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How to Teach by George Drayton Strayer and Naomi Norsworthy

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Quality 14.

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Quality 15.

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Quality 16.

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Quality 17.

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Quality 18.

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* * * * *

This table reads as follows: Quality four was written by five children
in the second grade and two in the third grade, quality five was written
by twenty-two children in the second grade, two children in the third
grade, three in the fourth grade, three in the fifth grade, none in the
sixth grade, one in the seventh grade, and none in the eighth grade, and
so on for the whole table.[24]

A scale for measuring ability in spelling prepared by Dr. Leonard P.
Ayres arranges the thousand words most commonly used in the order of
their difficulty. From this sheet it is possible to discover words of
approximately the same difficulty for each grade. A test could therefore
be derived from this scale for each of the grades with the expectation
that they would all do about equally well. There would also be the
possibility of determining how well the spelling was done in the
particular school system in which these words were given as compared
with the ability of children as measured by an aggregate of more than a
million spellings by seventy thousand children in eighty-four cities
throughout the United States. Such a list could be taken from the scale
for the second grade, which includes words which have proved to be of a
difficulty represented by a seventy-three percent correct spelling for
the class. Such a list might be composed of the following words: north,
white, spent, block, river, winter, Sunday, letter, thank, and best. A
similar list could be taken from the scale for a third, fourth, fifth,
sixth, seventh, or eighth grade. For example, the words which have
approximately the same difficulty,--seventy-three percent to be spelled
correctly by the class for the sixth grade,--read as follows: often,
stopped, motion, theater, improvement, century, total, mansion, arrive,
supply. The great value of such a measuring scale, including as it does
the thousand words most commonly used, is to be found not only in the
opportunity for comparing the achievements of children in one class or
school with another, but also in the focusing of the attention of
teachers and pupils upon the words most commonly used.[25]

One of the fields in which there is greatest need for measurement is
English composition. Teachers have too often thought of English
composition as consisting of spelling, punctuation, capitalization, and
the like, and have ignored the quality of the composition itself in
their attention to these formal elements. A scale for measuring English
composition derived by Dr. M.B. Hillegas,[26] consisting of sample
compositions of values ranging from 0 to 9.37, will enable the teacher
to tell just how many pupils in the class are writing each different
quality of composition. The use of such a scale will tend to make both
teacher and pupil critical of the work which is being done not only with
respect to the formal elements, but also with respect to the style or
adequacy of the expression of the ideas which the writer seeks to
convey. Probably in no other field has the teacher been so apt to derive
his standard from the performance of the class as in work in
composition. Even though some teachers find it difficult to evaluate the
work of their pupils in terms of the sample compositions given on the
scale, much good must come, it seems to the writer, from the attempt to
grade compositions by such an objective scale. If such measurements are
made two or three times during the year, the performance of individual
pupils and of the class will be indicated much more certainly than is
the case when teachers feel that they are getting along well without any
definite assurance of the amount of their improvement.

In one large school system in which the writer was permitted to have the
principals measure compositions collected from the sixth and the eighth
grades, it was discovered that almost no progress in the quality of
composition had been accomplished during these two years. This lack of
achievement upon the part of children was not, in the opinion of the
writer, due to any lack of conscientious work upon the part of teachers,
but, rather, developed out of a situation in which the whole of
composition was thought of in terms of the formal elements mentioned
above. The Hillegas scale, together with the values assigned to each of
the samples, is given below.

A SCALE FOR THE MEASUREMENT OF THE QUALITY OF ENGLISH
COMPOSITION

BY MILO B. HILLEGAS

VALUE 0. Artificial sample

_Letter_

Dear Sir: I write to say that it aint a square deal Schools is
I say they is I went to a school. red and gree green and brown
aint it hito bit I say he don't know his business not today
nor yeaterday and you know it and I want Jennie to get me out.

VALUE 183. Artificial sample

_My Favorite Book_

the book I refer to read is Ichabod Crane, it is an grate book
and I like to rede it. Ichabod Crame was a man and a man wrote
a book and it is called Ichabod Crane i like it because the
man called it ichabod crane when I read it for it is such a
great book.

VALUE 260. Artificial sample

_The Advantage of Tyranny_

Advantage evils are things of tyranny and there are many
advantage evils. One thing is that when they opress the people
they suffer awful I think it is a terrible thing when they say
that you can be hanged down or trodden down without mercy and
the tyranny does what they want there was tyrans in the
revolutionary war and so they throwed off the yok.

VALUE 369. Written by a boy in the second year of the high
school, aged 14 years

_Sulla as a Tyrant_

When Sulla came back from his conquest Marius had put himself
consul so sulla with the army he had with him in his conquest
siezed the government from Marius and put himself in consul
and had a list of his enemys printy and the men whoes names
were on this list we beheaded.

VALUE 474. Written by a girl in the third year of the high
school, aged 17 years

_De Quincy_

First: De Quincys mother was a beautiful women and through her
De Quincy inhereted much of his genius.

His running away from school enfluenced him much as he roamed
through the woods, valleys and his mind became very
meditative.

The greatest enfluence of De Quincy's life was the opium
habit. If it was not for this habit it is doubtful whether we
would now be reading his writings.

His companions during his college course and even before that
time were great enfluences. The surroundings of De Quincy were
enfluences. Not only De Quincy's habit of opium but other
habits which were peculiar to his life.

His marriage to the woman which he did not especially care
for.

The many well educated and noteworthy friends of De Quincy.

VALUE 585. Written by a boy in the fourth year of the high
school, aged 16 years

_Fluellen_

The passages given show the following characteristic of
Fluellen: his inclination to brag, his professed knowledge of
History, his complaining character, his great patriotism,
pride of his leader, admired honesty, revengeful, love of fun
and punishment of those who deserve it.

VALUE 675. Written by a girl in the first year of the high
school, aged 18 years

_Ichabod Crane_

Ichabod Crane was a schoolmaster in a place called Sleepy
Hollow. He was tall and slim with broad shoulders, long arms
that dangled far below his coat sleeves. His feet looked as if
they might easily have been used for shovels. His nose was
long and his entire frame was most loosely hung to-gether.

VALUE 772. Written by a boy in the third year of the high
school, aged 16 years

_Going Down with Victory_

As we road down Lombard Street, we saw flags waving from
nearly every window. I surely felt proud that day to be the
driver of the gaily decorated coach. Again and again we were
cheered as we drove slowly to the postmasters, to await the
coming of his majestie's mail. There wasn't one of the gaily
bedecked coaches that could have compared with ours, in my
estimation. So with waving flags and fluttering hearts we
waited for the coming of the mail and the expected tidings of
victory.

When at last it did arrive the postmaster began to quickly
sort the bundles, we waited anxiously. Immediately upon
receiving our bundles, I lashed the horses and they responded
with a jump. Out into the country we drove at reckless
speed--everywhere spreading like wildfire the news, "Victory!"
The exileration that we all felt was shared with the horses.
Up and down grade and over bridges, we drove at breakneck
speed and spreading the news at every hamlet with that one cry
"Victory!" When at last we were back home again, it was with
the hope that we should have another ride some day with
"Victory."

VALUE 838. Written by a boy in the Freshman class in college

_Venus of Melos_

In looking at this statue we think, not of wisdom, or power,
or force, but just of beauty. She stands resting the weight of
her body on one foot, and advancing the other (left) with knee
bent. The posture causes the figure to sway slightly to one
side, describing a fine curved line. The lower limbs are
draped but the upper part of the body is uncovered. (The
unfortunate loss of the statue's arms prevents a positive
knowledge of its original attitude.) The eyes are partly
closed, having something of a dreamy langour. The nose is
perfectly cut, the mouth and chin are moulded in adorable
curves. Yet to say that every feature is of faultless
perfection is but cold praise. No analysis can convey the
sense of her peerless beauty.

VALUE 937. Written by a boy in the Freshman class in college

_A Foreigner's Tribute to Joan of Arc_

Joan of Arc, worn out by the suffering that was thrust upon
her, nevertheless appeared with a brave mien before the Bishop
of Beauvais. She knew, had always known that she must die when
her mission was fulfilled and death held no terrors for her.
To all the bishop's questions she answered firmly and without
hesitation. The bishop failed to confuse her and at last
condemned her to death for heresy, bidding her recant if she
would live. She refused and was lead to prison, from there to
death.

While the flames were writhing around her she bade the old
bishop who stood by her to move away or he would be injured.
Her last thought was of others and De Quincy says, that recant
was no more in her mind than on her lips. She died as she
lived, with a prayer on her lips and listening to the voices
that had whispered to her so often.

The heroism of Joan of Arc was wonderful. We do not know what
form her great patriotism took or how far it really led her.
She spoke of hearing voices and of seeing visions. We only
know that she resolved to save her country, knowing though she
did so, it would cost her her life. Yet she never hesitated.
She was uneducated save for the lessons taught her by nature.
Yet she led armies and crowned the dauphin, king of France.
She was only a girl, yet she could silence a great bishop by
words that came from her heart and from her faith. She was
only a woman, yet she could die as bravely as any martyr who
had gone before.

The following compositions have been evaluated by Professor Thorndike,
and may be used to supplement the scale given above.

VALUE 13

Last Monday the house on the corner of Jay street was burned
down to the ground and right down by Mrs. brons house there is
a little child all alone and there is a bad man sleeping in
the seller, but we have a wise old monkey in the coal ben so
the parents are thankful that they don't have to pay any
reward.

VALUE 20

Some of the house burned and the children were in bed and
there were four children and the lady next store broke the
door in and went up stars and woke the peple up and whent out
of the house when they moved and and the girl was skard to
look out of the window and all the time thouhth that she saw a
flame.

And the wise monkey reward from going to the firehouse and
jumping all round and was thankful from his reward and was
thankful for what he got. $15. was his reward.

VALUE 30

A long time ago, I do not know, how long but a man and a woman
and a little boy lived together also a monkey a pet for the
little boy it happened that the man and the woman were out,
and the monkey and little boy, and the house started to burn,
and the monkey took the little boys hand, and, went out.

The father had come home and was glad that the monkey had
saved his little boy.

And that, monkey got a reward.

VALUE 40

Once upon a time a woman went into a dark room and lit a
match. She dropped it on the floor and it of course set the
house afire.

She jumped out of the window and called her husband to come
out too.

They both forgot all about the baby. All of a sudden he
appeared in the window calling his mother.

His father had gone next door to tel afone to the fire house.

They had a monkey in the house at the time and he heard the
child calling his mother.

He had a plan to save the baby.

He ran to the window where he was standing. He put his tail
about his waist and jumped off the window sill with the baby
in his tail.

When the people were settled again they gave him a silver
collar as a reward.

VALUE 50

A University out west, I cannot remember the name, is noted
for its hazing, and this is what the story is about. It is the
hazing of a freshman. There was a freshman there who had been
acting as if he didn't respect his upper class men so they
decided to teach him a lesson. The student brought before the
Black Avenger's which is a society in all college to keep the
freshman under there rules so they desided to take him to the
rail-rode track and tie him to the rails about two hours
before a train was suspected and leave him there for about an
hour, which was a hour before the 9.20 train was expected. The
date came that they planned this hazing for so the captured
the fellow blindfolded him and lead him to the rail rode
tracks, where they tied him.

VALUE 60

I should like to see a picture, illustrating a part of
L'allegro. Where the godesses of Mirth and Liberty trip along
hand in hand. Two beautiful girls dressed in flowing garments,
dancing along a flower-strewn path, through a pretty garden.
Their hair flowing down in long curls. Their countenances
showing their perfect freedom and happiness. Their arms
extended gracefully smelling some sweet flower. In my mind
this would make a beautiful picture.

VALUE 70

It was between the dark and the daylight when far away could
be seen the treacherous wolves skulking over the hills. We sat
beside our campfires and watched them for awhile. Sometimes a
few of them would howl as if they wanted to get in our camp.
Then, half discouraged, they would walk away and soon there
would be others doing the same thing. They were afraid to come
near because of the fires, which were burning brightly. I
noticed that they howled more between the dark and the
daylight than at any time of the night.

VALUE 80

The sun was setting, giving a rosy glow to all the trees
standing tall black against the faintly tinted sky. Blue,
pink, green, yellow, like a conglomeration of paints dropped
carelessly onto a pale blue background. The trees were in such
great number that they looked like a mass of black crepe, each
with its individual, graceful form in view. The lake lay
smooth and unruffled, dimly reflecting the beautiful coloring
of the sky. The wind started madly up and blew over the lake's
glassy surface making mysterious murmurings blending in with
the chirping songs of the birds blew through the tree tops
setting the leaves rustling and whispering to one another. A
squirrel ran from his perch chattering, to the lofty
branches--a far and distant hoot echoed in the silence, and
soon night, over all came stealing, blotting out the scenery
and wrapping all in restful, mysterious darkness.

VALUE 90

Oh that I had never heard of Niagara till I beheld it! Blessed
were the wanderers of old, who heard its deep roar, sounding
through the woods, as the summons to an unknown wonder, and
approached its awful brink, in all the freshness of native
feeling. Had its own mysterious voice been the first to warn
me of its existence, then, indeed, I might have knelt down and
worshipped. But I had come thither, haunted with a vision of
foam and fury, and dizzy cliffs, and an ocean tumbling down
out of the sky--a scene, in short, which nature had too much
good taste and calm simplicity to realize. My mind had
struggled to adapt these false conceptions to the reality, and
finding the effort vain, a wretched sense of disappointment
weighed me down. I climbed the precipice, and threw myself on
the earth feeling that I was unworthy to look at the Great
Falls, and careless about beholding them again.

A scale for measuring English composition in the eighth grade, which
takes account of different types of composition, such as narration,
description, and the like, has been developed by Dr. Frank W. Ballou, of
Boston.[27] For those interested in the following up of the problem of
English composition this scale will prove interesting and valuable.

Several scales have been developed for the measurement of the ability of
children in reading. Among them may be mentioned the scale derived by
Professor Thorndike for measuring the understanding of sentences.[28]
This scale calls attention to that element in reading which is possibly
the most important of them all, that is, the attempt to get meanings. We
are all of us, for the most part, concerned not primarily with giving
expression through oral reading, but, rather, in getting ideas from the
printed page. A sample of this scale is given on the following page.

* * * * *

SCALE ALPHA. FOR MEASURING THE UNDERSTANDING OF SENTENCES

Write your name here...............................
Write your age.............years............months.

SET _a_

Read this and then write the answers. Read it again as often as you need
to.

John had two brothers who were both tall. Their names were Will and
Fred. John's sister, who was short, was named Mary. John liked Fred
better than either of the others. All of these children except Will had
red hair. He had brown hair.

1. Was John's sister tall or short?.....................
2. How many brothers had John?..........................
3. What was his sister's name?..........................

SET _b_

Read this and then write the answers. Read it again as often as you need
to.

Long after the sun had set, Tom was still waiting for Jim and Dick to
come. "If they do not come before nine o'clock," he said to himself, "I
will go on to Boston alone." At half past eight they came bringing two
other boys with them. Tom was very glad to see them and gave each of
them one of the apples he had kept. They ate these and he ate one too.
Then all went on down the road.

1. When did Jim and Dick come?...................................
2. What did they do after eating the apples?.....................
3. Who else came besides Jim and Dick?...........................
4. How long did Tom say he would wait for them?..................
5. What happened after the boys ate the apples?..................

SET _c_

Read this and then write the answers. Read it again as often as you need
to.

It may seem at first thought that every boy and girl who goes to school
ought to do all the work that the teacher wishes done. But sometimes
other duties prevent even the best boy or girl from doing so. If a boy's
or girl's father died and he had to work afternoons and evenings to earn
money to help his mother, such might be the case. A good girl might let
her lessons go undone in order to help her mother by taking care of the
baby.

1. What are some conditions that might make even the best boy leave
school work unfinished?............................................
...................................................................
2. What might a boy do in the evenings to help his family?.........
3. How could a girl be of use to her mother?.......................
4. Look at these words: _idle, tribe, inch, it, ice, ivy, tide, true,
tip, top, tit,
tat, toe._

Cross out every one of them that has an _i_ and has not any _t_ (T) in
it.

SET _d_

Read this and then write the answers. Read it again as often as you need
to.

It may seem at first thought that every boy and girl who goes to school
ought to do all the work that the teacher wishes done. But sometimes
other duties prevent even the best boy or girl from doing so. If a boy's
or girl's father died and he had to work afternoons and evenings to earn
money to help his mother, such might be the case. A good girl might let
her lessons go undone in order to help her mother by taking care of the
baby.

1. What is it that might seem at first thought to be true, but really is
false?
.......................................................................

2. What might be the effect of his father's death upon the way a boy
spent
his
time?.................................................................
3. Who is mentioned in the paragraph as the person who desires to have
all lessons completely
done?..............................................
.......................................................................

4. In these two lines draw a line under every 5 that comes just after a
2,
unless the 2 comes just after a 9. If that is the case, draw a line
under
the next figure after the 5:

5 3 6 2 5 4 1 7 4 2 5 7 6 5 4 9 2 5 3 8 6 1 2 5 4 7 3 5 2 3 9 2 5 8 4 7
9 2 5 6
1 2 5 7 4 8 5 6

* * * * *

Many tests have been devised which have been thought to have more
general application than those which have been mentioned above for the
particular subjects. One of the most valuable of these tests, called
technically a completion test, is that derived by Dr. M.R. Trabue.[29]
In these tests the pupil is asked to supply words which are omitted from
the printed sentences. It is really a test of his ability to complete
the thought when only part of it is given. Dr. Trabue calls his scales
language scales. It has been found, however, that ability of this sort
is closely related to many of the traits which we consider desirable in
school children. It would therefore be valuable, provided always that
children have some ability in reading, to test them on the language
scale as one of the means of differentiating among those who have more
or less ability. The scores which may be expected from different grades
appear in Dr. Trabue's monograph. Three separate scales follow.

* * * * *

_Write only one word on each blank_
_Time Limit: Seven minutes_ NAME ..........................

TRABUE
LANGUAGE SCALE B

1. We like good boys................girls.
6. The................is barking at the cat.
8. The stars and the................will shine tonight.
22. Time................often more valuable................money.
23. The poor baby................as if it.....................sick.
31. She................if she will.
35. Brothers and sisters ................ always ................ to
help..............other and should................quarrel.
38. ................ weather usually................ a good effect
................ one's spirits.
48. It is very annoying to................................tooth-ache,
................often comes at the most................time
imaginable.
54. To................friends is always................the........
it takes.

_Write only one word on each blank_
_Time Limit: Seven minutes_ NAME..........................

TRABUE
LANGUAGE SCALE D

4. We are going................school.
76. I................to school each day.
11. The................plays................her dolls all day.
21. The rude child does not................many friends.
63. Hard................makes................tired.
27. It is good to hear................voice.......................
..........friend.
71. The happiest and................contented man is the one........
........lives a busy and useful.................
42. The best advice................usually................obtained
................one's parents.
51.................things are................ satisfying to an ordinary
................than congenial friends.
84.................a rule one................association..........
friends.

_Write only one word on each blank_
_Time Limit: Five minutes_ NAME ............................

TRABUE
LANGUAGE SCALE J

20. Boys and................soon become................and women.
61. The................are often more contented.............. the
rich.
64. The rose is a favorite................ because of................
fragrance and.................
41. It is very................ to become................acquainted
................persons who................timid.
93. Extremely old..................sometimes..................almost as
.................. care as ...................
87. One's................in life................upon so............
factors ................ it is not ................ to state any
single................for................ failure.
89. The future................of the stars and the facts of............
history are................now once for all,................I
like them................not.

* * * * *

Other standard tests and scales of measurement have been derived and are
being developed. The examples given above will, however, suffice to make
clear the distinction between the ordinary type of examination and the
more careful study of the achievements of children which may be
accomplished by using these measuring sticks. It is important for any
one who would attempt to apply these tests to know something of the
technique of recording results.

In the first place, the measurement of a group is not expressed
satisfactorily by giving the average score or rate of achievement of the
class. It is true that this is one measure, but it is not one which
tells enough, and it is not the one which is most significant for the
teacher. It is important whenever we measure children to get as clear a
view as we can of the whole situation. For this purpose we want not
primarily to know what the average performance is, but, rather, how many
children there are at each level of achievement. In arithmetic, for
example, we want to know how many there are who can do none of the
Courtis problems in addition, or how many there are who can do the first
six on the Woody test, how many can do seven, eight, and so on. In
penmanship we want to know how many children there are who write quality
eight, or nine, or ten, or sixteen, or seventeen, as the case may be.
The work of the teacher can never be accomplished economically except as
he gives more attention to those who are less proficient, and provides
more and harder work for those who are capable, or else relieves the
able members of the class from further work in the field. It will be
well, therefore, to prepare, for the sake of comparing grades within the
same school or school system, or for the sake of preparing the work of a
class at two different times during the year, a table which shows just
how many children there are in the group who have reached each level of
achievement. Such tables for work in composition for a class at two
different times, six months apart, appear as follows:

DISTRIBUTION OF COMPOSITION SCORES FOR A SEVENTH GRADE

======================================
| NUMBER OF CHILDREN
+-----------------------
| NOVEMBER | FEBRUARY
--------------+-----------+-----------
Rated at 0 | 0 | 0
1.83 | 1 | 1
2.60 | 6 | 4
3.69 | 12 | 6
4.74 | 8 | 11
5.85 | 3 | 4
6.75 | 1 | 3
7.72 | 1 | 2
8.38 | 0 | 1
9.37 | 0 | 0
======================================

A study of such a distribution would show not only that the average
performance of the class has been raised, but also that those in the
lower levels have, in considerable measure, been brought up; that is,
that the teacher has been working with those who showed less ability,
and not simply pushing ahead a few who had more than ordinary capacity.
It would be possible to increase the average performance by working
wholly with the upper half of the class while neglecting those who
showed less ability. From a complete distribution, as has been given
above, it has become evident that this has not been the method of the
teacher. He has sought apparently to do everything that he could to
improve the quality of work upon the part of all of the children in the
class.

It is very interesting to note, when such complete distributions are
given, how the achievement of children in various classes overlaps. For
example, the distribution of the number of examples on the Courtis
tests, correctly finished in a given time by pupils in the seventh
grades, makes it clear that there are children in the fifth grade who do
better than many in the eighth.

THE DISTRIBUTION OF THE NUMBER OF EXAMPLES CORRECTLY FINISHED
IN THE GIVEN TIME BY PUPILS IN THE SEVERAL GRADES

===================================================================
ADDITION | SUBTRACTION
No. OF |----------------------+ No. OF |------------------------
EXAMPLES| GRADES | EXAMPLES | GRADES
FINISHED| 5 | 6 | 7 | 8 | FINISHED | 5 | 6 | 7 | 8
--------+----+-----+-----+-----+----------+----+-----+-----+-------
0 | 12 | 15 | 5 | 4 | 0 | 6 | 2 | 2 | --
1 | 26 | 23 | 14 | 9 | 1 | 5 | 6 | 2 | 1
2 | 27 | 31 | 8 | 6 | 2 | 7 | 8 | 1 | --
3 | 31 | 27 | 27 | 9 | 3 | 13 | 21 | 3 | 1
4 | 25 | 28 | 19 | 16 | 4 | 21 | 18 | 13 | 2
5 | 16 | 23 | 16 | 15 | 5 | 26 | 30 | 12 | 7
6 | 15 | 22 | 12 | 12 | 6 | 17 | 27 | 15 | 9
7 | 1 | 11 | 8 | 9 | 7 | 15 | 27 | 18 | 9
8 | 3 | 4 | 6 | 11 | 8 | 15 | 20 | 12 | 12
9 | 1 | 2 | 3 | 8 | 9 | 10 | 13 | 9 | 12
10 | -- | -- | -- | 6 | 10 | 8 | 6 | 13 | 11
11 | -- | -- | 1 | -- | 11 | 6 | 2 | 3 | 12
12 | -- | -- | 1 | 2 | 12 | 3 | 1 | 7 | 9
13 | -- | -- | -- | -- | 13 | 2 | 2 | 3 | 5
14 | -- | -- | -- | -- | 14 | 1 | 1 | 3 | 7
15 | -- | -- | -- | 2 | 15 | -- | -- | 2 | 3
16 | -- | -- | -- | 1 | 16 | -- | -- | 1 | 2
17 | -- | -- | -- | -- | 17 | -- | 1 | -- | 1
18 | -- | -- | -- | -- | 18 | -- | -- | -- | 1
19 | -- | -- | -- | -- | 19 | -- | -- | -- | 4
20 | -- | -- | -- | -- | 20 | -- | -- | -- | 2
21 | -- | -- | -- | -- | 21 | -- | -- | -- | 1
22 | -- | -- | -- | -- | 22 | -- | -- | -- | --
--------+----+-----+-----+-----+----------+----+-----+-----+-------
Total | | | | | | | | |
papers |157 | 86 | 119 | 111 | |155 | 185 | 119 | 111
===================================================================

THE DISTRIBUTION OF THE NUMBER OF EXAMPLES CORRECTLY FINISHED
IN THE GIVEN TIME BY PUPILS IN THE SEVERAL GRADES

=======================================================================
MULTIPLICATION | DIVISION
------------------------------------|----------------------------------
No. of | GRADES |No. of | GRADES
Examples|---------------------------|Examples|-------------------------
Finished| 5 | 6 | 7 | 8 |Finished| 5 | 6 | 7 | 8
--------|------+-----+-----+--------|--------|------+-----+-----+------
0 . . .| 10 | 4 | -- | -- | 0 . . .| 17 | 7 | 1 | --
1 . . .| 10 | 4 | 3 | -- | 1 . . .| 19 | 17 | 2 | 1
2 . . .| 19 | 20 | 5 | 1 | 2 . . .| 18 | 22 | 8 | 4
3 . . .| 21 | 17 | 11 | 5 | 3 . . .| 21 | 26 | 6 | 2
4 . . .| 28 | 31 | 16 | 3 | 4 . . .| 25 | 27 | 8 | 6
5 . . .| 26 | 34 | 12 | 13 | 5 . . .| 21 | 27 | 11 | 7
6 . . .| 24 | 27 | 13 | 13 | 6 . . .| 9 | 15 | 12 | 4
7 . . .| 9 | 20 | 16 | 10 | 7 . . .| 10 | 15 | 16 | 18
8 . . .| 5 | 14 | 21 | 19 | 8 . . .| 6 | 7 | 20 | 9
9 . . .| 3 | 9 | 11 | 13 | 9 . . .| 4 | 7 | 11 | 6
10 . . .| -- | 4 | 6 | 10 |10 . . .| 4 | 9 | 7 | 13
11 . . .| 1 | -- | 2 | 9 |11 . . .| 1 | 3 | 3 | 7
12 . . .| -- | -- | 2 | 6 |12 . . .| -- | 2 | 10 | 10
13 . . .| -- | -- | 1 | 3 |13 . . .| -- | 2 | -- | 10
14 . . .| -- | -- | -- | 3 |14 . . .| 1 | -- | 1 | 4
15 . . .| -- | -- | -- | -- |15 . . .| -- | 1 | 2 | 9
16 . . .| -- | -- | -- | 1 |16 . . .| -- | -- | -- | 2
17 . . .| -- | -- | -- | -- |17 . . .| -- | -- | -- | 4
18 . . .| -- | -- | -- | 1 |18 . . .| -- | -- | -- | 2
19 . . .| -- | -- | -- | 1 |19 . . .| -- | -- | -- | 1
20 . . .| -- | -- | -- | -- |20 . . .| -- | -- | -- | 1
21 . . .| -- | -- | -- | -- |21 . . .| -- | -- | -- | 1
22 . . .| -- | -- | -- | -- |22 . . .| -- | -- | -- | --
--------+------+-----+-----+--------|--------|------+-----+-----+-------
Total | | | | | | | | |
Papers | 156 | 184 | 119 | 111 | | 156 | 187 | 118 | 111
=======================================================================

If the tests had been given in the fourth or the third grade, it would
have been found that there were children, even as low as the third
grade, who could do as well or better than some of the children in the
eighth grade. Such comparisons of achievements among children in various
subjects ought to lead at times to reorganizations of classes, to the
grouping of children for special instruction, and to the rapid promotion
of the more capable pupils.

In many of these measurements it will be found helpful to describe the
group by naming the point above and below which half of the cases fall.
This is called the median. Because of the very common use of this
measure in the current literature of education, it may be worth while to
discuss carefully the method of its derivation.[30]

[31]The _median point_ of any distribution of measures is that point on
the scale which divides the distribution into two exactly equal parts,
one half of the measures being greater than this point on the scale, and
the other half being smaller. When the scales are very crude, or when
small numbers of measurements are being considered, it is not worth
while to locate this median point any more accurately than by indicating
on what step of the scale it falls. If the measuring instrument has been
carefully derived and accurately scaled, however, it is often desirable,
especially where the group being considered is reasonably large, to
locate the exact point within the step on which the median falls. If the
unit of the scale is some measure of the variability of a defined group,
as it is in the majority of our present educational scales, this median
point may well be calculated to the nearest tenth of a unit, or, if
there are two hundred or more individual measurements in the
distribution, it may be found interesting to calculate the median point
to the nearest hundredth of a scale unit. Very seldom will anything be
gained by carrying the calculation beyond the second decimal place.

The best rule for locating the median point of a distribution is to
_take as the median that point on the scale which is reached by counting
out one half of the measures_, the measures being taken in the order of
their magnitude. If we let _n_ stand for the number of measures in the
distribution, we may express the rule as follows: Count into the
distribution, from either end of the scale, a distance covered by *_n/2_
measures. For example, if the distribution contains 20 measures, the
median is that point on the scale which marks the end of the 10th and
the beginning of the 11th measure. If there are 39 measures in the
distribution, the median point is reached by counting out 19-1/2 of the
measures; in other words, the median of such a distribution is at the
mid-point of that fraction of the scale assigned to the 20th measure.

The _median step_ of a distribution is the step which contains within it
the median point. Similarly, the _median measure_ in any distribution is
the measure which contains the median point. In a distribution
containing 25 measures, the 13th measure is the median measure, because
12 measures are greater and 12 are less than the 13th, while the 13th
measure is itself divided into halves by the median point. Where a
distribution contains an even number of measures, there is in reality no
median measure but only a median point between the two halves of the
distribution. Where a distribution contains an uneven number of
measures, the median measure is the (_n_+1)/2 measurement, at the
mid-point of which measure is the median point of the distribution.

Much inaccurate calculation has resulted from misguided attempts to
secure a _median point_ with the formula just given, which is applicable
only to the location of the _median measure_. It will be found much more
advantageous in dealing with educational statistics to consider only the
median point, and to use only the _n_/2 formula given in a previous
paragraph, for practically all educational scales are or may be thought
of as continuous scales rather than scales composed of discrete steps.

The greatest danger to be guarded against in considering all scales as
continuous rather than discrete, is that careless thinkers may refine
their calculations far beyond the accuracy which their original
measurements would warrant. One should be very careful not to make such
unjustifiable refinements in his statement of results as are often made
by young pupils when they multiply the diameter of a circle, which has
been measured only to the nearest inch, by 3.1416 in order to find the
circumference. Even in the ordinary calculation of the average point of
a series of measures of length, the amateur is sometimes tempted, when
the number of measures in the series is not contained an even number of
times in the sum of their values, to carry the quotient out to a larger
number of decimal places than the original measures would justify. Final
results should usually not be refined far beyond the accuracy of the
original measures.

It is of utmost importance in calculating medians and other measures of
a distribution to keep constantly in mind the significance of each step
on the scale. If the scale consists of tasks to be done or problems to
be solved, then "doing 1 task correctly" means, when considered as part
of a continuous scale, anywhere from doing 1.0 up to doing 2.0 tasks. A
child receives credit for "2 problems correct" whether he has just
barely solved 2.0 problems or has just barely fallen short of solving
3.0 problems. If, however, the scale consists of a series of productions
graduated in quality from very poor to very good, with which series
other productions of the same sort are to be compared, then each sample
on the scale stands at the middle of its "step" rather than at the
beginning.

The second kind of scale described in the foregoing paragraph may be
designated as "scales for the _quality_ of products," while the other
variety may be called "scales for _magnitude_ of achievement." In the
one case, the child makes the best production he can and measures its
quality by comparing it with similar products of known quality on the
scale. Composition, handwriting, and drawing scales are good examples of
scales for quality of products. In the other case, the scales are placed
in the hands of the child at the very beginning, and the magnitude of
his achievement is measured by the difficulty or number of tasks
accomplished successfully in a given time. Spelling, arithmetic,
reading, language, geography, and history tests are examples of scales
for quantity of achievement.

Scores tend to be more accurate on the scales for magnitude of
achievement, because the judgment of the examiner is likely to be more
accurate in deciding whether a response is correct or incorrect than it
is in deciding how much quality a given product contains. This does not
furnish an excuse for failing to employ the quality-of-products scales,
however, for the qualities they measure are not measurable in terms of
the magnitude of tasks performed. The fact appears, however, that the
method of employing the quality-of-products scales is "by comparison"
(of child's production with samples reproduced on the scale), while the
method of employing the magnitude-of-achievement scales is "by
performance" (of child on tasks of known difficulty).

In this connection it may be well to take one of the scales for quality
of products and outline the steps to be followed in assigning scores,
making tabulations, and finding the medians of distributions of scores.

When the Hillegas scale is employed in measuring the quality of English
composition, it will be advisable to assign to each composition the
score of that sample on the scale to which it is nearest in merit or
quality. While some individuals may feel able to assign values
intermediate to those appearing on the Hillegas scale, the majority of
those persons who use this scale will not thereby obtain a more accurate
result, and the assignment of such intermediate values will make it
extremely difficult for any other person to make accurate use of the
results. To be exactly comparable, values should be assigned in exactly
the same manner.

The best result will probably be obtained by having each composition
rated several times, and if possible, by a number of different judges,
the paper being given each time that value on the Hillegas scale to
which it seems nearest in quality. The final mark for the paper should
be the median score or step (not the median point or the average point)
of all the scores assigned. For example, if a paper is rated five times,
once as in step number five (5.85), twice as in step number six (6.75),
and twice as in step number seven (7.72), it should be given a final
mark indicating that it is a number six (6.75) paper.

After each composition has been assigned a final mark indicating to what
sample on the Hillegas scale it is most nearly equal in quality, proceed
as follows:

Make a distribution of the final marks given to the individual papers,
showing how many papers were assigned to the zero step on the scale, how
many to step number one, how many to step number two, and so on for each
step of the scale. We may take as an example the distribution of scores
made by the pupils of the eighth grade at Butte, Montana, in May, 1914.

No. of papers 1 9 32 39 43 22 6 2
Rated at 0 1 2 3 4 5 6 7 8 9

All together there were 154 papers from the eighth grade, so that if
they were arranged in order according to their merit we might begin at
the poorest and count through 77 of them (n/2 = 154/2 = 77) to find the
median point, which would lie between the 77th and the 78th in quality.
If we begin with the 1 composition rated at 0 and count up through the 9
rated at 1 and the 32 rated at 2 in the above distribution, we shall
have counted 42. In order to count out 77 cases, then, it will be
necessary to count out 35 of the 39 cases rated at 3.

Now we know (if the instructions given above have been followed) that
the compositions rated at 3 were so rated by virtue of the fact that the
judges considered them nearer in quality to the sample valued at 3.69
than to any other sample on the scale. We should expect, then, to find
that some of those rated at 3 were only slightly nearer to the sample
valued at 3.69 than they were to the sample valued at 2.60, while others
were only slightly nearer to 3.69 than they were to 4.74. Just how the
39 compositions rated on 3 were distributed between these two extremes
we do not know, but the best single assumption to make is that they are
distributed at equal intervals on step 3. Assuming, then, that the
papers rated at 3 are distributed evenly over that step, we shall have
covered .90 (35/39 = .897 = .90) of the entire step 3 by the time we
have counted out 35 of the 39 papers falling on this step.

It now becomes necessary to examine more closely just what are the
limits of step 3. It is evident from what has been said above that 3.69
is the middle step 3 and that step 3 extends downward from 3.69 halfway
to 2.60, and upward from 3.69 halfway to 4.74. The table given below
shows the range and the length of each step in the Hillegas Scale for
English Composition.

THE HILLEGAS SCALE FOR ENGLISH COMPOSITION

======================================================
STEP No.|VALUE or SAMPLE|RANGE OF STEP |LENGTH OF STEP
--------+---------------+--------------+--------------
0. . . .| 0 | 0- .91[32] | .91
1. . . .| 1.83 | .92-2.21 | 1.30
2. . . .| 2.60 |2.22-3.14 | .93
3. . . .| 3.69 |3.15-4.21 | 1.07
4. . . .| 4.74 |4.22-5.29 | 1.08
5. . . .| 5.85 |5.30-6.30 | 1.00
6. . . .| 6.75 |6.30-7.23 | .93
7. . . .| 7.72 |7.24-8.05 | .81
8. . . .| 8.38 |8.05-8.87 | .82
9. . . .| 9.37 |8.88- |
======================================================

From the above table we find that step 3 has a length of 1.07 units. If
we count out 35 of the 39 papers, or, in other words, if we pass upward
into the step .90 of the total distance (1.07 units), we shall arrive at
a point .96 units (.90 x 1.07 = .96) above the lower limit of step 3,
which we find from the table is 3.15. Adding .96 to 3.15 gives 4.11 as
the median point of this eighth grade distribution.

The median and the percentiles of any distribution of scores on the
Hillegas scale may be determined in a manner similar to that illustrated
above, if the scores are assigned to the individual papers according to
the directions outlined above.

A similar method of calculation is employed in discovering the limits
within which the middle fifty per cent of the cases fall. It often seems
fairer to ask, after the upper twenty-five per cent of the children who
would probably do successful work even without very adequate teaching
have been eliminated, and the lower twenty-five per cent who are
possibly so lacking in capacity that teaching may not be thought to
affect them very largely have been left out of consideration, what is
the achievement of the middle fifty per cent. To measure this
achievement it is necessary to have the whole distribution and to count
off twenty-five per cent, counting in from the upper end, and then
twenty-five per cent, counting in from the lower end of the
distribution. The points found can then be used in a statement in which
the limits within which the middle fifty per cent of the cases fall.
Using the same figures that are given above for scores in English
composition, the lower limit is 2.64 and the limit which marks the point
above which the upper twenty-five per cent of the cases are to be found
is 5.08. The limits, therefore, within which the middle fifty per cent
of the cases fall are from 2.64 to 5.08.

It is desirable to measure the relationship existing between the
achievements (or other traits) of groups. In order to express such
relationship in a single figure the coefficient or correlation is used.
This measure appears frequently in the literature of education and will
be briefly explained. The formula for finding the coefficient of
correlation can be understood from examples of its application.

Let us suppose a group of seven individuals whose scores in terms of
problems solved correctly and of words spelled correctly are as
follows:[33]

======================================
INDIVIDUALS|No. OF |No. OF WORDS
MEASURED |PROBLEMS|SPELLED CORRECTLY
CORRECTLY | |
-----------+--------+-----------------
A | 1 | 2
B | 2 | 4
C | 3 | 6
D | 4 | 8
E | 5 | 10
F | 6 | 12
G | 7 | 14
======================================

From such distributions it would appear that as individuals increase in
achievement in one field they increase correspondingly in the other. If
one is below or above the average in achievement in one field, he is
below or above and in the same degree in the other field. This sort of
positive relationship (going together) is expressed by a coefficient of
+1. The formula is expressed as follows:

(Sum x . y)
r = ------------------------------
(sqrt(Sum x^2))(sqrt(Sum y^2))

Here _r_ = coefficient of correlation.

_x_ = deviations from average score in arithmetic (or difference between
score made and average score).

_y_ = deviations from average score in spelling.

Sum = is the sign commonly used to indicate the algebraic sum (_i.e._
the difference between the sum of the minus quantities and the plus
quantities).

_x . y _= products of deviation in one trait multiplied by deviation in
the other trait with appropriate sign.

Applying the formula we find:
===================================================================
|ARITH-| | | SPEL- | | | |
|METIC | x | x^2 | LING | y | y^2 | x.y |
--+------+---+------------+-------+---+-------------+-------------+
A | 1|-3 | 9| 2|-6 | 36| +18|
B | 2|-2 | 4| 4|-4 | 16| +8|
C | 3|-1 | 1| 6|-2 | 4| +2|
D | 4| 0 | 0| 8| 0 | | |
E | 5|+1 | 1| 10|+2 | 4| +2|
F | 6|+2 | 4| 12|+4 | 16| +8|
G | 7|+3 | 9| 14|+6 | 36| +18|
| ___| | __| ___| | ___| __|
| 7 |28| |Sum x^2 = 28| 7 |56| |Sum y^2 = 112|Sum x.y = +56|
|Av. =4| | |Av. =8 | | | |
===================================================================
Sum x . y +56 +56
r = ---------------------------- = --------------------- = ---- = +1
(sqrt(Sum x^2)(sqrt(Sum y^2) (sqrt(28))(sqrt(112)) 56

If instead of achievement in one field being positively related (going
together) in the highest possible degree, these individuals show the
opposite type of relationship, _i.e.,_ the maximum negative relationship
(this might be expressed as opposition--a place above the average in one
achievement going with a correspondingly great deviation below the
average in the other achievement), then our coefficient becomes -1.
Applying the formula:

===================================================================
|ARITH-| | | SPEL- | | | |
|METIC | x | x^2 | LING | y | y^2 | x*y |
--+------+---+------------+-------+---+-------------+-------------+
A | 1|-3 | 9| 14|+6 | 36| -18|
B | 2|-2 | 4| 12|+4 | 16| -8|
C | 3|-1 | 2| 10|+2 | 4| -2|
D | 4| 0 | | 8| 0 | | |
E | 5|+1 | 2| 6|-2 | 4| -2|
F | 6|+2 | 4| 4|-4 | 16| -8|
G | 7|+3 | 9| 2|-6 | 36| -18|
| ___| | __| ___| | ___| __|
| 7 |28| |Sum x^2 = 28| 7 |56| |Sum y^2 = 112|Sum x.y = -56|
|Av. =4| | |Av. =8 | | | |
===================================================================

It will be observed that in this case each plus deviation in one
achievement is accompanied by a minus deviation for the other trait;
hence, all of the products of _x_ and _y_ are minus quantities. (A plus
quantity multiplied by a plus quantity or a minus quantity multiplied by
a minus quantity gives us a plus quantity as the product, while a plus
quantity multiplied by a minus quantity gives us a minus quantity as the
product.)

(Sum x.y) -56 -56
r = ------------------------------ = ------------------- = ---- = -1.
(sqrt(Sum x^2))(sqrt(Sum y^2)) (sqrt(28)sqrt(112)) = 56

If there is no relationship indicated by the measures of achievements
which we have found, then the coefficient of correlation becomes 0. A
distribution of scores which suggests no relationship is as follows:

=================================================================
|ARITH- | | | | | |
|METIC | x | x^2 |Spelling | y | y^2 | x.y
--+-------+----+-----------+---------+----+-------------+--------
| | | | | | | - +
A | 2 | -2 | 4 | 12 | +4 | 16 | -8 +6
B | 1 | -3 | 9 | 8 | 0 | | 0 +4
C | 4 | 0 | | 2 | -6 | 36 | 0 +4
D | 5 | +1 | 1 | 14 | +6 | 36 | -6
E | 3 | -1 | 1 | 4 | -4 | 16 | -14 +14
F | 7 | +3 | 9 | 6 | -2 | 4 |
G | 6 | +2 | 4 | 10 | +2 | 4 |
| ____| | | ___ | | |
| |28 | |Sum x^2=28 | 7|56 | | Sum y^2=112 | x.y=0
| AV.=4 | | | AV.=8 | | |
===================================================================

(Sum x.y) 0
r = ---------------------------- = ------------------- = 0.
(sqrt(Sum x^2)sqrt(Sum y^2)) (sqrt(28)sqrt(112))

In a similar manner, when the relationship is largely positive as would
be indicated by a displacement of each score in the series by one step
from the arrangement which gives a +1 coefficient, the coefficient will
approach unity in value.

===============================================================
ARITHMETIC| x | x^2 |SPELLING| y | y^2 |
---+------+----+-----------+--------+----+------------+--------
A |1 | -3 |9 |4 | -4 | 16 |+ 12
B |2 | -2 |4 |2 | -6 | 36 |+ 12
C |3 | -1 |1 |8 | 0 | |+ 4
D |4 | 0 | |6 | -2 | 4 |+ 4
E |5 | +1 |1 |12 | +4 | 16 |+ 18
F |6 | +2 |4 |10 | +2 | 4 |Sx.y=50
G |7 | +3 |9 |14 | +6 | 36 |
|Av. =4| |Sum x^2 =28|Av. = 8 | |Sum y^2= 112|
===============================================================

Sum x.y +50
r= -------------------------- = ---- = +.89.
sqrt(Sum x^2)sqrt(Sum y^2) 56

Other illustrations might be given to show how the coefficient varies
from + 1, the measure of the highest positive relationship (going
together) through 0 to -1, the measure of the largest negative
relationship (opposition). A relationship between traits which we
measure as high as +.50 is to be thought of as quite significant. It is
seldom that we get a positive relationship as large as +.50 when we
correlate the achievements of children in school work. A relationship
measured by a coefficient of +-.15 may _not_ be considered to indicate
any considerable positive or negative relationship. The fact that
relationships among the achievements of children in school subjects vary
from +.20 to +.60 is a clear indication of the fact that abilities of
children are variable, or, in other words, achievement in one subject
does not carry with it an _exactly corresponding_ great or little
achievement in another subject. That there is some positive
relationship, _i.e.,_ that able pupils tend on the whole to show
all-round ability and the less able or weak in one subject _tend_ to
show similar lack of strength in other subjects, is also indicated by
these positive coefficients.

QUESTIONS

1. Calculate the median point in the following distribution of
eighth-grade composition scores on the Hillegas scale.

Quality 0 18 26 37 47 58 67
Frequency 2 68 73 3

2. Calculate the median point in the following distribution of
third-grade scores on the Woody subtraction scale.

No. problems 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Frequency 2 2 2 3 3 5 4 5 8 16 16 16 23 20 21 11 22 11 2

22 23 24 +
1

3. Compare statistically the achievements of the children in two
eighth-grade classes whose scores on the Courtis addition tests were as
follows:

Class A--6, 5, 8, 9, 7, 10, 13, 4, 8, 7, 8, 7, 6, 8, 15, 6, 7, 0, 6, 9,
5, 8, 7, 10, 8, 4, 7, 8, 6, 9, 5, 7, 2, 6, 8, 5, 7, 8, 7, 8, 5, 8, 10,
6, 3, 6, 8, 17, 5, 7.

Class B--10, 4, 8, 13, 11, 9, 8, 10, 7, 9, 11, 10, 18, 7, 12, 9, 10, 8,
11, 10, 12,
9, 2, 11, 8, 10, 9, 14, 11, 7, 10, 12, 10, 6, 11, 8, 10, 9, 10, 17, 8,
11,
9, 7, 9, 11, 8, 12, 9, 13.

4. If the marks received in algebra and in geometry by a group of high
school pupils were as given below, what relationship is indicated by the
coefficient of correlation?

|GEOMETRY |ALGEBRA
|MARKS |MARKS
1. |80 |60
2. |68 |73
3. |65 |80
4. |96 |80
5. |59 |62
6. |75 |65
7. |90 |75
8. |86 |90
9. |52 |63
10. |70 |55
11. |63 |54
12. |85 |95
13. |93 |90
14. |87 |70
15. |82 |68
16. |79 |75
17. |78 |86
18. |79 |75
19. |82 |60
20. |70 |82
21. |52 |86
22. |94 |85
23. |72 |73
24. |53 |62
25. |94 |85

5. Compare the abilities of the 10-year-old pupils in the sixth grade
with the abilities of the 14-year-old pupils in the same grade, in so
far as these abilities are measured by the completion of incomplete
sentences.

(Note: 5 = 5.0-5.999.)

==================================================
NO. SENTENCES | |
COMPLETED | 10-YEAR-OLDS | 14-YEAR-OLDS
--------------+--------------+--------------------
24 |-- |--
23 |-- |--
22 |-- |--
21 |1 |--
20 |-- |--
19 |-- |--
18 |-- |--
17 |-- |1
16 |3 |--
15 |-- |2
14 |7 |4
13 |10 |3
12 |18 |7
11 |9 |10
10 |7 |9
9 |8 |10
8 |2 |10
7 |3 |10
6 |-- |2
5 |2 |3
4 |-- |2
3 |-- |--
2 |-- |1
1 |-- |--
0 |-- |--
===========================================

6. From the scores given here, calculate the relationship between
ability to spell and ability to multiply. Use the average as the central
tendency.

==============================
PUPIL|SPELLING|MULTIPLICATION
-----+--------+---------------
A |9 |22
B |10 |16
C |2 |19
D |6 |14
E |13 |24
F |8 |22
G |10 |17
H |7 |20
I |3 |21
J |2 |21
K |14 |20
L |8 |18
M |7 |23
N |11 |25
O |8 |25
P |17 |24
Q |10 |21
R |4 |16
S |9 |15
T |6 |19
U |12 |22
V |14 |19
W |8 |17
X |3 |20
Y |11 |18
==============================

* * * * *

INDEX

Achievements of children, measuring the,
and examinations,
in English composition,
in arithmetic,
arithmetic scale,
reasoning problems in arithmetic,
distribution of hand-writing scores,
handwriting scale,
spelling scale,
scale for English composition.
AEsthetic emotions,
appreciation and skill,
appreciation, intellectual factors in.
Aim of education, I
Analysis and abstraction, III.
Angell, J.R.
Appreciation,
types of,
passive attitude in,
development in,
value of,
lesson.
Associations, organization of,
number of.
Attention,
situations arousing response of,
and inhibition,
breadth of,
to more than one thing,
concentration of,
span of,
free,
forced,
immediate free,
immediate and derived,
derived,
forced,
and habit formation,
focalization of,
divided.
Ayres, L.P.

Ballou, F.W.
Bread-and-butter aim.

Classroom exercises, types of.
Coefficient of correlation,
calculation of,
values of.
Comparison and abstraction, step of.
Concentration, of attention.
habits of.
Conduct, moral social.
Consciousness, fringe of.
Correlation, coefficient of.
Courtis, S.A.
Culture as aim of education.
Curriculum, omissions from.

Deduction lesson, the,
steps in.
Deduction, process of.
Dewey, John.
Differences, individual,
sex.
Disuse, method of.
Drill,
lesson, the,
work, deficiency in.

Education, before school age.
Effect, law of.
Emotions, aesthetic.
Environment and individual differences.
Examinations,
limitations of.
Exceptions, danger of.

Fatigue and habits.
Formal discipline.

Gray, W.S.

Habit formation,
and attention,
laws of,
and instinct,
complexity of,
and interest,
and mistakes.
Habits, of concentration,
modification of the nervous system involved,
and fatigue,
and will power,
and original work.
Harmonious development of aim.
Heck, W.H.
Henderson, E.N.
Heredity and individual differences.
Hillegas, M.B.

Illustrations, use of.
Imagery, type of,
and learning,
productive, types of.
Images,
classified,
object and concrete.
Imagination.
Individual differences,
causes of,
and race inheritance,
and maturity,
and heredity,
and environment,
and organization of
public education
in composition
in arithmetic
in penmanship
Induction and deduction
differences in
relationship of
Induction, process of
Inductive lesson, the
Inquiry in school work
Instinctive tendencies
modifiability of
inhibition of
Instincts
transitoriness of
delayedness of
of physical activity
to enjoy mental activity
of manipulation
of collecting
of rivalry
of fighting
of imitation
of gregariousness
of motherliness
Interest
an end

Judd, C.H.
Junior high school, the

Kelly, F.J.
Knowledge aim

Learning
incidental
and imagery
curves
Lecturing
and appreciation
Lesson
the inductive

McMurry, F.M.
Maturity and individual differences
Measurement of group
comparison of seventh-grade scores in composition
comparison of scores in arithmetic
Measuring results in education
Median
calculation of
point
step
measure
Memorization
verbatim
whole-part method illustrated
Memory
factors in
and native retentiveness
and recall
part and whole methods
practice periods
immediate
desultory
rote
logical
and forgetting
permanence of
Miller, I.E.
Moral conduct
development of
Morality
defined
and conduct
and habit
and choice
and individual opinion
social nature of
and training for citizenship
and original nature
and environment
stages of development in
and habit formation
transition period in
direct teaching of
and classroom work
and service by pupils
and social responsibility
and school rules
Morgan, C.L.

Openmindedness
Original nature
of children
and racial inheritance
and aim of education
utilization of
and morality
Original work and habits

Payne, Joseph
Physical welfare of children
Play
theories of
types of
complexity of
characteristics of
and drudgery
and work
and ease of accomplishment
and social demands
supervision of
Preparation
steps of
Presentation
steps of
Problems as stimulus to thinking
Punishment

Questioning
Questions
types of
responses to
number of
appeal of

Reasoning and thinking
technique of
Recapitulation theory
Recitation
social purpose of
Recitation lesson, the
Repetition
Retention
power of
Review
Review lesson, the
Roark, R.N.

Satisfaction
result of
Scales of measurement
School government
participation in
Sex differences
education
Social aim of education
and curriculum
and special types of schools
Stone, C.W.
Study
how to
types of
and habit formation
and memorization
and interest
necessity for aim in
and concentrated attention
involves critical attitude
general factors in
for appreciation
involving thinking
use of books in
supervised
Substitution
method of

Thinking defined
Thinking
stimulation of
and problematic situations
by little children
and habit formation
essentials in process of
for its own sake
and critical attitude
laws governing
and association
failure in
and classroom exercises
Thorndike, E.L.
Thought
imageless
Trabue, M.R.
Training
transfer of
identity of response
probability of
amount of
Transfer of training

Will power and habits
Woody, Clifford
Work, independent
Work and play

Footnote 1: The nervous system is composed of units of structure called
neurones or nerve cells. "If we could see exactly the structure of the
brain itself, we should find it to consist of millions of similar
neurones each resembling a bit of string frayed out at both ends and
here and there along its course. So also the nerves going out to the
muscles are simply bundles of such neurones, each of which by itself is
a thread-like connection between the cells of the spinal cord or brain
and some muscle. The nervous system is simply the sum total of all these
neurones, which form an almost infinitely complex system of connections
between the sense organs and the muscles."

The word synapses, meaning clasping together, is used as a descriptive
term for the connections that exist between neurone and neurone.

Footnote 2: This is synonymous with James's Involuntary Attention,
Angell's Non-Voluntary Attention, and Titchener's Secondary-Passive
Attention.

Footnote 3: Educational Psychology, Briefer Course, pp. 194-5.

Footnote 4: Thorndike, Psychology of Learning, p. 194.

Footnote 5: How We Think, p. 6.

Footnote 6: The Psychology of Thinking, p. 98.

Footnote 7: How We Think, p. 66.

Footnote 8: How We Think, pp. 69-70.

Footnote 9: Psychology of Thinking, p. 291.

Footnote 10: How We Think, p. 79.

Footnote 11: Thorndike, Educational Psychology, Briefer Course, p. 172.

Footnote 12: Introduction to Psychology, p. 284.

Footnote 13: Thorndike, Origin of Man, p. 146.

Footnote 14: Racial Differences in Mental Traits, pp. 177 and 181.

Footnote 15: Thorndike, Educational Psychology, Briefer Course, p. 374.

Footnote 16: Thorndike, Educational Psychology, Vol. III, p. 304.

Footnote 17: Moral Principles in Education, p. 17.

Footnote 18: For a fuller discussion of this topic see next chapter.

Footnote 19: For a discussion of these scales see Chapter XV.

Footnote 20: The Courtis Tests, Series B, for Measuring the Achievements
of Children in the Fundamentals of Arithmetic, can be secured from Mr.
S.A. Curtis, 82 Eliot Street, Detroit, Mich.

Footnote 21: Measurements of Some Achievements in Arithmetic, by
Clifford Woody, published by the Teachers College Bureau of
Publications, Columbia University, 1916.

Footnote 22: Reasoning Test in Arithmetic, by C.W. Stone, published by
the Bureau of Publications, Teachers College, Columbia University, 1916.

Footnote 23: A Scale for Handwriting of Children, by E.L. Thorndike,
published by the Bureau of Publications, Teachers College, Columbia
University.

Footnote 24: A scale derived by Dr. Leonard P. Ayres of the Russell Sage
Foundation is also valuable for measuring penmanship, and can be
purchased from the Russell Sage Foundation.

Footnote 25: Copies of the Spelling Scale can be secured from the
Russell Sage Foundation, New York, for five cents a copy.

Footnote 26: A Scale for the Measurement of Quality in English
Composition, by Milo B. Hillegas, published by the Bureau of
Publications, Teachers College, Columbia University.

Footnote 27: The Harvard-Newton Scale for the Measurement of English
Composition, published by the Harvard University Press, Cambridge, Mass.

Footnote 28: Scale Alpha. For Measuring the Understanding of Sentences,
by E.L. Thorndike, published by the Bureau of Publications, Teachers
College, Columbia University.

Scales for measuring the rate of silent reading and oral reading have
been derived by Dr. W.S. Gray, of the University of Chicago, and by Dr.
F.J. Kelly, of the University of Kansas. Reference to the use of Dr.
Gray's scale will be found in Judd's Measuring Work of the Schools, one
of the volumes of the Cleveland survey, published by the Russell Sage
Foundation. Dr. Kelly's test, called The Kansas Silent Reading Test, can
be had from the Emporia, Kansas, State Normal School.

Footnote 29: Completion Test Language Scales, by M.R. Trabue, published
by the Bureau of Publications, Teachers College, Columbia University.

Footnote 30: The student who is not interested in the statistical
methods involved in measuring with precision the achievements of pupils
may omit the remainder of this chapter.

Footnote 31: This explanation of the method of finding the median was
prepared for one of the classes in Teachers College by Dr. M.R. Trabue.

Footnote 32: The third decimal place is omitted in this table.

Footnote 33: In order to discover the relationship which exists between
two traits which we have measured we would use many more than seven
cases. The illustrations given are made short in order to make it easy
to follow through the application of the formula.

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