Edward Lee Thorndike.

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Professor of Educational Psychology, Teachers College
Columbia University

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Reprinted from Teachers College Record, Vol. II, No. 2, March, 1910



(Statins (EuUpgp. Ql0lumbta ItntupraUy



Copyright 1910
Copyright 1912



1 . Introduction i

Part I. The Measurement of the Quality of Handwriting

2. The Construction of a Scale for Quality of Handwritings by

Children in Grades 5 to 8 4

3. The Nature of the Scale, including Qualities or Degrees of Merit

from that of Copy-Book Models down 7

4. Criticisms of the Scale 8

5. The Uses of the Scale 17

6. A Scale for Quality in Adult Women's Writing 19

7. The Derivation of the Scale 24

Part H. The Speed and Quality of Handwriting in
Seven School Systems*

8. Diflferences between Systems . . . '. 29

9. The Relation of Differences in Results to Differences in Means

and Methods of Teaching Handwriting 32

10. Differences between Individuals within the Same School System.. 33

11. The Relation Amongst Individuals between Speed and Quality.. 35

12. The Relation of the Quality of Slow Writing to the Quality of

Rapid W'riting by the Same Individual 36

13. Miscellaneous Comments 36

14. A Scale Based on Equally Often Noted Diflferences in Quality. . . 40

Scale A between pp. 10 and 1 1

Scale B " " 24 and 25

Scale C '' " 40 and 41







Section i. Introduction

Handwriting may profitably be studied from three points of
view : — that of the physiology and psychology of movement,^
that of the part it may play in the intelligently directed activities
of child life in schools,- and that of the direct examination of
the quality and speed of handwriting secured by various forms
of school training. But to any study of it there is one very
desirable preliminary — some means of measuring the quality
of a sample of handwriting.

At present we can do no better than estimate a handwriting
as very bad, bad, good, very good, or extremely good, knowing
only vaguely what we mean thereby, running the risk of shift-
ing our standards with time, 'and only by chance meaning the
same by a word as some other student of the facts means by it.
We are in the condition in which students of temperature were
before the discovery of the thermometer or any other scale for
measuring temperature beyond the very hot, hot, warm, luke-
warm, and the like, of subjective opinion. We opine roughly
that, at a fairly rapid rate, writing-movements in which the fore-
arm shares will produce a better quality of handwriting than
movements confined more exclusively to the thumb and fingers,
but no one could estimate with surety and precision hozu much
better the best rapid " free-arm " writing is than the best equally
rapid " finger-movement " writing. We opine roughly that drills
in which good writing serves some end of consequence to the

^_No attempt is made in tiiis article to report any results of physio-
logical or psychological analysis of the behavior involved in hand-
writing. The student of this aspect of the subject should consult
especially the investigations of Preyer. Judd and Freeman.

°_ No attempt is made in this article to report the experiences or
opinions of students of education with respect to the utilization of
the original tendencies of children so as to secure a rational and
economical cultivation of handwriting as an expressive art.


2 Handzvriting

children will be more efficient than drills for mere penmanship,
but no one could estimate hozv much more efficient they will be.
We know that some schools secure better writing at a given
speed than do other schools, but no one could tell hozv much
better in any terms sure of understanding and agreement ; for
we have no scale to measure handwriting by. No pupil, teacher,
or superintendent of schools knows how well any child, class,
or group of children writes in anything approaching the sense
in which we know how hot any liquid is or how long a wire is.

The main purposes of this monograph are to describe the
means by which a graphometer or scale for handwriting may be
made, to present such a scale for the handwriting of children
in grades 5, 6, 7, and 8, to explain how such a scale is to be
used, to present a similar scale for adult women's handwriting,
and to mention some of the facts and questions of importance
to which the discovery and use of these scales have led.

Many circumstances have combined to prevent me from giving
at this time anything like a perfect scale. The individual differ-
ences amongst competent judges in rating any example are so
great that to get for it a measure accurate within one per cent of
the difference in merit between the best and the worst of gram-
mar-school (i.e., grades 5 to 8) writing requires that at least 200
judges rate it. I have not been able to command the services
of so many. For the greatest practical convenience a scale
should have for any quality samples of all the common styles
of children's writings, and should include about ten qualities
differing each from the next by equal steps — equal, that is,
within, say, four per cent of a step or one half of one per
cent of the difference between the worst and the best grammar-
school writing. But to get such samples one would need to have
several thousand samples of each style of writing, and to have
about half a million ratings made. This means roughly four
thousand hours of labor. The final selections of samples for
the scale should properly be made from very many printed
reproductions such as will form the scale itself. The cost has
prohibited me from making many of these.

The scale is presented now, in spite of its imperfections, for
these reasons : It is the result of some twenty thousand ratings

Introduction 3

and ensures measurements far more accurate than anyone could
make without it. For the present needs of school practice
and educational research, a very precise instrument for measur-
ing handwriting is not required. The best way to get a more
perfect scale is by the use of this one as a starting point.

This scale is then offered as a preliminary scale w'hose imper-
fections the maker is, perhaps, more conscious of than any critic
will be. I beg the reader to bear this in mind, since, for the
sake of simplicity in description in w'hat follow^s, I shall not in
each case state the fact that a quality or point on the scale is
determined only to a certain approximation, and the fact that the
differences between successive qualities are only approximately


The Measurement of the Quality of Handwriting

Section 2. The Construction of a Scale for Quality of Hand-
writings of Children in Grades 5 to 8

If one selects from children's written work 1000 samples rang-
ing from the best to the worst handwriting found in grades 5
to 8 and tries to rank these 1000 samples in order of merit for
handwriting, one finds that he cannot make 1000 such ranks.
Some of the handwritings will be indistinguishable in " good-
ness " or " quality " or " merit." Nor can one make 100 such
ranks. Nor can one make 40. One can make about 20, but if
he so ranks the samples a number of times he gets substantially
the same average result as he gets when he ranks them a number
of times in 10 or 11 groups. To get an individual's judgment
of the relative merits of the 1000 samples it is sufficient to have
him rank them in 10 or 11 groups three or four times. If he
grades in 10 groups and tries to make the difference in
" goodness " or " quality " or " merit " all equal, — to make, that
is, the sample he puts in the highest group (call it 11) as much
superior to those in the next highest group (call it 10) as the
latter are to those he puts in the second from the highest group
(call it 9), etc., etc., — we have in the average^ result of his
groupings his judgment of the relative merits of the samples in
a specially convenient form. For instance, if he grades sample
217 as in group 5 three times, as in group 4 once, and as in
group 6 once, and grades sample 218 as in group 6 three times,
in group 5 once, and in group 7 once, he judges 218 to be " i "
better than 217, " i " being, in the individual's judgment, one
tenth of the difference between group i and group 11.

If thirty or forty individuals chosen from competent judges
of handwriting thus judge the 1000 samples, the average^ of all

' Except for certain factors which will be described in section 7.

The Measurement of the Quality of Handivriting 5

their gradings give approximately the relative merit of each
sample in the judgment of competent judges in general. If
they grade sample 317 in group 3 two times, in group 4 five
times, in group 5 thirteen times, in group 6 thirteen times, in
group 7 five times, and in group 8 two times, their average or
median grade for it is 5.5. If their average or median grade
for sample 318 is 6.4, they esteem 318 as .9 better than 317.
The .9 means, in their judgment, nine tenths of one tenth of the
difference between grade one and grade eleven.

If now from all the 1000 samples we could find some w^hich
were graded exactly i, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 by the
average or median^ judgment of 30 or 40 competent judges, each
grading the set into groups i to 11 by what he thinks are equal
steps in merit, we would have a very useful scale of merit in
handwriting. It would include all grades from the worst to
the best and would proceed by what were, by the average com-
petent opinion, equal steps. Or if we could find some graded
1.5, 2.4, 3.3, 4.2, 5.1, 6.0, 6.9, 7.8, 8.7, 9.6, and 10.5 we would
have a scale nearly as useful. It would not be so likely to in-
clude the very worst and very best samples, but would proceed
by equal steps, as before.

The scale which I shall proceed to describe was obtained by a
method in principle the same as the above.

Such a scale could be got in a different way, as follows : Sup-
pose competent judges to compare each sample with every other,
stating in each case which was better. If then w^e picked out
samples a, h, c, d, etc., such that a was judged better than h,
just as often as h was judged better than c, and just as often as
c was judged better than d, and so on, we could have, in samples
a, b, c, d, etc., a scale by equal steps, if two other conditions were
fulfilled by them. The first of these conditions would be that a
should not be judged better than b and worse than b equally
often. For if it were, a would be equal to b, b to c, e to d, and
so on, and we would have no extent to our scale. The second
of these_£onditions would be that a should not ahvays be judged
better than b. For, if it were, it might be just enough better
to barely be so judged, or it might be very, very much better.

^ Except for certain factors which will be described in section 7.

6 Handzvriting

Only if differences are not always noticed can we say that dif-
ferences equally often noticed are equal. But if we had, as
a result of the judgments, facts like those below, we could say
that a, b, c, d, etc., represented samples of writing progressing
by equal steps of difference in quality.

looo comparisons of a, b, c, d, etc., being made :

a was judged better than b in y^^ per cent., equal to & in ii
per cent., and worse than b in i6 per cent, of the judgments.

b was judged better than c in 73 per cent., equal to =

10 Handwriting

selecting, with the aid of thirty or forty competent judges, sam-
ples whose merit is exactly 8 or lo or 12 or 14 as the case may
be, and adding these to the scale. I shall be grateful to any one
who sends me collections of children's handwritings of styles not
represented in the scale.

Each such sample should be accompanied by a statement of all
the grades assigned to it on our scale by at least ten or twelve
competent observers, each of w4iom measures it with the scale
and rates it in complete ignorance of the ratings given by all the
other judges. It is desirable, though not necessary, that the
writings be on unruled paper.

In the second place, the qualities below 5 and above 17 should
perhaps be represented in the scale by actual children's writings.
This defect could be remedied by collecting children's handwrit-
ings that were superlatively bad and superlatively good. I shall
be grateful to anyone who sends me samples of children's writing
which are notably better than quality 17 or notably worse than
quality 5.

In the third place, although I have so far spoken of the quali-
ties 5, 6, 7, 8, 9, 10, etc., as if they might be absolutely these
amounts — as if the 13's might be all absolutely equal in merit and
all absolutely halfway between any one of the 12's and any one
of the 14's — this is not exactly the case. As was noted on page
3, the scale is only approximate. 16 on the scale does not
pretend to mean 16.00000, but between 15.9 and 16.1. 8 does not
pretend to mean 8.0, but between 7.9 and 8.1. And as a matter
of fact, although I have had a thousand samples graded and have
chosen as wisely as I could, some of the samples do vary in merit
from 7, 8, 9, 10, etc., by more than .1 plus or minus. Even after
one has picked samples that vary only that much, the relations
may be altered in the process of making the electrotypes from
which the scale is printed or in the process of printing itself.
This defect can be remedied by the expenditure of enough time
and money in getting more samples, having them graded by more
judges, reproducing more of them in electrotypes, and having
these reproductions graded again by more judges. In this work
I am now engaged. The defect is, however, of little consequence
to any use to which any of my readers is likely to put the scale.

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Online LibraryEdward Lee ThorndikeHandwriting → online text (page 1 of 4)