With reference to the problem of the most favorable distribution of single readings. . . I would say that the most general statement that can be made, taking all materials and methods of presentation into consideration, is that the most economical method is to distribute the readings over a rather lengthy period, the intervals between the readings being in arithmetical proportion. For example, with one individual, in memorizing a poem of twenty stanzas, the highest retentiveness was obtained by distributing the readings as follows: two hours, eight hours, one day, two days, four days, eight days, sixteen days, thirty-two days, etc. The practical bearing of the results obtained on education in general is that when associations have once been formed, they should be recalled before an interval so long has elapsed that the original associations have lost their color and cannot be recalled in the same shape, time, and order. In general it was found that the most economical method for keeping material once memorized from disappearing was to review the material whenever it started to fade. Here also the intervals were found to be, roughly speaking, in arithmetical proportion. For similar reasons the student is advised to review his lecture notes shortly after taking them, and, if possible, to review them again the evening of the same day. Then the lapse of a week or two does not make nearly so much difference. When once he has forgotten so much that the various associations originally made have vanished, a considerable portion of the material is irretrievably lost. (18: 161)

The results of the experiments by Leuba, Pyle, Ebbinghaus, Jost, and Lyon upon distributed practice versus more continuous practice should not be accepted as final and as furnishing entirely reliable guides for school programs without further critical study of the results of other experimenters. Such a critical comparison is furnished by Thorndike in his "Psychology of Learning” (9: 193–206), but the results are often so contradictory that the following tentative statement is the only general conclusion that he provides :

The experimental results obtained justify in a rough way the avoidance of very long practice periods and of very short intervals.

They seem to show, on the other hand, that much longer practice periods than are customary in the common schools are probably entirely allowable, and that much shorter intervals are allowable than those customary between the first learning and successive reviews in schools. (9: 194)

On the whole, however, so very few of the infinite number of ways in which any given total time can be distributed have been tested for even substitution tests and addition, that psychology has little yet to offer in advance of the experience of sagacious workers. (9: 206)

Empirical discussion of practice upon the piano. There is a large body of empirical or practical discussion of the principles of effective and economical practice. To a certain extent the conclusions reached by practical teachers are in harmony with the results of experimental investigations. As an exercise in further thinking about the results presented up to this point in the chapter, students may examine and evaluate the suggestions for practice contained in the following quotation from Josef Hofmann's book entitled "Piano Playing," from which other excerpts have been quoted above on pages 111-112. Under the head of General Rules, Hofmann writes as follows:

Now, as to Practice. Let me suggest that you never practice more than an hour, or at the most two hours, at a stretch, according to your condition and strength. Then go out and take a walk and think no more of music. This method of mental unhitching, so to speak, is absolutely necessary in order that the newly acquired results of your work may, unconsciously to yourself, mature in your mind and get, as it were, into your flesh and blood. (Compare Thorndike 9: 300-331)

After every half hour make a pause until you feel rested. Five minutes will often be sufficient.

A valuable little hint here, if you will allow me: Watch well that you actually hear every tone you mean to produce. Every missing tone will mean a blotch upon your photographic plate in the brain. Each note must be not mentally but physically heard, and to this

imperative requirement your speed must ever subordinate itself. It is not at all necessary to practice loudly in order to foster the permanence of impressions. Rather let an inward tension take the place of external force. It will engage, sympathetically, your hearing just as well.

With regard to finger exercises. Do not let them be too frequent or too long at the most a half hour a day. A half hour.daily, kept up for a year, is enough for anyone to learn to play one's exercises.

A rule for memory exercises. If you wish to strengthen the receptivity and retentiveness of your memory, you will find the following plan practical: Start with a short piece. Analyze the form and manner of its texture. Play the piece a number of times very exactly, with the music before you. Then stop playing for several hours and try to trace the course of ideas mentally in the piece. Try to hear the piece inwardly. If you have retained some parts, refill the missing places by repeated reading of the piece, away from the piano. When next you go to the piano (after several hours, remember), try to play the piece. Should you still get stuck" at a certain place, take the sheet music, but play only that place (several times, if necessary), and then begin the piece over again, as a test if you have better luck this time with those elusive places. If you still fail, resume your silent reading of the piece away from the piano. Under no circumstances skip the unsafe place for the time being and proceed with the rest of the piece. By such forcing of the memory you lose the logical development of your piece, tangle up your memory, and injure its receptivity.

With regard to technical work: Play good compositions and construe out of them your own technical exercises. In nearly every piece you play you will find a place or two of which your conscience tells you that they are not up to your own wishes — that they can be improved upon either from the rhythmical, dynamical, or precisional point of view. Give these places the preference for a while, but do not fail to play from time to time again the whole piece, in order to put the erstwhile defective and now repaired part into proper relation to its context. Remember that a difficult part may "go" pretty well when severed from its context and yet fail utterly when attempted in its proper place.

As to the number of pieces: The larger the number of good compositions you are able to play in a finished manner, the better grow your opportunities to develop your versatility of style; for in almost every good composition you will find some traits, peculiar to itself only, which demand an equally special treatment. To keep as many pieces as possible in your memory and in good technical condition, play them a few times each week. Do not play them, however, in consecutive repetitions. Take one after the other. After the last piece is played, the first one will appear fresh again to your mind. This process I have tested and found very helpful in maintaining a large repertory. (4: 19-27)

Conclusion of discussion of automatizing associations. This will include the third of the chapters which deal primarily with processes of association in teaching. Of these, Chapter IV treated the problem of forming correct motor responses to situations; Chapter V contained a discussion of the best methods of associating symbols and meanings. The present chapter has emphasized the most economical and effective methods of automatizing or making permanent various types of associations. A summary of the important factors in such economical automatizing is found at the beginning of this chapter. In the next chapter we shall take up the third type of learning which we are to consider, namely, reflective thinking.

BIBLIOGRAPHICAL NOTES

General discussions of practice or drill. I. BAGLEY, W. C. The Educative Process. (The Macmillan Company, 1905.) Pp. 328–331. A very influential chapter.

2. COLVIN, S. S. The Learning Process. (The Macmillan Company, 1911.) Pp. 40-46, 64–70, 159-178. Brief reliable summaries of experimental evidence.

3. COLVIN, S. S. The Practical Results of Recent Studies in Educational Psychology. School Review, May, 1913. Vol. XXI, pp. 307–322.

4. HOFMANN, JOSEF. Piano Playing. (Doubleday, Page & Company, 1908.) Pp. 19-33. Very readable essays.

5. KIRKPATRICK, E. A. Genetic Psychology. (The Macmillan Company, 1909.) Pp. 111-140. General discussion of habit formation.

6. LADD, G. T., and WOODWORTH, R. S. Elements of Physiological Psychology. (Charles Scribner's Sons, 1911.) Pp. 572-582. Brief summary and interpretation of experimental data.

7. MEUMANN, E. The Psychology of Learning. (D. Appleton and Company, 1913.) Pp. 231–364. Extended summary and interpretation of the experimental evidence by the leading contemporary German authority.

8. STRAYER, G. D. pany, 1911.) Pp. 41-50. 9. THORNDIKE, E. L. The Psychology of Learning, being Vol. II of Educational Psychology. (Teachers College, 1913.) The standard critical summary in English of experimental investigations of practice. Should be studied by all instructors. Too difficult for undergraduates.

The Teaching Process (The Macmillan Com-
Good pedagogical discussion.

10. WATT, H. J. The Economy and Training of Memory. (Longmans, Green & Co., 1910.) An excellent little manual based on results in experimental psychology.

Special experimental investigations. II. ABBOTT, E. A. On the Analysis of the Factor of Recall in the Learning Process. Psychological Review Monograph Supplements, 1909, Vol. XI, pp. 159–177. Experimental justification of the use of recall.

12. BOOK, W. F. The Psychology of Skill. Bulletin No. 53, Psychological Series, No. 1. (University of Montana publications, 1908.) Extended report of elaborate experiments on practice in typewriting.

13. BRYAN, W. L., and HARTER, N. Studies in the Physiology and Psychology of the Telegraphic Language. Psychological Review, 1897, Vol. IV, pp. 27–53, and 1899, Vol. VI, pp. 345–375. A widely quoted study.

14. DEARBORN, W. F. Experiments in learning. Journal of Educational Psychology, 1910, Vol. I, pp. 384–387. Experiment on memorizing vocabularies.

15. EBBINGHAUS, H. Memory. (Published 1885, translated 1913, Teachers College, Columbia University.) The pioneer experimental investigation of memorizing.

16. LAKENAN, MARY E. The Whole and Part Methods of Memorizing Poetry and Prose. Journal of Educational Psychology, April, 1913, Vol. IV, pp. 189–198. Verifies earlier work on poetry and includes work on prose to three hundred words.

17. LEUBA, J. H., and HYDE, W. An Experiment in Learning to make Hand Movements. Psychological Review, Vol. XII, pp. 351–369. Shows superiority of distributed practice in learning German script.