Students
First Exam.
Sec. Exam.
Third Exam
I
60
100
70
2
55
90
55
3
SO
80
80
4
45
95
55
S
45
85
70
6
40
95
50
7
40
80
50
8
35
70
65
9
35
85
45
10
30
75
60
II
30
80
50
12
30
90
75
13
25
95
30
14
25
90
60
IS
20
90
55
16
20
85
55
17
20
8e
35
18
15
100
50
19
15
65
40
20
10
80
45
21
10
85
35
22
5
85
45
23
5
60
30
24
75
25
Answer the following questions: —
1. Who is responsible for the low grades in the first examination and
the high grades in the second examination ? Do the grades mean that
the students loafed before the first examination and studied hard
before the second ? Or do they mean that the first examination was too
hard or too long and the second too easy or too short? Or do they
mean that the course of study was poorly organized at the beginning
and the teaching was poor at the start and after the poor showing in
the first examination the teacher "woke up" and "got busy" and did
good teaching?
Who, then, is primarily responsible for the grades in the first exami-
nation ranging from 60 to o and in the second examination from
100 to 60?
2. Which grade represents the greater ability, 60 given in the first
examination or 80 given in the second? 60 is 20% inferior to 80, of
course. But, on the other hand, only one student received 60 in the
first examination and none received a higher rating, whereas in the
second examination 5 students received 80 and 14 more received
higher grades than 80.
142 INTRODUCTORY PSYCHOLOGY FOR Tl'ACHEKS
3. If we arrange the students by order of merit according to their
grades in the three examinations, we find that the
best student got 60, 100 and 80, respectively,
the 1 2th student got 30, 85 and 50, respectively, and
the poorest student got o, 60 and 25, respectively.
Are 60, 100 and 80 equal then? or 30. 85 and 50? or o. 60 and 25?
4. In grading examination papers should we grade in terms of the
"ideal" paper, the best paper, the paper of an average student, or the
poorest paper? With which one of these standards is the teacher
most Ukely to be familiar? Which one is most likely to fluctuate
from year to year?
5. What final grades would you give these 24 students on the basis
of the three examinations? Plot the surface of distribution for the
grades you assign.
6. Are your final grades fair to the students? to the instructor? to
students in other classes in the institution? to other instructors? to
the institution as a whole? Explain.
Hand in your report at the next class-hour.
LESSON 28— METHODS OF GRADING STUDENTS*
The matter of grading students in a class is a subject that is inti-
mately connected with the subject of individual differences. It is
introduced here as an illustration of how this subject is related in
still another way to educational theory and practice.
SYSTEMS OP MARKING STUDENTS.
Grading on Percentage Basis with Prescribed Passing Mark. One
of the two most universally used systems of grading students is to give
students grades ranging from o to lOO, with some grade as 50, or 60,
or 75, or even 80, as a passing mark.
The theory underlying the granting of percentages is that the
student is graded in terms of absolute proficiency. If he gets 90 in
an examination in arithmetic or spelling, he has done 90% of the
examination correctly. The system works fairly well here. But it
falls down completely in such subjects as English Composition, or
history or geography, etc. For who knows what is absolute profi-
ciency in composition work for 5th grade children? How does such
a standard differ from the 4th grade, or from the 6th grade ? Actuall\-
in ordinary practise the grades represent at best only a certain per-
centage of what the teacher considers the class can do. It is based
on two very variable things — the teacher's estimate of what the class
can do, and second — the class itself. If the class is better than usual,
the teacher's grades stand for better work than usual ; if the class is
poorer than usual, the teacher's grades represent poorer work than
usual. Despite the best efforts of any teacher his grades are not
standardized on the basis of a fixed absolute standard but vary with
the calibre of his pupils. It is impossible under such conditions to
ever expect that a "85" will represent a definite standard of work in
a particular course. The 85 will vary from year to year with the
same teacher, and it will vary with every two teachers, depending
on those teachers' estimates of what a class can do. (All of these
statements have been substantiated in every investigation on this
subject and are no longer open to argument.)
Grading on Bcisis of Five Groups. The other most universally used
system of grading students is to give the students grades in terms of
about five letters or numbers, such as A, B, C, D, and F ; or E, S, M,
•CLASS-HOUR
IN CLASS
WRITE UP
READ
38
29
Discuss, Lesson 27
Experiment, Les. 39
Lesson 29
Lesson 2S
143
144 INTRODUCTORY PSYCHOLOGY i'OR 'iKACill-RS
I. and F; or again i, 2, 3, 4, and 5. The A, E, or i is given to the
best students ; the B, S, or 2, to the next best group ; etc. The F or
5 is considered as failure. Sometimes the fourth grade, D. 1, or 4 is
'•not passing" and sometimes it is considered as "conditioned"' requiring
another examination. At still other institutions D is a passing grade
but entitles the student to but 8ofo credit, so that in a 5-hour course
the student with a D will receive but 4 hours credit.
It is because of insurmountable difficulties pointed out above in
connection with the percentage system of marking that this system of
grading students with five letters has arisen. The whole scheme of
grading students on the basis of an absolute standard of perfection
is thrown away, or almost thrown away* The teacher then roughly
divides the class into five groups, the excellent students, the good, the
fair, the inferior, and the failures. More or less of the old scheme
survives in the case of deciding just what will constitute a passing
standard as distinguished from a failure. The essential thing, how-
ever, is the division of the class into five groups in terms of their
general ability and performance in the particular class.
Anyone familiar with the laws underlying individual differences
immediately realizes that these five groups should not contain an equal
number of students; — that the largest number of students should be
in the middle group, and that relatively few should be in the two
extreme groups, the excellent students and the failures. But the
study of how teachers grade students shows clearly that teachers diflfer
enormously as to how they distribute their grades under this scheme.
In Table X is shown the distrbution of grades in seven courses in
the University of Missouri prior to 1908. It is clear from this table,
and it represents conditions in every institution of that time and most
institutions today, that a student could quite easily win "honors," or
a scholarship, or make Phi Beta Kappa by electing Philosophy, Eco-
nomics, etc., but would have an extremely small chance of obtaining
these honors if he grouped in Chemistry. Yet an "A" counted
equally toward these honors whether obtained in Philosophy or Chem-
istry III. In the same way a poor student would have little trouble in
passing Philosophy but would stand a good chance of being "flunked" in
English II or Chemistry III. The problem educators are now facing
in regard to grading students is how to make an "A" or "F" mean the
same thing whether given by Prof. Smith or Prof. Brown, whether
given in Philosophy or Chemistry, whether given in 1915 or 1917.
•Of course, in those cases where a teacher marks a student by these five letters but
always translates the letter into a numerical figure, so that A equals 100 to 95; B, 95 to
85; etc.; he is practically following the first scheme and not the second. When the
second scheme is used properly there are no numerical values attached to the letters.
LESSON 28 145
TABLE X. SHOWING THE RELATIVE FREQUENCY OF FOUR
GRADES A. B, C, AND F. AS FOUND BY MAX MEYER IN
THE UNIVERSITY OF MISSOURI, IN 1908.
;Table based on Max Meyer, "The Grading of Students," Science, August
21, 1Q08, p. 3.)
Total No.
Course Distribution of Grades of Students
A B C F Considered
Pbilosophy 55 33 10 2 623
Economics 39 37 I9 5 ^"i
German II 26 38 25 11 941
Education 18 38 35 9 266
Mechanics 18 26 42 14 495
English II 9 28 35 28 1098
Chemistry III in 60 28 1903
An important step toward obtaining equitable grading has been to
apply the conception of our normal surface of distribution to the prob-
lem. Any group of students (barring exceptional cases considered be-
low) will divide themselves up into inferior, average, and superior
students and these three groups will approximate 259^0, 50% and
25% in size, respectively. They will do so if the method of grading
them is fair. If, however, the examination is too easy or too difficult
there will appear not a normal distribution but one in which there are
too many superior or too many inferior students, respectively. If in
two classes of 100 students, Prof. Smith and Prof. Brown require a
fair amount of work, then 25% of the students will do superior work,
50% average work and 25% inferior work. If Prof. Smith requires
too much and Prof. Brown too little, then it may appear that the
former has 40%) inferior and 10% superior students whereas the
latter has 10% inferior and 40% superior students. If we require
each professor to grade 25% of his students superior, 50% average,
and 25% inferior, then we recognize (i) that one class of students
taken as a whole is about equal to any other class and (2) that
students are graded in terms of what an average student will do and
not in terms of a variable standard of what is required by diflferent
instructors. In such a case we know that a "superior" student for
Prof. Smith has actually done better work than % of the students in
his class and that a "superior" student for Prof. Brown has likewise
excelled % of his class. A given grade is not then a grade in terms
of any absolute standard of perfection but is a grade in terms of
what average students can do.
With such a requirement the irregular grading shown in
Table X was eliminated to a large extent at the University
of Missouri. The average of all the grades for the under-
graduate courses became in 191 1, 23.7% superior, 49.9% average,
146 INTRODUCTORY PSYCHOLOGY FOR TEACHERS
and 26.4% inferior. Nineteen of the instructors distributed their
grades as shown in Table XL Comparison of the individual
instructor's gradings in this table with those in Table X shows an
enormous improvement in the way of uniform grading on the part of
the faculty. An '"E" now means nearly the same high grade of
scholarship whether given by one instructor or another. The gradings
in Table XI are, however, still too irregular as respecting Grades "I"
and ''F" to be entirely satisfactory.
The Missouri System of Grading. As can be seen from Table XI,
the Missouri system of grading students provides first of all for the
students being divided into three groups, — superior, average, and
mierior, — so that the first group comprises the best 25% of the >tu-
denls, the second group the middle 50%, and the third the remainder.
The superior and inferior are further divided so that in effect there
are five grades of E (excellent), S (superior), M (medium), I (in-
ferior), and F (failure). As illustrated in Plate XX the surface of
TABLE XI. SHOWING THE RELATIVE FREQUENCY OF THE FIVE
GRADES E, S, M, I, AND F, AS USED BY VARIOUS INSTRUCTORS
IN THE UNIVERSITY OF MISSOURI IN 191 1.
(Based on the "Report of the Committee on Statistics on the Grading sf the
Semester," Closing Feb., 191 1.)
Instructors
% E
% S
% u
% I
% F
A
7
29
51
8
5
B
5
23
52
15
5
C
3
21
51
21
4
D
7
21
56
8
8
E
6
15
60
13
6
F
I
22
55
17
5
G
2
17
64
II
6
H
3
21
52
18
6
I
3
24
46
21
6
J
3
20
51
20
6
K
3
20
S3
16
8
L
3
23
47
17
10
M
2
19
55
14
10
N
4
19
45
23
9
5
20
43
21
11
P
7
21
47
9
16
Q
3
13
52
19
13
R
5
II
43
29
12
S
3
15
47
20
15
Average
f
19.7
1
n
16.8
1
?
23.6 51.0 25.3
distribution is so divided that the difference in ability represented
by Grades E and S is equal to the difference between S and M, or
LKSSON 28
147
Grades 7
Plate XX. A normal surface of distribution divided up Into
five groups showing five grades of scholarship. At the
University of Missouri thes^ five grades are called P (fail-
xire). I (inferior), M (ra^dium) , S (superior), and B (ezoel-*
lent). At Peabody College the grades are called F (failure),
D (inferior), C (average), B (superior), and A (excellent.!
M and I, or I and F. The standard which all instructors are ex-
pected to reach in their grading is then that $0% of the students
shall receive an M, 22% an S, 22% an I, 3% an E, and 3% an F.
One objection to this scheme will immediately occur to some readers.
Maybe half the class has actually failed and you have given most of
them a C or D. Will that method of marking be fair? Yes, cer-
tainly; for if half the class fails, who is to blame? Undoubtedly, in
practically every case, no one but the teacher. The examination was
too difficult, or too long, or because of poor discipline the students
had not studied. This system throws the blame for poor work in the
class on the person who deserves the blame — the teacher. Of course,
sometimes a group of students will not work, then the only final resort
is to "flunk" them. But such cases are rare as compared with those
where the trouble lies in the main with the instructor.
Here are the faculty rules at George Peabody College for Teachers
on this subject. They make plain that the above system applies di-
rectly to large classes and only indirectly to small classes, and possibly
not at all to exceptional classes, such as in graduate courses.
''It is fair to assume that the average student in any undergraduate course is
equal in ability to the average student in any other undergraduate course. Con-
sequently it is fair to expect that all members of the faculty will in the long run
148 INTRODUCTORY PSYCHOLOGY FOR TEACHERS
(when they have marked 500 students, say) give approximately the same per
cent, of students each of the five grades.
"It is also fair to assume that the calibre of classes does vary, and that this is
particularly true in the case of very small classes. Consequently it is fair to
expect that the mcmlurs (if the faculty will vary considerably in the way they
mark the members of particular classes.
"We expect then in the long run that the members of the faculty will all use
the same standards. We also expect, on the other hand, that there will be
noticeable variation in the way individual classes will be marked. In the light
of these assumptions, the following rules are laid down:
"1. The quality of the student's work in a course shall be reported to the regis-
trar by use of the following grades : A, B, C, D, and F.
"2. The grade of "C" is designed to represent the performance of the mid-
dle 50% of the class. The grades of "B," and "D" represent work that is su-
perior and inferior, respectively, to that of the middle group. The grade of
"A" is reserved for markedly superior work, while the grade of "F" is de-
signed for those who have failed and shall receive no credit for their work.
Students receiving the grade of "D" will receive but 80% of the full credit at-
tached to the course, i. e., in a five-hour course such a student will receive but
four hours credit.
"3. It is recognized that the more advanced the student the more selected is
the class with which he will be grouped and the system of marking will vary
proportionately.
"4. Experience has shown that in the long run the instructor will give approxi-^
mately 3% of his students an "A," 22% of his students a "B," 50% a "C,"
22% a "D," and 3% an "F'."
Such a uniformity of grades from the members of a faculty is
highly desirable and is to be expected so long as it can be assumed
that the calibre of students in one class is equivalent to those in an-
other class. If an instructor gives proportionately more low or high
grades in his classes than this ideal, he declares in so doing that his
students are poorer or better than the students in other classes. This
's, of course, in many cases an actual fact, and when so, an instructor
should mark accordingly. But in the ordinary course of events one
class is pretty nearly equivalent to another class as far as ability of the
students composing it is concerned.
Varying the Amount of Credit with the Grade Given. The Uni-
versity of Missouri further provides that students shall obtain varying
amounts of credit for their work according as they obtain high or low
grades. At the present time in a one hour course, a student obtaining
an E earns 1.15 hours credit, a student obtaining an S earns i.io
hours credit, a student obtaining an M earns i.oo hour credit, a student
obtaining an I earns 0.85 hour credit, and a student obtaining an F
earns o credit. Prof. Max Meyer, who has been responsible for the
adoption of the Missouri scheme of grading, is now advocating that
the grades shall carry these amounts of credit: — E (1.2 hrs. credit),
S (i.i hrs. credit), M (i.o hr. credit), I (0.9 hr. credit), and P
(poor) (0.8 hr. credit). A student "who ought to repeat the course
LESSON 28 149
before his attainments are recognized, and who therefore is marked
F by his teachers, would receive no credit toward graduation.*
PRESENT TENDENCIES IN GRADING.
Among colleges and universities the tendency is away from the
percentage system to the group system and to a limited extent toward
the Missouri system, which has been adopted more or less entirely in
a number of institutions.
Among secondary schools, today, 30% employ percentage systems
and 65% the group system. Of those using the group system, 44%
have three grades above passing, 52% have four grades, and 4% have
five grades. The National Conference Committee on Standards of
Colleges and Secondary Colleges recommends 'that, ("if a group
system is used, the letters A, B, C, or A, B, C, D be employed to indi-
cate passing grades, and that E or F, or both E and F, be reserved
for failure. The committee calls attention to the fact that the
majority of colleges use four groups above passing, and that the
tendency in schools appears to be in that direction.
"The committee recommends that schools using a percentage sys-
tem follow what appears to be the most common practice, of using 60
as the passing grade.**
So in school grades any student must be compared with his class
and with the average of the class, not with the best one in the class,
aiid fortimately, as investigations have shown that the average per-
formance in one class is approximately the same as that in other
classes, we do have quite a stable standard from which to measure.
DISCUSSION OF THE PROBLEM ASSIGNED IN LESSON 27.
With these general considerations before us let us turn now and
consider the problem which was assigned in Lesson 27.
The Surfaces of Distribution ; What They Show. The grades from
the three examinations given in Lesson 27 are plotted in surfaces of
distribution in Plate XXL The three surfaces approximate the nor-
mal surface of distribution. The first one is long drawn out: the
effect obtained when the exam'ination is too difficult. The low grades
show the same fact. The second distribution is skewed — most of the
grades are bunched at the upper end. This is characteristic of too
easy an examination or one where nearly all could answer the ques-
tions in the alloted time. If the time had been cut in half the distribu-
tion would have resembled that of the third examination.
If we followed the old scheme of marking where, say, 60 was the
passing mark, we would, in the first examination, if we were true to
•Max Meyer, The Administration of College Grades, School and Society, Oct, 23, 1915.
••Report in School and Society, March 1, 1918, by Headmaster Ferrand.
ISO
INTRODUCTORY PSYCHOLOGY FOR TEACHERS
our Standards and had the requisite courage, fail all but one in the
class. In the second examination we would pass every one, and in the
third we would fail 17, or 71% of the class. Averaging the three
sets of grades we obtain the results given at the bottom of Plate XXI,
These grades would necessitate our failing 14 members of the class, or
58%. If the passing grade were 75 but one of the class would pass.
If it were 50 then 7 would fail, or 29%.
f
i>
c
n u
B
A
t}2l <f
l^f^n 1
7 S
VL
ItUii
iS i3 I* i
• y 5 a
1
f I> C B A
uii
n 2t
IS
• r H,
IT 13
zt
7 1
ii. »>
ii
Z3
If S M>
4 i-
z 7
1
1
C B h
1
lUy
Ziiit tS
lilt
Z» 1 f
It S
.J1
13 .7 i^
4 » z
10 Si )i
3
F P C B A
><
ly
u
•9
It
II If
Its
li
16
.0 i
*» 3
wii.i
!.^ 3 ,7
V J
»
Plat^ Jul* The ezamliiati on grades glTan in
Table U and the oomptited final- grades
plotted In snrfaaes of die-tribution, to-
gether with their conversion into Srades
A, B, C, D and F.
LESSON 28 151
This example Ls an extreme one, but is based on an actual case.
It is, however, useful here as it points out in an exaggerated form the
real situation that confronts the majority of instructors in their mark-
ing of students' papers. The grades a class actually receives, con-
sidering the class as a whole, are dependent on the instructor and him
alone. If the examination is difficult the class as a whole gets low
grades, if the examination is easy the class as a whole gets high
grades. Instructors who mark low are generally instructors who
require much from their students, while instructors who mark high
do not require enough. Of course, there are many exceptions to this
rule. To set up a standard such as 60 or 75 as a passing mark is to
postulate that the instructor is omnipotent, that he knows exactly
how easy or difficult to make an examination. Such an assumption is
preposterous.
The only method now known to education whereby the standard of
a class may be determined is to assume that the average student in one
class is equal to the average student in another. This assumption
is correct remarkably often, as determined by actual investigation.
When this is done, the middle half of the class, regardless of whether
they obtain 30. 85, or 50, are graded C. The upper fourth are graded
A or B, and the lower fourth, D or F. Just how that is done is in<B-
cated in Plate XXI. Theoretically 3% should receive an A and an
equal number an F. In actual practice, an instructor should feel
free to give no A or F, or several, depending on the circumstances of
the case. On the basis of Plate XXI,
I student would receive an A, or 4%
6 students would receive a B, or 25%
10 students would receive a C, or 42%
5 students would receive a D, or 21%
2 students would receive an F, or S%
The A and F grades must depend on circumstances.
In this particular case Student i is so far ahead that he alone
would be given an "A" unless the work of the class, including I's
work, was not very good. In the same way no grade of "F" might be
given if the work of 23 and 24 was acceptable ; or if the work was poor
19 might also be given an "F." But in the long run, the instructor
should give grades approximately as follows: — A-3%, B-22%, C-50%,
D-22% and F-3%.
Hoiv to Grade Papers. There are undoubtedly many good methods
of grading a student's paper. Circumstances will determine whether
one will read the whole paper thru and grade it as a whole, or whether
one will grade each part and then total the parts. The two give
152
INTRODUCTORY PSYCHOLOGY FOR TEACHERS