11= .93
M13-M12=1.10
M13M10=2.75
1.88
2.98
. 136
. 117
TABLE XXV
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
MULTIPLICATION RIGHTS IN ARKANSAS CITY
SCORES
Age
Total
X1
X2
X3
0
1
2
3
4
5
6
7
8
9
10
11
12
X9
11
-
-
10
11
12
13
14
8
4
1
51
14
8
4
61
51
14
63
41
49
30
44
21
25
18
24
40
38
22
24
22
50
24
6
21 15
31 22
30 22
9
28
28
6
16
16
2
2
24
8
4
4
298
258
296
245
2
3
1
6
8
2
4
1
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
0.00
0.00
.89
.098
.127
10
11
12
13
.36
1.71
3.20
4.51
06
. 14
. 15
.19
1.78
3.84
5.13
6.88
M11-M10=1.35
M12-M11=1.49
M13-M12=1.31
M13--M10=4,15
1.92
2.08
2.43
.97
. 150
2.01
. 126
48
Study of Achievement in Country and Town Schools
TABLE XXVI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC Tests
MULTIPLICATION RIGHTS IN SALINA, KAN.
SCORES
Age
Total
X1 X2 X3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 X9 X10
9 911011
-
-
1
1
-
-
1
1
1
16
3
3
1
1
-
-
i
!
-
10
11
12
13
22
16
3
1
48 31 27 20 23 48 48 24|101 91 4 4
22 19 17 22 23 21 52 22 8 10 17 4 5 2 2
16 8 8 11 29 29 45 51 19 33 27 19 19 3 7 1
3 6 8 13 11 31 27 46 29/28/19)10 15 7 4 8
334
267
333
275
-
.
2
4
2
2
2
---
---
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
3. 13
4.54
6.28
6.81
. 18
.18
. 16
.20
5.32
6.23
8.84
9.18
0.00
1.39
4.18
4.86
2.66
2.44
2.33
2.66
M11-M10=1.41
M12-M11=1.64
M13-M12= .53
M13-M10=3.68
. 155
. 148
. 156
.162
TABLE XXVII
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC Tests
MULTIPLICATION RIGHTS IN HIBBING, MINN.
SCORES
Age
Total
X2 X30
2
3
4
5 6 7
89
10
11
12
13
21
14
15
16
17 X9 X10
.
1
+
-
1
1
.
!
t
t
10
11
12
13
18 35 34 23 29 35 20 21 16 12 95
16 19 11 24 25 23 42 25/ 191 10 15
7 10 12 171 271 291 271 261 181 18
3 6 4 12 12 13 13 17 16 11
4
8
10
12
1
1
3
12
1
2
9
8
2
6
3
1
1
261
244
230
181
4
2
4
33
4
-
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
•
10
11
12
13
2.77
5.09
6.48
8.65
.18
.17
.18
.32
5.17
6.92
8.97
12.59
.41
2.62
4.42
5.63
2.38
2.15
2.27
3.48
M11--M10=2.32
M12/M11=1.39
M13-M12=2.17
M13-M10=5.88
140
.140
.220
.220
As is the case in addition and subtraction, the ranking in order of
gain made in ability for the three-year period from ages 10 to 13 inclu-
sive does not correspond exactly with the ranking in order of ability of
TOTAL GAIN
MEDIANS
SCHOOL SYSTEMS
10 to 13
inclusive
13-year-old
children
1
1
I
1
-
--
-
-
-
-
I
-
1
1
-
-
-
Hibbing-
Arkansas City
Salina.
Louisville..
Madison County, 9-month schools-
Louisiana..
Madison County, 6-month schools..
-
-
-
-
5.88
4.15
3.68
3.61
2.92
2.75
.47
8.65
4.51
6.81
7.43
3.86
2.98
.98
Achievement Measured by Courtis Arithmetic Tests
49
13-year-old children. The measure of gain made is probably the
more significant measure, as for addition and subtraction.
It must be borne in mind that the steps of improvement are not
necessarily of equal value. It may be more difficult to teach a child
who cannot multiply to multiply well enough to do one example cor-
rectly than it is to teach a child who can do one example correctly to do
two examples correctly. In other words, because Hibbing makes twice
as much improvement as Louisiana does not necessarily mean that the
teaching in Hibbing is twice as good as that in Louisiana. This dif-
ficulty in evaluating the results of this test is not due to the fact that
a difference between the median abilities of age-groups is used as a
measure, but rather to the manner in which the test is constructed.
The unit in which the result is stated is not one of the relative diffi-
culty with which those results are obtained.
The following summary shows the gain for each yearly age period
in the systems studied :
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
-
-
- -
-
-
-
!
-
-
Hibbing-
Arkansas City-
Salinan
Louisville...
Madison County, 9-month schools.
Louisiana
Madison County, 6-month schools.
2.32
1.35
1.41
2.16
.76
.72
.11
1.39
1.49
1.64
1.07
1.36
.93
.31
2.17
1.31
.53
.38
.80
1.10
.05
-
1
-
-
Total..
8.83
8.19
6.34
The variations in amount of yearly gain are as great as they are in
addition and subtraction. The greatest gain seems to be between
ages 10 and 11 in this case, while in both addition and subtraction the
greatest gain seems to come between ages 11 and 12. The smallest
gain appears between ages 12 and 13.
The conclusions in regard to multiplication are the same as those for
addition (p. 38) and subtraction (p. 44).
SECTION 4. DIVISION
The data presented in division are from the same sources as those
for addition, subtraction and multiplication, and the same method of
treatment has been followed.
50
Study of Achievement in Country and Town Schools
Table XXVIII gives the facts in regard to division in the 6-month
schools of Madison County.
TABLE XXVIII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC Tests
DIVISION RIGHTS IN THE 6-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1
X2
0
1
2
3
4
5
6
7
8
X9
X10
X11
1
-
1
10
11
12
13
10
6
3
2
17
10
6
3
-
98
83
78
70
7
15
16
16
OOO en hoe
1
5
7
5
2
2
6
1
1
4
139
126
138
123
2
4
11
1
1
2
4
2
Median
P. E, true
- obtained
median
75 per-
25 per-
P.E.
centile
centile
.78
10
11
12
13
43
.56
.76
.80
.03
.04
.09
.94
2.05
2. 15
0.07
.18
.32
.36
.35
.38
.86
.89
M11--M10= .13
M12-M11= 20
M13-M12= .04
M13-M10= .37
.028
.053
.078
.072
. 10
In these schools the median ability in division of each of the age-
groups from ages 10 to 13 inclusive is between 0 and 1. For the ages 10
and 11 the 75 percentiles are in the same interval. It seems that in
division, as in multiplication, the majority of the children under 14
years of age in the Madison County 6-month schools are unable to
work correctly any of the examples given in the Courtis Standard
Research Tests in Arithmetic Series B for division.
The total gain in ability to divide during the three-year period from
ages 10 to 13 inclusive is from .43, the median for the 10-year-old chil-
dren, to .80, the median for the 13-year-old children, a difference of .37.
The P.E. of this difference is .072-about 20 per cent of the gain.
This gain is very small for so long a period of time at the age when
material progress is being made in this ability in other school systems.
As would be expected where the total improvement is so small, the
yearly gains are very small and uneven. From ages 10 to 11 the gain
is .13; from ages 11 to 12 it is .20; and from ages 12 to 13 it is .04.
The P.E. of the gain from ages 12 to 13 is .072, which is almost twice
as much as the gain. This means that the gain in this year is almost
negligible.
Table XXIX gives the facts in regard to division in the Madison
County 9-month schools.
Achievement Measured by Courtis Arithmetic Tests
51
TABLE XXIX
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN THE 9-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
SCORES
Age
Total
X1 X2
0
1
2
3
4
5
6
7
8
9
10
11
12
13 X9 X10
X11
1
10
11
12
13
9
1
3
5
16
9
1
3
60
46
45
17
5
6
13
15
8
11
9
8
5
3
10
11
9
7
13
7
4
2
11
6
3
2
8
6
1
2
8
3
1
4
2
3
1
1
1
3
1
1
1
1
124
96
129
99
1
1
8
2
1
1
1
1
-
Median
P.E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.61
10
11
12
13
.82
.12
.16
.21
.33
2.37
2.90
5.31
6.37
.11
.30
.63
.98
2.27
3.13
1.13
1.30
2.34
2.69
M11-M10= .21
M12-M11=1.45
M13–M12= .86
M13–M10=2.52
. 122
. 190
.264
.210
In these schools the 25 percentile of each of the age-groups from ages
10 to 13 inclusive falls between 0 and 1, and the medians for the 10-
and 11-year-old groups each fall in the same interval. A much larger
proportion of the children reported are able to work some of the ex-
amples correctly than is the case in the 6-month schools.
The total gain from ages 10 to 13 inclusive in this case is 2.52 as
against .37 in the case of the 6-month schools in the same county. The
P.E. of the gain for the 9-month schools is .21, about 8.5 per cent of the
gain. The probable actual deviation of the true measure of gain from
the measure of gain given is almost three times as great as the like
probable deviation in the case of the 6-month schools, but the gain in
the case of the 9-month schools is so much greater that proportion-
ately the probable deviation is smaller.
As in the 6-month schools, so in these, the yearly gains are unequal.
From ages 10 to 11 the gain is .21; from ages 11 to 12 it is 1.45; and
from ages 12 to 13 it is .86. The gain for each year after the first is
much greater than the total gain in the 6-month schools for the entire
three-year period.
Tables XXX to XXXIV inclusive give comparative data from other
school systems in regard to division. In the following summary the
total gain in ability to divide during the three-year period from ages 10
to 13 inclusive is given for each of the systems studied, and also the
median ability of the 13-year-old children in the respective systems.
The schools are listed in the order of the amount of improvement
made.
In this table it is interesting to note that the ranking in order of
amount of total gain corresponds exactly to ranking in order of the
52
Study of Achievement in Country and Town Schools
TABLE XXX
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN CERTAIN WHITE SCHOOLS OF LOUISVILLE, Ky.
SCORES
Age
Total
X1 X2 X3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 X9
10
5
-
-
-
-
-
-
10
11
12
13
16
10
5
4330 24 31 24/32 21 20 13 9 11 31 31 41 2 1
16 23 12 16 23 28/25 22 20 18 19|21|12121 91 7 3 3
10 16 12 15 18 22 22 23 27 27 23 23 10 1711 12 9 3
5 11 9 13 16 13 21 34 23 30 25 26 25 18 13 612 6
NONI
1
4
1
3
2
1
1
297
308
319
336
---
26
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.19
10
11
12
13
2.82
5.84
7.61
8.76
.24
.23
.21
5.60
9.68
10.83
12.05
.17
2.68
4.17
5.80
2.71
3.50
3.33
3. 12
M11-M10=3.02
M12-M11=1.77
M13–M12=1.15
M13–M10=5.94
. 192
.204
. 191
. 176
TABLE XXXI
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN CERTAIN WHITE SCHOOLS IN LOUISIANA
SCORES
Age
Total
X1
X2 X3
ol
1
2
3 4
5
6
7
8 9
10
11
12
13
14 X9 X10 X11
-
.
1
-
24
14
7
2
.
.
10
11
12
13
-
1
1
43
24
14
7
59 106 16 17 9 4 41
43 90 27 19 161 16 9
24 103 32 31 22 23 13
14 751 371 181 15 261 22
2
76
817
13 10
1
3
8
12
1
3
7
6
1
1
4
2
1
286
282
305
281
1
1
1
16
1
1
-
-
1
1
3
1
-
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.16
.83
10
11
12
13
.66
1.14
2.41
.02
.09
.12
.19
2.70
3.80
5.85
0.00
0.00
.30
.65
33
1.35
1.75
2.60
M11-M10= .50
M12-M11= .48
M13–M12=1.27
M13–M10=2.25
.060
.092
. 138
120
0
TABLE XXXII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN ARKANSAS CITY
SCORES
Age
Total
X1 X2 X301
3
3
4
5
6
7
8
9
10
11
12
13
14
15 X9
1
10
11
12
13
16
8
4
1
49
16
8
4
60 86 43
49811 38
16 82 45
8421 29
22
10
37
25
9
16
19
23
7
9
19
19
2
9
11
25
6
15
23
5
12
15
1
7 1
6 10
5 8
2
9
10
295
257
294
248
1
3
5
1
1
1
Median
P. E. true
obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.26
.053
10
11
12
13
.68
1.82
3.85
04
.08
.14
.20
1.23
2.07
4.50
6.43
0.00
0.00
.55
1.24
.61
1.03
1.97
2.59
M11--M10= .42
M12 M11=1.14
M13--M12–1.83
M13-M10=3.39
. 102
. 150
. 121
Achievement Measured by Courtis Arithmetic Tests
53
TABLE XXXIII
AGE DISTRIBUTION, 10 TO 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN SALINA, KAN.
SCORES
Age
Total
X1 X2 X30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 X9 X10
il
-
.
-
-
-
-
-
!
1
10
11
12
13
16
3
3
21
16
3
3
47 48 41 39 27 28 21 21 9 12 2. 2 1
21 36 21 29/37 17 29 16 16 25 7 5 41 4 5 2 2
16 22 18 28 25/32/33 29 25 281 9 21 8/10) 5 2 1 2
3 11 17 20 272529 31 14 20 11 18 141 8 10 2 2
2
-
-
335
297
322
275
-
--
1
2
5
2
2
-
+
-
--
1
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
15
10
11
12
13
.21
1.86
3.60
5.45
6.80
4.43
6.85
8.26
9.56
0.00
.95
2.86
3.54
2.21
2.95
2.80
3.01
M11-M10=1.74
M12-M11=1.85
M13—M12=1.35
M13-M10=4.96
. 19
22
. 158
. 176
.176
. 166
TABLE XXXIV
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF COURTIS SERIES B ARITHMETIC TESTS
DIVISION RIGHTS IN HIBBING, MINN.
SCORES
Age
Total
X2 X3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 X9 X10
16
-
.
-
.
-
-
-
-
1
1
-
-
3598 11 14 11/17 11 12 11 41 41 5 1 5 2 1
16160 22 21 16 13 15 13 13 11 10 12 7 9 11 1 1 1
28/10 20 12 26 19 18 13 14 16 13 4 13 31 31 5 3 2
14 10 4 4 11 8) 9 13 12 9 10 5 10 8 6 2 1 2
.
10
11
12
13
-
258
243
229
178
1
1
1
1
4
32
1
2
---
4
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
· 13
.74
10
11
12
13
.79
3. 15
5.97
9.44
17
. 27
.27
.45
4.50
7.48
9.73
15. 12
2.18
3.37
3. 38
4.92
M11-M10=2.36
M12-M11=2.82
M13--M12=3.47
M13-M10=8.65
2.96
5.18
172
.220
.327
. 172
size of the median for the 13-year-old children. This is not true in
the case of addition, subtraction, or multiplication, though in each case
there is a marked similarity in the ranking.
TOTAL GAIN
MEDIANS
SCHOOL SYSTEMS
10 to 13
inclusive
13-year-old
children
Hibbing
Louisville...
Salina-
Arkansas City ---
Madison County, 9-month schools.
Louisiana
Madison County, 6-month schools..--
8.65
5.94
4.96
3.39
2.52
2.25
.37
9.44
8.76
6.80
3.65
3.13
2.41
.80
- -
-
-
-
54
Study of Achievement in Country and Town Schools
The following table shows the yearly gain in ability to divide in each
of the systems studied :
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
Hibbing-
Louisville
Salina---
Arkansas City
Madison County, 9-month schools..
Louisiana..
Madison County, 6-month schools..
2.36
3.02
1.74
.42
.21
.50
.13
2.82
1.77
1.85
1.14
1.45
.48
.20
3.47
1.15
1.35
1.83
.86
1.27
.04
1
1
-
-
-
Total...
8.38
9.71
9.97
The variations in amount of yearly gain in the different systems is
as great as it is in addition, subtraction and multiplication. The
greatest gain seems to be between ages 12 and 13, but the gain from
ages 11 to 12 is almost as great. The gain from ages 10 to 11 is some-
what less. It seems that division is taught when the children are a lit-
tle older than when addition, subtraction and multiplication are taught.
CONCLUSIONS
1. The difference in performance in arithmetic, as measured by the
Courtis Standard Research Tests in Arithmetic, can be obtained for
school children of different ages.
2. Since the fundamental processes measured by this test are largely,
if not solely, imparted by school training, this difference is a reliable
measure of school efficiency.
3. Since the improvement measured by this test is stated in terms of
examples solved in a given time rather than in terms of difficulty for
the children, the differences obtained must be considered in connec-
tion with the number of examples solved by the groups of children of
different ages.
4. The differences obtained may be compared for two systems of
schools, even though the testing was done at different times in the
respective systems.
5. The differences obtained are valid, even though there are con-
stant errors in the giving of the tests, such as might be caused by hav-
ing the tests given by the teachers.
Achievement Measured by Courtis Arithmetic Tests
55
6. Material gain may be made in these fundamental processes of
arithmetic during any part or all of the age period from 10 to 13 in-
clusive.
7. The results in the 6-month schools of Madison County, Kentucky,
are uniformly poorer than in any of the other systems studied.
CHAPTER V
ACHIEVEMENT AS MEASURED BY THE THORNDIKE SILENT
READING SCALE ALPHA 2
THE Thorndike Silent Reading Scale Alpha 2 was used to measure
reading in the schools of Madison County at the same time that the
tests were given in Language and Arithmetic. This scale is designed
to be used as a group test, and the directions for scoring are given on
the basis of groups of pupils such as would be found in one room of a
city school system. In country schools such groups do not exist, and
therefore individual scores were assigned each pupil, on the basis of
tables prepared by Dr. Truman Lee Kelley1
Using the individual scores assigned on the basis of these tables, the
remaining problems involved in finding the differences in performance
in reading of different age-groups are practically the same as in the
work with the Trabue Language Scale and the Courtis Standard Re-
search Tests in Arithmetic. Distributions for the respective age-
groups are completed on the same assumptions, and the same age-
groups are used throughout. Scores used are in terms of difficulty as
assigned by Thorndike.
Table XXXV gives the facts in regard to reading in the Madison
County 6-month schools. The table reads, there are estimated to be
8 children 10 years old in the first grade (X1) whose scores in read-
ing are unknown, 10 children 10 years of age with scores unknown
are estimated to be in the second grade (X2), 1 child 10 years old
made a score of 2.0, 5 made a score of 2.2, 3 a score of 2.6, 3 a score
of 2.9, 2 a score of 3.2, etc.
The total gain in ability to read for the three-year period from ages
10 to 13 inclusive is from 4.50 to 5.26, a difference of .76. The P.E. of
this difference is .09, or about 12 per cent of the total. This gain is
very small for a three-year period, and the P.E. of the gain is relatively
quite large.
The improvement from year to year is very uneven. From ages 10
to 11 it is .03; from ages 11 to 12 it is .59; and from ages 12 to 13 it is
.14. The results indicate rather indefinite work in reading.
1
Kelley, T. L.: "Thorndike's Reading Scale Alpha 2 Adapted to Individual
Testing,” Teachers College Record, XVIII: 253ff. (May, 1917).
56
TABLE XXXV
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF THORNDIKE SILENT READING SCALE ALPHA 2 SCORES IN THE 6-MONTH WHITE SCHOOLS OF MADISON COUNTY, Ky.
SCORES
Age
-
-
-
X1 X2 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.04.14.24.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.66.76.8 6.9 7.0 7.1 7.2 7.37.417.5 7.6 7.7 X9 X10 X11
//(|////////
8 10 1
5
3
3
2 6
4 1
11 12 1 2 21 11
2 18 3 5 4 1 2 2 2 4 2
1 1
1 1
4 8
2 1
4
4 5
5 1
1 5 5
9
1 2 9 1 5 7 1 1
2
3
3
2
2
2 1
1 1
3 4
1
4
1 6
1 10 1) 3 10 5) 10 8 24 2 3 3 1
1 4
2 4
72
3 1
3
1
1
2 식
​1 3
1
1
2
2
1
2
5 21
71 10 1 8 4 2 3 1 2 4 2 2 7
2. 7 1
3
1
1 31
-
-
1
-
-
1
-
-
-
-
1
-
---
1
-
1
.
1
-
NI
--
-
-
--
-
-
i
10
11
12
13
-
-
1
1
---
NNN
-
-
.
-
NA
I
-
.
-
6.
4
; iܝܢ
O O
.
-
-
-
0
-
-
!
1
-
-
-
-
.
-
---
-
-
1
.
--.
Age
Total
Median
P. E. true
---obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
.89
10
11
12
13
122
107
131
117
4.50
4.53
5.12
5.26
. 10
. 12
.09
.11
5.01
5.23
6.06
6.59
3.22
3.24
4.37
4.59
.99
.84
1.00
M11-M10= .03
M12-M11= .59
M13–M12.14
M13—M10.76
09
.09
.09
.09
TABLE XXXVI
AGE DISTRIBUTION, 10 to 13 -
INCLUSIVE, OF THORNDIKE SILENT READING SCALE ALPHA 2 SCORES IN THE 9-MONTH WHITE SCHOOLS OF MADISON COUNTY, KY.
SCORES
Age
X1 X2
1 X2
0 2.2 2.32.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7|3.8 3.9 4.04.1/4.24.3/1.4/4.5|4.64.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.916.06.116.2.6.36.46.5) 6.66.716.816.97.0 7.1 7.2 7.37.417.57.67.77.8/7.918.08.1 8.2 8.3 8.4 8.5 8.6 8.7 x9
X10 X11
6
2
1
8
-
2
1
5
.
13
6
11 1
1
-
-
2
2
1
-
-
-
-
-
1
I
5
1
3
2
1
1
1
5
2
3
3
3
1
11
1
2
1
ܕ ܟܬ ܟܬ
1
2
1
3
4
-
-
4
1
2
2
10
11
12
13
2
-
-
-
-
ܟܬ ܘܬ ܘܬ
-
-
1
-
1
4
5
2
1
7
5
3
2
3
1
2
3
-
2
3
5
2
5
5
3
4
1
IN
1
2
4
2
1
1
4
3
لما المسط ما
3
4
6
3
1
1
ܙܟܬ ܟܝ
1
4
6
3
3
1
5
7
2
1
31._
2 3
1
2
1
3
1
2
1
1
3
3
1
1
1
3 2
1
1
1
.
1
1
1
1
NNN
1
-
1
-
1
2
1
7
4
2
-
-
3
2
3
2
1
NA
1
-
1
1
1
1
1
2
---
2
1
;
-
-
3
-
-
-
2
-
-
1
-
-
-
-
-
-
.
-
1
-
-
-
Age
Total
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
. 15
10
11
12
13
109
84
107
83
4.55
5.30
5.86
6.45
. 17
5.51
6.25
6.65
7.01
2.98
3.75
4.95
5.14
1.26
1.25
.85
.93
M11-M10= .75
M12-M11= .56
M13-M12= .59
M13--M10=1.90
.14
. 13
10
. 12
.10
. 13
TABLE XXXVII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF THORNDIKE SILENT READING SCALE ALPHA 2 SCORES OF CERTAIN WHITE SCHOOLS IN LOUISVILLE, Ky.
Age
SCORES
X1 X2 X3 0 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.415.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 X9 X10 X11
2.782.8/2
15.0
5.81
816.9
1
1
1
-
.-
-
1
1
.
1
3
2
1
1
1
1
10
2
1
2
2
10
11
12
13
7
4
2
2
1
1
1
1
2
1
14] 34
101 14
21 10
1 2
-
-
9
6
-
.
1
ܟܬ ܟܬܢ
2
4
2
3
7
61
3
8
2
2
1
2
1
5
3
4
4
6
2
5
2
NHA AO
1
8 11
3 7
4 9
2 1
1
1
1
1
1
8
6
4
4
4
7
8
5
1
-
1
2
1
3 3
2 9
31 12
2 9
1
!
4 2 8
7 10 9
3 4 8
2 31 12
5 6 2
7 13 8
71 14 9
5 71 25
-
2
8
7
8
1 3
4 7
81 10
8 17
-
4 1
2 6 1
31 10 8 3
71 181 101 10
1
2
4
2
1
-
-
.
2
1
2
7
1
-
NN
1
!
-
1
1
1
13
4
7
---- --
1
1
-
18 1
-
-
1
1
3
1
1
1
1
1
1
Age
Total
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
5.09
10
11
12
13
203
194
201
218
.17
.08
07
.04
6.03
6.45
6.90
5.95
6.66
6.96
7.34
1.91*
4.86
5.46
6.37
2.02
.90
.75
.48
M11-M10= .94
M12-M11= .42
M13-M12= .45
M13—M10=1.81
*The 25 percentile for the 10-year-old children is calcu-
lated on the assumption that the scores of children reported
under captions X1, X2 and X3 are distributed evenly be-
tween 0 and 2.2.
. 12
.06
.05
.11
TABLE XXXVIII
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF THORNDIKE SILENT READING SCALE ALPHA 2 SCORES OF HAMILTON TOWNSHIP, N. J.
SCORES
X1 X2
le
0 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.815.916.0 6.1 6.2 6.316.4 6.5 6.616.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.6*1 X9
5.916.
6.566.66.
17.01
18.388.418.5/8.618.768.818.9.0.0
1
2
-
1
2
1
-
1
.
-
-
-
.
6
3
1
1
1
4
2
1
1
1
3 10
5
4
2
-
1
-
1
1
1
1
-
-
-
18
6
3
1
.
-
3
1
1
2
11
9
6
---
---
---
--
---
3
6
2
1
5 14 12 10 6
2 6 7 10 7
2 2 2 71 10
3 2 3 2 9
1
5
6
2
9
6
2
2
3
8
5
8
8
9
O COO
6
4
2
2
10 7 7 3 5
9 8 12 11 13
8 13 7 7 16
8 7 5 4 9
3
2
5
2
6
4
8
6
2 4 4
8 12 8
8 13 12
6 9 13
6 4 6
8 6 6
8 21 17
9 121 11
1 1
2 1
2 6
1
2 2
2 4
5 3
4 11
1
-
-
-
.
;;
-
1
2
3
ONN
1
U
-
1
1
1
2
4
11.1
1 2
---
--
;
1
2
$
1
4
1
2
1.
11
Age
Total
Median
P. E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
*Note that the scale is not charted from 9.1 to 9.6.
10
11
12
13
223
222
213
206
5.19
5.91
6.25
6.77
.06
.06
.05
.06
6.04
6.58
6.80
7.30
4.53
5.11
5.61
5.95
.75
.73
.59
.67
M11-M10= .72
M12-M11= .34
M13-M12= .52
M13—M10=1.58
04
.04
.05
.05
TABLE XXXIX
AGE DISTRIBUTION, 10 to 13 INCLUSIVE, OF THORNDIKE SILENT READING SCALE ALPHA 2 SCORES FOR AMSTERDAM, N. Y.
SCORES
Age
X1 X2 X3 o 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.616.7 6.8 6.917.0/7.1 7.2 7.37.4 7.5 7.6 7.7 7.8 7.9 8.018.1 8.2 8.3 8.4 8.5 8.6 8.7 8.818.919.0 X9
////////|///|/
.1
-
3
-
-
-
i
-
-
-
2
1
.
--
2
2
1
1
1
7
.
18
8
5
1
1
1
1
2
-
2
3
11
2
8
1
i
-
31 61
18 31
81 18
5 8
--
10
11
12
313
-
5
9
1
-
-
.
-
.
2
1
1
1
3
5
1
3
1
14
1 11
4
4
1
6
2
1
3
1
5
3
6
1
3
1
4
9
1
3
7
9
8
9 8
5 14
4 4
3 8
4.
4
3
2
5
3
4
5
8
6
3
2
1
4
7
4
5
1
4
7
6
1
1
1
1
1
4
6
4
4
-
2
4
1/ 13
31 11
2 1
2 8
-
3 6
61 17 6 6 3 8
4 14 5) 10 5
6 7 14 5 121 11
1
-
2
4
4
71
-
-
-
1
1
-
1
1
A
2
3 7
5| 15
-
3
7
---
1
4
6
or
8
3
2
1
8
2
2
4
-
1
3
1
.
-
2
1
1
2
.
1
2
Age
Total
Median
P.E. true
-obtained
median
75 per-
25 per-
Q
P.E.
centile
centile
10
11
12
13
242
255
193
211
3.70
5.37
5.99
6.55
.17
.08
.09
.08
5.55
6.32
6.87
7.21
1.21*
3.77
4.53
5.29
2.17
1.27
1.17
.96
M11-M10=1.67
M12-M11= .62
M13-M12= .56
M13-M10=2.85
. 12
08
.08
. 12
*The 25 percentile for 10-year-old children is calculated on
the assumption that the scores of children reported under
captions X1, X2 and X3 are distributed evenly between 0
and 2.2.
Achievement Measured by Thorndike Reading Scale
57
Table XXXVI gives the facts in regard to reading in the 9-month
schools of Madison County.
The total gain for the three-year period in this case is from 4.55,
the median ability of the 10-year-old children, to 6.45, the median
ability of the 13-year-old children, a difference of 1.90. This gain is
just 2.5 times as great as that made in the 6-month schools of the
same county. The median abilities of the 10-year-old children are
about alike. The comparison of amount of gain in the two cases is
valid, since the scores given are in terms of difficulty for the children.
It must be remembered, however, that there is no proof that the gain
in each case can be attributed solely to school work. It is possible
that influences outside of the school contribute materially to the re-
sult. The conclusion can only be that school influence on reading and
other possible influence on reading accomplish between them 2.5 times
as much in places having a 9-month school term as do the same in-
fluences in places having a 6-month school term.
The P.E. of the gain in the 9-month schools (1.90) is .12, about
7 per cent of the gain. The probable actual deviation of the true dif-
ference from the obtained difference in these schools is a little larger
than the like deviation in the 6-month schools, but in proportion to the
gains made in the respective schools the deviation is less in the 9-month
schools.
The yearly gains are much more nearly uniform than in the 6-month
schools. From ages 10 to 11 the gain is .75; from ages 11 to 12 it is
.56; and from ages 12 to 13 it is .59.
Tables XXXVII to XXXIX inclusive give comparative data in re-
gard to reading from certain other school systems. The data from
Louisville are based upon tests given by the Psychological Laboratory
of the Louisville Board of Education. Data for Hamilton Town-
ship, New Jersey, were collected by the Psychology Department of
the Trenton State Normal School. The data from Amsterdam, New
York, were collected by the Department of Educational Administra-
tion of Teachers College, Columbia University.
In the following summary the total improvement in silent reading dur-
ing the three-year period from ages 10 to 13 inclusive is given for each
of the school systems studied, and also the median ability for the re-
spective groups of 13-year-old children. The schools are listed in the
order of the amount of improvement made.
58
Study of Achievement in Country, and Town Schools
TOTAL GAIN
MEDIANS
SCHOOL SYSTEMS
10 to 13
inclusive
13-year-old
children
1
Amsterdam
Madison County, 9-month schools ---
Louisville
Hamilton Township-
Madison County, 6-month schools._.
- -
.
2.85
1.90
1.81
1.58
.76
6.55
6.45
6.90
6.77
5.25
-
The ranking in order of amount of improvement for the three-year
period from ages 10 to 13 inclusive does not correspond exactly with
the ranking in order of ability of 13-year-old children. As has been
pointed out in the case of language and arithmetic, the medians for
13-year-old children may be affected by constant errors in any of the
respective systems, such as a tendency to overrun the time allowance,
a little greater leniency in scoring papers in one place than in another
either by the teachers or by the examiner, in giving directions, etc.
Such errors are compensating when the difference between the medians
for two ages is used as a measure, since these errors would be constant
for any given place and time for pupils of the different ages. In view
of this, it is probable that the ranking in order of total gain in the above
table is the more significant ranking.
The amount of gain in the respective systems is directly comparable,
since the scale used is expressed in terms of units of difficulty for the
children. We can say that the results in Amsterdam for the three-
year period from 10 to 13 inclusive are about four times as good as
are the results in the Madison County 6-month schools, and about
twice as good as the results in Hamilton Township. However, not
all of the improvement noted is known to be the result of school pro-
cedure. A good share of the gain in ability to read silently may be
due to forces outside of the school, such as library facilities, home in-
fluence, newspapers, etc. Indeed, it is sometimes charged that school
work in reading stresses oral work too much. The conclusion from
the above table is therefore limited to the statement that the sum of
school influence in reading and outside influences in reading is about
four times as great in Amsterdam as in the Madison County 6-month
schools for the equal period of time from ages 10 to 13. If equality
of outside influences making for improvement in silent reading might
be assumed for the different systems studied, there would be left the
single variable element in the school work on silent reading. It does
? For an example of this see Klapper, Teaching Children to Read.
Achievement Measured by Thorndike Reading Scale
59
not seem probable, however, that influences other than those of the
school which make for improvement in silent reading are equal in
cases such as Amsterdam, New York, and the smaller schools of Mad-
ison County, Kentucky.
The following summary shows the gain for each age period of a
year in the systems studied:
YEARLY GAINS
SCHOOL SYSTEMS
10 to 11
11 to 12
12 to 13
-
-
-
Amsterdam..
Madison County, 9-month schools.
Louisville..
Hamilton Township-
Madison County, 6-month schools
1.67
.75
.94
.72
.03
.62
.56
.42
.34
.59
.56
.59
.45
.52
.14
-
-
Total
4.11
2.53
2.26
The variations in the amount of yearly gain are large, as is the case
in language and arithmetic. The greatest gain seems to be from ages
10 to 11, and each year after this shows less gain than the preceding
year. It appears that greater gain is made by younger children than
by older ones within the limits of the age-groups studied.
1
CONCLUSIONS
1. The difference in ability in silent reading, as measured by the
Thorndike Silent Reading Scale Alpha 2, can be obtained for children
of different ages.
2. Since the function measured by this scale may be improved by
influences outside of the school, as well as by school training, this dif-
ference cannot be considered as a wholly reliable measure of school
efficiency in teaching silent reading.
3. This difference does give a reliable measure of the improvement
in silent reading due to all causes during the three-year period from
ages 10 to 13 inclusive.
4. Since the improvement measured by this scale is stated in terms
of. difficulty for the children, the differences obtained in the respective
systems studied may be compared directly.
5. The differences obtained may be compared for two systems of
schools, even though the testing was done at different times in the re-
spective systems.
60
Study of Achievement in Country and Town Schools
6. The differences obtained are valid, even though there may be
constant errors in the giving of the tests, such as might be caused by
having the tests given by the teachers.
7. Greater gain in silent reading seems to be made by the younger
children within the age limits studied (ages 10 to 13 inclusive).
8. Material gain in silent reading may be made during any part or all
of the period from ages 10 to 13 inclusive.
9. The results in the Madison County 6-month schools are much
poorer than in any other system studied.
10. The results in the Madison County 9-month schools compare
favorably with those in the other systems studied.
CHAPTER VI
SUMMARY AND CONCLUSIONS
This study was undertaken with four specific objects in mind.
These objects are set forth in Chapter II, and are stated as follows:
First: To show that the difference in performance in school sub-
jects of children of different ages can be obtained.
econd: To show that this difference is a measure of school effi-
ciency which may be used to measure schools or school systems.
Third: To apply this measure to a system of country schools.
Fourth: To compare the results in this country school system with
the results in certain city school systems.
The results of the study are considered in the light of these aims.
Sections 1, 2, 3 and 4 of this chapter deal respectively with the pur-
poses stated.
SECTION 1
The purpose as stated is "to show that the difference in perform-
ance in school subjects of children of different ages can be obtained.”
With the tests used such differences have been obtained for chil-
dren from 10 to 13 years of age inclusive. As the work progressed,
certain difficulties became apparent which seem to justify the following
statements :
The tests to be used in obtaining age differences in performance
must be of such a nature that identical tests can be given in identical
manner to all of the grades tested. Such a spelling scale as that de-
vised by Ayres could not give age differences because the 12-year-old
child in the third grade would have a score on a test different from
the test used for the 12-year-old child in the sixth grade. The results
for children of like age, but in different grades, would be in terms that
could not be directly compared.
The tests should be given in as many as possible of the grades of
the elementary school. The tabulations in this study include results
for grades 3 to 8 inclusive and in some cases for grades 4 to 8. With
results from children in these grades it was found necessary to esti-
mate the number of children in the lower grades of the respective
ages studied, and it seemed unwise to attempt to find medians for
61
62
Study of Achievement in Country and Town Schools
groups of children under 10 years of age because of the limited num-
ber of children of the lower ages tested. If the tests could have been
given in grade 2, it would have been possible to calculate medians for
children under 10, and the necessity of calculating the probable num-
ber of 10-to-11-year-old children in grade 2 would have been avoided,
and scores could have been assigned them.
Full age-grade tables of all the children in all the grades of the
systems studied should be prepared. Such tables give a very desirable
check on the number of children tested, and furnish a basis for esti-
mation of the number of children of any given age in grades not tested.
Tests used should be such as will test the ability of the children in
the lower grades as well as the ability of those in the higher grades.
The work with Courtis Standard Research Tests in Arithmetic showed
that these tests do not measure the ability of lower grade children,
since a great many children were unable to work correctly even one
of the examples given. A test that includes problems less difficult than
those of this series would be desirable.
Tests used must be individual tests rather than group tests; at least
it must be possible to assign individual scores on the basis of the tests
given. This is necessary in order that the individual scores of chil-
dren of any given age may be taken from the different grades in which
these children are tested and thrown into a single distribution on an
age basis.
For work in country schools there is an added need for individual
tests rather than group tests, since groups of children of like age or
grade in any given country school are likely to be small.
The above statements may be summarized as a set of directions for
the guidance of those giving tests which are to be tabulated on an age
basis. The concise directions are as follows:
1. Select tests that are identical for all the grades to be tested.
2. Test as many of the grades as possible.
3. Make full age-grade tables of all the children in all the grades.
4. Select tests that measure the ability of all the children.
5. Use individual rather than group tests.
SECTION 2
The second purpose of this study as stated is "to show that this dif-
ference is a measure of school efficiency which may be used to meas-
ure schools or school systems."
In so far as the tests used measure functions affected solely, or even
Summary and Conclusions
63
largely, by school training, the difference in performance of children
of different ages seems to furnish a measure of school efficiency. In
the case of the Trabue Language Scale B the function measured has
not been shown to be fundamentally one dependent on school training
In the case of the Courtis Standard Research Tests in Arithmetic
Series B it seems that the function measured is to a very large degree
at least one dependent on school training; therefore in this case the
difference obtained is one that is chiefly the direct result of the school
training received by the children and of elimination, and for that rea-
son may be considered a measure of the effectiveness of that training
and of elimination. In the case of the Thorndike Silent Reading Scale
Alpha 2 the function measured is one which is greatly affected by
school training, but which may also be greatly affected by influences
outside of the school.
Even though the function measured be one which is affected by in-
fluences other than school training, it may be argued that the work
of the school should so supplement other influences brought to bear
upon the children as to secure for them reasonable development of
the function considered. If this conception of the work of the school
is accepted, the difference between performance of children of differ-
ent ages seems a sound measure of the degree to which the school has
succeeded in its effort to secure the desired development.
In any case in which the difference in performance of children of
different ages is considered as measuring some function other than
one dependent on school training for its improvement, the difficulty
lies in the nature of the test rather than in the fact that the age-differ-
ences are used. The same criticism would apply to the same
urement if grade standards were used.
There are a few advantages that the use of age-differences as a
measure of school efficiency seems to have over the use of grade
standards. One of these is that the testing may be done at any con-
venient time in the school year, with the possible exception of the first
three or four weeks of the school term. This is due to the fact that
the birthdays of any age-group of children, say the 10-year-olds, are
distributed throughout the year in the same way as are the birthdays
of any other age-group, say the 13-year-olds. This means that the loss
of children from the group because they reach a higher age will be
compensated by the accretion of other children from the next lower
age-group. Moreover, this loss and accretion continues throughout
the school year and for each age-group, so that the difference between
neas-
64
Study of Achievement in Country and Town Schools
any two age-groups is a constant quantity. During the first few weeks
of school there may be a slightly uneven loss in school ability due to
the vacation period, since it has never been shown that the retaining
power of children of different ages is the same. After school is once
well under way this uneven loss is overcome, and the testing may be
done at any convenient time.
Another advantage in the use of age-differences as a measure
of school efficiency lies in the fact that errors such as those caused by
having the tests given by the teachers are compensated, since such er-
rors are identical for children of all ages.
A further advantage in the use of age-differences lies in the fact
that the effects of poor grading or great retardation are considered in
the measurement of improvement. The necessity of correcting grade
results for retardation is avoided, since the score of the retarded child
of any given age has entered into the measurement of that age-group.
The advantages mentioned above are of particular significance for
work in country schools. The difficulties involved in giving tests
where the schools are scattered, the grading poor, and the groups of
children frequently very small, make it especially desirable to give
tests in these schools at the most convenient time of the year and to
have the tests given by the teacher.
SECTION 3
The third purpose of this study as stated is “to apply this measure
to a system of country schools."
This purpose has been accomplished and the results given in the
treatment of the respective tests.
SECTION 4
The fourth purpose of this study as stated is “to compare the re-
sults in this country school system with the results in certain city
school systems."
The Madison County 6-month schools have been compared through-
out this study with the schools in the same county having a 9-month
school term. In addition to this comparison, the results of the Trabue
Language Scale B have been compared with results from Louisville,
Kentucky; Paterson, New Jersey; and St. Paul, Minnesota. As has
already been pointed out, this comparison concerns the results of
school training and also other influences. The 9-month schools in
Madison County made a gain in the ability to complete sentences 53
Summary and Conclusions
65
per cent greater than the gain made over the same three-year period
in the 6-month schools. None of the systems studied made a gain so
great as that of the Madison County 9-month schools, and all of them
except St. Paul made gains greater than did the Madison County
6-month schools. St. Paul made practically the same gain as did these
schools.
If the comparison is made on the basis of the final ability attained
by the children (medians for 13-year-olds), the Madison County 6-
month schools are poorer than any of the others studied. Louisville
13-year-old children possess 50 per cent greater ability to complete
sentences than do those in the smaller schools of Madison County.
The children of the same age in the 9-month schools possess 25 per
cent greater ability than do the children of the 6-month schools. The
10-year-old children in Louisville possess greater ability to complete
sentences than do the 13-year-old children in the 6-month Madison
County schools, and so do the 12-year-old children in the 9-month
schools, the 11-year-olds in Paterson and the 10-year-olds in St. Paul.
Whichever basis of comparison is used, the Madison County 6-
month schools are at the bottom. If the age achievement is used
as the basis of comparison, the Madison County 9-month schools are
only kept from the bottom by the presence of the 6-month schools
among the systems compared.
In comparing the work in arithmetic it must be remembered that
the results are in terms of examples worked correctly in a given length
of time, and that it cannot be assumed that it is twice as difficult to
add 8 examples as it is to add 4 in the same time. Bearing in mind
this caution, it seems, on the basis of the results obtained, that while
the pupil in the Madison County. 6-month schools is increasing his
ability to add to such an extent that he can add one more example in
the time allowed, the pupil in the Madison County 9-month schools is
increasing his ability to add by 1.6 examples, the pupil in Louisiana by
2.2, the one in Arkansas City by 2.7, the one in Salina by 3.0, the one in
Louisville by 3.4, and the one in Hibbing by 5.7 examples.
In subtraction the situation is much the same. While the pupil in
the Madison County 6-month schools is improving his ability to sub-
tract by 1 example, the one in the 9-month schools of the same county
is improving his ability by 3.1, the one in Salina by 3.2, the one in
Louisiana by 3.3, the one in Arkansas City by 4.2, the one in Louis-
ville by 4.8, and the one in Hibbing by 5.8 examples.
66
Study of Achievement in Country and Town Schools
While the pupil in the 6-month schools of Madison County is im-
proving his ability to multiply to such an extent that he can multiply
one more example in the time allowed, the pupil in Louisiana improves
his ability so that he can multiply 5.8 more examples in the time al-
lowed, the pupil in the Madison County 9-month schools improves by
6.2 examples, the one in Louisville by 7.7, the one in Salina by 7.8,
the one in Arkansas City by 8.8, and the one in Hibbing by 12.5 ex-
amples.
In division the situation is even worse. While an improvement of
one example is being made by the pupil in the Madison County 6-
month schools, there is an improvement of 6.1 by the pupil in the
Louisiana schools, of 6.8 in the Madison County 9-month schools, of
9.1 in Arkansas City, of 13.4 in Salina, of 16.1 in Louisville, and of
23.4 in Hibbing
If the comparison be put on the basis of achievement of 13-year-old
children, the situation in the Madison County 6-month schools does
not seem to be much better. The median 13-year-old child in these
schools can neither add, subtract, nor multiply as well as the median
10-year-old in Hibbing, and he can barely divide as well. The Madi-
son County 9-month schools do better on this basis, but the median for
the 13-year-old children is below the median for the 11-year-old chil-
dren in Hibbing in addition, subtraction, multiplication and division.
The comparison of the results of the Thorndike Silent Reading
Tests shows conditions which are not quite so disastrous for the
Madison County 6-month schools in that the differences are not so
great. On the basis of improvement, while the pupil in the Madison
County 6-month schools is improving his ability to read by one step
on the Thorndike scale, the pupil in Hamilton Township improves 2.1
steps, the one in Louisville 2.4, in the Madison County 9-month schools
2.5, and in Amsterdam 3.7 steps. On the basis of age achievement
the median 13-year-old child in the Madison County 6-month schools
is poorer than the median 11-year-old child in Hamilton Township,
Louisville, and Amsterdam, and almost as poor as the median 11-year-
old child in the Madison County 9-month schools.
The comparison of the Madison County 6-month schools with the
other schools tested may be summed up in the statement that the chil-
dren in these schools have less ability along every line tested than have
the children of the same ages in other schools, and that they are learn-
ing more slowly, except that the children in St. Paul are improving as
slowly as they do in language.
Summary and Conclusions
67
FINAL SUMMARY
The following four statements seem justified concerning the four
purposes for which this study was undertaken:
First: The difference in performance in school subjects can be ob-
tained for children of different ages.
Second: This difference is a measure which may be used to meas-
ure schools or school systems, and has certain advantages for this pur-
pose, especially in rural schools.
Third: This measure has been applied to a system of country
schools.
Fourth: The Madison County 6-month schools compare unfavor-
ably with all of the other schools measured. The Madison County
9-month schools compare more favorably.
APPENDIX
For the convenience of any who may wish to supplement the re-
port made in Chapter I of scientific studies on the results of instruc-
tion in rural schools, or who may later wish to bring this report up to
date, this statement of the educational literature investigated is made.
As a first step in searching for such data the following surveys were
studied. In each case the tables showing the results were investigated
to find what scores might be included from rural schools in the com-
parisons made.
SURVEYS
Akron, Ohio.
Connecticut (counties).
Alabama (three counties).
Dansville, N. Y. (High School).
Alabama. *
Dayton, Ohio.
Alton, I11.
Delaware. I
Amsterdam, N. Y.
Delaware (School Buildings).
Anderson, Ind.
Denver, Col.
Arizona.*
Detroit, Mich. (Recreational).
Ashland, Ore.
Elyria, Ohio.*
Atlanta, Ga.
Evansville, Ind. (Vocational).
Baltimore, Md.
Framingham, Mass.
Binghamton, N. Y.
Gary, Ind.*
Blaine, Wash.
Gary, Ind. I
Bloomington, Ind.
Georgia (Counties).
Boise, Idaho.
Grafton, W. Va.
Boston, Mass.
Grand Junction, Col.
Bridgeport, Conn.
Grand Rapids, Mich.
Buffalo, N. Y.
Great Neck, L. I.
Brookline, Mass.
Greene County, Ind.
Butte, Mont.
Greenwich, Conn.
Chicago, Ill. (Educational Commission). Hammond, Ind. (Industrial).
Cincinnati, Ohio.
Harrisburg, Pa.
Cleveland, Ohio.
Herkimer, N. Y.
Cleveland, Ohio.
Huron County.
Colorado.
Illinois (State).
Cold Springs, N. Y. (Haldane School). Indiana (Vocational).
Colorado (rural schools).
Janesville, Wis.
Columbia, S. C.
Jefferson County, Ind. (Vocational).
Connecticut (Educational Commission). Kansas (high schools).
*United States Bureau of Education.
fRussell Sage Foundation.
General Education Board.
68
Appendix
69
Lane County, Ore.
Los Angeles, Cal.
Leavenworth, Kan.
Louisville, Ky.
Maricopa County, Ga.
Maryland (State). I
Memphis, Tenn.*
Minneapolis, Minn. (Vocational).
Missouri (Saline County).
Montclair, N. J.
Nassau County, N. Y.
Newburgh, N. Y.
New Orleans, La. (Vocational).
Newton, Mass.
New York City.
North Dakota.*
Oakland, Cal.
Ogden, Utah.
Ohio.
Oklahoma.
Oklahoma (county).
Oswego County, N. Y.
Paducah, Ky.
Paterson, N. J.
Port Townsend, Wash.
Portland, Ore.
Reading, Pa.
Rochester, Minn.
Rockford, Ill.
St. Louis, Mo.
St. Paul, Minn.
Salt Lake City, Utah.
San Antonio, Texas.
San Francisco, Cal.
San Mateo, Cal.
Saskatchewan, Canada.
Solvay, N. Y.
South Bend, Ind.
South Dakota.*
Stamford, Conn.
Syracuse, N. Y.
Travis County, Texas.
Utica, N. Y.
Van Wert, Ohio.
Vermont.
Virginia (Educational Commission).
Washington.*
Waterbury, Conn.
Westchester, N. Y.
Wilmington, Del.*
Windsor County, Vt.
Wisconsin (State).
Winston-Salem, N. C.
Wyoming.*
The next step in the search for data bearing on the objective results
of instruction in rural schools was a study of A Selected Bibliography
of Certain Phases of Educational Measurements, prepared by Edna
Bryner and published in the Seventeenth Year Book of the National
Society for the Study of Education, 1918. The titles listed were
examined, and whenever there seemed any possibility that the article
might contain any data concerning country schools the article was stud-
ied. One bulletin by E. J. Ashbaugh, entitled The Arithmetical Skill
of Iowa School Children, University of Iowa Extension Bulletin, No.
24, November, 1916, was not found. In all, twenty-eight of the ref-
erences were examined, and of these five were found to contain data.
As a final step in the search for material bearing on the comparison
of country and city schools by the use of objective standards, a study
was made of the monthly lists of current educational publications pre-
*United States Bureau of Education.
*Russell Sage Foundation.
General Education Board.
70
Study of Achievement in Country and Town Schools
pared by the United States Bureau of Education, beginning with the
list for June, 1917, and extending through the list for October, 1920.
In this study every title and subtitle was considered, and in case
there seemed a possibility that objective data might be found, the
reference was investigated. In this study only two articles which
seemed to bear in any way on this topic were not found. These refer-
ences are: (1) Johnson, W. E., “Reading, Writing, Arithmetic and
Spelling in City and Town Schools of South Dakota in 1917-1918,”
Bulletin of the Northern Normal and Industrial School at Aberdeen,
S. D., Vol. XII, No. 2 (October, 1918); and (2) Heckert, J. W.,
"The Cleveland Survey Tests in Arithmetic in the Miami Valley,"
Elementary School Journal, XVIII: 447-457.
VITA
NORMAN FROST, born in Oberlin, Ohio, June 23, 1887. Son of
William G. and Louise Raney Frost.
Academic Training: Berea College Academy, 1901-1905; Berea
College, 1905-1906; Bates College, 1906-1908; Oberlin College, 1908-
1909; University of Chicago, summer sessions, 1910 and 1911; Teach-
ers College, Columbia University, 1912-1913; summer sessions, 1914
and 1915, 1916-1917; fall semester, 1918 and 1919; B.A., Oberlin,
1909; M.A., Columbia University, 1914.
Professional Experience: Principal of Public Schools, Fountain,
Minn., 1909-1910; Superintendent of Schools, Stephen, Minn., 1910-
1912; Specialist, United States Bureau of Education, 1913; District
Superintendent of Schools, Waterbury, Vt., 1914-1916; Professor of
Rural Education, Peabody College for Teachers, Nashville, Tenn.,
1917-
Author of A Statistical Study of Public School Systems of the
Southern Appalachian Mountains, United States Bureau of Education,
Bulletin, 1915, No. 11.
!
UNIVERSITY OF MICHIGAN
FULLAN ALLE
3 9015 07416 4966
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