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Grouping -
An Experimental study

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APR 1 1323
AN EXPERIMENTAL STUDY OF GROUPING, BY
SIMILARITY AS A FACTOR IN THE
TEACHING OF SPELLING
Important Facts Revealed by the Investigation, and Methods of :::
Computation That Give a Basis For Comparative
Interpretation of Results From Experi-
mental Pedagogy, Are Also
Included
A Thesis Presented to the Faculty of the Graduate School of
the University of Pennsylvania in part fulfillment
of the requirements for the Degree of
Doctor of Philosophy
CHARLES A. WAGNER
BY
West Chester, Pa.
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AN EXPERIMENTAL STUDY OF GROUPING BY
SIMILARITY AS A FACTOR IN THE
TEACHING OF SPELLING
Important Facts Revealed by the Investigation, and Methods of
Computation That Give a Basis For Comparative
Interpretation of Results From Experi-
mental Pedagogy, Are Also
Included
A Thesis Presented to the Faculty of the Graduate School of the
University of Pennsylvania in part fulfillment of the
requirements for the Degree of Doctor of
· Philosophy
BY »
CHARLES A WAGNER
West Chester, Pa.
June 1, 1912
AN EXPERIMENTAL STUDY OF GROUPING BY
SIMILARITY AS A FACTOR IN THE
TEACHING OF SPELLING
By CHARLES A. WAGNER
West Chester, Pa.
AN INVESTIGATION TO DETERMINE THE EFFICIENCY OF TEACH-
ING SPELLING IF THE WORDS BE GROUPED ACCORD-
ING TO “GROUP" DIFFICULTY IN SPELLING.
I. INTRODUCTION.
An investigation conducted by myself, for Doctor Yocum's
Seminar in Pedagogy, in 1908, yielded the tentative conclusion
that “Etymology is an effective help in spelling after considerable
of the Grammar of the Classical languages is known." This
raised the question of the effectiveness for spelling of forms of
grouping other than Etymological, as phonetic difficulty, similar
silent letters, and so on.
The next year an investigation of special devices in spelling,
such as rhymes or jingles for "ie” and “ei” words, brought to
light the existence of a large number of such devices among
educated people. This result gave further impetus to the ques-
tion, "What is the degree of efficiency of 'group' association in
spelling"?
In most instances spelling books have the words arranged into
groups. The groups are either words of the same degree of
difficulty or else of names of things "found in the parlor”, “in the
iaitic”, and so on. To learn the names of all the things in the
s parlor becomes easy from such a list, but it is the words and not
o their spelling that seems to be helped by the grouping, unless it
* should be found that in some way the recollection of the words
in such a "contiguous" list also helps the spelling of these words.
The principle of grouping applied in this experiment is the princi-
īple of analogy or similarity of spelling difficulty.
Doctor J. M. Rice, in discussing his findings in his well-known
spelling investigation in American cities, says (Forum, vol. 23,
Kpage 417): “ ... the course [in spelling] is open to
simplification by separating words that may be learned collectively
from those that must be learned individually . . . That
little advantage is now taken of rules in spelling is indicated by
4.-17-23, g

ge 417) in by separating worded individually
is indicated by
-
Eras
the fact that, broadly speaking, as many errors were made on
words governed by rules as on those to which rules do not apply.”
These considerations pointed the way to this investigation.
What is the measurable advantage, under actual school conditions,
of teaching the spelling of words grouped according to a common
'difficulty in their spelling? It seemed both desirable and possible
to arrange a test to measure such efficiency: the selection of two
classes of children, in the same set of schools, alike in grading and
school age, must, of course, be the laboratory in which the test is
to be made. If one class of children study their spelling words in
the usual way, and the other class study the same words, but
study them according to groups on the basis of similar difficulty in
spelling, the difference of advantage one way or the other would
be likely to appear. The attempt was made, in the experiment,
to keep all the conditions alike, except the spelling lessons. In
one class the source of the words determined their place in the les-
sons, in the other class, it was the kind of spelling difficulty found
in the word. It was also hoped that the test might show the rela-
tive advantages among the kinds or groups of spelling difficulty
selected in classifying the words for the second class.
Does such method tend to build up a habit of associating new ,
words with the groups learned ? seemed another important prob-
lem upon which it was hoped some light might be found. Be-
cause such an investigation must extend over years, it was impos-
sible to get any light on the formation of such a tendency. Were
such a tendency sure to follow from the method, and there seenis
much reason for believing that it does, it would be more valuable
than the results found by this investigation. The spelling of his
vocabulary 'is not nearly so valuable to the child as the habit of
learning new words as he encounters them. This is surely to be
aimed at by all teaching of spelling.
No method is simple. All methods are complex, made up of
many factors. When the final method of teaching spelling is
formulated, therefore, shall the grouping of words according to
similarity of spelling difficulty be one of those factors ? became
the final problem of this study.
II. WHERE CONDUCTED.
The schools of a borough in Pennsylvania with supervision by
the School Principal were available for the experiment, and of-
fered favorable conditions. There are two school buildings in
the town. The buildings are about half of the length of the town
apart. This was of advantage since it hindered the exchange of
experiences by the pupils in the twoʻclasses while the experiment
was in progress. Each of the buildings had a class of sixth
grade pupils, boys and girls in each class. The teaching ability :
of the teachers who had charge of these rooms was rated as about
1
TI
A
.
.
.
.
.
.
.
equal by the Principal, who assisted in the conduct of the inves-
tigation. At first, the intention had been to include seventh and
eighth grade pupils also, to find if possible, how far these older
children use reasoning power in spelling. In the schools selected
there were no parallel grades seven and eight in the two schools,
so this part of the search had to be given up. Making deduc-
tions for absence from the tests, in one class, that which studied its
words grouped according to likeness of spelling difficulty, there
were twenty-eight (28) pupils; in the report this class is called
Class A. In the class which studied the words in the usual way,
there remained twenty-two (22) pupils. This class will be
called Class B.
III. THE WORDS CHOSEN FOR THE TEST.
Two hundred words were agreed upon as the test. A smaller
number, it was feared, might be remembered by association by
contiguity alone. That number seemed to be enough to test the
efficiency of grouping; it would give enough groups and would
permit of considerable variation in the sizes of the groups. This
seemed necessary to bring the “group” difficulty into active use
both in learning and in recalling the words. A larger number
would have made a serious interference in the regular work of
these classes in their schools. Alsu it would have required too
much time to complete, and it seemed that the work as here plan-
ned and described would yield tentative results of value. If
grouping in study has any efficiency in learning and recalling the
spelling of words, it seemed likely to appear as the result of the
experiment as here planned, even if larger and more important
results must be neglected.
The words for the test were selected from the other text books
studied by these classes. Their reader, history, geography, physi-
ology and grammar texts were carefully examined, and words
were chosen from those parts of these texts which had already
been gone over that term. This was done to make sure of con-
tent or meaning for the words, and it also made as sure as condi-
tions permitted that the words in the spelling lists would not come
up and be studied in other lessons during the time of the test.
For Class A, the words were arranged into thirty (30) groups,
each group having the same spelling difficulty. Then ten (10)
: lessons were arranged, each lesson containing from one to three
words from each of six or eight of the different groups. This
was done to conform to the practice of the school, twenty (20)
words to the spelling lesson. In Class B there were also twenty
(20) lessons arranged, chiefly according to the order in which
the words were selected from the text books. In the preliminary
test and in the final test, the children spelled fifty (50) words
1
in
5
.
each day for four days. The total time taken for the tests and
Jessons was thus exactly twenty (20) days, just a school month.
IV GROUPING THE WORDS.
Thirty bases of grouping were chosen, and the words put into
the group which seemed to represent the greatest difficulty in the
word. The smallest group had two words, the largest had
sixteen (16) words. With such a small number of words it was
impossible to include all the words of like difficulty that might
belong to any group. The method of selection excluded all
words not found in the text books, hence choosing from spellers
or dictionaries, just to secure an exhaustive list, was precluded.
It seems probable that the group containing the group difficulty
called the “line” group, Group one, approaches very closely to
containing all the words commonly used. The words them-
selves and the grouping, as well as the "group" difficulties
selected, will all be shown in the table of results, and are there-
fore omitted here.
The continuous repetition of the "group" difficulty, as provided
in the lessons for Class A, seemed necessary, to secure the highest
possible degree of certainty that the "group" difficulty should be
learned, that the words in the group should be associated with it,
and so that dependence upon it should have a chance to develop.
It is believed, for instance, that to have learned all the words of a
few groups as a single lesson, and not to have repeated the group
after that, would have afforded a mimimum chance for any ad-
vantage of grouping to show itself. To train the child to depend
upon grouping, he must use grouping frequently, so that "group"
analogy shall function certainly and quickly.
V. PRELIMINARY TEST.
A preliminary test was decided upon as a basis from which to
measure the improvement of each class. Both classes were given
the entire list of two hundred (200) words to spell, in lessons of
fifty (50) words each, without any fresh study of them. The
results attained in this test are the basis from which improvement
is reckoned. The regular teachers conducted these tests. The
children were not told what was in progress, except that it was
review work in spelling. This probably secured normal condi-
tions and the children's best effort. Only the results for the
classes as a whole are shown. In the report to the Seminar, no
difference by sexes was noticeable, hence they are here omitted.
VI. METDOD OF PRESENTATION OR TEACHING THE WORDS.
After the preliminary test, actual study of the entire list of
words, was begun by each class. In Class A, the “grouping".
class, each word of a twenty (20) word lesson was written upon

6
the black-board by the teacher. If any child could use the word
in a sentence or give its meaning so that the entire class under-
stood, then the class was assumed to know the meaning of the
word. If no child could tell its meaning, the teacher, by sug-
gestion or hint, tried to recall the connection where the class had
met the word, and thus, if possible, secured the recall of a mean-
ing already learned. Meaning, or content for the word, even if
but partial, being thus assured, each of the following steps was
taken if the learning of groups had gone ahead far enough to
require it:
(1) To which group of our list may this word be added ?
(2) What words have we already learned that will help us
to remember this ?
(3) Name all the words already learned that will help you
to remember this one ?
Then each word was written two times, to conform to the regu-
lar practice of this class and teacher.
In Class B, the proceeding was the same while making sure
that the words had meaning or content. Then some pupil was
asked to point out the hard part of the word, or'the place where
one would be likely to make a mistake in spelling. Some likely
mistake was always found. Had the teacher been instructed to
point out the difficulty for the children, it was feared that stress
might be put upon the same difficulty in both classes. The results
seem to show that the class that studied its words in ordinary lists
yet hit upon group spelling difficulty as the “hard part” of the
word..
Next each word was written three times, to conform with the
lisual custom of this class and teacher. In both classes this so-
called writing the words means the writing of each word in imme-
diate succession. Should the writing of the words two times in
one class and three times in the other be regarded as a serious
variation? Since it was Class B that wrote them oftener, and
since it was Class A that was trying the “grouping," it seemed
clear that whatever advantage there might be in the three writ-
ings, must accrue to the Class B, which studied its words in the
ordinary groups. Therefore this conformity to usual school con-
ditions seemed better: it gave the children no chance to become
- curious or suspicious that something unusual was going on.
Normal states of mind and attitude toward the work were thus
secured and maintained. Since favorable results, if any, would
be against "grouping” rather than in favor of it, the variation is
here mentioned merely as an explanation, not with the belief that
it caused any disturbance whatever in the results.
VII. THE SPELLING LESSONS.
All spelling lessons, and all the test exercises, were given in the
first period of the afternoon session of the school, between 1.45
and 2.15 p.m. The first ten minutes were given to the pre-
sentation of the words after the plan already described. Then
followed the writing of the words—the study: for this study or
writing, twenty minutes, or as much of it as was needed, was
given to the writing or practicing from the black-board copy.
Then the lesson of twenty words was pronounced to be spelled
in the usual way. All papers were then collected. The teachers
and the investigators marked the papers. Papers were not re-
turned to the children.
Each teacher noted the words misspelled in the lessons. When
the entire list of words had been studied and spelled, these lists of
inisspelled words were treated as two new lessons, each word be-
ing again presented as if it were a new word. The papers of the
review lessons were not kept, the errors were not counted, and no
record of them is included here. Since each class of children
gave extra study to those words which appeared more difficult, it
seems permissible to omit this phase of the work. The mis-
spelled words were restudied to conform to the practice of the
school. This variation told against Class B if it made any dif-
ference, since that class missed the larger number of words in the
daily lessons. Probably this difference is so slight as to be en-
titled to mention only and not to actual consideration or computa-
tion.
VIII. MARKING AND COUNTING ERRORS.
Two classes of errors were arranged as the basis for tabulation
and comparison. Misspelling of any kind made a word wrong.
Next, words that were wrong were examined for the kind of mis-
take or mistakes that had been made. Any error due to not
knowing or not using the “group' difficulty was called a group
error. All other kinds of errors, such as omitted letters, wrong
letters, and so on, were called "non-group" errors. For instance,
the word "conscience," if written consience,” was counted wrong
and the error was regarded a "grouping" error; if written
"consciense,” the error was called a "non-grouping” error. This
classification of errors furnished the basis for determining the ef-
fectiveness of “grouping" in eliminating "group" errors, and
also for the comparison of the groups as to relative efficiency.
There were, of course, many more errors than misspellings:
that is, some words had several mistakes in them, some having as
many as four errors in the preliminary test. In computing the
class standing, only the number of misspelled words was counted.
in computing the efficacy of the groups and of the grouping, the
number of errors was also included.
8 .
In marking the words, the singular difficulty came to light that
some words might with equal propriety be included under several
“groups" of clifficulty. Thus “conception," although actually in-
cluded in the etymological group, might also have been included
in the "group" "tion as shun." In such cases, the error was
counted as a grouping error if the "group". difficulty under which
the word was studied was not used in the spelling. Thus, an
crror resulting from not reineinbering “cept” as the group diffi-
culty for “conception," was regarded as a group error, and any-
thing else in this word as a non-group" error. Words omitted
in the lessons or tests by any pupils, or words substituted for
those pronounced by the teacher were all counted as “non-group-
ing” errors.
The group of words ending in “y” in the singular seems to pre-
sent no group clifficulty; in the plural the rule for spelling “y”
plurals was used, so that rules of spelling, as suggested by Rice,
have had a small trial here.
Many perplexing decisions had to be made in marking the
papers and in classifying the errors. “Graphophone” was most
frequently misspelled by writing it “graphone.” It had been
grouped with the “graph” words: the “graph” is present, bút
shall we call it a grouping or a non-grouping error ? Did the
child write "graph one” or “gra phone”? As the words had not
been written in syllables, we could not tell absolutely. For safe-
ty's sake—to avoid the suspicion of trying to make out a case for
the experiment—all such errors were counted as non-grouping.
Only clear and unmistakable cases of ignorance or non-use of the
"group' difficulty were counted "grouping" errors: all others
were counted as “non-grouping.”
IX. MARKING THE PAPERS.
First the teachers marked the papers: then the investigators:
looked them over, confirmed the markings, and classified the
errors. Then the counts were taken. This precaution seemed
best to guard against any disposition to find errors in favor of the
test, namely,"group" errors. In the tables of results, the
"grouping errors" are called "g” errors, and the “non-grouping"
errors are called “ng” errors.
* X. RESULTS.
For convenience of all kinds, the figures for both tests are
placed side by side in the tables. The words are there arranged
into groups as they were listed for the “grouping" class, under
their respective "group" headings. The table is intended to
show just what were the results for each word, for each group of
words, and for each class, in both tests.
-
.
..
.
.
The results of the daily spelling lessons do not appear in the
table. For the sake of completeness, they are stated here. Class
A, 28 pupils, missed a total of 109 words, during the time of daily
iessons. Class B, in the same time, missed 110 words, but it had
only 22 pupils. The average for Class A is thus 3.9 words per
pupil for the ten lessons, and for Class B it is 5 words per pupil.
In the preliminary test, it will be noticed, that Class A had the
poorer, showing, so that this difference at once becomes a differ-
ence in favor of the "grouping” here tried.
The attendance of the pupils during the time of the lessons was
as follows:
Class A: 3 pupils absent for one lesson each, 2 pupils absent for
2 lessons each, and 2 pupils absent for 4 days each, a total of 15
days..
Class B: 4 pupils absent for 1 day each, and one pupil absent 2
days, a total of 6 days.
Class A thus was present less that 91% of the learning time,
and Class B was present nearly 98% of that time. Class A, the
"grouping" class, made the poorer showing at the start, was
present a smaller percentage of the learning time, yet it made
the better showing in the lessons. As an indication this differ-
ence is entitled to statement here.
Since each class had two days of review, and since the reviews
are not counted in the results of the daily lessons, it is only the
trend of the lessons that may be summarized.
Tabulation of results, showing misspellings and numbers of
the several kinds of errors:
CLASS A.
CLASS B.
(GROUPING METHOD OF STUDY.) : (NON-GROUPING METHOD OF STUDY.)
28 Pupils in Class.
22 Pupils in Class.
MISSPELLINGS
ERRORS
MISSPELLINGS
Grouping Non-grouping
Grouping Non-grouping
Prel. Fin. Prel. Fin.
GROUP 1, "line" as base; 4 words:
lineage
11
12
linear
ERRORS
Prelim. Final
Test. Test.
Prelim. Final
Test. Test.
Prel. Fin.
Prel.
Fin.
16
10
11
13
o
18
16
2
lineal
lineament
21
24
Tono
to c
44
1
21
78
GROUP 2, "que" as k; 6 words:
new cool and como
28
her
3
25
s
o
arabesque
grotesque
oblique
opaque
picturesque
pique
or on
med
Inco E ICIN OWN WINHO
B
vlonoro el noroo
43
GRQUP 3, "verd” as green, as base; 4 words:
21
0 40 2
R
16
ܟܬ ܢܙ ܗ ܝܙ ܙ ܣ
Angora
1
ܝܙ ܗ̇ ܘܿ ܐ ܣ
Cape Verde
verdant
verdure
Vermont
-aasto
64 9
30 &
3511
19
TO.
CLASS A.
(GROUPING METHOD OF STUDY.)
28 Pupils in Class.
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Test Test. Prel. Fin. Prel. Fin.
GROUP 4, "ch” as k; 11 words:
0
CLASS B.
(NON-GROUPING METHOD OF STUDY.)
22 ·Pupils in 01988.
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Test. Test. Prel. Fin. Prel. Fin.
14
1
11
catechism
chasm
chemist
choleric
chord
chorus
Christian
Christmas
chrysalis
monarch
patriarch
INONN & HOROONPOON NA
3
16
OWSE 8100 SAHA O oo whom
176 21.
8 148 19
GROUP 5, “ci” as sound of sh; 4 words:
25
14
1
1
1
19
ow.
17
12
17
capacious
ferocious
precious
vicious
5
ง
4
69
41 5 48
GROUP 6, “geon" as jon; 5 words:
23 1
23
0
O
3
.5
ñ
R
bludgeon
dungeon
pigeon
surgeon
sturgeon
0
2
1 .
12
.
. al --O.
574
73 g
GROUP 7, “tyr" as ter; 3 words:
9 2 30
ll'
1
martyr
martyrdom
satyr
TO HA ESTAT FINDE ET
܂ ܦܣ | ܗ
13. :"
TETE
42 6
GROUP 8, “ti”
277
20.
as sh; 6 words:
22 0
0 1
0
I WONDOR
insatiate
martial
partial
patience
patient
quotient
ܪܘܝ | ܝ ܗܝܕܝܢ
en MO W DOE JOAN
NH O mol
a WHMOND-01.00 NO
GROUP 9,"ant" as ent; 7 words:
27
O
10
027
8
1 - 2
3
.
w
buoyant
claimant
gallant
informant
radiant
tenant
truant
aloo on and on
S1600Noora
12
a
03
-
0
17
85 6
GROUP 10, *cept" as base; 6 words:
15
11
8
:0
221
16
7::
Hwa w
1
101: 22
accept
conception
exception
intercept
precept
reception
n
HON OH a
11
.
7
10
0
0
7
0
0
34
content
IT:
CLASS A.:.
(GROUPING METHOD OF STUDY.)
28 Pupils in Class.
MISSPELLINGS
ERRORS
Prelim. Final. Grouping Non-grouping
Test. Test.
Prel. Fin. Prel. Fin.
GROUP 11, "ph" as f; 8 words:
15
15
CLASS B.
(NON-GROUPING METHOD OF STUDY.)
22 Pupils in Class.
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Test. Test. Prel. Fin. Prel. fin.
1
0
7
2
201
3
1
0
8 “ ප ප - ඒ ස ස 3 ක්
4
cipher
elephants
phalanx
phantom
physic
sulphur
sapphire
triumph
2
2
2
3
4
loon.
com
0
0
0
0
10
0
16
110
-
0
1
0
TONOOMOO
16
senten
89
GROUP 12, "graph' as base; 10 words:
16
0
.0
0
autograph
biography
geography
graphic
graphite
graphophone
paragraph
phonograph
photograph
telegraph
2
OOOOHOO 19.
Tow w w but the coon
glio
o look
olooo cloOoO-HODOH
.
102
1
GROUP 13, “gyp” as jip; 3 words:
§ © 28
0
0 0 1
1
Egypt
gypsum
sypsy
2
0
2
.
6
14
GROUP 14, "BC" as 8; 8 words:
0
0
'
1
0
6
O
o loco e o GO ON
0
0
abscess
descent
fascinate
scenic
scenery
scepter
science
scissors
1
, UNA DE LES AC.CO Dolors
t.
TOO #cool locatoris
.
GROUP 15, "h" silent; 5 words:
28
26
10
10
1
1
aghast
dahlia
honest
rhubarb
shepherd
8 60
0
looo-oo NUOHOOH NlOOOON 01 HONOWO
GROUP 16, "eigh" as long a;
O
0
Ő
inveigh
neigh
neighbor
sleigh
weight
Ó
Ö
:
X GROUP 17, "mission" as base; 6 words:
10
LANCHO Ô Lowo
.
in
0
0
11
-
10
0
0
2
2
0
0
admission
mission
intermission
missionary
permission
remission
0
0
9
.
.
$100
0
0
9
8
0
0
1
0
0
0
0 0
2 0
0
10 - Î
1
0
0
À
0
1
0
ī
50 ö
ö iö
12
CLASS A.
CLASS B
(GROUPING METHOD OF STUDY.)
(NON-GROUPING METHOD OF STUDY.)
28 Pupils in Class.
22 Pupils in Olass.
MISSPELLINGS
ERRORS
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Prelim. Final Grouping Non-grouping
Test. Test. Prel. Fin. Prel. Fin.
Test. Test. Prel. Fin. Prel. Fin.
GROUP 18, "y" preceded by a constant, plural nouns; 9 words:
5 0 2 0 canaries
canopies
colonies
deliveries
quantities
securities
0 stories
1 tapestries
O tributaries
H vs ở
a los ES to noon
lovnoc w O O OF
SI NO ERA NON
oooOOO ON
8 3 9 10 9 +
30
GROUP 19, "ie" as long e; 10 words:
1
.
o 51 Now O OIHANA & Loga Oonari
0
I LO HA wa wowo
O
w w w co w
>OH pod O HO
believe
chief
fiend
fierce
grieve
piece
pierce
thief
wield
1
SI NONON FOR
83 899 9 9 Hos
0
I had w w
GROUP 20, "scio," to know, as base; 2 words:
2 0
conscience
conscious
o
8
3
8 J1 4
18
GROUP 21, singular "y"! preceded by a conso nant nouns (no grouping for these); 9 words:
canary
canopy
colony
delivery
quantity
security
story
tapestry
tributary
ooohan come
Novo
HwOOOH
ܝܙ ܗ ܟ ܝܕ ܟ ܝܕ ܢܪܘ ܢܪ | ܣ
0 0
GROUP 22, “ea” as long e; 5 words:
A
12
bereave
eager
easel
fearful
weasel
I wooco e
6.
0
:
2
.
ܟ ܘܝܪܝܕ ܗ | ܬ
1 ANNAMOS NO ON DHAONNAST NAHORONAS
GROUP 23, “tion" as shun; 12 words:
oooooo OOONOOO AY OOI
A OHY
-
Si cu o wo wo wo 010 0003
home or 0000OOO
i na nown
affliction
completion
direction
exertion
irrigation
objection
observation
perfection
reflection
suffocation
transaction
vegetation
INNHO
ܗ ܘܗ ܟܘ ܘܺܘ ܢܢܘܘ ܝܕܘ ܟ | ܦ
19.
CLASS. A.
(GROUPING METHOD OF STUDY.)
28. Pupils in Class.
MISSPELLINGS
ERRORS. .
Prelim. Final : Grouping Non-grouping
“ Test.' Test. Prel. Fin. Prel. Fin.
GROUP 24, "ojsilent; 9 words:
CLASS B.
(NON-GROUPING METHOD OF STUDY.)
22 Pupils in Class.
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Test. Test.
Prel. Fin. Prel. Fin.
R 100.000.000
ܟܬ ܗ ܟ ܗ ܟ ܗ ܢܙ ܗ ܛ | ܪ
almond
balky
calm
chalk
embalm
Lincoln
palm
psalm
salmon
OOOOHO
-
13
C
.
OWO
GROUP 26, “dg” as j; 16 words:
acknowledge
begrudge
0.0 2 0 bridge
6 0 12 0 cartridge
dodge
drudge
0 1 - 0 fledge
00:
00 fudge
grudge.
hedge
knowledge
ledger
pledge :
jo
ridge
sledge
wedge
low on doing on OHV DO NOWO
RONOOO ovoito C CO HONNNA
ܝܙ ܗ ܤ ܗ ܗ ܚ ܘܗ ܢܙ ܗ ܢܙ ܢܙ ܟܬ ܘܹܢܹܙ ܂1
loooonnoo hod OHHONO al 0 HOOOOOH
ܟ ܟܙ ܟ ܟܬ ܚ ܗ ܢܙ ܗ ܗ ܟ 7 ܗ ܟ ܢܝܙ ܘ ܟ | $
aloOoOHOOONO NA ONO ovlawin OOOOO
hand paid woN NO WA
1 ::.
1
1
0
.:1
291 591
GROUP 27, “gh” silent; 7 words:
:: 2
1 bough
60
blight
haughtily
plight
thought
through
0 tight
too
ܢܚܕ ܘܢܕܘܢܙ ܝ
05
olooooo oloooo Ho Toowo- olooo00oo w 1000 OHMOO0000000 100000000-
ܟ ܘ ܬ ܩ ܟܬ ܘ ܝܙ ܐ 8_
oloood
Ö ONN VON
O 1 One Owo
GROUP 25, "m's silent; 5 words:
0
..
ܟܬ ܤ
8
OOO
autumn
column
condemn
hymn
solemn
DONDOO
6
lowo
oloooo Dolcow OT Mod . oo low
1
1
GROUP 28,
bert
meaning direction; 4 words:
0
o eastern
northern
0
southern
western
1'
1
otoooo
o::adowo
ܐ ܝܕ
GROUP 29, "gh” as f; 5 words:
il
:
O
O
60
10000010
enough
laugh
rough
slough
tough
.
CON
0
:0
:1
olos
• is too
6) N
N
Ho 1o
in
CLASS B.
(NON-GOU UPING METHOD OF STUDY.)
. 22 Pupils in Class.
MISSPELLINGS
ERRORS
Prelim. Final Grouping Non-grouping
Test. Test. Prel. Fin. Prel. Fin.
CLASS A.
(GROUPING METHOD OF STUDY.)
28 Pupils in Class.
MISSPELLINGS : ERRORS
Prelim. Final Grouping Non-grouping
Test: Test. Prel. Fin. Prel. Fin.
GROUP 30, "head” as base; 6 words:
0
0 behead
0 deadhead
1 forehead
.0 'headache
headlong
hogshead
0
o
·
1
0
olooooo
olooooo
Col Wwoo
ܗ ܗ ܝܢ ܚܙ ܗ ܗ |ܫ
I WODOW
5
GROUPS
SUMMARIES BY GROUPS.
CLASS A, 28 Pupils.
CLASS B, 22 Pupils.
Words
Errors,
Words
Errors,
Missed. Grouping. Non-gr'ping. Migsed. Grouping. Non-grºping.
Prel. Fin. Prel. Fin. Prel. Fin. Prel. Fin. Prel. Fin. Prel. Fin.
78
54 3
60
44
21
99 10
87 14 74
55 12
11
No. of
GROUPS. words
in gr'p.
1. line ....... 4
2. que ....... 6
3. verd
4. "ch"
6. “ci”
50
1
43
35
27
Nov
6. geon
7. tyr.
4
8. "ti”
9. ant
10. cept
11. "ph"
12. graph
13. gyp ....
14. "BC"
15. "h"
16. eigh ..
17. sion
18. ies plur. .. 9
19. “ie" ..... 10
20. scio ...... 2
21. "y" sing...
22. "ea"
23. tion
24. "1"
25. “n”
26. “dg."
27. “gh"
28. ern ..
29. “gh” (1).. 6
30. head ......
0
6
at we are on Goor o co co co a vow on
NH CONDOOMOOOONOHA O oo w Ovo
OOOOHOOOA OHON A MOTH OR DO
1 WOOOWA W J WOONT COHNN COOW COO v
OOOOH
DONO
8
1772
2
160
0
980
0
66
8
1246
3
120
§
1177
4
282
i
728
Totals:
200
109
747
196
.
r
5.7
COMPARISON: I. OF SPELLINGS.
GROUP A (28 Pupils).
GROUP B (22 Pupils).
Preliminary. Final.
Preliminary. Final.
Total words to spell...
5600
6600
4400
4400
Total words mispelled........
1772
160
1177
282
Average mispelled per pupil...
63.3
63.5
12.8
Standing of elass..........
73.25% . 93.6%
That is, Class A rose from 68.36%, in the preliminary to
97:14% in the final test, and Class B rose from 73.25% in the
preliminary to 93.6% in the final test.
68.86%
97.14%
1.5
Class
Class
Linear Representation of Results
B
97.14
T
C
936 %
The results of the tests as expressed in percent-
ages are here shown in lines drawn on a similar scale.
Point B in each line represents the percentage
made in the Preliminary Test ; point C represents the
percentage made in the Final Test; distance B C
shows the gain made by each class.
Improvement for each class must be measured
from point B. Class A began its improvement lower
and ended higher, a fact thus made clear and con-
spicuous to the eye.
73.25 %
68.36
A-
No method of computing the gain having heretofore been pro-
posed, the following plan of comparison and computation is
adopted. As far as known, the two classes represent approxi-
mately children of the same average ages and of the same rela-
tive school advantages. It would seem therefore as if Class B,
having reached a higher mark in the preliminary test, must repre-
sent the better acquisitive power, in the ratio of 73.25 to 68.36.
According to the preliminary test, again, Class A had 100%
minus 68.36%, or 31.64% to learn; in the same way, Class B had
but 26.75% to learn. Here, then, is another inequality, and it
seems as if the chances of learning must be in proportion to the
16
quantity to be learned, or as if Class A's chances of learning were
to Class B's as 31.64 to 26.75. This ratio appears warranted by
the consideration of the fact that all the children study all the
words. Therefore the group having most words to learn has the
better chance to make gain or to learn words and to spell those
words correctly in the final test which were misspelled in the pre-
liminary test. Compounding these ratios, we get that-
Class A's rate of gain should be to Class B's rate of gain as,
68.36 to to 73.25, and as 31.74 is to 26.75. If we now assume
that B, being the group which uses the usual method, has a rate of
gain of 1, we get a compound ratio that-
A : B : A : B
:: 68.36 : 73.25
X : I 1 :: 31.64 : 26.75
which worked out gives, X equals 1.1, meaning that the rate of
gain in Class A must be 1. I times as great as that of Class B if it
is to show equal efficiency, and that whatever rate of gain greater
than 1.1 Class A may show represents the relative efficiency of
grouping as a factor in learning to spell.
The rate of gain of the two classes might be shown in each of
several ways, such as the percentage of improvement in the final
test, if the preliminary test be used as base, or in terms of what
seemed unknown in the preliminary test. The latter plan is used
here since that is the only process possible if a class start with an
entirely unknown mass of facts. To adopt the "unknown of
the preliminary test” as the basis for computing rate of learning
will give uniformity between investigations where parts of the
matter is known and those where none of it is known.
. Class A had 31.64% of the original list to learn after the pre-
liminary test, Class B had 26.75% to learn. As already shown
Class A improved its standing in the final test by 28.78%; this is
a rate of 91% of its unknown, of the 31.64% unknown. Class
B. improved its standing by 20.35%, or at the rate of 70% of its
unknown. A mere arithmetical difference here would show
Class A doing better by the difference between 91%, A's rate of
gain, and 70%, B's rate of gain, or 21% larger rate of gain in
favor of Class A.
If the initial difference between the classes, as already pointed
out and equated in the proportion of an earlier paragraph be
valid, however, we should compare the classes with all possible
inequalities eliminated. That proportion gave us the ratio of
1. I rather than as absolute equality, and means that to do as
well as Class B, Class A must show a rate of gain at least 1. I
times that of Class B. Now, Class B’s rate of gain was 70%.
Therefore to do as well as Class B, Class A must make 1.1 times
70%; or 77% of its unknown. Class A learned 91% of its un-
rate of 70% of it
gain, and sing better by the clical difference
17
known, which is 14% better than 77%, and which is just 20%
of B's own rate of gain better when all inequalities have been
eliminated.
To learn words grouped according to similarity of difficulty in
spelling thus seems about 20% better than the usual way,
whether the advantage be computed as an arithmetical ratio or as
an arithmetical difference. If this single factor of word-group-
ing thus adds 20% to the efficiency of teaching of spelling, it
should certainly be included in the arrangement of spelling lessons
of all kinds. Joining this unmistakable advantage as thus shown
by the comparison of the tests to what was so clearly foreshad-
owed by the daily lessons, it seems proved that,
THE STUDY OF WORDS ARRANGED INTO GROUPS ACCORDING TO
SIMILARITY IN SPELLING DIFFICULTY IS 20 PER CENT. BETTER
THAN THE USUAL NON-GROUPING METHOD OF ARRANGEMENT
AND STUDY.
II. COMPARISON OF ERRORS.
CLASS A (28 Pupils)
CLASS B (22 Pupils).
Preliminary Test. Final Test. Preliminary Test. Final Test.
1. 2. 3. 1. 2. 3. 1. 2. 3. 1. 2. 3.
Total % of Av. Total % of Av. Total •% of Av. Total % of Av.
No. of whole per No. of whole per No. of whole per No. of whole per
errors. No. pupil. errors. No. pupil.
Grouping...... 980 44 35. 66 35.6 2.36
Non-grouping.. 1246 56 44.5 120 64.5 4.3 747 51 34. 195 49.0 9
1
errors.
No. pupil. errors. No.
728
49
33.1
109
326
5
REDUCTION OF ERRORS:
CLASS A
CLASS B
Grouping, from an average of 35 to 2.36, or 93.3% : from 33.1 to 5, or 85. %;
Non-grouping, from an average of 44.5 to 4.3, or 90.4% : from 34.0 to 9, or 73.5%;
This shows the reduction per pupil for each class.
· The fact that Class A had 44% of its errors of the grouping
variety, and Class B 49%, in the preliminary test, shows that the
grouping according to difficulty had been made quite successfully.
As already stated, many words could quite properly have gone
into other groups of this set, and in an attempt to incorporate this
grouping idea into the arrangement of spelling lessons con-
sisting of words grouped according to spelling difficulty that is
what must be done.
The grouping errors were very considerably reduced in both
classes; this shows that Class B must quite regularly have
pointed out the group difficulty as “the place where you are likely
to make a mistake” while preparing to study the words...
In Class A the non-grouping errors increase from 56% in the
preliminary to. 64.5% in the final test, which shows very mark-
edly the good effect of the grouping for that kind of errors, and
also confirms the statement that words having more than one
difficulty must be studied in more than one group. In Class B
the reverse toak place. The non-grouping errors fell from 51%
18
to 49%. Apparently, the plan of having the children point out
the difficulty in the word occasionally brought out some other
than the group difficulty. The testimony of the teachers cor-
roborates this indication. This comparison by errors brings out
a fact which may be of great importance in the teaching of spell-
ing, namely, the pedagogical mistake of calling a word wrong
and deducting but one point of credit for each misspelled word,
without regard to whether there was one or more than one error
in the misspelling. Long standing practice and custom has es-
tablished it as the right way, but it is at least worth asking,
whether the desire to do well and to stand well in spelling would
not be helped if the pupil knew that it was possible to lose more
than one point for a misspelled word in case he made more than
one mistake in it. Great difficulties would be encountered in at-
tempting to apply such a method, as, for instance, shall we count
the literal or the phonic errors? or, how shall we count omitted
words? It seems probable that to count each word wrong as one
point wrong being both easy to apply and having high practical
value, may, therefore, be tolerated. Just as an example in an
arithmetic test may be right “in principle” but wrong in compu-
tation, and therefore is refused full credit, so it would seem un-
fair to pupils who misspell words by but a single letter to suffer
as much loss of credit as do pupils who have two or three errors
in each misspelled word. Because the problem seems difficult is
no reason for dismissing it, however. If one plan of marking
and counting mistakes will arouse a more earnest and a higher
pitch of effort to secure sustained excellence in spelling, that
method should be developed as soon as possible. The act of
calling the attention of the child to the particular difficulty which
the word presents to him is certainly the first step toward'helping
him conquer that difficulty. It is doubtful whether we do that
in our present way of marking and counting errors.
III. INCIDENTAL RESULTS.
As a matter of curiosity it will be worth while to state that four
words were not missed in either test; they are direction, laugh,
neighbor, weight. There were seven words not missed at all in
the first test, and 54 words not missed at all in the final test. A
remarkable fact came to light in tabulating the errors for the final
test. It was discovered that in both classes there were mis-
spellings of words in the final test which had been spelled cor-
rectly in the preliminary test. In Class A there were 53 such
misspellings and in Class B there were go of them. Mere mass
statistics could not have disclosed this fact. It came to light only
when a record was compiled showing each pupil's work for each
word in the preliminary and in the final test. Just what is the
significance of this fact ?
-----
--
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
19
verage the san the wor vali
iminaten av and the ato
Evidently that guessing was present in the preliminary test;
that the 28 pupils guessed right on 53 words in the preliminary,
and wrong in the final; the 22 pupils guessed right on 90 words
in the preliminary test, and and wrong in the final test. While it
may be true that some of the mistakes in the final may have been
mistakes of incoördination, yet on the whole the figures indicate
the error that may creep into investigations of this kind by as-
suming, as is often done, that "the errors in the one group will
offset the errors in the other," or, that in either group “the correct
and incorrect guesses will offset each other.” This could be
true only in cases where the chances of error and of correctness
were exactly even. That is, if there were but one wrong and one
right way to spell a word. Since there is but one right way, and
since there are innumerable possibilities of getting it wrong, the
chances are very uneven, and the assumption of offset is not to be
admitted. Scientific investigation must get the facts. In this
investigation the 28 children averaged a trifle less than 2 right
guesses in the preliminary test, and the same wrong guesses in the
final test: the 22 children averaged a little more than 4 right
guesses in the preliminary test and the same wrong guesses in the
final test, and this after having studied the words rather inten-
sively. It would certainly be interesting and valuable to find
what would appear if there were no study of words or matter be-
tween two tests.
While this number of children was small, only fifty in all, it
does not seem reasonable to suppose that it would equalize itself
if the number were larger, say 1,000 or 10,000. The real wrong
of the assumption is not that an equal number of children may be
uncertain and guess; for the sake of the argument that may be
conceded, just as we concede the insurance man's claim that so
many people out of a thousand of a given age will die in any one
year. If true, however, the difficulty, whether in spelling or in
arithmetic, comes from assuming that those who guess or err
have just as many chances to be right as to be wrong !The chances
of error are greater than the chances of right, entirely independ-
ent of the number of children that do the guessing. In is the fact
of hundreds of chances of wrongness to the one chance of right-
ness that decides the matter in favor of error.
XI. WORDS CORRECTLY SPELLED IN THE PRELIMINARY TEST
BUT MISSPELLED IN THE FINAL TEST.
The table showing such variation in misspelling is included for
reasons that will appear presently.
T
*
!.
.
20,.
.
CLASS B
CLASS A
MISSPELLINGS.
In the Final Test.
Same words Different
as in words from
Prelim. Test. Prelim. Test.
In the
Preliminary
Test.
75
Individual
pupils in
numerical
order.
MISSPELLINGS
In the Final Test.
In the Same words Different
Preliminary as in words from
Test. Prelim. Test. Prelim. Test.
38
74
*********** ******
115
57
79
103
The No. of
several pupils
numbers of missing
diff. errors. this No.
SUMMARY:
CLASS A
TOTAL MISSPELLINGS.
No. of
Final Test.
pupils
Prelim. Same Different missing
Test. words. words. this No.
404
514
12
256
CLASS B
TOTAL MISSPELLINGS.
Final Test.
Prel. Same Different
Test. words. words.
97
162
208
13
od Act
44
138
-..on
333
OH OH O
vaatwa
10
.
103
35
84
90
150
09
50
65
14
1.9
AVERAGES FOR EACH GROUP OF "NUMBERS OF DIFFERENT WORDS MISSED IN FINAL”:
57.7
32.3
2.0
51.4
1.2
40.5
3.3
- 85.3
3.0
52.0
8.0
44.0
2.0
68.0
83.3
10.3
54.0
10.0
103.0
16.0
57.0
4.0
74.0
2.0
35.0
4.0
84.0
12.0
90.0
23.0
75.0
22.5
6.0
oo wo or HA CONDO
FURTHER CONSIDERATION OF THE VARIATION.
There seems no discoverable relation between initial correct
spelling and the likelihood of misspelling words in the final test
that were not misspelled in the preliminary test, which shows the ---
l
21
presence of the factor of guessing. It might be supposed that the
poorer spellers do most guessing, but the records hardly bear out
this supposition. Thus, pupils No. 2 and No. 27 in class A both
misspelled 74 words in the preliminary test. Pupil No. 2 missed
none in the final, but pupil No. 27 missed 8 in the final, 6 of
which he had not missed in the preliminary test. Pupil No. 2
certainly did less, or perhaps better, guessing than pupil 27.
Again, the group missing 6 different words in Class B had an
average misspelling of but 35 words in the preliminary rest,
which was the next to the lowest average of any group in either
class, and very much lower than the o group in Class A, which
had an average of 57.7 in the preliminary test.
The chances of correct guessing and of incorrect guessing in
such work as this can be worked out actually for these two groups
of children. In Class A, 7 pupils missed only words in the final
which had also been missed in the preliminary, and 21 missed dif-
ferent words in the final. Correct guessing, if present, seems to
have hit it in proportion of I to 3. The 21 pupils missed 53 such
words, or an average of 2.52 errors per pupil. If among the
pupils the proportion was I to 3, and each pupil making an error
made 2.52 errors, the chances of correct to incorrect guessing
that actually materialized here were 3 times 2.56 or 7.68 to
every correct guess. In Class B, the chances among the pupils
are 3 correct to 19 incorrect, or 6.33; now the 19 pupils missed
90 words, an average of 4.74 words each. Since 6.33 times
4.74 equals just about 30, we have here 30 chances of error to I
of correctness that is actually realized. Thus the assumption of
correct and incorrect guessing on the part of contrasted groups of
children, or between contrasted methods, is shown to be entirely
untrustworthy and unscientific. The incorrect guesses of the
one group certainly did not offset those of the other. The Class
B, which were the better spellers at the start, make almost twice
as many such errors as Class A. Incidentally, this constancy,
whether positive knowledge or merely a keener guessing power,
seems to further show the advantage of the grouping method of
study, since Class A had much the smaller percentage of such
errors.
XII. VALIDITY OF PRELIMINARY TEST.
This variation very certainly casts doubt on the absolute de-
pendence upon the results of the preliminary test as measuring
the point from which advance is made. If the preliminary tests
were corrected for each of the two classes, Class A would lose
1% of its preliminary standing, and Class B about 3%. No
correction of the results has been made to incorporate these va-,
riations. The final test would certainly show some variations,
22
.
therefore the results are presented with this mere statement of the
fact that a trifling variation is present. This is probably the as-
tronomer's "personal equation.” It may be of value, however,
to suggest that some future investigation should be made to as-
certain, if possible, what is the percentage of variation that must
be allowed in preliminary tests. It is of course greater than in
final tests after teaching and drill on a subject. Its approximate
value can be cletermined by several trials of a test with the same
groups of children, and will be a valuable factor to know in all
experimental pedagogical work.
XIII. THE EFFICACY OF THE RESPECTIVE GROUPS OF WORDS.
Besides the value which this investigation may have in the light
it throws upon "grouping vs. non-grouping” as a method of
study, an analysis of the effectiveness of the several kinds of
grouping here resorted to may be of value in suggesting the
kinds of grouping to use in the method, since not all the groups
appear to have been equally effective. Therefore, the following
table of results in Class A, the children who studied by the group-
ing method, will indicate whatever efficacy any group had.
THE COEFFICIENT OF EFFICIENCY OF GROUPING.
It seemed desirable to compare the respective groups with each
other as to efficiency; to do so, a standard must be fixed, and a
method of comparison worked out which should resolve itself
into a single amount or number, indicating efficiency as com-
pared with the standard group. Since original and final status
should appear in the computation, the following method of com-
puting the coefficient was decided upon.
An inspection of the entire 30 groups showed two very de-
·sirable qualities inherent in the results for group 17. First, it is
almost the methematical median of the entire 30, and second, in
the final test all its words were spelled correctly, so that its effi-
ciency is 100%, which means that all was learned that could be
learned in that group. This group having been fixed upon for
the standard, the average number of misspellings of the words in
the group in the preliminary test was found, and it was 8.33 :
this then was treated as the standard of difficulty of the words,
and the comparative difficulty of the words in any other group,
for these 28 children, of course (and not for the world in gen-
eral) was found by dividing the average misspellings in any
other group by this 8.33. Thus, group 2 it will be seen has an
average of 16.5 misspellings, which means, according to the
comparison here proposed, that the words of group 2 were twice
as difficult at the start as those of the standard group-group 17:
this becomes one factor of the coefficient of efficiency.
23
.90%
Next, the percentage of improvement in each group must be
compared with the percentage of improvement in the standard
group: out of these comparisons, a compound proportion grows
which is easily resolvable, and workable by a simple rule. Group
2 showed an improvement of 90%, and if we compare groups
17 and 2 we get this proportion:
Av. Misspell. Improvement.
Group 2................ 16.5.
" 17... ............ 8.33
100%
If group 17 be now called an efficiency of 1, what efficiency has
group 2 shown? Here is the answer:
X:1:: 16.5 : 8.33
90. : 100, which may be simplified into this
X:I:: 2:1
9:1, which yields us the result-
x=1.8, as the efficiency of group 2, and also the simple
rule that degree of difficulty multiplied by the decimal ratio of
their percentages of improvement will yield the coefficient of effi- .
ciency. It is by this method and by this rule that the coefficients
of the following table were computed:
Group.
Gain.
%
94.84
90.
78.
16.
88.2
89.
87.6
86.
Coefficient
of efficiency.
2.22
1.79
1.5
1.7
1.66
1.53
1.42
1.44
1.36
1.32
1.09
1.13
1.01
1.56
1.53
1.06
96,
93.
93.
87.95
92.15
86.2
.75
AVERAGE MISSPELLING.
Preliminary.
Final.
19.5
• 1.00
16.5
1.80
16.
1.75
1.98
15.5
1.75
14.6
1.8
14.
2.
12.5
.5
12.14
1.4
11.85
1.2
10.38
1.25
10.2
.8
97
(8.87
1.33
8.8
.00
8.33
.00
8.11
1.00
7.7
6.5
6.45
1.11
6.
5.6
5.11
4.8
1,2
4.63
4.14
1.75
1.4
1.33 .
91.7
4
95.5 V
100
8.8
100
87.52
1.
78.
92.3
86.1
100.
78.1
96.
75.
.43
bone
.55
98.65
89.9
43
87.
It may be of interest, and even of added value, that the group
chosen as standard has an average of misspellings, almost equal
1
24.
N
.
...
."
13
.
.
11.11
.
1V+. ..-.'
to that of the average of misspellings of the entire list, which is
8.86, or just about the same as group 14. -
It appears that both the most and the least effective group is •
etymological, that is group 1, with a coefficient of 2.22, and
group 30 with a coefficient of .12. Groups 18 and 21 offer a
striking contrast: Group 18, the nouns ending in "y," singular,
preceded by a consonant, for whose spelling there is an easy rule,
is .85, and for group 21, the singulars of the same nouns, for
whose spelling there is no rule, the coefficient is but .66. Seem-
ingly, here is another corroboration in favor of the study by
ingly, here is anoth to spelling difficultyjad little or not
O
The size of the groups seems to have had little or nothing to do
with the efficiency; group 4, with 11 words, is more efficient than
group 5, with 4 words. The etymological groups clearly do not
show a marked higher efficiency, for they are found scattered
quite evenly throughout the table, in places 1, 3, 10, 12, 17, 20, 28,
30. Since most of the other groups wëre phonetic or the equiva-
lent of phonetic, the same conclusion must be drawn for that
kind of grouping. It seems probable, however, that with older
pupils there might have been evidence of higher efficiency of the
etymological grouping, since that appeals to reasoning as well as
to analogy of literal form. In sixth grade children this form of
comparison and association is just beginning to show itself. The
earlier habits of the children were at least as strong as the factor
which the investigation was bringing consciously into opera-
tion in their study. Group 26, the largest group in the lot, con-
taining 16 words, is near the end of the list, with an efficiency of
.55. Group 23, with 12 words, shows an efficiency of but .52.
In both cases, however, it is not the size of the group, but the in-
effective grouping that is the cause. In both groups, the group-
ing errors are but a small part of the actual errors, which once
again emphasizes the necessity of including the same word in
different groups according to the number of difficulties of actual
spelling which it contains.
XIV: SUMMARY.
1. Preliminary Tests are not absolutely but only approximately
correct as a point from which to measure improvement due to a
method of instruction.
X : 2. Grouping words into lessons according to spelling difficulty
is better than the ordinary plan of spelling lessons. It secures
better daily lessons, better final results, and greater steadiness or
constancy of correct spelling.
3. Computation of gain or improvement should be upon the
basis of the "unknown" in the preliminary test, so as to secure
comparable results from all experimental investigations.
25 .
1
4. A word should be grouped with as many separate groups as
it contains real spelling difficulties. In any one group this
• focuses the attention upon but one difficulty, making mastery of
that more probable, and in the end all its difficulties will be mas-
tered.
5. It is not safe to assume that variations to right and wrong
"offset" each other in large numbers of children, unless the
chances of error and of correctness are exactly equal. Where
the chances of error outnumber the chances of correctness, even if
the average number of guesses on the two sides be equal, the
errors will outnumber the correct variations.
6. Grouping shows its effectiveness by every test to which we
submit the figures, even among the groups themselves.
7. A coefficient of efficiency for the matter of instruction can
be found by adopting a standard mass or unit, and then, through
the results of a preliminary test, ascertain the relative difficulty
Cf other units or masses, and multiply this ratio of difficulty by
the ratio of improvement between the standard mass or unit and
any other unit, as shown by the final test.
8. Is our present plan of counting each. misspelled word as but
one wrong, regardles of the number of errors it may contain,
conducive to the highest efficiency of method in spelling? Would
not the counting of the actual errors, by calling attention to each
error specifically, result in having most effort applied at the point
of greatest resistance?
9. A method is proposed to equate original difference of groups
of children, so as to secure a basis for comparison of contrasted
methods. The rates of gain should be to teach each other as the
percentages of standing in the preliminary test, and also as the
percentages of “unknown” in the preliminary test. Equating the
percentages of the preliminary test equalizes acquiring power, and
equating the unknown of the preliminary test equalizes the chances
of learning. This applies only to tests where the entire field or
Lody of matter comprehended in the preliminary test is also cov-
ered in the teaching or learning of the two contrasted groups.
This method of computing enables us to show what one class
should do in terms of the other, thus giving us a ratio of com-
parison before final results are known. Prediction of the result
thus becomes possible with a high degree of probability of its
approximate tendency in the right direction.
10. THE STUDY OF WORDS ARRANGED INTO GROUPS ACCORD-
ING TO SIMILARITY IN SPELLING DIFFICULTY IS 20. PER CENT.
BETTER THAN THE USUAL NON-GROUPING METHOD OF ARRANGE-
MENT AND STUDY.
26
Gaylord Bros.
Makers
Syracuse, NY.
PAT. JAN. 21, 1908
UNIVERSITY OF MICHIGAN
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DI AULA ILLUMINATION
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