HoUinga: Corp.
pH8.5
The Ages of Pupils and Their Progress
Through the Elementary Grades
FIRST STEPS IN STATEWIDE EDUCATIONAL ACCOUNTING,
SECOND PAPER. APRIL 1918
BY W. A. AVERILL, A. B., CONSULTING OFFICE-ORGANIZER
AND STATISTICIAN
Formerly Inspector in Elementary Education, New York State Education
Department, and Expert in School Investigation, New York
Bureau of Municipal Research
A hand-book showing the statistical technique, tabulation and
graphic presentation of the salient features of Age- Progress
problems in elementary schools.
The first paper of this series of educational accounting reports
was pubUshed in October 191 7 in order to have ready for distribution
such returns from a request sent to the schools of the State in May
19 1 7 as were compiled at the time of the 19 17 Convocation of The
University of the State of New York. The limited edition of the
first paper was soon exhausted and to meet the subsequent demand
for copies, this second paper will contain the salient features of the
first.
For the study of age and progress conditions of elementary school
pupils, the cities, villages and union free school districts of the State
are divided into nine groups, the basis of which division is the size
of the elementary school enrolment, reported in this case on May 21,
19 17. The groups of communities are:
6 cities enrolling over 5000 elementary pupils
8 cities enrolling 3000 to 4999 elementary pupils
7 cities and i village with 2000 to 2999 elementary pupils
16 cities and 8 villages with 1000 to 1999 elementary pupils
4 cities, 16 villages and 28 union free school districts with 500 to 999 elementary
pupils
3 villages and 61 union free school districts with 300 to 499 elementary pupils
I village and 76 union free school districts with 200 to 299 elementary pupils
153 union free school districts with 100 to 199 elementary pupils
175 union free school districts with less than 100 elementary pupils
563 communities reporting data, including 41 cities, 29 villages and 493 union
free school districts.
TTri..».,,..».ii'r^
u^
\\
<^5
Table i
Progress percentages of 286,207 pupils in 41 cities, 29 villages and 493 union
free school districts
PUPILS
PER CENTS
Rapid
Normal
Slow
Total
Rapid
Normal
Slow
Total
Less than lOO
987
I 078
864
1 271
2 217
3 123
2 681
4 483
10 424
6 724
II 090
II 574
13 674
17 566
18 118
10 937
18 361
66 375
3 732
6 183
6 541
7 104
9 96s
9 691
6 071
8 389
26 984
II 443
18 351
18 979
22 049
29 748
30 932
19 689
31 233
103 783
8.62
5.82
456
5-77
7.3
10.09
i3-6i
14-35
10.04
58. 76
60.8
61.
62.
59.3
58.57
55-5
58.79
63.96
32.62
33-352
34.44
32.23
33-4
31.33
30.83
26-86
26.
100
100
200- 299
100
100
100
100
100
100
Over sooo
100
Total '. . .
27 128
174 419
84 660
286 207
9.48
60.94
29-58
100
Figure i
Each column represents 100 per cent of the entire enrolment in each group
of school systems. The groups themselves vary in size but this variation is
not shown in the figure which shows only the relative percentages of rapid,
normal and slow-progress pupils in each group and not the actual number of
pupils. Late reports received after figure was drawn reduce the slow progress in
the second column to 34 per cent.
The blank which was sent to the schools of the vState in May, 19 17,
requesting the information on which the tables in this paper are based,
called for the number of years of schooling assignable to the pupils
in each grade and the number of pupils in each grade who
had attended each different period of schooling. For example, the
report in the fifth grade as sent out called for the number of pupils
who had to their credit 4-A^ea^jpf»^hooling, 5 years of schooling, 6
APR 28*-*i91i>
years of schooling, etc. In the fifth grade those who reported only
4 years of schooling were called rapid-progress pupils, those reporting
5 years were called normal and those, who reported a total attendance
of more than 5 years, including the school year ending June 19 17,
were reported as slow-progress pupils. On this basis the tables in
this pamphlet have been prepared, except where otherwise specified.
Table i gives the total results for 286,207 pupils in 563 communities
throughout the State. This figure does not represent the entire
elementary school enrolment of the State, as New York City is
omitted together with several of the smaller communities whose
reports for various reasons could not be used.
Note that these tables do not refer to overage but to progress alone.
In this respect they are incomplete in that they present only one
phase of retardation, namely the time-in-school factor, whereas the
complete statement of the retardation situation requires along with
this time factor, the age factor expressed in three subdivisions for
underage, normal age and overage.
A glance at the slow-progress percentages of table i shows that
they are, as a whole, unusually low. They are in all probability
about 4 per cent lower than the percentages which would be obtained
by an analysis of the situation in which both age and time in school
are considered, and compiled to show conditions either at the beginning
or after the close of the school year. The figures were reported as
of May 21, 19 1 7 and do not include in the slow-progress element
those pupils who were not promoted in June 191 7. Pupils who
left school prior to May 2 ist do not appear on the reports, which
again tends to understate the slow-progress number. A third factor
tending to reduce the stated amount of slow progress was the date
of the collection of the data, late in the school year, at which time
many communities were obliged to gather the figures hurriedly;
it is probable that a portion of the time in school for some of the
pupils was omitted.
The difference between the reported slow progress in September
19 16 and May 19 17 is shown in table 2 for ten cities which col-
lected figures at both times, the total of which shows the slow-
progress percentage to be 4.4 higher in the report at the beginning
of the school year, which is the best time to assemble age and
progress data.
For purposes of comparison outside New York State, superin-
tendents making these surveys as per September 1 9 1 8 or February
19 1 9 should deduct at least 5 per cent from their total slow progress
percentage. This does not apply to tables 16 and 17, on pages
31 and 32, nor to figure 10 and table 29. In other words, September
Table 2
Progress reported by ten cities by two methods, September 1916 and May 1917
PUPILS
PERCENTAGES
Rapid
Normal
Slow
Total
Rapid
Normal
Slow
I
13
49
291
379
380
237
684
665
1.9
7-4
42.5
57-
55.6
35.6
Sept.
May
1916
1917
77
133
689
766
514
359
I 280
I 258
6.1
10.6
53.8
60.9
40.1
28.5
Sept.
May-
1916
1917
3
i6s
216
731
645
289
223
I 185
I 084
13.9
19-9
61.7
59. 5
24.4
20.6
Sept.
May
1916
1917
'4
i6s
159
623
666
540
479
I 328
I 304
12.4
12.2
46,9
51. 1
40.7
36.7
Sept.
May
1916
1917
5
144
196
S5I
661
375
207
I 070
I 064
13.4
18.4
51.4
62.1
35.2
19. 5
Sept.
May
1916
1917
6
210
133
521
532
302
398
I 033
I 063
20.3
12.5
50.4
50.
29.3
37.5
Sept.
May
1916
1917
7
44
30
I 349
I 251
860
902
2 253
2 183
2.
1.3
59.9
57.4
38.1
41.3
Sept.
May
1916
1917
8
112
121
608
731
362
203
I 082
I 055
10.3
II. 5
56.2
69.3
33.5
19.2
Sept.
May
1916
1917
42
30
263
259
199
186
504
475
8.3
6.2
52.2
54.6
39. 5
39.2
Sept.
May
1916
1917
10
17
25
423
337
194
227
634
589
2.7
4-3
66.7
57.2
30.6
38.5
Sept.
May
1916
1917
Total
989
I 092
6 049
6 227
4 015
3 421
II 053
10 735
9.
lO.I
54.7
38.0
36.3
31.9
Sept.
May
1916
1917
or February figures are directly comparable with tables 16, 17, 29
and figure 10; the slow progress percentages obtained in September
or February will be about 5 per cent greater than the figures of
May 191 7, shown in the other tables. For example, if a superin-
tendent should prepare a table similar to table 16 in September or
February for a system containing between 500 and 999 elementary
pupils finding a total slow progress of 35 per cent, the position of
that city in table 7 on page 10, would be 30 per cent slow progress
approximately at the first quartile instead of 35 per cent at the
median.
City totals
Tables 3 to 11 show the progress figures and percentages reported
by individual cities and villages in the various groups, beginning
with cities enrolling more than 5000 elementary pupils. Attention
is called to the fact that the total or average of any group actually
conceals the conditions which exist in the separate components of
the group.
Table 3
Progress reports from six cities enrolling more than 5000 elementary pupils
CITY
RAPID
NORMAL
SLOW
TWO OR
MORE
YEARS
SLOW'
TOTAL
A
613
3 SOS
I 86s
3 363
74S
9 887
8 737
IS 634
26 171
2 926
3 020
2 006
3 286
5 172
12 324
I 768
2 428
333
698
831
4 089
391
792
12 SO6
IS 528
22 671
41 858
5 439
5 781
B
c
D
E
F..
Total
10 424
66 375
26 984
7 134
103 783
Total .
Corresponding percentages
4-90
79.06
16.04
2.66
22.57
56.26
21.17
4.49
8.23
68.96
22.81
3.66
8.03
62.53
29.44
0.76
13.69
53.79
32.52
7.18
5. 76
52.24
41.99
13.70
10.04
63.96
26.00
6.87
From table 3 it is seen that the slow-progress percentage of 26
for the group of cities with over 5000 elementary pupils in table i
represents a range of slow-progress percentages from 16 to 42. In
the same manner, the percentage of pupils reported two or more
years slow ranges from 2.6 to 13.7.
When a niimber of measurements of any sort are arranged in any
given order, as in this case, in the order of slow-progress percentage,
the entire number of measurements is called a series or an array, and
it is customary to locate the middle member or midpoint of the series
and call it the median (Md) and to use this median in many instances
in place of the average.
The median of this series of six measurements is the average
between the third and fourth members, which is 26.13 per cent. The
average of the six percentages is 28.16 per cent, while the average
figured from a total of all six cities is 26 per cent. Superintendents
will find the median the most convenient measure both to determine
and to use in making comparisons with other cities of the same
group.
' Included in '"slow"; total equals the sum of rapid, normal and slow in all tables.
Table 4
Progress reports from cities enrolling 3000 to 4999 elementary pupils
CITY
RAPID
NORM.'VL
SLOW
TWO OR
MORE
YEARS
SLOW
TOTAL
A
561
639
821
773
669
470
136
414
2 071
2 143
2 461
2 998
2 146
1 720
2 814
2 008
453
586
827
I 196
894
993
I 805
I 635
109
100
186
317
207
223
523
527
3 085
B '.
3 368
C
4 109
4 967
3 709
D
E
F
3 183
G
4 755
H
4 057
Total
4 483
18 361
8 389
2 192
31 233
Percentages corresponding to above figures
A
18.17
18.97
19-98
15.65
18.03
14.77
2.93
10.51
67.13
63.62
59.88
60.35
57.8s
54-04
59-17
49-49
14.7
17.39
19.34
24.00
24.10
31.19
37.90
40-. 00
3.533
2.969
4.520
10.275
5.581
7 .000
16.142
17.082
B
C
D
E
F
G
H
Total
14.35
58.79
26.86
7.01
This table shows a range of reported slow progress from 14.7 to
40 per cent. In this series there are eight members and the median is
the average between the fourth and fifth measures, or 24.05 per cent.
Table 5
Progress reports from seven cities and one village enrolling 2000 to 2999
elementary pupils
CITY
RAPID
NORM.-VL
SLOW
TWO OR
MORE
YEARS
SLOW
TOT.\L
A
728
000
693
166
394
534
30
136
1 278
2 127
I 112
I 626
I 416
I 174
I 353
851
361
465
649
795
806
918
861
I 216
106
104
213
197
193
274
275
379
2 367
2 592
2 454
2 587
^ 616
B
c
D
E
F
-> 626
G
2 244
2 203
H
Total
2 681
10 937
6 071
I 741
19 689
Percentages corresponding to above figures
Total .
30.75
00.0
28.23
6.41
15.06
20.33
1.33
6.17
13-62
53-99
82.06
15.25
17.93
45-31
62.8s
26.44
30.73
54-12
30.81
44-7
60.29
38.62
34.9s
38.36
55. 2
30.83
4.47
6.53
8.67
7.61
7.37
10.43
12.25
17 .20
8.76
r>E'RCtnTA^Er AF- SL6W J>fe0^fet5S '« iZZ ettME-MTAfeY SYST&MS
*o 50
LLINO ht-TW6-6-N
300-500
MlrblArH-34
500-1000
M&blANl-SSo/
1000-3000
ME-blAh-
3000
E'blAM-ZI-o/j
SOOO
MCBe-Twe&M
5C»00
•/.
zsy.
AMO
Ak&IM/!.M~5^6«
Figure 2
Each horizontal Hne represents the percentage of slow-progress pupils in one
elementary school system. The total enrolment in each system if represented
graphically would be shown in each case by a line extending entirely across the
diagram. The pupils represented by the black line are retarded and all the
others in each system are making normal and rapid progress.
In this series of seven cities and one village, the percentages of
slow progress range from 15.25 to 55.2. This series, however, hav-
ing eight measures has no single middle member and the median
30.05 per cent is determined by taking the average of the two middle
members in this array, namely, the fourth and fifth.
Table 6
Progress reports from sixteen cities and eight villages enrolling 1000 to 1999
elementary pupils
CITY
RAPID
NORMAL
SLOW
TWO OR
MORE
YEARS
SLOW
TOTAL
A
43
00
121
560
196
216
122
54
219
281
00
186
133
141
S3
62
I2S
178
159
133
49
16
56
20
930
I IIS
731
933
661
64s
97S
I 050
980
S93
928
624
766
829
I 030
847
796
539
666
532
689
727
338
194
60
III
204
356
209
22s
336
332
306
295
337
311
361
412
497
443
502
399
481
400
. 576
701
675
I 162
8
32
117
44
43
80
39
92
83
93
69
120
134
102
174
184
III
122
102
i8s
238
328
463
I 033
B
I 226
C
I 056
D
I 849
E
I 066
P
I 086
G
I 433
H
I 436
I
I 505
J
I 169
K... :.;.:::.:::::
L..
I 26s
I 121
M
I 260
V
I 382
6
I 580
p
I 352
Q.,.
I 423
R
I 116
S
I 306
T
I 06s
U
I 314
V
T z]/]/]
W.
I 069
X
I 376
Total
3 123
18 118
9 691
2 963
30 932
Percentages corresponding to above figures
A
4.2
0.0
ii-S
30.4
23-7
19.9
8.6
3-4
12 .9
24.1
0.0
16.7
10. S
10.8
3.4
4.6
8.8
16.
12.2
12. 5
3.8
I.I
S-3
1.9
90.
91-
69.3
50.4
S6.8
59-5
68.1
73.2
63 -7
50.8
73 -S
55-7
61.
60.
65.3
62.7
56.
48.3
5I-I
SO.
52. 5
50.4
31.7
14. 1
5.8
9.
19.2
19.2
19.5
20.6
23.3
23-4
23-4
25.1
26.5
27.6
28.5
29.2
31-3
32.7
35-2
35-7
36.7
37.5
43.7
48.5
63.
84.
I
3
6
4
4
6
3
6
7
7
6
10
10
6
13
13
10
9
10
14
17
31
45
100
B
C. .
D
E.. . . .
F
— Qi=Ji.28
G..
H...
I
J
K
L
— Md=28.os
M
N...
P. . . ...
Q
R..:.:;.; : :
—03=36.45
S. .
T
U
v
W
X
Total
10.09
58. 57
31.33
9.57
In this series of twenty-four cities we may add two other points
to the median (Md) in the center. These points are located just
half way between the median and the extremes and are called
the first and third quartiles. The first quartile (Qi) is that point
along the series which has one-fourth of the measures in front of it
and three-fourths of the measures following it. The third quartile
(Q3) is preceded by three-fourths of the measures and followed by
one-fourth of them. In this series of twenty-four measures, the
extremes of slow-progress percentage range from 5.8 to 84. The
first quartile located between the sixth and seventh measures, is
21.28 per cent. The median is the average between the twelfth
and thirteenth measures, or 28.05 per cent. The third quartile
located between the eighteenth and nineteenth measures, is 36.45
per cent.
Between the two quartile points lie just half of the measures; in
other words, the quartiles inclose the middle half of the series in the
order of the item measured with the median in the center. In general
terms, a superintendent may consider his system to be normal if
his city schools are within the quartile range, but if his system's
rating places his schools in the first or the last fourth of the series,
there is occasion for further study of the local situation.
The school systems tabulated thus far are those with 1000 elemen-
tary pupils and upwards. They have been tabulated in small groups
as the total number of systems of this size in the State is not large.
The tables which follow comprise smaller school systems from 999
elementary pupils downwards. The details of rapid, normal and slow
progress for these systems will appear in tables 19 to 2 7, which give
these figures for the different grades. For the purpose of showing
the range of slow-progress percentages reported by the larger number
of small cities and villages in these groups, the tables which follow
indicate merely the percentage of slow progress reported and the
number of cities which report each different per cent.
Thus four columns of figures appear in each table. The first
colimm consists of all the percentages of total slow progress hsted in
increasing order. The second column is the number of cities and
villages reporting each per cent. The third column consists of the
percentages of pupils retarded two or more years and the fourth
column gives the niimber of places reporting each per cent. The
first and third columns constitute what is known as the measure,
while the second and fourth columns constitute the frequency.
Measure is indicated by " m " and frequency is indicated by " f ".
lO
Table 7
Slow-progress percentages reported by 4 cities, 16 villages and 28 union free
school districts with an elementary enrolment between 500 and 999
SLOW-PROGRTTSS PERCKNTAGE REPORTEO
NUMBER OF
CITIES
REPORTING
PER CENT
TWO OR MORE
YEARS
RETARDED
NUMBER OF
CITIES
REPORTING
Meiisiire (m)
II
17
18
22
23
2^
25
26
2k.'.'.'.'.'.'.'.'.'.'.'.]'.'.'.'.'.
— 0i=28.S
30
31
32
33
34
35
— Md=3S . 5
36
37
38
39
40
—03=40.75
41
42
43
44
45
46
47
49
63
Frequency If)
Measure (m)
Less than i
6 Oi
7
8
9
10- Md
II
12
13
14
IS
16-Q3
17
18
Fre.juency {/)
The range of this series is from 11 to 63 per cent for total slow
progress and from less than i to 25 per cent for two-year retardation.
The medians and quartiles are indicated. The medians do not
lie in the exact center of the printed columns because certain per
cents occur several times, but they are the exact middle point on
the scale of measures from one extreme to the other. The quartiles
are the exact quarter points.
IJ
Table 8
Slow-progress percentages reported by three villages and sixty-one union free
school districts with an elementary enrolment between 300 and 499
SLOW-PROGRESS PERCENTAGES REPORTED
im)
6
10
II
18
20
21
22
23
24
25
26
27-Qi
28
29
31- . ■
32
33
34-Md
35
36
37
38
39
40-Q3
41
42
45
46
47
48
61
72
NUMBER
REPORTING
(/)
PER CENT
TWO OR MORE
YEARS
RETARDED
(m)
Less than
5
6-O1
7
8-Md
9
10
II
12-O3
13
14
15
17
18
20
23
33
NtnUBER
REPORTING
(/)
[2
Table 9
Slow-progress percentages reported by one village and seventy-six union free
school districts with an elementary enrolment between 200 and 299
SLOW-PROGRESS PERCENTAGES REPORTED
PER CENT
NUMBER
TWO OR MORE
NUMBER
REPORTING
YEARS
RETARDED
REPORTING
I
5
I
I
2
2
2
2
3-Qi
6
I
4
3
I
5
6
I
6
6
2
7-Md
7
2
8
9
I
9
5
2
10-Q3
4
3
12
3
I
13
2
3
14
3
4
15
2
2
16
I
3
17
I
2
18
2
2
23
I
3
24
2
3
3
3
6
I
3
I
I
4
6
12 ... .
13
16
17. . . .
18
19
20. . . .
22. . . .
23
24-O1 ■
2S
26
27
28
29
30
31. . . •
32-Md
33
34
35
36....
37. . . .
38. ...
39-O3.
40
41
42 ... .
43
44
47
48....
49
SI
52
61
70
In this table of 7 7 measures the median is the thirty-ninth measure
or the " last " of the three measures of 32 per cent for total slow
progress and the first of the seven measures of 7 per cent for two or
more years slow.
The quartile points are located 19I measures along the scale from
either end; the first quartile is one-half of the "way" from the
nineteenth measure of 24 per cent to the twentieth measure of 25
per cent, or 24.5 per cent. The third quartile is 19I points from
the bottom or " within " the twentieth measure of 39 per cent. For
the two-year retardation, the quartiles are 3 and 10 per cent
respectively.
13
Figure 3
In both of the diagrams each horizontal Hne represents the slow-progress
percentage reported by one elementary school sj^stem.
14
Table lo
Slow-progress percentages reported by one hundred and fifty-three union free
school districts with an enrolment between lOO and 199
TWO YEARS OR
MORE
SLOW
-PROGRESS
PERCENTAGES
SLOW PROGRESS
(m)
(/)
(m)
(/) {m)
(/)
41
I
4
10
42
8 I
6
13
44-Q^
4 2
6
15
45
4 3
9
16
46
3 4-Qi
13
17
47
6 5
5
18
3
48
3 6
17
19
2
49
6 7
10
20
4
50
3 8-Md
ID
21
3
51
I 9
9
22
2
52
2 10
II
23
I
54
3 II
7
24
6
56
I 12
7
25
I
57
2 13-Q3
7.
26
3
61
I 14
4
28
3
64
I 15
5
29-Q.
6
89
I 16
5
30
9
90
I 18
3
31
5
19
3
32
6
20
5
33
3
21
I
34
8
22
I
35-Md
6
23
2
36
3
24
I
37
3
27
I
38
4
43
I
39
5
40
7
N=i53
N= 153
The columns beginning with o and ending with 90 headed m mean
that villages reported slow-progress percentages ranging from noth-
ing to 90. Zero per cent, 10 per cent, 13 per cent, 15 per cent, and 16
per cent were reported by one village each ; 1 7 per cent was reported
by four villages, 18 per cent by three, 19 per cent by two, and 20
per cent by four, etc.
The column headed / indicates how many villages reported each
per cent. This is called the "frequency." There were in all 153
village elementary school systems reporting with an enrolment
between 100 and 199. If the villages were " lined up in a row "
in the order of their slow-progress percentages, the extremes would
be o and 90. The middle village would have 35 per cent. The
village which is one-fourth of the way along the line would report
29 per cent, and the village three-fourths of the way through the
series would report 44 per cent. The middle percentage of 35 is
called the median of the series or " array " and the 29 per cent and
44 per cent are called the first and third quartiles respectively.
Table 11
Slow-progress percentages reported by one hundred and seventy-five union
free school districts with an elementary enrolment below 100
SI.OW-PROGRESS PERCENTAGES REPORTED
NUMBER
REPORTING
PER CENT
TWO OR MORE
YEARS
RET.^RDED
NUMBER
REPORTING
S . ■
7. . .
8. . .
9- . .
11 . . .
12 . . .
13. . •
14. . .
15. . ■
16. . .
18. . .
19. . .
20. . .
21 . . .
22-Ql.
23 . . .
24. . .
25
26
27. . .
28
29 . . .
30
31. . .
32-Md
33 . ■ . .
34- • •
35 ... .
36. . . .
37 ... .
38. .. .
30. . . .
40 ... .
41. . . .
42-Q3.,
43 ... .
45
46....
48 ... .
50. . . .
51. . . .
52. . . .
53. . . .
54. . . -
58. . . .
59. . . .
63 ... .
73 ... •
76....
3-0!
4
5
6
7-Md
TI-Q3
12
13
14
15
16
17
18
25
46
i6
S\ow Progress
Percentages In J 75
vSy>stem3 With Less Than
lOO Element^sry pupils Each
Percen+3 Twt? or
More Vear^ 5/o\*/
Figure 4
^7
Slow-progress Figures not Basis for Criticism
Thus far in tables 3 to ii inclusive we have arranged the city and
village communities of the State in nine groups according to the
size of the elementary enrolment and within each group we have
placed the members in a row in the order of their reported slow-
progress for the purpose of seeking out the^jxiiddle member of each
row and the two members which are located in the one-quarter and
three-quarter points in the series. These points are indicated in the
preceding tables and by means of them each superintendent may'
detenhine his relative standing with reference to the other com-
munities of his particular group. As is indicated in the first paper
of this series, there is no actual nor inferred criticism of those systems
which happen to have reported large slow-progress conditions. The
problem of retardation is one which exists throughout the State and •
the relative number of slow-progress pupils is a very precise measure
of that problem and its difficulty for the local superintendent, prin-
cipals and teachers. But when it comes to criticizing the efficiency-
of the schools on the basis of reported slow progress, so many other
conditions may enter into this complex problem as to render the mere'
position of the school system on a progress-percentage list a very
unsafe criterion for drawing conclusions about the character of the.
work carried on in the schools. Some of these other features which
influence the " standing " of a school system with respect to retar-'
dation are: . - ..;
a The late entrance of pupils into the first grade
b Varying practice in promoting children into and out of the first
grade
c Different standards of promotion from grade to grade
d Differences in the health of pupils while at school
e Varying degrees of regularity of attendance
/ Different degrees of familiarity with the English language
g Differences in the mentahty of normally intelligent children
h The presence of mentally subnormal children in regular classes
7 Physical defects of children
k Differences in the maturity of children
/ Differences in the home environment of children
ni Differences in the amount of time which children may devote to
the preparation of lessons outside of school •
n Circimistances incident to the moving of families from place
to place
i8
The transfer of pupils from one school to another and from
parochial to public schools within a city
p Differences in the type of pupil left in the system when others
have been removed
q Differences in the extent to which communities offer inducements
for pupils to leave school
Some of them are so general as to affect nearly all schools alike
and others, while affecting different classrooms, will not materially
change the result throughout city and village systems as a whole,
and they are presented by no means as excuses for retarded conditions.
If a superintendent finds that his reported rating places his schools
in front of the first quartile in the series, or above the median, a
brief account of any features of his organization, plan of supervision
and methods of teaching which in his opinion many have contributed
to the success of his system and resulted in the low slow-progress
percentage, might be of service to other superintendents by way of
suggestion. If a sufficient number of memoranda are received on
this point, they will be assembled into a bulletin, returned to the
contributing superintendents and distributed to all the communities
participating in this research.
While as a general rule throughout the State it may be probable
that the better organized systems will be found in the schools above
the median, a relatively high position in the series does not neces-
sarily mean a superior school system. The reverse of this proposition
is even more true because we know from other sources that in many
cases some of the very best work in the State is being done in com-
munities where circumstances apparently beyond the control of the
schools militate against the achievement of a normal amount of
successful progress through school.
Medians and Quartiles for Nine Groups of Communities
A single table showing the slow-progress percentages reported by
these 563 communities in detail would be confusing rather than illumi-
nating. For the sake of brevity it is customary to describe the con-
ditions shown in a whole series of these measurements by tabulating
five figures, the two extremes, the two quartiles and the median.
This condensed table is shown for the nine groups of cities and
villages which have been reported in the foregoing tables.
19
Table 12
Extreme, median and quartile percentages of slow progress in communities
grouped according to elementary enrolment
ELEMENTARY
ENROLMENT
SLOW-PROGRESS PERCENT.\GES
Lower
extreme
First
quartile
Median
Third
quartile
Higher
extreme
Quartile
range
Quartile
deviation
0\eT 5000. . .
3 000-4 999.
2 000-2 999 .
I 000- I 999 .
500- 999 .
300- 499 ■
200- 299 .
TOO- 199-
Below 100 . . .
16
14
15
5
1 1
6
4
7
25
8
19.13
18.36
22.18
21.275
28.5
27.
24-5
29.
26.13
24 . 05
30.05
28.05
35. 5
34-
32.
35.
32.
34
35
36
36
40
40
39
44
42
89
4
6S
45
75
42
40
55
84
63
72
70
90
76
2
15
17
14
IS
12
13
14
IS
20
76
04
47
17s
25
5
7
8
7
7
6
6
7
10
88
52
24
S8
125
5
25
5
The two columns of extremes show that the greatest variation in
slow progress occurs in the very small systems, the range being from
4 to 70, from o to 90 and from 2 to 76 per cent, while the total range
for the two highest groups of cities is from 16 to 42 and 14.7 to 40
per cent.
Since extremes are very unsafe criteria, it is customary to charac-
terize a series of measurements by indicating the two percentages
between which the middle half of the measures lie, that is, the range
in per cent between the two quartiles, the object being to find how
large a distance on the scale contains the middle half of the series.
This is known as the interquartile range and is given in the next to
the last column of the table.
The two columns of extremes show that the total range increases
as the systems grow smaller. This last column but one shows that
the position on the scale of the middle half of the measures does not
bear this inverse ratio to the size of the systems but that the least
variation among the middle half of the measures occiurs in the two
adjacent groups of systems from 300 to 499 and 500 to 999, in which
groups the difference between the communities which stand one-
quarter of the way from the top and the systems three-quarters of
the way toward the bottom is only thirteen percentage points. This
means that more uniform conditions of retardation are to be found
in these two groups of communities than in the other seven groups of
the above table, in which the middle half of the measures are scattered
over a wider range of percentage points.
In statistical tables it is customary to express this variation by
dividing the quartile range by two in order to show the amount of
deviation from the midpoint or median. This distance on the
20
scale between the quartiles divided by two is called the quartile
deviation or semi-interquartile range and is given in the right-hand
column of the table. In general, when a nurnber of large groups
of measurements are tabulated for comparison, the groups with
the least quartile deviation are supposed to represent more uniform
conditions than those groups which show large deviations and the
general inference is that this uniformity means probable similarity
in organization and administration.
Median May Not Be Proper Measure
Attention should again be called to the fact that the slow-prog-
ress percentages reported by these 563 communities are based
on their own local standards of promotion and teaching and we can
only assume that in the uniform course of study pursued throughout
the State and in the high character and ability of superintendents
and principals, which we confidently believe is likewise statewide,
we have the assurance that these tables present fairly reliable
estimates of superintendents, principals and teachers who are
doing all in their power for the welfare of the children in the schools.
On the other hand, the fact that the median point of a group
of 24 cities is 28 per cent slow progress and the median point of
77 villages is 32 per cent slow progress, is no proof that these
points indicate what the amount of slow progress actually ought to
be. Certainly no one would suggest that in the group of 24 cities
the 12 above the median with slow-progress percentages less than
28 per cent should begin increasing their retardation until the
median was reached. With reference to the school systems in the
lower half of any series, we can not say that the median is the
goal toward which that city should work, because we know
practically nothing about the character of the school work repre-
sented by this median and we have no reason to believe that what
happens to be the reported achievement of the middle community
in a list of a score or a hundred is any where near the proper measure
for the entire group. To be content with obtaining these median
retardation rates would indeed be following a line of least resistance
to the neglect of much that ought to be done for the progress of the
school children. The scrutiny with which many superintendents
in various parts of the country have subjected their systems to
the most thoroughgoing examination has revealed both praise-
worthy features and remedial and preventive defects in their schools,
often in their own offices, to such an extent that we can no
21
longer conclude that the average attainment-results of any number
of different localities represents all that ought to be expected from
most of them. Appraising the work of a school system by such
a standard is akin to the rather widespread but quite precarious
procedure of figuring the school budget on the basis of what happened
to have been spent the year before rather than on the basis of the
modern budget carefully analyzed by function, character, object
and location.
Some retardation will of course always be present, and from
these figures we can not determine the extent to which school systems
might reasonably be expected to reduce their slow-progress per-
centages. As already pointed out, the percentage of slow progress
which actually exists in the schools is probably 4 or 5 per cent higher
throughout the State than the figures reported by the schools of
the State in May 19 17 here presented.
These tables constitute merely the first general statewide state-
ment of conditions showing what the schools of the State say about
themselves, and enabling each city and village superintendent
and union school district principal definitely to locate the place
which his schools occupy among all the other self-reported ratings
of the State and in particular among the school systems which
enrol about the same number of elementary pupils. All this is
of course only the first of a half dozen or more steps in the direction
of securing for all the schools of this State definite and reliable infor-
mation about the conditions of the pupils and the results of
educational effort, the information finally obtained being of such
a character as to be a help rather than a burden to the superintendents
and principals who contribute it.
The next step is to determine by much more carefully collected
data exactly what the rapid, normal and slow progress conditions
are when measured by the latest methods of modern statistical
research. This second step has been in progress in a number of
cities and villages during the present school year. The first results
of this investigation will be' to show the difference in conditions
reported in May 19 17 and those found to exist in September 19 17
and February 19 18.
A third step in this program of educational accounting after
the schools have been rated by their own standards is the measure-
ment of these school systems by the common measure of the standard
classroom tests by means of which the school ability of the pupil
can be definitely appraised in addition to his general condition of
retardation or acceleration, as determined by his age and promotion
22
from grade to grade. In addition to the many uses which progressive
superintendents and principals have found for these now thoroughly
tried and permanently established standard tests in the regular
program of supervision throughout the school year, these definite
measurements constitute a most valuable appraisal of local school
and classroom standards which are particularly applicable in the
analysis of the children of a school system considered in the nine
standard age and progress groups in which these children find
themselves placed by reason of their past school life and their
apparent success or failure with local teachers. At present it is
planned to send to the superintendents and principals of the State
shortly after the opening of schools in the fall of 19 18 the results
of an amount of research work sufficient to illustrate adequately
the complete correlation of age and progress locally found with
the corresponding abilities of pupils as shown by standard class-
room tests. The titles of 84 tests for elementary grades are here
included for reference.^
Tests for Elementary Grades
Arithmetic
Guhin's Bobbit's
Courtis's B Monroe's
Starch's A Woody's
National busi- Thompson's
ness ability tests
Gray's
Kansas
Starch's
Gray's
Monroe's
Brown's
Starch's English
vocabulary
Boston fractions
Stone's fundamental
Courtis's reasoning
Bonser reasoning
Silent reading
Courtis's research
Thorndike's visual
Haggarty's visual
Oral reading
Cleveland survey
Stone's reasoning
Rice's reasoning
Buckingham's reasoning
Courtis's series A
Haggarty's
Jones's
Courtis's series R 2
Thorndike's understanding
Minnesota scale Beta
Fordyce's achievements
Price's
Spelling
Buckingham's Ayres's Courtis's
Monroe's timed lists Iowa dictation
Nebraska Rice's Starch's
National business ability
Jones's concrete
Writing
Gray's
Breed & Downs
Ayres' (children)
Ayres Gettysburg
Ayres' (adults)
Thorndike's
Courtis's
Freeman's
Johnson's & Stones
Zaner & Blossom
1 Details of procedure and addresses for obtaining these tests are given in
full in " Educational Tests and Measurements " by Monroe, Kelley and De Voos
(Houghton Mifflin Company) and in part 2 of the 1 7th Year Book of the National
Society for the Study of Education (Public School PubHshing Company, Bloom-
ington. 111.). See also an article, " Measurement and Diagnosis as an aid to
Supervision," by Haggarty, in " School and Society," volume 6, September
1917, page 271.
23
Nassau county
Willi -g's
Breed & Frostic
National busi-
ness ability
Language
Hillegas Courtis's
Trabue completion
Buckingham grammar
Charter's grammar
Starch's grammar
Thompson's research
Boston
Thompson's standardized
Geography
Buckingham
Hahn-Lackey
Thorndike's extension
Harvard-Newton
Haggarty's grammar
Starch's grammar scales
Starch's punctuation
Boston copying
Witham's standard
Starch's series A
History
Buckingham Boll & McCollum's
Harlan's information American history Starch's American history
Drawing
Thorndike's
Music
Seashore's talent chart
After a school system has been properly measured by the age-
progress record of the pupils and this measure checked with the
standard classroom tests as indicated in the preceding types of
measurement, a fourth step is the correlation of the pupils' age-
progress ratings and tested abilities with their individual health
and physical records. A very limited amount of research along this
line is under way and will be distributed when completed.
A corollary to this work with physical and health records is the
application of actual intelligence and psychological tests to small
groups of children found markedly deficient in all the preceding tests.
Necessarily on a still smaller scale at the present time, this
phase of work has already been undertaken and a limited quantity
of data will be forthcoming when the schools open in the fall of 1918.
Pupils Schooled Locally and Elsewhere
When a superintendent or principal is confronted with a retardation
table of his system, he naturally seeks an explanation at least for
a portion of the retardation among the conditions listed on page 1 7 .
Neither the head of a school system nor the teachers are responsible
for all the schooling of all the pupils, since the local system always
contains a very considerable number of pupils who come to that
system after previous schooling elsewhere. In accordance with
this idea, 88 school systems with elementary enrolments ranging
from 25 to 500 pupils, reported progress figures at the close of the
school year 19 16-17, both for all pupils who had been educated
exclusively in the public school system in which they were enrolled
when this canvass was made, and those who had been partially
educated elsewhere. The results are shown in the following tables:
24
Table 13
Total earolment and pupils schooled locally in eighty-eight communities with
slow-progress percentage of each
COMMUNITY
3-
4-
S-
6.
7.
8.
9.
■TO.
I I .
12 .
13-
14-
15.
16.
17.
18.
19.
20.
21 .
22 .
2-1.
25.
26,
27.
28,
29.
30
31
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
SO
51
52
53
54
55
56
57
S8
59
60
.61
62
63
64
TOTAL
PUPILS
KNROLI.ED
54
2S1
St
95
55
281
117
212
123
49
28s
279
192
568
.130
28
83
304
139
lor
82
500
320
62
268
204
14s
206
67
IIS
108
3'73
222
299
131
149
45
218
168
269
547
464
307
290
432
SO
180
214
147
238
197
254
96
79
28
476
292
368
124
552
332
314
31
96
PUPILS
SCHOOLED
LOCALLY
32
263
34
81
34
223
71
156
71
168
174
122
426
277
10
59
236
93
78
34
318
253
62
175
139
77
141
41
64
72
290
207
168
79
78
26
146
107
238
490
292
233
194
314
26
ISI
124
88
162
146
213
66
49
15
311
177
234
84
318
232
175
12
■ S8
PER-
CENTAGE
SCHOOLED
LOCALLY
59
94
67
85
62
79
65
74
58
57
59
62
64
75
64
36
71
78
67
77
41
64
79
100
65
68
53
68
6i
56
67
78
93
56
60
52
58
67
64
89
90
63
76
67
72
52
84
58
60
68
74
84
69
62
54
66
61
64
68
58
70
56
44
60
PERCENTAGES OF
SLOW PROGRESS
Among
all
pupils
enrolled
Among
pupils
locally
schooled
25
Table 13 (concluded)
Total enrolment and pupils schooled locally in eighty-eight communities with
slow-progress percentage of each
COMMUNITY
6S .
66
67
68
69
70
71
72
73
74
75
76
77
78
70
80
81
82
83
84
85
86
87
88
Total
TOTAL
PUPILS
ENROLLED
97
322
126
66
55
30
243
189
156
39
59
88
439
41
208
109
257
107
40
56
183
183
126
105
PUPILS
SCHOOLED
LOCALLY
03
200
67
66
44
19
243
JIG
126
23
48
63
330
41
i6t
77
23 s
62
24
27
iSi
380
PER-
CENTAGE
SCJiOOLED
LOCALLY
62
53
100
80
63
100
58
81
59
81
72
75
100
77
71
91
58
60
48
83
63
67
95
PERCENTAGES OF
SLOW PROGRESS
Among
all
pupils
enrolled
Among
pupils
locally
schooled
27
38
o
42
32
SO
44
21
31
30
48
45
45
48
32
44
37
37
45
S3
42
68
90
It will be noted that in the case of some of the small schools there
is a greater percentage of retarded pupils among those schooled
entirel}^ in that school than among the entire enrolment. This
apparent impossibility is due to the chance advancement of the
pupils schooled in part elsewhere, who are sufficiently advanced
to reduce the retardation of the entire school below that of the
pupils who have never been elsewhere. This is of course exceptional.
Table 13 shows that of 17,104 pupils enrolled in 88 schools,
12,380, or 72 per cent, were schooled exclusively in the school where
they were enrolled at the time the tabulation was made. The
schools in this table are listed in the order of the reported percentage
of slow-progress pupils, hence any relation between retardation
and the percentage of pupils locally schooled is not apparent. As it
is possible to arrange a given table in the order of but one factor
at a time, this was chosen as the most important.
Table 14 shows the retardation reported in each case for the
entire school listed according to the per cent of pupils locally
schooled.
26
P^F^CE-hTAGE OP SLOW P^I^OGt>E'SS f^VP^ILS
pjE-r^Of^TE-b BY 88 COMMVNITIErS-
ALL F>UP>ILS tnfeOLL&b
PE-ffC&MTAOe- OF- £>tOW PKOOR&SS
IP Zo 30 40 SC 60 TO ao 90 lOO
QVAfiT^li' ^5
ME-b AN
'/o
- 54-yJ
aa Ql/AftTILE-
4Zo/,
Figure 5
Each horizontal hne represents the slow-progress percentage among all pupils
enrolled in one elementary school system. The schools in this figure are the
same as in figure 6.
27
SLOW i::>t>OG[>B'SS r>tfeCE'riTAGe5 OP tAJt>\lS
bChOOltb tXCLUSIVE-LY Ih OhB- WbUC
SCHOOL SYSTtM- 88 COMnV/MITIES feer^fetSEMTEb
P&RCtMTAGeS OP- SLOV/ PROCRtSS — •
IP lo 3o 40 60 SO TO 8$ 25 Ljo
STOl'AtJTILEr-
/AlrblA
35«>ov//^fiTll,e' 3(Wo
ri-27 o/o
I90J0
Figure 6
Each horizontal hne represents the percentage of slow-progress pupils in one
elementary school system. The. four systems at the top represent no slow
progress pupils or zero per cent. These are the same school systems shown
in figure 5. Note that in the case of these pupils who have received all their
schooling in the local pubHc system in which they were found when this survey
was made, the slow-progress percentages are lower than those shown m figure 5.
28
Table 14
Slow-progress percentages arranged according to the per cent of pupils locally
schooled
PER CENT OF ALL PUPILS SCHOOLED
LOCALLY
30-39 . .
40-49 . .
50-59. .
60-69. .
70-79. .
80-89. .
90-100 .
88 schools.
ALL PUPILS ENROLLED
Percentages of retardation
Lowest
1st
quart ile
Median
auartile
Highest
50
49
56
48
50
88
In table 15 the progress percentages reported by schools are
arranged in four wa^^s, each in a double column of figures in which
the first figure is the per cent of slow-progress pupils and the second
figure is the number of villages reporting the percentage represented
by the first figure.
Age-progress and School Locations
It is of course expected that those pupils who have not moved
about from place to place will make more satisfactory school progress
than those who have done any considerable amount of moving.
The division of the pupils of a public school system into groups
for the study of retardation on this basis of locations is not so simple
and is by no means limited to the two groups representing pupils
who have been schooled elsewhere and those who have not.
When we go into this matter of the location of pupils' schooling
we encounter the following groups of pupils which have to be
analyzed separately as to rapid, normal and slow progress:
1 Pupils who have never been to school in any other building
except the one in which they were found at the time of
the age-progress survey
2 Pupils schooled entirely in two or more schools of the local
pubhc system
3 Groups I and 2 combined, constituting all pupils schooled
within the local public system
4 Pupils partly schooled in local parochial and other private
schools
5 Pupils partly schooled in any type of schools in other cities
6 Pupils partly schooled in foreign countries
29
Table 15
Slow-progress percentages reported by villages
Reading across the top of the page, the first Hne items in this table means that
9 per cent retardation among all pupils enrolled was reported by one village;
o per cent retarded two or more years was reported by six villages; o per cent
retarded at all among pupils exclusively schooled locally was reported by 3 vil-
lages; and o per cent of two-year retardation among pupils locally schooled was
reported by 9 villages. The "first figure in each double column is the reported
percentage of slow progress and the second figure is the number of villages which
report each particular per cent.
ALL PUPILS ENROLLED
TOTAL
RETARDATION
Per
cent
9
II
14
I . . . .
17. . ..
18
19
20. . . .
21 ... .
22 ... .
23
24
25-Q. .
26. . . .
28
29
30
31
33
34-Md
35- • • •
36....
37
38....
39
40
41
42-Q3 .
43
44- ■ ■
45 ■ ■ ■ .
46...
47 • • •
48...
49 . . .
50
54
.56.. .
Fre-
quency
N=88
TWO YEARS
RETARDATION
Per
cent
-Qi
3-
4-
5-
6.
7. ...
8-Md
9. .. .
10. . . .
12. . . .
13-Q3 .
14. .. .
15. .. .
16
18. .. .
20. . . .
23
Fre-
quency
N=88
PUPILS SCHOOLED LOCALLY
TOTAL
RETARDATION
Per
cent
o. . . .
•3 —
5
7
8 . .. .
9
II ... .
12 ... .
13
14
16. . . .
17
18
19-Q1 .
20. . . .
21 . . ; .
22 . . . .
23
25
26. . . .
27-Md
28. . . .
29
30
31
32
35
36-Q3 .
37
38....
39
41
42
44
45
48 ... .
50
53
68
90
Fre-
quency
TWO YEARS
RETARD.\TION
Per
cent
0. . . .
1 . . . .
2. . . .
3-Q. ■
4. .. .
5-Md
6
7
8
9-Q3.
10. . . .
II ... .
12 ... .
13- •- •
14. .. .
15. .. .
16
17
18
20. . . .
Fre-
quency
6
13
II
12
6
I
5
3
3
I
3
2
3
I
I
3
30
As it is not worth while to make an analysis in this detail without
securing complete information about pupils, the record of each
pupil's age was secured, as well as a record of his progress through
school. As a pupil may be young, normal or overage and may
make rapid, normal or slow progress through school, the following
well-known arrangement of nine age-progress groups is necessary
to tell the whole truth about any group of pupils under consideration.
In point of age, the pupil is classified according to whether he is
young, normal or old with reference to the standard which is as
follows for heeinninv the work of each grade:
I B, 6 ^■ears hut less than 7
1 A, 6r
2 B, 7
2 A, ^h
3 B, 8
3 A, 8^
4 B, 9
4 A, 9h
I vears
1\' "
lO
5 B, lo vears but less than ii
5A, lor " III
6B, II " 12
6 A, III " 12^
7 B, 12 " 13
7 A, I2| « 13I
8 B, 13 " 14
8 A, 13I " \\\
years
It is important to note that " being in a grade " is not an accurate
measure for determining progress.
The circumstances of age and progress result in nine categories of
pupils :
1 Underage and rapid progress
2 Normal age and rapid progress
3 Overage and rapid progress
4 Underage and normal progress
5 Normal both as to age and progress
6 Overage and normal progress
7 Underage and slow progress
S Normal age and slow progress
9 Overage and slow progress
These are best shown in the following arrangement of the groups :
UNDERAGE AND RAPID
PROGRESS
NORMAL AGE AND RAPID
PROGRESS
OVERAGE AND RAPID
PROGRESS
UNDERAGE AND NORMAL
PROGRESS
NORMAL BOTH AS TO
AGE AND PROGRESS
OVERAGE AND NORMAL
PROGRESS
UNDERAGE AND SLOW
PROGRESS
NORMAL AGE AND SLOW
PROGRESS
OVERAGE AND SLOW
PROGRESS
According to this plan the results of the statistical research in the
cities undertaking this work during 19 16-17 are given.
31
Under A^e
Normal
Over A0e
Total
Rapid
®
©
(2) ©
Normal
:■■ ..\;\;s:^i'sis;\:^s.:,\K>^
Progress
^^1^^
^^^^^^ci^:^y'^^v<
Slow
Progress
^^^^^^^^^^1
lE^I
Jz6.J
K -34.' jj
Totil
@
( 44.M
( \00%
Figure 7
Age and progress of elementary pupils
This age-progress percentage chart represents the nine groups of pupils shown
in the text just preceding table 16. The figures show percentages alone and
not the actual number of pupils and correspond to table 16, to which additions
were made after the figure had been drawn, which slightly changed the decimals
in some of the percentage figures. The total of 100 per cent is the sum of the nine
groups, not of the 15 other circles in the figure, 6 of which, 3 at the right and 3
at the bottom, are subtotals.
Table 16
46,000 pupils in twenty-two cities in New York State
NUMBERS
PERCENTAGES
PUPILS
Under-
age
Normal
age
Over-
age
Total
Under-
age
Normal
age
Over-
age
Total
Rapid progress. . . .
Normal progress . . .
Slow progress
1 356
2 710
315
I 195
16 220
3 148
820
7 921
12 338
3 371
26 851
15 801
2.9
5.9
.7
2.6
35.3
6.8
1.8
lei
7.3
58.4
34-3
Total.
4 381
20 563
21 079
46 023
9.5
44-7
45 8
100
32
Table 17
Age-progress analysis of 3665 elementary pupils by school location
Table A — All pupils enrolled
NUMBERS
PERCENTAGES
PUPILS
Under-
age
Normal
npie
Over-
age
Tot.al
Under-
age
Normal
age
Over-
age
Total
Rapid nrogress
Normal progress . . .
Slow progress
120
370
119
96
641
353
lOI
431
I 43-1
317
I 442
I 906
3-3
10.
2.6
17.5
9.6
2.8
II. 8
39 I
8.7
39.3
50
Total
609
I 090
I 966
3 665
16.6
29 7
53-7
100
Table B — 228^ pupils schooled entirely in local public schools
Rapid progress . . .
Normal progress .
Slow progress . . . .
Total.
95
323
100
59
500
275
35
208
694
189
I 031
I 069
4.2
14. 1
4-4
2.6
21.8
12
1.5
9.1
30.3
8.3
45
46.7
518
834
937
2 289
22.7
36.4
40.9
100
Table C — 836 pupils schooled entirely in two or more local public schools
Rapid progress . .
Normal progress .
Slow progress ....
Total.
19
82
60
II
148
98
8
lOI
309
38
331
467
2.3
9.8
7.2
1.3
17.7
II. 7
I.O
12.2
36.9
4.6
39.6
55.8
161
257
418
836
19.2
30.7
50.1
100
Table D — • 1453 pupils schooled entirely in one school
Rapid progress. .
Normal progress .
S}ow progress . . . .
Total.
76
241
40
48
352
177
27
107
38s
ISI
700
602
5
17
3
3
24
12
2
7
27
10
48
42
357
577
519
I 453
25
39
36
100
Table E — /S^ pupils schooled partly in local nonpublic schools
Rapid progress . .
Normal progress .
Slow progress . . . .
5
24
9
14
66
45
42
133
447
61
223
501
.6
31
1 . 2
1.8
8.4
5-7
5.3
16.9
57
63.9
38
125
622
785
4.9
15.9
79-2
100
Table F — 45S pupils partly schooled in other cities
Rapid progress
Normal progress . . .
Slow progress
18
20
10
21
66
29
21
66
207
60
152
246
3-9
4-4
2.2
4.6
14.4
6.3
4.6
14.4
45.2^
13-1
33.2
53-7
Total
48
116
294
458
10.5
23-3
64. 2
100
Table G — 133 pupils partly schooled in foreign countries
Rapid progress . .
Norma! progress .
Slow progress . . . .
Total .
2
2
3
7
2
2
3
9
24
36
2
6
18
4
86
90
3
65
5
15
113
133
4
II
85
33
^e-r^Ce-MTAGeOP t>Vi:>IL5
horn oveji-ACE- a 5Low-prifltfee6!>
3 >
ALL PVf'lCS
E-MI»OLLf-b
4-407.
A7o/„
^30/ >>\/6l.lC SCHOOLS
C4 3
»>V(»1L* SCHOOL&b
6-HTit»ErLY IH LOCAL
P>VM,lC SCHOOLS
f>VI»ll,S SCHOOLE-b
S-NTIR6-LY >K ON6-
OvbL>C SCHOOL
30o/,
Figure 8
This figure should not be misinterpreted as showing the relative number of
pupils who have been schooled entirely in the local system or have come into
it from the outside. It represents groups of pupils based on the location of
their previous schooling, ranging in size from 133 pupils partly schooled in foreign
countries to the grand total of 3665 found in the public schools at the time of
the survey. Each circle represents 100 per cent of its own group and the black
sector shows the percentage of these that are retarded.
There are three points in each of these tables which should interest
the local superintendent. These are (i) the percentage of overage
pupils; (2) the percentage of slow-progress pupils; (3) the per-
centage of pupils who are both old and slow for their grade.
In this particular total group of 3665 pupils, the overage situation
may be stated as follows:
Overage, for all pupils enrolled 53.7 per cent
For pupils schooled entirely within the local
public system 40 . g per cent
34
For pupils who have moved from school to school
within the local public school system 50. i per cent
For pupils who have always attended the same
public school 36 per cent
Pupils who have come into the system from
parochial or private schools 79. 2 per cent
Pupils entering from other cities 64.2 per cent
Pupils entering from foreign schools 85 per cent
The corresponding percentages for slow progress and for both
overage and slow progress are:
GROUP OF PUPILS
All pupils enrolled
Schooled locally in public schools . .
In two or more local public schools.
In one school only
Partly parochial
Partly out of town
Partly foreign
PER CENT
SLOW
PROGRESS
PER CENT
BOTH OVERAGE
AND SLOW
PROGRESS
52
39-1
46.
7
30.3
55.
,8
36 -9
42
27
63.
9
57
53 •
•7
45-2
68
65
This table shows that at the very start, there are three types
of location factors which have to be analyzed quantitatively before
the superintendent can even Ijegin to interpret his own age-progress
figures: (i) changes within his system, (2) the combination of
public and parochial schooling, and (3) the combination of local
and out-of-town schooling.
The great difference between the number of pupils who are over-
age, who are slow and who are both old and slow shows the inadequacy
of either age or years-in-school alone as a measure of retardation,
and the handicap under which those superintendents are working
who have not the aid and support of a complete system of individual
permanent record cards, so essential to the demands of modem
supervision considered locally and entirely apart from any collective
research such as this discussion.
Even this sevenfold table does not tell the complete story of local
and outside retardation, to determine both of which requires the
correlation of each pupil's progress with the proportion of his total
schooling received in the local public system and obtained elsewhere,
a task which, while somewhat involved, is quickly accomplished by
means of the mechanical tabulation of these statistics with electrical
35
machines. The detailed data for this type of correlation are already
assembled for a number of cities in New York State and will doubtless
be given to the superintendents early in the fall.
Analysis of Progress by Grades
The tables and discussions thus far presented in this paper refer
to the progress percentages reported by communities in the form
of one figure representing the per cent of all the pupils in one com-
munity who were reported by that community as having made
retarded or slow progress at the time the figures were collected.
In tables 2 to 6 each community reported three figures, one for
rapid progress, a second for normal progress and a third for its slo^^'
progress per cent. The remaining tables have presented slow
progress alone giving one percentage figure for each community with
reference to the total retardation in that system and another per-
centage figure with reference to the retardation which amounted to
two or more years and were likewise for the entire school system.
As the total slow-progress percentage of 32.4 for union free school
districts with less than 100 elementary pupils gives no idea of the
variety of conditions shown in the first column of table 11 where
the slow progress ranges from 2 per cent to 76 per cent, so do all
the slow-progress percentages for school systems as a whole fail to
give any notion whatever of the variety of retardation conditions
which exist within each of these 563 communities.
The reports received from all these cities and villages had
the information contained in them arranged separately by grades.
On the basis of this division of each school system into the
eight regular grades of the elementary schools, the tables which
follow have been prepared, showing first for the State as a
whole and subsequently for each of the nine groups based on the
size of the elementary enrolment, the nimibers of pupils and per-
centages of rapid, normal and slow progress, likewise separately
tabulated for each grade. For example, the figures for the first
grade in table 18 were obtained by adding together the figures
for the first grades in all the 563 communities reporting. In the
same manner the first grade figures in the nine tables reporting
the nine groups of cities were obtained by adding first grade figures
reported by the cities in each group.
Figure 9 represents pupils in elementary schools arranged in
eight coltmms to correspond to the eight regular grades. The
shading in the columns indicates the relative amount of rapid.
normal and slow progress in each grade, expressed in per cents.
Each column represents loo per cent for each grade. The columns
are of equal length to bring out the relative proportions of rapid,
normal and slow progress in the different grades at a glance. This
figure does not show the relative size of the different grades, as it
is concerned with percentages alone and not with the ntunbers
enrolled in each grade. There is no rapid progress reported in the
first grade, but, beginning with the second grade, the rapid progress
is seen to increase with each succeeding grade, through the eighth.
The solid black shading indicating normal progress is affected by
the increasing rapid-progress, and the slow-progress elements which
increase from the start and reach a maximum in the fifth grade.
The decrease in slow progress in the sixth, seventh and eighth is
due to the withdrawal of retarded pupils from these grades as well
as to improved school conditions, but the relative weight of these
factors has not been studied in this research. The chief purpose
of the diagram is to bring out the fact that there is a wide variation
in the amount of rapid, normal and slow progress from grade to
grade which is not revealed in an average or median figure for a
community as a whole, and the careful determination and inter-
pretation of these differences by the local superintendent are
essential to the intelligent and effective analysis of the situation
in each community.
Table i8
Progress percentages of 286,207 pupils in 41 cities, 29 villages and 493 union
free school districts
GRADE
RAriD
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
38 112
28 026
24 796
21 599
18 81S
16 402
13 875
12 798
7 SOI
8 900
8 120
9 247
8 990
7 963
6 126
4 709
841
2 108
2 325
2 964
3 109
2 684
I 693
I 298
154
357
631
923
I 053
801
416
274
19
83
180
296
306
217
67
72
10
24
41
84
58
28
II
6
8
10
19
14
12
I
8 531
II 479
II 309
13 533
13 222
II 609
8 314
6 355
46 643
41 730
39 018
38 905
36 497
32 579
27 043
23 792
2
3
4
5
6
7
8
2 225
2 917
3 773
4 152
4 568
4 854
4 639
Total..
27 128
174 419
61 556
16 925
4 608
I 240
259
70
84 660
286 207
Percentages
81.69
67.16
63-54
55-51
51-55
50.34
51.31
53-77
16.07
21.31
20.81
26.09
24-63
24-44
22.65
19-79
1.8
5-OS
5-95
7-62
8.52
7-94
6.26
5-46
.33
.852
1. 617
2.372
2.885
2.458
1-53
I. IS
-047
.198
.461
.76
.838
.666
.247
.300
m-7
.012
.019
.025
.049
.038
.036
.004
18.3
27-51
28.98
34-78
37-07
35-63
30.74
26.71
2
3
4
5
6
7
8
5-33
7.47
9.67
11-37
14.02
17-94
19.49
057
105
215
158
088
04
08
100
100
100
100
100
100
100
Total..
9.48
60.94
21. 51
5-91
1.608
■ 433
.091
.025
29-58
100
37
Rapid, Normal & Slow Progress Percentages
Reporfed By 5€>3 School S^itejA^ In
New York ^tate Representing o.To^'al of
2.66,207 Elementary Pupils
More Than
Progress
Grades ~*1
I
I I
Two ^BArs
-SO
One. Vceetr
5 l6>vl/
-50
Rapid
4 5" 6
Figure 9
8«-GrQdes
Table 19
Progress percentages of 103,783 pupils in six cities with an elementary enrol-
ment of over 5000
GRADE
RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YE.\RS
SLOW
6 YE.\RS
SLOW
TOTAL
SLOW
TOTAL
IS 296
10 604
9 615
8 181
7 078
6 150
4 950
4 501
2 044
2 769
2 040
3 019
3 021
2 982
2 268
I 706
197
483
437
906
I 070
981
672
424
47
75
112
302
354
311
155
109
8
18
23
87
III
91
29
42
I
6
7
26
24
6
2
I
4
2
5
4
3
I
2 297
3 354
2 621
4 345
4 584
4 374
3 127
2 282
17 593
2
3
4
5
6
7
8
I 041
I 302
I 492
I 576
I 638
I 814
I 561
14 999
13 538
14 018
13 238
12 162
9 891
8 344
Total..
10 424
66 375
19 849
5 170
I 464
409
73
19
26 984
103 783
38
Percentages
86.94
70.69
71 .01
58.36
54-15
50-56
49 63
53-94
II. 6
18.46
15.07
21. IS
22.92
21.94
20.41
15-87
i-iS
2-97
4-05
5 -24
6-27
4.81
3-36
2-28
.302
.508
.885
2.15
1.94
I . II
.578
-455
.078
.113
-170
-550
.431
.316
.070
.109
.009
.011
-055
. 106
.101
.014
.011
.011
.047
.013
13-05
2I-36
19-36
30.98
34-11
35 96
31-87
27-34
100
2
3..
4
5
6
7
g
7-94
9-62
10.64
11.72
13-46
18.48
18.71
100
100
100
100
100
100
100
Total..
10.04
63.96
19-10
4-97
1-4
-393
.070
.018
26
100
Table 20
Progress percentages of 31,233 pupils in eight cities with an elementary enrol-
ment from 3000 to 4999
GRADE
RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
I
3 873
3 136
2 862
2 374
2 068
I 544
I 417
I 087
736
890
I 004
988
935
814
484
346
79
243
286
283
3SS
249
104
75
10
30
6S
86
91
68
19
19
2
8
27
19
18
25
3
3
3
3
8
3
3
I
I
I
2
828
I I7S
I 386
I 386
I 402
I 159
610
443
4 701
3
4
5
6
276
416
60s
747
771
904
764
4 587
4 664
4 365
4 217
3 474
2 931
8...
2 294
Total..
4 483
18 361
6 197
I 674
388
lOS
20
5
8 389
31 233
Percentages
82-04
68-36
61-36
54-38
49 04
44-44
48-34
47-38
15-65
20.05
22.20
23-SS
22-26
24-88
17-68
iS-28
1-787
5-66
6-63
7.01
8-8r
7-61
3-55
3-26
.235
.637
1-475
2-193
2.36s
1.983
.73S
-845
.047
. 196
.653
.487
•474
.781
.116
.148
.023
.073
.073
. 204
.079
-097
.023
.024
-024
-osi
17-613
25-621
29-716
31-752
33-246
33-362
20.8t2
19. 311
100
2
3
4
5
6
6.01
8.91
13.86
17-71
22-19
30.84
33-30
100
100
100
100
100
100
8
100
Total. .
14-35
58-78
19-84
5-36
1.242
.336
.064
.016
26.86
100
Table 21
Progress percentages of 19,689 pupils in seven cities and one village with an
elementary enrolment between 2000 and 2999
GRADE
R.A.PID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
1
2
3
4
5
6
7
8
00
323
337
400
393
492
424
312
2 645
I 824
I 610
I 167
I 229
985
843
634
493
624
734
646
634
523
382
294
49
121
214
260
198
177
112
94
6
22
76
84
74
46
42
21
I
9
21
21
29
13
4
8
I
3
9
8
6
2
I
I
I
I
4
2
551
780
I 054
I 020
945
763
S4I
417
3 196
2 927
3 001
2 587
2 567
2 240
I 808
I 363
Total..
2 681
10 937
4 330
I 225
371
106
30
9
6 071
19 689
39
Percentages
I
82.8
56.52
15.43
21.32
I -534
4-136
.188
-753
.031
.375
031
103
.031
-034
17.245
33.46
100
2
10.
100
3
11.23
53.7
24-45
7-14
2-532
.700
300
35.122
100
4
IS. 46
45.15
24-97
10. OS
3-247
.813
309
■ 039
39.428
100
s
15.31
47.84
24.7
7-72
2.885
I. 13
234
-156
36.82s
100
6
21.95
44.
23.34
7.91
2.053
.581
089
.089
34.062
100
7
23-45
46.6
21 . 12
6.20
2.322
.221
05 s
29.918
100
8
22.90
46.50
21-57
6-89
1-54
.587 . . -
30.587
100
Total..
13.62
55-55
21-99
6.22
1.884
-539
152
.046
30.831
100
Table 22
Progress percentages of 30,932 pupils in sixteen cities and eight villages with
an elementary enrolment between 1000 and 1999 pupils
GRADE
RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
S YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
I
2
3
4
5
6
7
8
000
234
376
434
462
546
510
S6i
3 87s
2 971
2 476
2 269
2 025
I 845
I 429
I 228
900
I 001
983
I 02s
964
788
620
447
143
261
386
332
362
292
179
140
24
62
114
120
143
8S
52
23
4
13
40
61
44
II
II
3
5
5
17
14
3
I
I
3
6
2
I
I 072
I 342
I 531
I 561
I 529
I 180
863
613
4 947
4 547
4 383
4 264
4 016
3 571
2 802
2 402
Total..
3 123
18 118
6 728
2 095
623
187
45
13
9 691
30 932
Percentages
I
00.00
5. IS
8.58
10.17
11.50
15.28
18-20
23-35
78.38
65-33
56.47
S3. 21
50.40
51.68
51.00
51.13
18.19
22.02
22.41
24.04
24.00
22.06
22. 12
18.61
2.89
S.74
8.81
7.79
9.02
8.18
6.39
5.83
.485
1.363
2.601
2.815
3.564
2.380
1.8SS
.957
.08
.286
.913
1.430
1.095
.308
.392
.125
.000
. no
.114
.399
.349
.084
.036
.000
020
21.62
29.52
34.95
36.62
38.10
33.04
30.80
25.52
100
3
4
5
6
7
8
068
141
050
028
000
000
100
100
100
100
100
100
Total. .
10.09
58-57
21.75
6.772
2.014
.6m
.145
.042
31.33
100
Table 23
Progress percentages of 29,748 pupils in four cities, sixteen villages and twenty-
eight union free school districts with an elementary enrolment between 500
and 999
GRADE
RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YE.'i.RS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
I
3 732
2 787
2 689
2 222
I 804
I 708
I 427
I 197
I 126
I 036
877
I 054
994
808
6S4
532
151
279
266
447
353
256
178
146
24
36
100
137
138
102
43
28
4
12
29
SO
30
28
5
6
6
4
6
2
I
3
2
I
I 313
I 368
I 282
I 696
I SI7
I 196
881
712
5 045
2
3
4
5
6
7
8
100
160
316
381
418
433
409
4 255
4 131
4 234
3 702
3 322
2 741
2 318
Total..
2 217
17 566
7 08 1
2 076
608
164
27
9
9 965
29 74S
40
Percentages
74
65.2
6s.i
32. 5
48.7
SI. 3
52.1
31.7
22.3
24.3
21 .2
24.9
26.8
24-3
23-9
23
3
.48
I. 31
2.42
3.24
3.72
3.06
1.37
I. 21
.08
.28
.70
I. 18
.81
.84
.18
.26
26
32.5
30 -5
40.1
41. 1
36.2
32.1
30.7
3
4
5
6
7
8
2.3
3.9
4.7
10.2
12. 5
15.6
17.6
6
6
10
9
7
6
6
5
4
5
7
9
5
7
.09
.17
.14
.03
.06
.04
.02
.06
.05
.03
100
100
100
100
100
100
Total . .
7-3
59-3
23.6
7
2. II
.55
.09
.03
33.4
100
Table 24
Progress percentages of 22,049 pupils in three villages and sixty-one union
free school districts with an elementary enrolment between 300 and 499
GR.\DE
R.^PID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
S YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
I
2 690
2 155
I 799
I 778
I 530
I 299
I 131
I 292
729
719
750
801
758
549
504
202
86
213
235
244
275
204
155
126
17
37
51
78
94
87
33
16
7
17
28
38
22
4
3
I
I
I
8
5
2
I
I
833
977
I 05s
I 160
I 172
864
696
347
3 523
3 179
2 961
3 IIO
2 89s
2 416
2 040
I 925
2
3
4
5
6
47
107
172
193
253
213
286
8
Tr.taL.
I 271
13 674
5 012
I 538
413
119
18
4
7 104
22 049
Percentages
76 A
20.70
22 .60
25.32
25.74
26.20
22.72
24.70
10.48
2.44
6.70
7.93
7.8s
9.50
8.45
7.60
6.53
.48
1. 16
1.72
2.51
3.25
3.60
1 .62
.83
.22
.57
.90
1.31
.91
. 196
.156
.028
.031
.034
.257
.173
.083
.034
.032
.069
23.648
30.711
35.618
37.289
40.50
35.763
34.116
17.996
2
3
4
5
6
7
1.48
3.61
5-53
6.67
10.47
10.44
14.84
67
60
57
52
53
55
67
8
8
2
9
8
5
100
100
100
100
100
8
Total..
5.77
62
22.71
6.98
1.87
.54
.082
.018
32.20
100
Table 25
Progress percentages of 18,979 pupils in one village and seventy-six union free
school districts with an elementary enrolment between 200 and 299
GRADE
RAPID
NORMAL
I YEAR
SLOW
2 YE-iVRS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOT.\L
I
2 293
I 759
I 542
I 481
I 277
I 178
I 059
985
740
675
686
644
690
624
495
. 452
81
213
180
171
193
150
122
125
9
37
39
38
42
35
26
25
830
931
914
867
937
816
644
602
3 123
2 741
2 503
2 449
2 334
2 no
I 896
I 823
-,
51
47
101
120
116
193
236
6
7
10
II
5
■ I
3
4
5
6
7
2
3
I
2
I
8
Total..
864
II 574
5 006
I 235
251
40
8
I
6 541
18 979
, 41
Percentages
T
1.86
1.87
4.12
5 -14
S-S
10.18
12.94
73-5
64.2
61. 5
60.4
54-7
55-9
55-9
49.1
23.7
24.6
27.4
28
29-5
29.6
26. 1
24.8
2-59
7.77
7.18
6.98
8.27
7.12
6.44
6.86
2.88
1-35
1.56
1-55
1.80
1.66
1-37
1-37
26.257
33-946
36 . 498
37.10
30.085
38.682
33.963
33 -03
->
.219
■ 279
.408
-472
-237
.053
3-
4-
5-
6.
.079
. 122
.043
-095
-04
100
100
100
100
8.
To
tr.' .
4-S6
61
26.4
6.18
6. SI
.132
.042
.005
41-057
100
Table 26
Progress percentages of 18,351 pupils in 153 union school districts with an
elementary enrolment between 100 and 199
GR.-VDE
RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOT.-*L
I
2
3
4
5
6
7
8
000
76
63
120
154
193
222
250
2 428
I 774
I 367
I 304
I 008
981
972
I 256
337
820
694
613
632
543
450
441
14
205
215
200
199
182
104
95
45
48
55
82
48
30
16
7
15
12
16
18
9
3
2
7
I
4
7
5
I
I
I
6
351
I 080
979
882
934
804
598
555
2 779
2 930
2 409
2 306
2 096
I 978
1 792
2 061
Total . .
I 078
II 090
4 530
I 214
324
80
26
9
6 183
18 351
Percentages
2.34
2.6x
5-21
7-35
9-76
12.39
12.13
87-4
61 .4
56.75
56-6
48-15
49-65
54-25
60.8
12 . 12
27 .20
28.8
26.57
30.15
27.45
25.12
21.4
-54
7-29
8-93
8.68
9.50
9.21
5-81
4.61
12.66
35-777
40.675
38.437
44-553
40.658
33-381
26.915
2. . . .
3
4..-.
5- • - ■
6....
7....
8
I
I
2
3
2
I
55
99
58
91
43
67
•76
387
623
521
754
911
502
041
290
043
191
354
279
042
042
043
048
303
100
100
100
100
100
-ri^
Total
5.82
60.8
24.44
6.5
1-78
.442
. 140
-05
33-352
100
Table 27
Progress percentages of 11,443 pupils in 175 union free school districts with
an elementary enrolment below 100
GRADl
: RAPID
NORMAL
I YEAR
SLOW
2 YEARS
SLOW
3 YEARS
SLOW
4 YEARS
SLOW
5 YEARS
SLOW
6 YEARS
SLOW
TOTAL
SLOW
TOTAL
1. . . .
2. . . .
3.-..
4....
6.'.'.'.
7.--.
S....
77
109
133
126
141
141
260
I 280
I 016
832
823
796
712
647
618
396
366
352
457
362
332
269
289
41
90
106
121
104
96
67
73
17
13
26
23
35
19
16
17
3
I
8
9
4
I
4
I
7
2
I
I
I
456
472
487
616
510
453
354
384
I 736
I 565
I 428
I 572
I 432
I 306
I 142
I 262
Total
987
6 724
2 823
698
166
30
12
I
3 732
II 443
42
Percentages
I
2. . .
3...
4...
4-92
7.6l
8.47
8.8
10.8
12. 35
20.6
■70 S
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