 

GROWTH AN‘D imi‘émﬂTiON EN REA’DENG

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MICI'HGAN STATE COLLEGE
Faye Lucile [{unkie
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This x. to certify that the

theeie entitled

Growth and l’rediction in Reading Achievement

presented by

Faye Lucile Xunkle

bu been accepted towards fulfillment
of the requirements for

LA. degree in Educat ion

Major professor

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GROWTH AND PREDICTION
IN READING ACHIEVEMENT

A Theeia
Presented to
the Faculty of the Department of Education
Michigan State College

In Partial Fulfillment
of the Requirements for the Degree

Master of Arte

by
Faye Lucile Kunkle
December 1950

”duals

LIST OF TABLES
TABLE PAGE
I. Average Number of Tastings and Average
Span.....................'7
II. Comparison of Boys' and Girls' Predicted
Scores with Stanford Norms . . . . . . . . . . 12
III. Constants from Equations for Unmatched Groups. . 18
IV. Constants from Equations for Matched Groups . . 23
V. Comparison of Predicted Scores of Upper Boys,
Upper Girls, Lower Boys and Lower Girls . . . 26

i
J!
ea
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b-hr.

LIST OF FIGURES

FIGURE

1.

5.

4.
5A.
5B.
SC.
SD.
5E.
5F.
5G.
5H.
51.
53.
SK.

5.

Distribution of Deviations of Predicted Reading
Scores from.Actual Stanford Scores . . . . . .
Comparison of Stanford Norms with Curves of
Constants . . . . . . . . . . . . . . . . . .
Theoretical Reading Achievement Curves of Nine
Unselected Girls . . . . . . . . . . . . . . .
Distribution of I. Q.'s . . . . . . . . . . . .
Distribution of kl . . . . . . . . . . . . . . .
Distribution of k2 . . . . . . . . . . . . . . .
Distribution of k3 . . . . . . . . . . . . . . .
Distribution of 01 . . . . . . . . . . . . . . .
Distribution of 02 . . . . . . . . . . . . . . .
Distribution of tl . . . . . . . . . . . . . . .
Distribution of t2 . . . . . . . . . . . . . . .
Distribution of r1 . . . . . . . . . . . . . . .
Distribution of r2 . . . . . . . . . . . . . . .
Distribution of b1 . . . . . . . . . . . . . . .
Distribution of b2 . . . . . . . . . . . . . . .

Comparison of Composite Curves of Upper Boys,

Lower Boys, Upper Girls and Lower Girls . . .

PAGE

13

15
19
19
19
19
20
2O
2O
2O
21
21
21
21

27

INTRODUCTION

Much has been said in methods textbooks, periodical
literature and teacher training courses concerning provision
for individual differences in teaching of reading. Studies
have developed steps or stages through which individuals
pass in the process of learning to read.1' By stating such
e series, there is the implication that all individuals
traverse the same path. However, the progressive differen-
ces in the achievement levels of individuals follow a much
more sensitive classification. Children arrive at the vari-
ous stages at differing times and'ggg; toward individual
maturity levels at unique rates.

The type of investigation which has revealed the
necessity for provision of individualized instruction has
been primarily of the cross-sectional type. By development
of norms based on measurement of different children in dif-
ferent grades at the same time, a grosser type of scale has
been devised than would seem.feasible to apply to the study
of a single individual. The need is for successive measure—

ment of the same children over a period of years--the

 

1National Society for the Study of Education, Reading
in the Elementary School, Forty-Eighth Yearbook, Part I ,
C'EiTago: University or“ Chicago Press, 1949, pp. 19-22.

2
longitudinal study technique. Gray2 and Traxler5 have sums
marized several thousand studies of reading, but few tackle
the problemuwith the longitudinal approach. Studies such as
those carried out in the Harvard and Iowa growth studies
should become the general practice. This study has been
carried out for the purpose of contributing to the understand-
ing of the nature of reading progress and the factors which

affect reading achievement.

22299868:

The investigation has five purposes: (1) to shoe
the individuality of growth in reading; (2) to shoe the
patterns of growth in preadolescent and adolescent reading;
(3) to shoe sex differences in reading growth; (4) to
shoe effect of intelligence on reading growth; (5) to

state generalizations based on data analysis.
General Setting:

The children used as subjects were in attendance at

the Henry Ford School, Dearborn,‘Michigan. Children in this

 

zGray, W. 8., Elementary School Journal, University
of’Chicago Press, Chicago, 111. (Summary appears in October
or March 1 ssue .)

aTraxler, A. E.,”Ten'Years of Research in Reading,“
Educationa Records B letinpﬁg..§§, Educational Records

ureau, ew York, Marc , 1941.

3
school are, in general, typical of the higher level of social
status in an industrial community. Few of the cases are rep-
resentative of social extremes.

Eighteen boys and eighteen girls were used for the
study. This is a relatively small group, but since the growth
measured is individually analyzed, the small number of cases

is not important.

MEI'HOD 0F ANALYSIS

In this study the attempt has been made to describe
growth in reading in mathematical terms by fitting an equa-
tion to the observed data. By computing the equation from
the observed data, it is possible to predict growth beyond
the range of actual testing.

The equation used here has been widely used in stud-
ies in biological science. To Courtis“who adopted the
technique frothompestz' ”LII of Biologic Growth" is given
the credit for introducing growth technique in educational
research. Data which follow a logarithmic curve when plotted
on rectangular coordinate graph paper will graph as a
straight line when plotted on graph paper in.which the hori-
zontal scale remains uniform and the vertical scale is laid
off in logarithmic units. The Courtis technique uses a
specially constructed graph paper on which the horizontal
scale remains uniformly spaced but the vertical scale rep-
resents peroentages of maximum devlepment.

The equation of the straight line as plotted on
Courtis' isochronic graph paper is determined in units of

percentages of time required to complete the cycle. The

equation is of the form.Y - KkErt + q. The portion of

 

4Courtis, S. A., The Measurement 2; Growth, Brumfield
and.Brumfield,.Ann.Arbor, Michigan, 1932.—

5
the equation in brackets can be recognized as the equation
of a straight line. "r” is the slope of the line and is
found by dividing the change in isochrons between two points
by the time required for the change to take place. "t" is
the time, the abscissa on the graph; and "i” (incipiency)
is the value of the ordinate when ”t” is zero, or the inter-
cept on the vertical scale. Values obtained by solving
this portion of the equation yield isochronic values. The
cross-bars on the first bracket sign indicate that this
quantity is to be translated to percentages of maximum be-
fore multiplying by "K", the score achieved at maturity by
the individual.

In describing growth which seems to mature in more
than one cycle, the equations are combined to produce the

following formula:

‘13; cycle Egg cycle
Y 3 K1 {1‘11 4- 11] + K2 {Inst + 12]

Experience leads to the expectation of a two-cycle
phenomenon in the development of height and weight in child-
ren. Pubertal changes are evident in the acceleration of
the rate of growth. These changes are also to be noted in

growth curves of dentition, intelligence, and other forms

of growth as shown by Huggett and Millard.5 Longitudinal
curves in reading resemble closely those of other functions
and should be regarded as a portion of the total develop-
ment of the child.

Millard6 has shown that a single cycle equation des-
cribes preadolescent growth in reading achievement. However,
to portray the total growth of the individual, it is necessary
to represent further growth beyond the preadolescent maximum

by a second cycle equation.

 

5Hu
. ggett A. J. and Millard C. V. Growth; Learning
Ln he Elementary Schodl, D. 0. Heath 8c Coz, Doston, l 4 .

6M111ard, o. v., "The Nature and Character of Pre-
Adolescent Growth in Reading Achievement," Child Develo ment,
Vol.11, No. 2, pp. 71-114, 1940.

METHOD OEIMEASUREMENT

Description 93 Data:

 

The data used for analysis consisted of Stanford
reading scores, for eighteen boys and eighteen girls.
Three hundred eighty scores were available for this group
of thirty-six children. The average number of testings and

average spans are given in Table l which follows.

Table 1. {Average Number of Testings

and Average Span.

 

Box! Girls 2219.].- $129.39.
.Averags number 10.4 10.7 10.5

of testings

Average Age Span
of testing

 

 

109 e2'172e5 97.1-15705 103e2'164e9

 

 

All children.were in attendance at the Henry Ford School,
Dearbcrn, Michigan, during the course of the testing.

'1!

1 0121222922:

1. An equation for the growth of each individual
was derived from the actual measurements (Appen-

dices A and.B)

 

7Scores used represent the average interpolated score
of paragraph meaning and word meaning, as indicated by Stan-
ford scoring instructions.

8
2. These equations were solved for values for each
individual at the ages at which the tests were
given.
3. Comparison was then made between computed scores

and actual scores as obtained on the tests.

.Ldeguacz 9;.Derived gguation :

Comparison of actual scores with the predicted scores
obtained as described above showed the mean deviation of pre-
dicted from.actua1 to be 2.7 in 380 predictions. Forty-four
per cent of these predictions showed an error of less than
1.4. In view of the variability which might be expected due
to uncontrollable factors in the testing situation, the limits
of the tests themselves, and variability of individual per-
formance, it seems remarkable that individual performance can
be anticipated with such accuracy. Figure 1 shows the dis-

tribution of errors in prediction.

wwwoom do wwwng

110-

100

90-

70-

60'

40

20-

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Figure l.

M6311 -- 207

Average error with sign -- +.32

 

 

. iron . . . . l, a
-20 -15 ~10 -5 O 5 10 15

Distribution of Deviations of Predicted Reading

Scores from Actual Stanford Scores

10

Comparisonigg Stanfgrd Norma with.Bgyg' and Girls' Curves
g; Constants:

. ”Curves of Constants" were obtained for boys and
girls as described by Courtis.8 To obtain these equations,
the means of the constants of the individual equations were
utilized. ‘Using the resulting equations, scores were com»
puted at tenementh intervals (Table 2) and plotted on the
same axes as the Stanford norms (Figure 2).

It is apparent that the progress of these two groups
is not as uniformly linear as that expected from.reference
to the norms. The reading achievement of the studied groups
is observed to accelerate rapidly in the beginning stages of
growth, reach a plateau period, then spurt upward again
rapidly. .L second cycle of achievement is apparent begin-
ning near puberty, 136 months for the girls and 146 months
for the boys.

Since the curves of constants differ so markedly from
the Stanford norms curve, and resemble so much more closely
the individual curves of achievement (see Appendix C), the
injustice done many pupils by computation of reading quotient
(educational age divided by chronological age) is readily

 

8Courtis, S. A., ”The Derivation of Norms,” Section
I§& Education, American Association for the Advancement of
clones. 1932, pp. 237-242.

11
apparent. A.child may show a lag in comparison to the Stan-
ford norms, when, in actuality, if given a little more time,
and allowed to continue at his own growth rate without undue

pressure, he may soon surpass the norm.

12
Table 2. Comparison of Boys' and Girls' Predicted Scores

with Stanford Norms

 

Stanford Girls' Boys'

Age Norms Predicted Scores Predicted Scores
6- 8 --- 4.4 ---
7- 6 19 23.7 ---
8- 4 28 49.3 2.7
9- 2 39 65.3 16.e
10- 0 50 73.2 38.3
10-10 62 78.4 57.7
11- 8 72 85.2 71.0
12- 6 80 92.3 81.9
13- 4 86 96.7 ss.e
14- 2 91 99.0 92.8
13- 0 96 100.0 94.5
13-10, 101 100.4 95.7

16- B 108 100.5 96.3

13

Boys' Curve.—___.
Girls' Curve. ------ .
Stanford Norms._ _.

Boys' Co osite Equati n:
y I 78eﬁe790t * 6le4 + 18e8{0696t 9' '72s];

Girls' Composite Equat on:
y a 79.6f.897t «- 52.3 + 21.2%.8691; - 9343

120 L

110-

‘.
‘.
4
it
4

100

so. "’ V

C
70' ,r’ /‘
60’ / /.
50 * .’ e/

wwwOOM uwowzbam
\.
\

.
20 ’ I’./

10 F I!" /

‘1'6 100 120 L 140 ‘ ids ‘ iso ‘ zoo

 

Figure 2. Comparison of Stanford Norms with Curves cf Constants

INDIVIDUAL DIFFERENCES IN READING PERFORMANCE

Through the study of large groups of students, stand-
ards of achievement have been established, the existence
and importance of individual differences has been made known
and the concept of individual needs has developed. 0n the
other hand, it has been shown that data obtained on large
groups of children of a given age used in establishing norms,
obscure variation in growth that are evident in individual
growth curves.

It has been shown.that individuals differ greatly by
studying the reading growth curves of nine unselected girls.
No two curves originated at the same age level, and no two
curves attained the same maximum.levsl. Some followed
nearly parallel for a period, then suddenly deviated marked-
ly. By reference to Figure 3, the fallacy of judging the
performance of one child by that of another who at any
particular point rates at approximately the same level is

apparent.

15

.manao ompocaomob coax Ho mobaoo pooaopoﬁmom mcﬂcmom Hecapcaooma .n caowam

 

 

\\

 

 

 

 

 

 

 

 

SEX DIFFERENCES IN READING PERFORMANCE

Many studies have been made of effects of intelli-
gence on reading achievement. Individual differences have
already been discussed. However, one other important fac-
tor in individual differences has been neglected in most
studies. Certainly sex differences should be studied as a
part of an analysis of reading in order to provide for
another possible factor in individual differences. School
achievement scores have indicated superiority for girls in

10 concluded that

linguistic skills at all ages.9 Millard
”Although there are characteristics of the reading achieve-
ment curve which can be attributed to the effect of sex,
differences in rates of growth, differences in time at
which maturity is reached, and differences in maxima, there
is no basic difference in achievement when all of these
factors are taken into consideration."

Comparison of constants from the composite equations
for boys and that for girls will reveal differences in read-

ing achievement along many lines.

First of all is the difference in maxima--girls excel

 

9
Gray, N. 8., "Reading" Encyclogedia_ of Educational
Research. New York: The Mac Millan Co., 1941, pp. 591-926.

1QMillard, C. V., ”The Nature and Character of Pre-
Adolescent Growth in Reading Achievement," Child Development
Vol. 11, No. 2, p. 91,1940.

17
in levels attained in both cycles by 1.5 at the termination

of the first cycle, by 2.9 in the second cycle, and by 4.4
in the overall analysis.

Girls again function at a higher level than boys
when the rate of growth is studied.

Girls begin each cycle at an earlier age than boys,
require less time for completing the cycle, and arrive at
maturation at an earlier age.

Thus is shown the superiority of girls over boys in
all aspects of reading achievement. Table 3 presents the
data upon.which the above statements are based.

Frequency distributions for the growth constants
show again that, despite the superiority of girls over

boys, wide degrees of variability occur.

 

 

Table 3. Constants from.equations for unmatched groups.
Constant boys girls

kl preadolescent maximum 78.1 79.6
kg adolescent maximum. 18.8 21.7
k3 total maximum 96.9 101.3
r1 preadolescent rate .790 .897
r2,adolescent rate .696 .869
tl age of preadolescent

maturation 161.6 149.2
t2 age of adolescent maturation 225.8 201.2
b1 age of beginning preadolescent

cycle 85.2 74.2
b2 age of beginning adolescent

cycle 121.2 119.7
°1 time required for completion

of preadolescent cycle 76.3 74.9
oz time required for completion

of adolescent cycle 104.7 82.0
03 140.6 127.0

time required for total growth

18

 

Uldrﬂdtsn3 t+c> riai’ilnta

owwopm Ho Havana

Boys

V

 

Boys ..___.._...

Mean I. Q.

104.0

Girls 110.5

S.D.
12.4
12.1

 

Girls ----- 19

HNGPOOQO

Moan K1 SeDe
Boys 78.1 14.6
Girls 79.6 11.0

 

 

Fig. 4. Distribution of I.Q.'s. Fig. 5A. Distribution of k1.

Boys
Girls

 

Mean kg
18.8
21.7

 

'2 25 28 31

“0811 K3 SeDe
Boys 96.9 16.5
Girls 101.9 9.2

 

 

I
I

40 so so 70 so so 160 .120

 

 

Fig. SB. Distribution of k2. Fig. 5C. Distribution of k3.

20

Boys 76.3 21.1 Boys 104.7 32.2
Girls 74.9 17.9 Girls 82.0 31.7
6 .

 

 

 

 

 

0 130

Fig. 5D. Distribution of °1' Fig. 5E. Distribution of ca

Mean t1 S.D. Mean t2 S.D.
Boys 161.6 16.6 Boys 223.8 27.0
Girls 149.2 17.4 Girls 201.2 27.1

 

 

PMS‘O‘OQ

 

 

 

110 130 15c 176 190 210 160 200 240 sec 300
Fig. 3F. Distribution of t1. Fig. 5G. Distribution of t2-

21

 

    

 

 

 

Mean 1'1 SeDe Mean 1‘2 Se De
Boys .790 .286 Boys .696 .257
Girls .897 .258 Girls .869 .323
10» 10f
8. 8"
6.
4.
2
:"x
e3 07 e9 10]. 1.5 e3 .5 e7 09 1e]. 13 L5 1”

Fig. 5H. Distribution of r1. Fig. 51. Distribution of re

mean b1 S.D. Mean b2 S.D.
Boys 85.2 10.4 Boys 121.2 12.3
Girls 74.2 12.2 Girls 119.7 15.6
10- 10k
a a
i.
e * 6 *
4 . 4 t
2 ,t' 2 "

         

I --".‘~‘

g _- a a a “ a J l l A;
50 60 7O 80 90 100 110 90 100 120 140 160
Fig. 5J. Distribution of b1. Fig. 5K. Distribution of be.

 

 

j

 

EFFECT OF INTELLIGENCE ON READING ACHIEVEMENT

Division of boys and girls into groups by I.Q. was
made. Five cases were used in each of the following groups:
upper girls, upper boys, lower girls, lower boys.

Comparisons will now be made between upper I.Q. boys
(mean I.Q. 115.2) and lower 1.9. boys (mean I.Q. 100.5),
upper I.Q. girls (mean I.Q. 115.6) and lower I.Q. girls
(mean 1.9. 100.1), upper boys and upper girls, and lower
boys and lower girls.

Comparing upper boys with lower boys shows the fol-
lowing: upper boys have a higher preadolescent maximum,

a lower adolescent maximum, but a higher total reading
maximum. Upper boys have a higher preadolescent rate of
growth, but a lower adolescent rate of growth. Upper boys
begin both cycles at an earlier age, complete both cycles
at an earlier age, and require less time for completion of
cycles.

Comparing upper girls with lower girls: upper gh:1s
have a higher preadolescent maximum, a lower adolescent
maximum, but a greater total maximum. Upper girls have a
lower preadolescent rate, but a higher adolescent rate.
Upper girls complete the preadolescent cycle later than
lower girls, but complete the adolescent cycle at an earlier

age. Upper girls and lower girls vary only slightly in age

23

 

 

 

Table 4. Constants from equations for matched groups.
BOYS GIRLS
Constant Upper Lower Upper:;pwer

k1 preadolescent maximum 87.6 76.2 ' 87.0 72.4.
k2 adolescent maximum 17.8 18.6 20.2 22.8
kg total maximum 105.4 94.8 107.2 95.2
r1 preadolescent rate .943 .862 .843 .943
r2 adolescent rate .728 .839 .839 .774
tl age of preadolescent

maturation 149.3 166.4 152.1 146.6
t2 age of adolescent maturation 214.5 223.3 202.6 212.9
bl age of beginning pre-

adolescent cycle 83.2 90.0 73.0 73.5
b2 age of beginning adolescent .

cycle 122.2 124.3 120.0 119.1
01 time required for completion

of preadolescent cycle 66.1 76.4 79.2 73.2
02 time required for completion

of adolescent cycle 92.3 99.0 82.6 95.4
05 time required for total

growth 131.3 133.3 129.6 139.4

 

24
of beginning cycles, with the upper girls having the advan-
tage in the preadolescent cycle and the lower girls in the
adolescent cycle. Upper girls require more time to complete
the preadolescent cycle, but less time for the adolescent
cycle and less time for the total growth in reading.

Comparing upper boys and upper girls lessens the
differences found in comparing unmatched boys and girls.
Upper boys and girls have nearly identical preadolescent
maxima, with the girls having the adolescent advantage and
attaining a slight overall advantage. Preadolescent boys
achieved at a higher rate, but adolescent girls regained
the advantage. Preadolescent maturation occurred earlier
for the boys, but adolescent maturation was attained with
a decided advantage of nearly a year for the girls. Pre-
adolescent girls began reading earlier, and also began the
adolescent cycle earlier, but lost much of the advantage in
the second cycle. The boys required less time for comple-
tion of the preadolescent cycle, but more for completion of
the adolescent cycle, with a slight overall disadvantage.

Comparison of lower boys with lower girls shows
essentially the same results with the following exceptions.
lower boys had a lower preadolescent rate of growth than
the girls, and a higher adolescent rate of growth. Lower

girls completed the preadolescent cycle earlier than the

25
lower boys. Lower boys required more time to complete the
preadolescent cycle, and less time for the total growth.

The conclusion to be drawn from the above discussion
is that while, in the unmatched groups, the girls have the
advantage in all phases of reading growth, the advantage
is divided in comparison of groups matched by 1.9. Too,
the upper groups of both boys and girls have the overall
advantage over the lower groups. Data for the above con-
clusions are shown in Table 4.

Scores were predicted at ten-month intervals from
upper and lower boys' and girls' composite equations and
are listed in Table 5. Figure 6 interprets these results

graphically.

26

 

 

 

Table 5. Comparison of Predicted Scores of Upper Boys,
Upper Girls, Lower Boys and Lower Girls.
Girls' Boys'
Predicted Scores Predicted Scores
A8. Upper lower Upper lower
6-8 2.6 2.2 --- ---
7-6 20.0 17.4 7.1 ---
8-4 46.1 42.0 32.8 8.4
9-2 66.1 58.6 59.7 44.5
10-0 77.4 66.7 75.5 51.8
10-10 83.7 71.6 83.9 65.2
11-8 90.6 78.4 90.5 74.4
12-6 97.5 86.0 96.3 82.8
13-4 102.3 90.3 100.4 89.0
14-2 105.0 92.9 102.9 92.0
15-0 106.1 94.1 104.1 93.3

 

 

Computed from the following composite equations:

Upper Boys -- y o 87.6 {.9461: - 64.1] 4- 17.8 f.728t -

Lower Boys -- y - 76.2 {.862t .. 64nd + 18.6 {.869t
Upper Girls - y - 87.0 {.846t - dead 4- 20.2 {.8391;
Lower Girls - y . 72.4 f.943t - 68.3 + 22.8 {.774t

I

9 9
(D (O
O m
e 0
.EL

80.1000) “HOHBGCO'UJ

2‘7

Figure 6. Comparison of Composite Curves of Upper Boys,

 

Lower Boys, Upper Girls, and Lower Girls.

Upper Girls ——-
Lower Girls —.—-

Upper Boys assess

 

Low er Boys ------
110 . I...
/ .‘uuwv‘
/‘__,.-'
/ ‘,s.s:::f
90 ’ / .nnifr'tt"""
W" '
. Z/ . 9’ o
80 /./
70 ~ /-/ . ""13?
/O/a"’.” 0’ '
so . / ,4»
/s", v"!
50 ' /.’/. "9""
t" ’
40 ~ /,-‘ ./
4!!
30 * ﬂ", '/ i,
so . / I ./
/ .3 ’
10 P /,o". /
k"
80 100 120 140 160 180

Chronological Age

28

Generalizations and Implications from the Stud:

The following characteristics of the pattern of read-
ing growth have been revealed or verified by the results of
this investigation.

1. All children tend to traverse similar routes
as reading abilities mature.

2. Although all children go through similar pat-
terns of development, there is wide variation
in rate, time, and maximum of development.

3. That certain inherent factors, or early es-
tablished determinants, influence growth in
reading is borne out by the adequacy of des-
cription of the curves of reading achievement
by mathematical equations.

4. Reading growth follows a curvilinear pattern
with an adolescent cycle succeeding the pre-
adolescent cycle.

5. Reading growth is a part of the total develop-
ment of the organism.and presents a developmen-
tal pattern similar to those familiar ones of
physical develOpment including a pause and an
acceleration near puberty.

6. Patterns of individual or small group progress

deviate markedly from the existing norms.

10.

29
Girls, on the average, develop earlier and
exhibit a higher developmental level at any
given age than do boys.
Although girls tend to be superior in the
preadolescent cycle, much of their final
superiority is due to growth during the
adolescent cycle.
Intelligence is an important factor in read-
ing growth.
When I. Q. is made constant, much of the
variability in favor of the girls tends to

disappear.

Generalizations and Implications for Educationa;HPractices

Revealed pg Verified.p1_the Study

1.

2.

3.

4.

Single measures of achievement appear useless
for evaluation.

.A number of successive measurements are necess-
ary for prognosis.

The need for maintenance of longitudinal records
by schools is pointed out. Growth patterns are
essential for evaluation and must cover the
entire developmental career to be valid.
Possible short-time fluctuations due to instruc-

tional level have little effect upon the final

30
achievement of the individual.

5. Possibilities for a better basis for group-
ing for instructional purposes are indicated
by this type of investigation.

6. The present system of grades needs a thorough
study for possible alteration in view of growth
analysis of children. Study tOpio placement
may need revision in order to place new ma-
terial in the curriculum at a time when rapid
growth is taking place, and not at a time of
plateau in the learning curve.

7. The individuality of learning is emphasized
and indicates the need for individualized
instruction.

8. The apparently predetermined nature of read-
ing growth indicates that reading instruction
in the school should emphasize development ct
wide interests, literary taste, discrimination,

and reading for special purposes.
Implications for Further Study

That study in this area is at a beginning and leaves
much for the future is apparent. Some questions yet to be

investigated follow.

1. Study is needed to determine effect of

2.

31
preadolescent cycle upon the adolescent
cycle.
Interrelationship between factors of growth
are still to be investigated.
Follow-up studies are needed to indicate the
extent to which prediction is possible.
Relationships between patterns of development
in reading and other mental and physical

traits should be traced.

B IB LI OGRAPHY

52
BIBLIOGRAPHY

Courtis, S. A. The Measurement of Growth, Brumfield.&
Brumfield, Ann.Arbor, Michigan, 1932.

, "The Derivation of Norms," Sectionig. Education,
American Association for the Advancement of Science.
1932, pp. 237- 242.

Gray, W. 3., Elementary School Journal, University of
Chicago Press, Chicago, 111. (Summary appears in
October or'March issue.)

_______, "Reading" Encyclopedia‘pg Educationa; Research.
New York; the MacMillan Co., 1941, pp. 891-926.

Huggett, .A. J. and C. V. Millard, Growth.& learning in
the Elementarz School, D. C. Heath.&.Co., Boston,
1946.

Millard, C. 7., "The Nature and Character of PreAdoles-
cent Growth in Reading.Achievement,” Child Develop-
ment, Vol. 11, No. 2, pp. 71-114, 1940.

Traxler, A. E., "Ten.Years of Research in Reading,"

Records Bureau, New'York, March, 1941.

National Society for the Study of Education, Reading_ in
the Elementary School, Forty-Eighth Yearbook, Part _II,
Chicago: Uﬁiversity of Chicago Press, 1949, pp. 19-22.

APPENDIX

33

 

 

APPENDIX A. Boys' Reading Scores - Equation Constants
Case
Number k1 r1 11 b1 °1 tl k2 r2
10M 97 .908 53.3 74.9 67.3 142.2 12 .919
19MC 74 .824 50.8 79.5 74.4 153.9 17 .738
21M 72 .803 56.6 88.8 76.3 165.1 17 .486
26M 78 .982 72.4 88.7 62.4 151.1 16 1.374
28M 90 .978 80.0 96.8 62.7 159.5 20 .612
31M 87 .706 49.4 90.8 86.8 177.6 22 .745
34M 84 1.105 79.5 85.3 55.4 140.7 24 .632
36M 64 .573 32.7 82.7 107.0 189.7 14 .540
44M 92 .923 62.9 84.1 66.4 150.5 20 .680
45M 92 .742 43.1 78.0 82.6 160.5 13 .443
52M 75 .980 64.6 80.9 62.5 143.4 20 1.032
55M 82 .612 31.1 74.8 100.1 174.9 22 .485
61M 90 .725 42.7 79.2 84.5 163.7 18 .593
63M 80 1.244 108.7 99.1 49.3 148.4 24 1.049
80M 83 .681 37.1 68.7 89.9 158.7 28 .429
100M 33 .475 19.8 72.6 129.0 201.6 10 .471
180M 60 .797 66.3 101.6 76.9 178.5 26 .408
223M '72 1.550 155.5 107.8 59.2 147.1 16 .887

APPENDIX.A. (continued)

 

 

Av. Age No. of
12 b2 c2 t2 k3 Dev. Range Scores
93.7 118.0 66.7 184.7 109 2.68 95-146 9
60.7 102.2 83.0 185.3 91 4.288 98-157 10
36.9 106.2 126.1 232.2 89 3.3 107-166 11
166.7 132.0 115.1 247.1 94 1.7 110-168 10
63.7 128.2 100.1 228.3 110 1.71 121-183 12
82.6 130.7 82.2 212.9 109 1.53 107-181 13
62.8 122.8 96.9 219.7 108 2.6 105-167 11
47.7 115.7 113.4 229.1 78 2.02 115-174 10
73.2 129.3 90.1 219.4 112 2.02 101-179 12
36.1 114.7 138.3 253.0 105 2.7 99-181 12
116.8 127.4 59.3 186.7 95 2.629 94-153 9
42.4 117.9 126.3 244.2 104 3.159 97-167 11
50.0 109.1 103.3 212.4 108 3.856 1091180 11
129.1 137.0 58.4 195.4 104 2.007 115-175 8
35.6 117.2 142.9 260.1 111 2.98 109-173 10
46.5 129.9 130.1 260.0 43 4.15 136-188 9
38.0 96.8 182.7 279.5 86 2.96 120-191 10
114.7 145.9 69.1 215.0 88 1.58 128-172 9

35

 

 

APPENDIX B. Girls' Reading Scores - Equation Constants
Case
No. k1 r1 11 b1 01 t1 k2 r2
2! 100 .711 30.2 63.1 86.2 149.34 10 .658
4F 70 1.341 84.0 76.3 45.7 119.3 30 1.190
8F 76 .725 32.6 65.3 84.4 149.7 20 .610
16F 74 .930 82.6 104.7 65.8 170.5 22 .901
18F 66 1.408 104.4 84.6 44.6 129.2 24 1.229
21? 70 .985 60.2 76.1 62.2 138.3 30 .765
22! 82 .779 29.7 57.0 78.7 135.6 10 .823
24F 70 1.263 70.0 67.0 48.6 115.6 30 .780
25F 90 1.205 85.5 83.1 50.9 134.0 24 1.137
32F 70 .901 59.2 67.4 85.0 152.4 20 .343
38? 78 .729 36.5 70.3 84.0 154.4 30 .714
41! 84 .703 32.2 66.8 87.1 153.9 28 .725
42F 64 .955 68.5 87.2 64.2 151.3 18 .869
45F 100 .676 32.2 69.5 90.6 160.1 12 .701
49F 90 .532 15.8 57.3 115.2 172.5 14 .492
58F 74 .643 38.2 82.2 95.3 177.5 30 .710
71F 95 1.050 82.2 92.3 58.3 150.6 15 1.233
82F 80 .603 27.5 70.0 101.6 171.6 24 1.758

APPENDIX B. (continued)

36

 

 

Av. Age No. of
12 b2 cg t2 k5 Dev. Range Scores
56.1 107.4 93.1 200.5 ’ 110 1.513 84-135 9
112.9 107.3 51.4 158.7 100 3.47 90-141 9
46.9 101.0 100.4 201.4 96 3.498 94-145 9
104.4 132.2 68.0 200.2 96 2.8 115-166 10
145.4 130.3 49.8 180.1 90 2.8 99-157 11
78.5 121.9 80.0 201.9 100 2.29 97-159 12
67.5 99.8 74.4 174.2 92 3.33 79-138 11
64.2 101.2 78.6 179.8 100 2.868 80-139 11
119.0 117.6 53.8 171.4 114 4.198 94-153 11
21.1 104.5 178.6 283.1 90 2.82 100-159 11
74.3 124.7 85.8 210.5 108 1.95 100-158 11
71.7 119.2 84.5 203.7 112 2.66 102-164 '12
106.6 124.3 85.8 210.1 82 3.41 107-177 12
67.2 116.9 87.4 204.3 112 1.8 104-162 11
38.1 107.3 124.6 231.9 104 2.04 98-160 12
83.9 139.0 94.3 225.3 104 4.39 100-182 12
176.3 154.9 49.7 204.6 110 1.19 112-172 9
240.5 145.2 34.8 180.0 104 2.422 93-168 9

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37

 

 

 

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Chronological Ages

 

 

 

 

APPENDIX 0 (Continued) 38
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80 100 120 140 160 180
Chronological Ages

40
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