Memorizing is a form of mental work that is susceptible of management, and several principles of scientific management have been worked out that may greatly assist in the learning of a long and difficult lesson. The problem has been approached from the angle of economy or efficiency. Suppose a certain amount of time is allowed for the study of a lesson, how can this time be best utilized?

The first principle of economy has already been sufficiently emphasized: observant study, directed towards the finding of relationships and significant facts, is much more efficient than mere dull repetition.{339}

The value of recitation in memorizing.

"Recitation" here means reciting to oneself. After the learner has read his lesson once or twice, he may, instead of continuing simply to read it, attempt to recite it, prompting himself without much delay when he is stuck, and verifying his recitation by reference to the paper. The question is whether this active reciting method of study is or is not economical of time in memorizing, and whether or not it fixes the lesson durably in memory. The matter has been thoroughly tested, and the answer is unequivocally in favor of recitation. The only outstanding question is as to how soon to start attempting to recite, and probably no single answer can be given to this question, so much depends on the kind of material studied, and on peculiarities of the individual learner. Where the sense rather than the exact wording of a lesson has to be learned, it is probably best to recite, in outline, after the first reading, and to utilize the next reading for filling in the outline.

The results of one series of experiments on this matter are summarized in the adjoining table.

Three facts stand out from the table: (1) Reading down the columns, we see that recitation was always an advantage. (2) The advantage was more marked in the test conducted four hours after study than in the test immediately following the study. To be sure, there is always a falling off from the immediate to the later test; there is bound to be some forgetting when the lesson has been studied for so short a time as here; but the forgetting proceeds more slowly after recitation than after all reading. Recitation fixes the matter more durably. (3) The advantage of recitation is less marked in the meaningful material than in case of nonsense syllables, though it is marked in both cases. The reason is that meaningful material can better be read observantly, time after time, than is possible with nonsense material. Continued reading of nonsense material degenerates into a mere droning, while in repeatedly reading meaningful material the learner who is keenly interested in mastering the passage is sure to keep his mind ahead of his eyes to some extent, so that his reading becomes half recitation, after all.

Whence comes the advantage of recitation? It has a twofold advantage: it is more stimulating, and it is more satisfying. When you know you are going to attempt recitation at once, you are stimulated to observe positions, peculiarities, relationships, and meanings, and thus your study {341} goes on at a higher level than when the test of your knowledge is still far away, with many readings still to come. You are also stimulated to manipulate the material, by way of grouping and rhythm.

On the side of satisfaction, recitation shows you what parts of the lesson you have mastered and gives you the glow of increasing success. It shows you exactly where you are failing and so stimulates to extra attention to those parts of the lesson. It taps the instincts of exploration, manipulation, and mastery much more effectively than continued re-reading of the same lesson can do. The latter becomes very uninteresting, monotonous and fatiguing.

Perhaps, after all, the greatest advantage of reciting is that it makes you do, in learning, the very act that you have later to perform in the test; for what you have finally to do is to recite the lesson without the book. When reading, you are doing something different; and if it were altogether different, it probably would not help you at all towards success in the test. But since intelligent reading consists partly in anticipating and outlining as you go, it is a sort of half recitation, it is halfway doing what you are trying to learn to do. Memorizing consists in performing an act, now, with assistance, that you later wish to perform without assistance; and recitation first stimulates you to fashion the act conformably to the object in view, and then exercises you in performing that act.

Spaced and unspaced repetition.

Another question on the economical management of memorizing: Is it better to keep steadily going through the lesson till you have it, or to go through it at intervals? If you were allowed a certain time, and no more, in which to prepare for examination on a certain memory lesson, how could the study time be best distributed? This question also has received a very definite answer.{342}

Spaced repetitions are more effective than unspaced. In an experiment of PiÉron, a practised subject went through a list of twenty numbers with an interval of only thirty seconds between readings, and needed eleven readings to master the list. But a similar list, with five-minute intervals, was mastered in six readings; and the number of readings went down to five with an interval of ten minutes, and remained the same for longer intervals up to two days. With this particular sort of lesson, then, ten minutes was a long enough interval, and two days not too long, to give the greatest economy of time spent in actual study.

In a somewhat different experiment in another laboratory, lists of nonsense syllables were studied either two, four, or eight times in immediate succession, and this was repeated each day till a total of twenty-four readings had been given to each list; then, one day after the last reading of each list, the subjects were tested as to their memory of it. The result appears in the adjoining table.

The widest distribution gave the best score. Undoubtedly, then, if you had to memorize a poem or speech, you would get better value for time spent if you read it once or twice at a time, with intervals of perhaps a day, than if you attempted to learn it at one continuous sitting. What exact spacing would give the very greatest economy would depend on the length and character of the lesson.

Spaced study also fixes the matter more durably. Every student knows that continuous "cramming" just before an {343} examination, while it may accomplish its immediate purpose, accomplishes little for permanent knowledge.

When we say that spaced repetitions give best results in memorizing, that does not mean that study generally should be in short periods with intervals of rest; it says nothing one way or the other on that question. The probability is, since most students take a certain time to get well "warmed up" to study, that fairly long periods of consecutive study would yield larger returns than the same amount of time divided into many short periods. What we have been saying here is simply that repetition of the same material fixes it better in memory, when an interval (not necessarily an empty interval) elapses between the repetitions.

Whole versus part learning.

In memorizing a long lesson, is it more economical to divide it into parts, and study each part by itself till mastered, or to keep the lesson entire and always go through the whole thing? Most of us would probably guess that study part by part would be better, but experimental results have usually been in favor of study of the whole.

If you had to memorize 240 lines of a poem, you would certainly be inclined to learn a part at a time; but notice the following experiment. A young man took two passages of this length, both from the same poem, and studied one by the whole method, the other by the part method, in sittings of about thirty-five minutes each day. His results appear in the table.

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Here there was an economy of eighty-three minutes, or nearly twenty per cent., by using the whole method as against the part method. Similar experiments have regularly given the same general result.

However, the matter is not quite so simple, as, under certain conditions, the results tend the other way. Let us consider a very different type of learning test. A "pencil maze", consisting of passages or grooves to be traced out with a pencil, while the whole thing was concealed from the subject by a screen, was so arranged that it could be divided into four parts and each part learned separately. Four squads of learners were used. Squads A and B learned the maze as a whole, squads C and D part by part. Squads A and C learned by spaced trials, two trials per day. Squad B learned the whole thing at one sitting; while squad D, which came off best of all, learned one part a day for four days, and on the fifth day learned to put the parts together. The results appear in the adjoining table, which shows the average time required to master the maze by each of the four methods.

When the trials were spaced, the whole method was much the better; but when the trials were bunched, the part method was much the better; and, on the whole, the unspaced part learning was the best of all. Thus the result stands in apparent contradiction with two accepted laws: that of the advantage of spaced learning, and that of the advantage of whole learning.

This contradiction warns us not to accept the "laws" {345} too blindly, but rather to analyze out the factors of advantage in each method, and govern ourselves accordingly. Among the factors involved are the following four:

(1) The factor of interest, confidence and visible accomplishment--the emotional factor, we might call it. This is on the side of part learning, especially with beginners, who soon feel out of their depth when wading into a long lesson, and lose hope of ever learning it in this way. This factor is also largely on the side of unspaced as against spaced learning, when the part studied is of moderate length and when there are recitations to keep up the interest; for when the learner sees he is getting ahead, he would rather keep right on than wait for another day to finish. To have a task that you can hope to accomplish at once, and to attack it with the intention of mastering it at once, is very stimulating.

(2) The factor of recency, of "striking while the iron is hot". When an act has just been successfully performed it can easily be repeated, and when a fact has just been observed it can readily be put to use. This factor is clearly on the side of unspaced learning; and it is also on the side of part learning, since by the time you have gone through the whole long lesson and got back to where you are now, the recency value of what you have just now accomplished will have evaporated.

(3) The factor of meaning, outlining and broad relationships. This is on the side of whole learning, for it is when you are going through the whole that you catch its general drift, and see the connections of the several parts and their places in the whole. This factor is so important as to outweigh the preceding two in many cases, especially with experienced learners dealing with meaningful material. Even if you should prefer the part method, you would be wise to begin by a careful survey of the whole.{346}

(4) The factor of permanency. This is something "physiological", and it is on the side of spaced learning. The muscles profit more by exercise with intervals of rest than by a large amount of continuous exercise, and no athlete would think for a moment of training for a contest of strength by "cramming" for it. Apparently the neurones obey the same law as the muscles, and for that reason spaced learning gives more durable results than unspaced.