In the whole method the arrows indicate that the end of each line becomes associated with the beginning of the next, which is as it should be. In the part method, by which stanza A is repeated by itself until memorized, the last arrow indicates that the end of line 4 of stanza A becomes associated with the beginning of line I of the same stanza. This is an association that we do not care to build up. Hence time is wasted in building up an association which we do not want, and which, later on, will interfere with the association that we do want, namely, of the end of line 4 of stanza A with the beginning of line I of stanza B.

Greater concentration of attention by the whole method. — The other factor in explaining the superiority of the whole method of memorizing over the part method is the fact that the whole method secures greater concentration of attention. If small parts are repeated until memorized, after one or two repetitions the repeating may continue mechanically, with relatively little attention to what is being repeated. Such repetitions without concentration of attention are relatively wasteful, as we noted above. On the other hand, if the whole is repeated every time, when the learner approaches each part it retains certain aspects of novelty or unfamiliarity which are helpful to spontaneous attention. Furthermore, students often remark that the whole method "seems harder " than the part method. This means that greater effort is put forth during the process of memorizing by the whole method, and effort, when associated with spontaneous attention, is also conducive to the economical automatizing, or fixing, of associations, as was noted above on page 152.

5. Drill on real process; do not waste time on accessories. Thumbing dictionaries. - An important point in economy in learning is to waste as little time as possible on activities which are not an essential part of the activity that is being practiced. The most striking neglect of this principle is found in studying a foreign language largely by means of the dictionary. In

learning a foreign language the connections, or associations, that we desire to automatize are associations of foreign symbols with their meanings, and vice versa. From the standpoint of economy in learning, the more quickly the association can be started the better; but when the student meets new words in his reading and has to look up their meaning in a dictionary, a large part of the time is spent before the association which we desire to build up is even started. Moreover, having found the English equivalent, he notes it for a moment and starts to search for the next word to be looked up. Hence, a large part of his time is spent on an accessory process, namely, thumbing the dictionary, while the real process of concentrated repetition of the association is slighted.

Experiments on memorizing vocabularies demonstrate waste. The significance of this waste of time becomes apparent when we consider the large vocabulary that can be learned in a very short time if the material for the associations is provided outright and does not have to be gathered by the student. Thus, Dearborn experimented upon memorizing vocabularies provided by students in the form of parallel columns of French words and English equivalents. In presenting the tabulated results, he says:

Subject 1, for example, learned fifty French words daily for twenty-one days. . . . As a result of the practice over one thousand new words were learned, at least for the time being, in less than six and one-half hours. The ordinary vocabulary, with the exception of paradigms and declensions, usually learned in a semester's work in university classes is, I am told, less than half of this. (14: 386. Cf. 9: 142-143)

English equivalents and notes should be easily accessible. -If the translation method of teaching a foreign language is to be used, it is evident from such investigations that devices should be adopted to eliminate the waste of time in using a dictionary. If a systematic course covering at least

two years is worked out, it would be quite practicable to devise a series of textbooks that would give the English equivalent of each foreign word in some convenient, accessible form the first four or five times the word occurred. In some books this has been done by interlinear translation. If there is objection to this, the new vocabulary for each page can be printed at the bottom of the page. Certainly the explanatory notes should be printed there. Think of the hours of time wasted by millions of students in finding the notes printed in the back of readers and editions of the classics! It is far better that a few editors and printers should spend some time arranging material for economical use than that the time of students should be wasted.

Another ex

Flash cards save much time in drilling. ample of the possibility of avoiding waste of time on accessories is the use of "flash cards " for various forms of drill. In the elementary school this practice is very common in the work in arithmetic and reading. Thousands of arithmetical combinations are arranged on cards and "flashed" by the teacher before the class one at a time and very rapidly. When a pupil is called upon, he is expected to give the answer immediately. The same method could be used for rapid oral drill on many of the processes in algebra. It is being used for vocabulary drills in Latin in several places. By use of such a device practically all of the class are doing alert, rapid mathematical or linguistic thinking during the whole period of drill. No time is wasted in getting the associations or problems before their attention, and every member must be alert in expectation of being called on. Additional stimulus to attention is commonly provided by introducing the game spirit and recording the time taken to run through a given set of cards. Groups of pupils at certain ages become intensely interested in improving their own records or beating the records of other groups and succeed in accomplishing astonishing results in a short time.

6. What is the best distribution and length of practice periods? Writing German script. — In order to get some evidence concerning the best distribution of time for economical practice or drill, Leuba and Hyde carried on an experiment with some twenty-six subjects who were learning to write German script. (17: 351–369.) The practice periods were twenty minutes long. Six subjects practiced two periods a day, namely, at 8.40 A.M. and 1.30 P.M. Seven practiced one period a day, at 1.40 P.M. Six practiced one period every other day. Seven practiced one period every third day.

The following table shows the relative achievements after an equal number of periods of practice :

It is quite evident from this table that the once-a-day subjects achieved much more after a given number of periods of practice than did the twice-a-day subjects.

Learning to use new alphabets. - Another experiment to determine the most economical amount of time to spend each day in practice was described by Pyle in the Journal of Educational Psychology (1913). The practice material consisted of arbitrary new alphabets of twenty-six characters each. Practice with a given alphabet consisted in translating ordinary printed material into it. This is known by psychologists as a substitution test. In summing up the results from several subjects who carried on such practice with varying amounts of time per day, Pyle says:

On the whole our experiments warrant some such conclusion as the following: In habit formation [in the case of simple substitution

experiments] an adult can practice profitably for something like thirty minutes daily. The length of time for practice doubtless varies with individuals and with the stage of fixation of the habit. If practice is extended beyond thirty minutes, there may be some return for the extra time, but it is relatively small. It is quite probable that in the later stages of habituation the length of practice period could be shortened and the interval lengthened with practically as much return. A second practice on the same day is not quite as beneficial as the first practice. After a few practices, further practice on the same day is useless. (19: 158. Cf., however, 19 a)

Distributed repetitions best in memorizing.

In the inves

tigation of memorizing it has also been found that distributed repetitions are more economical than continuous repetitions. Thus, Ebbinghaus found that when the repetitions of series of nonsense syllables were distributed over three days, each series required thirty-eight repetitions, while sixty-eight repetitions were necessary for a series when they were all performed at a single sitting. (7: 265.) Another German investigator named Jost

devoted thirty repetitions without pause to the learning of a series of syllables; in another case he employed ten repetitions on each of three successive days. In both cases he tested accuracy of retention twenty-four hours after the repetitions had been completed. He found that the syllables which had been learned with distributed repetitions were retained better than those which had been learned with the same number of accumulated repetitions. Jost also attempted to determine how far the distribution of repetitions may be carried without giving rise to a deleterious result. He found that when the material to be learned is of large mass, the most extensive distribution is the most advantageous, both as to rapidity of learning and permanence of retention. (7: 266)

Lecture notes and readings should be reviewed soon after first repetition; later at increasing intervals. - Lyon, who has specialized upon the study of economy in memorizing, gives the following practical conclusion: