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mentally with three-place numbers continuously, for two to twelve
hours with Miss Whitley's ('11) subjects who did three similar
problems a day for twenty days. The outcome was in favor of
the distributed practice, but probably only slightly so when allow-
ance is made for the effect of fatigue in the continuous work.

In general, relatively short periods of work in simple associative
learning are probably the most economical. It would be unwise
in the absence of more extensive experimental studies, to generalize
to all types of learning and particularly to the learning of school
subjects. What the most productive periods for learning reading
or spelling or Latin or English composition are, will have to be
determined experimentally in each case. All that we can say at
present is that each type of learning probably has its optimum
length and distribution of practice periods. Lyon has stated the
matter in the following manner as a result of his studies on this
problem:

"With reference to the problem of the most favorable distribution of
single reading. ... I would say that the most general statement that
can be made, taking all materials and methods of presentation into con-
sideration, is that the most economical method is to distribute the read-
ings over a rather lengthy period, the intervals between the readings
being in arithmetical proportion. For example, with one individual, in
memorizing a poem of twenty stanzas, the highest retentiveness was
obtained by distributing the readings as follows: two hours, eight hours,
one day, two days, four days, eight days, sixteen days, thirty-two days,
etc. The practical bearing of the results obtained on education in general
is that when associations have once been formed, they should be recalled
before an interval so long has elapsed that the original associations have
lost their color and cannot be recalled in the same shape, time, and order.
In general it was found that the most economical method for keeping
material once memorized from disappearing was to review the material
whenever it started to fade. Here also the intervals were found to be,
roughly speaking, in arithmetical proportion. /For similar reasons the
student is advised to review his lecture notes shortly after taking them,
and, if possible, to review them again the evening of the same day^ Then
the lapse of a week or two does not make nearly so much difference.
When once he has forgotten so much that the various associations orig-
inally made have vanished, a considerable portion of the material is
irretrievably lost." ('13, p. 161.)

b. Forgetting. Learning is, in a certain sense, a fortification
against forgetting, and from the practical side, it is important to



THE RATE AND PROGRESS OF LEARNING



157



know how frequently and in what manner the fortifications should
be strengthened in order to resist the attacks of forgetting. Only
a few experimental studies have been made on the rate and factors
of forgetting. Ebbinghaus ('85) learned nonsense syllables until
he could give them once correctly, and then measured the rate of
forgetting by the amount of time required for relearning them at
different intervals after the original memorizing. Radossawlje-
witch ('07) used nonsense syllables and poetry, Bean ('12) used
series of letters, and Magneff ^ used poetry. The curves of for-



100

90

80

70

,60

■^50

u

Uo

30
20
10



k






tbed curved




' ' ' ' '



5 10 15 20 26 30 35 , 40

Days

Fig. 47. — Curves of forgetting.

getting obtained by these investigators are presented in Figure 47.
They agree in showing a very rapid rate of loss at first, followed
by a very gradual decline afterwards. In retaining syllables,
Ebbinghaus found that he forgot as much in the first twenty min-
utes as in the following thirty days; in remembering a poem which
had been learned to the point of two perfect repetitions, Rados-
sawljewitch found that his subjects forgot as much in the first
two days as in the next twenty-five days.

Inquiry into the rate of deterioration of connections through
lack of practice have also been made by Book ('08), Rejall,^ Swift

^ As reported by Radossawljewitch.
^ Reported by Thorndike, II, p. 309.



158 EDUCATIONAL PSYCHOLOGY



and Schuyler ('07) in the case of typewriting, and by Swift in the
case of tossing balls. These seem to indicate much greater per
manency in sensori-motor connections than in the memory of syl-
lables or poetry.

The experimental work on forgetting is too limited as yet to
permit of much definite application in the practical procedure of
learning school material. The one suggestion that may possibly
be made would be this: Since the rate of forgetting is very rapid
at first and more gradual later on, it probably would be highly
advantageous to have relearning of a given material come very
frequently at first and more rarely later on. Thus the facts of a
lesson in history or the newly acquired words of a spelling lesson
should be reviewed the next day or perhaps preferably on the
same day, then again two or three days later and then a week or
ten days later, and so on.

The effect of long vacations upon the retention of school material
has been investigated only partially. Measurements of skill in
arithmetical operations in June and September show heavy losses
(see page 403) and raise the question as to whether long vacations
are really profitable or detrimental.

c. Concentration, Effort, and Zeal. "Practice makes perfect,"
is only a half truth. Only practice with zeal and effort is likely to
bring improvement. A great deal of practice and repetition may
continue day in and day out without the slightest gain. While
the factor of zealous attention and interest has long been recog-
nized as a matter of common-sense observation, its real value,
however, has never been appreciated until experimental studies
pointed out its actual significance. Bryan and Harter have called
attention to this point in a very emphatic manner as follows:

" A fact which seems to be highly significant is that years of daily prac-
tice in receiving at ordinary rates will not bring a man to his own max-
imum ability to receive. The proof of this fact is that men whose re-
ceiving curve has been upon a level for years, frequently rise to a far
higher rate when forced to do so in order to secure and hold a position
requiring the higher skill. That daily practice in receiving will not
assure improvement is further seen in the fact that in many cases in-
ferior operators after being tolerated for years are finally dropped be-
cause they do not get far enough above the dead line. One conclusion
seems to stand out from all these facts more clearly than anything else,
namely, that in learning to interpret the telegraphic language, it is in-
tense effort which educates. This seems to be true throughout the whole



II



THE RATE AND PROGRESS OF LEARNING 1 59

length of the curve. Every step in advance seems to cost as much as the
former. Indeed, each new step seems to cost more than the former. In-
quiry at the telegraph school and among operators indicates that between
si.\:ty and seventy-five per cent of those who begin the study of telegraphy
become discouraged upon the plateau of the curve just below the main-
line rate. As a rule, ordinary operators will not make the painful effort
necessary to become experts. Facts of an analogous character will be
recalled from other fields.

"The physiological, psychological and pedagogical implications of this
conclusion are manifestly important. If in our educational methods in
the past, we have often made the pace that kills, there is possibly the
danger on the other hand that we shall make school work all play, and so
eliminate the intense effort which is necessary for progress." ('97, p. 50.)

A great deal of learning is done without any real zeal or effort
toward improvement. The usual way in which a great many
children learn to play the piano illustrates how much practicing
and learning consists in dawdling with more attention upon the
clock than upon the music sheet. A great deal of learning of school
material is done with the same lack of interest and effort.

d. Specific Practice in the Functions to be Improved. One of the
striking discoveries of experimental investigations is the very
rapid progress in specific functions when the practicing is done on
the particular connections to be established. A surprisingly large
percentage of pupils make little or no progress in an entire year's
work in such subjects as reading, writing, and the like, while the
remaining pupils make only a part of the progress that they could
make if their efforts were squarely directed at the material to be
learned or at the associations to be established.

The numerous practice experiments that have been conducted
in psychological laboratories during the last two decades furnish
overwhelming evidence of the tremendous improvement ob-
tained under experimental conditions. Only a few examples will
be cited.

The writer found that eight persons, practicing mental multi-
plication of three-place numbers by one place-numbers for about
15 minutes a day for 14 successive days, made enormously large
gains as shown in the following table:



i6o



EDUCATIONAL PSYCHOLOGY



TABLE 40
Improvement in mental multiplication. After Starch ('11)



Individual


Examples Done

PER 10 MiNuriiS

ON 1st Day


Examples Done

PER 10 Minutes

ON Uth Day


Gross Gain


Percentage
Gain


s

St

F

V


25

37-7

23.8

41.7

14.7

37

25

23-4


62.5
81

45-4
71-4
29
100
29.8
66


37-5
43-3
21.6
29.7
14-3
63
4.8
42.6


150

115

91

71

97

170

19
182


w

H

Si

B



These subjects gained in approximately four hours of practice
per person over 100%, varying, of course, from one person who
made Httle gain up to two persons who gained nearly 200%.

Wells found the amounts of gain from 150 minutes of practice
in addition on the part of ten adults as follows:



I



TABLE 41
Improvement in addition: adults. After WeUs ('12)



Individual and Sex


NuMisEB OF Additions in Five Minutes


Percentage which

Amount Done on 30th

Day was of Amount

Done on 1st Day




First Day


30TH Day


Gross Gain


if


150
180
200
220

225
22s

23s
250
260

2QO


280
380
430
380
368
460
570
440
540
540


130
200
230
160
143
235
335
190
280
250


187

211

21S

173 1

164 1

204

243
176
208


2 m

3 m

4f


cm


6 m

7f

8f

of


10 m


1 86



The gains show approximately a doubling in efficiency in the
course of thirty days.

Dearborn used vocabularies and poetry in learning experiments
and reported the following results :



I



THE RATE AND PROGRESS OF LEARNING i6l

TABLE 42
Improvement in ability to memorize. After Dearborn ('10)

Total Prac- Amount Number of Total Time Re- Time Re-
Subject TiCE Time Learned Days of Amount quired on quired on
IN Hours Daily Practice Learned P'irst Day Most Effi-
cient Day
Learning the English meanings of French or German words:

1 61/3 50 21 1050 30 13

2 6 35 20 700 30 12

3 6 35 18 630 30 14

4 81/10 30 22 660 S3 15

5 72/3 30 20 600 40 15

I^earning poetry:

7 31/3 32 15 480 38 7

8 32/3 18 16 288 30 8

10 4I 17 13 221 30 12

Similar results have been reported by Bair in tossing shot, by
Swift and Batson in tossing balls, by Whitley in drawing lines in a
maze, by Wells in tapping, by Kline, Wells, and Whitley in can-
cellation tests, by Thorndike, Wells, and Kirby in adding, by
Swift, Book, Rejall in typewriting, by Ebert and Meumann,
Winch, Sleight, Dearborn, and Fracker in memory — in fact in all
experimental work in which practice enters. Improvement of
mental functions through practice is well-nigh universal and the
amount of improvement through specific training under experi-
mental conditions is almost incredible, particularly when we con-
trast with it the gains made in school functions in from 50 to 150
hours devoted to a subject in the course of a year.

The average gain made by pupils in school activities in the
course of a year's practice as indicated by the standard scores
derived from measurements with tests and scales is shown in the
following percentages of gain at the end of the eighth grade as
compared with the end of the seventh grade:

' Approximate.



l62 EDUCATIONAL PSYCHOLOGY

TABLE 43
Based upon published scores for the various tests



Reading: speed, words jier second

Reading: comprehension, words written.

Writing: speed letters per minute

Writing: quality, Thorndike scale

Addition: Courtis Series B — rights

Subtraction: " " " "

Multiplication: " " " "

Division: " " "

Reasoning: Starch Arith. Scale A

Language: Starch Gram. Scale A

Composition: Hillegas Scale



Per Cf.nt
Gain



7TH


s™


3-6


4.0


45 -o


50.0


75-0


83.0


10.4


10.9


6.5


8.0


8.5


10.0


6.5


8.0


7.0


9.0


II .0


12.6


8.0


S.3


41.0


46.0



5

23
17
23
28

IS
4



These gains arc surprisingly trivial when compared with the
gains, often running over 100%, reported in connection with
experimental investigations of practice.

Definite experimental results are not at hand to substantiate
the following assertion, which may seem doubtful but which is
not impossible from the present indication of other measurements,
such as those presented by Dearborn in Table 42 or by the writer
in Table 9 (Experiments), namely, that the average high school
pupil could learn in 20 minutes a day for thirty days, all the Latin
words (500 words) that he would need in an entire year of Latin.
He could learn in 30 minutes a day for one-half the school year,
all the Latin words (approximately 2,000) that he would use in his
entire study of four years of high school Latin.

The difficulty with the material of school subjects is that we do
not, and in some instances we cannot, specify with sufficient def-
initeness just wherein the improvement is to be made. We can
point out specifically to a child whether or not he spells a word
correctly and what part of the word may be incorrect, but we have
not until recent years made any attempt at determining which
particular words a child really ought to know how to spell. The
pupil was given a Hst of words selected more or less on the basis
of their unusualness and difficulty rather than upon the basis of
usefulness or frequency of occurrence. The idea seemed to be that
if he learns to spell a sufficient number of difficult and useless words,
he will know how to spell all other words in the English language.
The school has virtually said, "Learn to spell," but has not said



l\



THE RATE AND PROGRESS OF LEARNING 163

what a child should learn to spell. Even in a subject in which the
associative bonds may be precisely defined so that they can be
directly attended to, we have not done so. The same situation
obtains in practically all other subjects with the added difficulty
that in some subjects the material is of such a nature that specific
directions and specific material or specific bonds to be formed,
cannot easily be isolated. This is particularly true of such a sub-
ject as English composition which represents the opposite extreme
from spelling and arithmetic. The child is told to improve his
style, or his language, or his expression, or his originality, or his
imagination; but he is not told very definitely how he may do this,
or just what he is to do. The school should, therefore, aim to
specify exactly what sort of learning is to be done so that a definite
notion on the part of the learner may be formed of the precise bonds
and connections to be made.

e. Definite Knowledge of Success and Error. Much experimental
work implies that the feeling of satisfaction resulting from success-
ful trials of a task facilitates the formation of the connections con-
cerned. It seems obvious therefore as a practical matter that pre-
cise knowledge of the success or failure on the part of the learner
is exceedingly important. It will not only serve to arouse the
feeling of satisfaction but also help to define the particular bonds
to be established. Feelings of dislike on the part of the learner
toward the material to be learned undoubtedly interfere with the
rapid formation of the connections, and frequently the feeling
of dislike is accompanied by an attitude of unwillingness or stub-
bornness indicated by such statements as "I know I can't learn
languages; I never could." "I never was able to get mathematics."
"I can't memorize anything." A concrete case that came under
the writer's observation was that of a man considerably older than
the average university student, who in the experiment on the trans-
ference of training (Chapter XI, Experiments in Educational
Psychology) reported that he was unable to learn vocabulary and
that the net result of half an hour's work on the first list was ten
words. The average student is able to learn the entire list of thirty
words in from twelve to fifteen minutes. He further stated that
he had always had great difficulty in learning languages. In order
to ascertain, if possible, the real status of his memory and other
abilities, he was tested by Terman's revision and some additional
tests, all of which indicated that he was of average intelligence and
that his memory was not defective, but approximately average.



164 EDUCATIONAL PSYCHOLOGY

He was informed of the results of the tests, that his defective
memory was largely illusory, and that probably his real trouble
lay in his contrary attitude toward certain tasks, which was also
indicated by his own statements concerning his work. The general
effect upon his later attitude in learning was a distinctly whole-
some one. This case is cited because it exemplifies many similar
instances of persons who feci incapable of learning certain things.

/. Interest in Improvement. One important element in the re-
markably large amount of gain through practice in specific func-
tions, is the fact that the progress is directly observable and
definitely measureable which in turn produces a real zeal toward
improvement and toward outstripping the preceding records.
In an experiment such as the substitution test or the practice ex-
periments in arithmetical operations, the observation of a definite
gain is possible so that the learner can see just how much progress
he is making. The practical value of this suggestion would be the
creation of circumstances for the learning of school subjects similar
to the conditions of learning in laboratory experiments by intro-
ducing forms of measurement through which the progress may be
determined at frequent intervals, so that the pupil may see what
progress he is actually making.

In a certain elementary school a series of standard tests ^ was
applied every month throughout the entire school year. Tests in
reading, writing, spelling, and arithmetic were given at monthly
intervals to determine the progress made. Each pupil knew his
own record in each test and compared it from month to month.
This condition developed a remarkable interest and zeal in striving
to surpass the record of the preceding month. The condition
created thereby was similar to that of a learning experiment under
laboratory conditions. Each pupil kept his own score and knew
what gain he was making each month. This condition had a re-
markable effect upon the total progress made during the school
year as shown in the accompanying graphs. These results show
that the pupils made on the average a gain in some studies
twice as great as that made ordinarily in the course of a school
year. This gain cannot be attributed to familiarity with the test
material since, in the case of reading, different passages were used
in each successive test; in writing, a different sentence was used

1 The tests were made in The Alice School, Hibbing, Minnesota, by Principal L. J.
Coubal, and reported in an unpublisjjed thesis in the library of the University of Wis-
consin. The tests were carried out under the direction of Professor V. A. C. HenmoQ.



THE RATE AND PROGRESS OF LEARNING



i6s



each time; in spelling, the author's six lists were used in rotation,
one at a time; and in arithmetic the three sets in the Courtis Series
A were used and rotated so that there was a recurrence of the same



40



30



20



10






Sept. Oct. Nov. Dec. Jan. Feb. March April May
Fig. 48. — Progress in speed and comprehension of reading combined into
single scores as measured by monthly tests (Starch reading tests) upon 4th grade
pupils. The continuous curve represents the progress of the class. The straight,
broken line is the progress for schools generally based upon the standard scores
for June of the 3rd grade and June of the 4th grade.

test every three months, but it is very unlikely that this contributed
any appreciable share toward the gain shown. It would seem,
therefore, highly desirable if there could be introduced into the
schoohroom a similar atmosphere of motivation such as obtains



40
30


























y






;;r_-






^-





\^








20
10


— "



















Sept. Oct. Nov. Dec. Jan. Feb. March April May

Fig. 49. — Progress in speed and quality of writing (Thorndike scale). Other
facts same as for Fig. 48.

in learning experiments in the laboratory. The knowledge of one's
actual ability and of the actual amount of gain serves as an ex-
ceedingly powerful spur for the learner to surpass his own previous
performances. The popular dictum "Nothing succeeds like sue-



i66



EDUCATIONAL PSYCHOLOGY



cess" may be partly justified by such experimental results as the
ones here cited. To see oneself gaining tends to stimulate greater
efforts toward gain. The educational measuring scales and tests



fiO
40
30
































y






.^







-^






20



















Sept. Oct. Nov. Dec. Jan. Feb. March April May

Fig. 50. — Progress in spelling (Starch test) of 3rd grade class. Other facts
the same as for Fig. 48.

ought to serve a useful purpose at this juncture. They will pro-
vide means whereby the pupil may be able to see for himself in
definite terms the gains he is making.




Sept. Oct. Nov. Dec. Jan. Feb. March April May

Fig. 51. — Progress in the fundamental operations in arithmetic (Courtis
tests). Other data same as for Fig. 48.

g. Mental Imagery. After the early studies on mental imagery
became known, there followed considerable theorizing as to types
of persons and types of learners, and with it came the resulting



THE RATE AND PROGRESS OF LEARNING 167

endeavors to make applications of these theories to methods of
teaching. Thus it was said that if a pupil has difficulty in learning
to spell or in learning a foreign language he may be devoid of, or
weak in visual imagery; or if he has trouble in learning to write,
he may be short on motor imagery; or if he finds it hard to learn
the pronunciation of words, he may be defective in auditory and
motor imagery; and if he fails in the academic subjects he was sus-
pected of being devoid in visual and auditory images and strong
in motor imagery and should therefore turn to manual training.
The proposed remedy was that the material to be learned should
be presented to a different sense organ so that the pupil might use
the imagery natural to him. All these inferences may possibly
be true; but later additions to our knowledge of mental images
make us more hesitant regarding the real part played by them in
learning and concerning the actual differences produced by present-
ing material to different sense avenues.

Before we can make changes in practice we must be sure of the
principles upon which the practice is to be based. It is important,
therefore, to examine at least the following three considerations:

In the first place, more careful studies of the sorts of images
employed by different individuals show that the classification of
persons into visuals, audiles, motiles, and so on, is fundamentally
misleading. Studies by Betts ('09) and others have helped greatly
to clarify the matter by showing that pure types rarely exist.
During the last six years several hundred students have performed
the imagery tests outlined in Chapter VII of the author's Experi-
ments ('17). Among this entire number not more than two or three
persons were found whose images either were practically all of
one type, or who had one or another commonly prevalent class
almost entirely missing. The facts for 95% of all persons are sub-



Online LibraryDaniel StarchEducational psychology → online text (page 13 of 41)