learning a given amount or the amount learned in a stated period of

time. We may do this for the learning of any material, whether it be

Greek verbs or typewriting. All that is necessary is to decide upon

some method by which progress can be noted and expressed in numerical

units. This, you will observe, constitutes a statistical approach to

the processes of study, such as is employed in science; and just as the

statistical method has been useful in science, so it may be of value in

education, and by means of statistical investigations of learning we

may hope to discover some of the factors operative in good learning.



Progress in learning is best observable when we represent our

measurements graphically, when they take the form of a curve, variously

called "the curve of efficiency," "practice curve," "learning curve."

We shall take a sample curve for the basis of our discussion, showing

the progress of a beginner in the Russian language for sixty-five days

(indicated in the figure by horizontal divisions). The student studied

industriously for thirty minutes each day and then translated as

rapidly as possible for fifteen minutes, the number of words translated

being represented by the vertical spaces on the chart. Thus, on the

tenth day, twenty-five words were translated, on the twentieth day,

forty-five words.



[Illustration (graph): STUDY OF RUSSIAN]



In making an analysis of this typical curve, we note immediately an

exceeding irregularity. At one time there is extraordinary

improvement, but a later measurement registers pronounced loss. This

irregularity is very common in learning. Some days we do a great amount

of work and do it well, but perhaps the very next day shows marked

diminution in our work.



The second characteristic we note is that there is extremely rapid

progress at the beginning, the curve slanting up quite sharply. This is

common in learning, and may be accounted for in several ways. In the

first place, the easiest things come first. For example, when you are

beginning the study of German, you are given mostly monosyllabic words

to learn. These are easily remembered, hence progress is rapid. A

second reason is that at the beginning there are many different

respects in which progress can be made. For example, the beginner in

German must learn nouns, case endings, declension of adjectives, days

of the week; in short, a vast number of new things all at once. At a

later period however, the number of new things to be learned is much

smaller and improvement cannot be so rapid. A third reason why learning

proceeds more rapidly at first is that the interest is greater at this

time. You have doubtless many times experienced this fact, and you know

that when a thing has the interest of novelty you work harder upon it.



If you will examine the learning curve closely, you will note that

after the initial spurt, there is a slowing up. The curve at this point

resembles a plateau and indicates cessation of progress if not

retrogression. This period of no progress is regarded as a

characteristic of the learning curve and is a time of great

discouragement to the conscientious student, so distressing that we may

designate it "the plateau of despond." Most people describe it as a

time when they feel unable to learn more about a subject; the mind

seems to be sated; new ideas cannot be assimilated, and old ones seem

to be forgotten. The plateau may extend for a long or a short time,

depending upon the nature of the subject-matter and the length of time

over which the learning extends. In the case of professional training,

it may extend over a year or more. In the case of growing children in

school, it sometimes happens that an entire year elapses during which

the learning of an apparently bright student is retarded. In a course

of study in high school or college, it may come on about the third week

and extend a month or more. Something akin to the plateau may come in

the course of a day, when we realize that our efficiency is greatly

diminished and we seem, for an hour or more, to make no progress.



Inasmuch as the plateau is such a common occurrence in human activity,

we should analyze it and see what factors operate to influence it. It

is interesting to note that the plateau generally occurs just before an

abrupt rise in efficiency. This is significant, for it may mean that

the plateau is necessary in learning, especially just before reaching

the really advanced stages of proficiency. Accordingly, when you are

experiencing a plateau in the mastery of some accomplishment, you may

perhaps derive some comfort from the prospect of an approaching rise in

efficiency. On the theory that it is a necessary part of learning, it

has been regarded as a resting place. We are so constituted by nature

that we cannot run on indefinitely; nature sometimes must call a halt.

Consequently, the plateau may be a warning that we cannot learn more

for the present and that the proper remedy is to refrain for a little

while from further efforts in that line. We have possible justification

for this interpretation when we reflect that a vacation does us much

good, and though we begin it feeling stale, we end it feeling much

fresher and more efficient.



But to stop work temporarily is not the only way to meet a plateau, and

fatigue or ennui is probably not the sole or most compelling

explanation. It may be that we should not regard the objective results

as the true measure of learning; perhaps learning is going on even

though the results are not apparent. We discovered something in the

nature of unconscious learning in our discussion of memory, and it may

be that a period of little objective progress marks a period of active

unconscious learning.



Another meaning which the plateau may have is simply to mark places of

greater difficulty. As already remarked, the early period is a stage of

comparative ease, but as the work becomes more difficult, progress is

slower. It is also quite likely that the plateau may indicate that some

of the factors operative at the start are operative no longer. Thus,

although the learning was rapid at the beginning because the material

learned at that time was easy, the plateau may come because the things

to be learned have become difficult. Or, whereas the beginning was

attacked with considerable interest, the plateau may mean that the

interest is dying down, and that less effort is being exerted.



If these theories are the true explanation of the plateau, we see that

it is not to be regarded as a time of reduction in learning, to be

contemplated with despair. The appropriate attitude may be one of

resignation, with the determination to make it as slightly disturbing

as possible. But though the reasons just described may have something

to do with the production of the plateau, as yet we have no evidence

that the plateau cannot be dispensed with. It is practically certain

that the plateau is not caused entirely by necessity for rest or

unconscious learning. It frequently is due, we must regretfully admit,

to poor early preparation. If at the beginning of a period of learning

an insecure foundation is laid, it cannot be expected to support the

burden of more difficult subject-matter.



We have enumerated a number of the explanations that have been advanced

to account for the plateau, and have seen that it may have several

causes, among which are necessity for rest, increased difficulty of

subject-matter, loss of interest and insufficient preparation. In

trying to eliminate the plateau, our remedy should be adapted to the

cause. In recognition of the fact that learning proceeds irregularly,

we see that it is rational to expect the amount of effort to be exerted

throughout a period of learning, to vary. It will vary partly with the

difficulty of subject-matter and partly with fluctuations in bodily and

mental efficiency which are bound to occur from day to day. Since this

irregularity is bound to occur, you may well make your effort vary from

one extreme to the other. At times, perhaps your most profitable move

may be to take a complete vacation. The vacation might cover several

weeks, a week-end, or if the plateau is merely a low period in the

day's work, then ten minutes may suffice for a vacation. As an adjunct

to such rest periods, some form of recreation should usually be

planned, for the essential thing is to permit the mind to rest from the

tiresome activity.



If your plateau represents greater difficulty of subject-matter and

loss of interest, your duty is plainly to work harder. In exerting more

effort, make some changes in your methods of study. For example, if you

have been accustomed to study a certain subject by silent reading,

begin to read your lessons aloud. Change your method of taking notes,

or change the hour of day in which you prepare your lesson. In short,

try any of the methods described in this book, and use your own

ingenuity, and the change in method may overcome the plateau.



If a plateau is due to our last-mentioned cause, insufficient

preparation, the remedy must be drastic. To make new resolutions and to

put forth additional effort is not enough; you must go back and relay

the foundation. Make a thorough review of the work which you covered

slightingly, making sure that every step is clear. This process was

described in an earlier chapter as the clarification of ideas and is

absolutely essential in building up a structure of knowledge that will

stand. Indeed, as you take various courses you will find that your

study will be much improved by periodical reviews. The benefits cannot

all be enumerated here, but we may reasonably claim that a review will

be very likely to remove a plateau, and used with the other remedies

herein suggested, will help you to rid yourself of one of the most

discouraging features of student life.



READING AND EXERCISE



Reading: Swift (20) chapter IV.



Exercise I. Describe one or more plateaus that you have observed in

your own experience. What do you regard as the causes?