1100 1000 900 800 700 600 500 400 800 200 100 FIG. 16. 80 85 40 45 50 5 10 15 20 25 LEARNING CURVE SHOWING PROGRESS MADE IN BALL-TOSSING. The horizontal axis represents days. The vertical axis represents the number of balls caught. (From The Mind in the Making, by Edgar James Swift. Courtesy of Charles Scribner's Sons.) Copyright, 1908. Number of Solutions per Unit of Time 1 2 84667 9 10 11 12 FIG. 17. CURVE SHOWING PROGRESS MADE IN SOLVING PUZZLES. that all curves are of this sort. Most curves showing the acquisition of skill by human beings are of this kind. Most of the curves show rapid progress followed by slower progress. In some cases of learning, there may be but little apparent progress made at first but more rapid progress later. 16. Laws of Economical Learning Learning is a process of forming associations. In rote learning, the associations are formed between series of words or events. Many experimental studies have been made for the purpose of determining the most effective way of estab lishing these connections. From these studies, several important laws have been derived. 1. Other things equal, learning is conditioned by the number of attentive repetitions. Even after learning is apparently complete, added repetitions will strengthen the tendency to retain. 2. Other things equal, learning capacity increases up to maturity and then remains constant until the onset of old age. 3. If repetitions are distributed over several days, the learning is more effective than when repetitions are accumulated on a single day. The most effective distribution of repetition is conditioned by circumstances. 4. After intensive study of new material, there should be a pause or rest before taking up some other activity. The impressions made in the first instance are likely to be interfered with by the second activity unless the effects of the first activity have had time to "set." 5. Although there is some experimental evidence to the contrary, learning a selection by the whole method is generally regarded as a better procedure than learning it part by part and then piecing it together. Some investigators recommend a combination whole-part-whole procedure. 6. Other things equal, learning is most economical when the rate of repetition is adapted to the individual's abilities and peculiarities. Either a too rapid or a too slow repetition is wasteful. 7. Where rhythm can be employed its use facilitates the formation of bonds or connections. 8. Intention to recall facilitates learning. 9. When ideas have been learned in one connection, it is more difficult to learn them in another connection. Learning anything incorrectly, for example, makes correct learning more difficult. Wrong associations inhibit the establishment of correct associations. However, if the first set of associations were completely learned, the formation of others of the same kind may be made easier. 17. Adjusting Work to Suit the Ability of the Children [FREEMAN, Frank N., How Children Learn, p. 47. Boston, Houghton Mifflin Co., 1917.] This form of distribution of abilities corresponds to the distribution of different degrees of physical traits as, for example, height and weight. It may be used in a practical way in assigning school grades, provided we use a system of relative marks; or in calculating the extent to which any uniform mode of treatment will be likely to suit the different persons of a group. If school grades are so given that half the class receive the highest grade, or a third fail to pass, it is clear that the marks are not so distributed as to correspond with the differences in ability of the pupils. Yet such extremes of these may be found in the marks given by teachers in the same school. If, again, a school system is so arranged that one half the children cannot do the work which is planned and keep up with their grade, while only two or three per cent can do work which is superior to that which is supposed to be suited to the majority of the children, it is evident that the work is not adjusted to suit the ability of the children. 18. Interest in Improving [THORNDIKE, E. L., Educational Psychology, Vol. II, p. 225. New York Teachers College, Columbia University, 1913.] On the whole, though the interpretation of all of these facts is somewhat uncertain, I cannot but believe that they testify to the very great potency of interest, whereby the added zeal and satisfaction at success which come from adding for improvement primarily, rather than simply to provide an investigator with material on hunger or pause-length, increase the rate of gain notably. 19. The Importance of General Principles [THORNDIKE, E. L., The New Methods in Arithmetic, p. 45, Copyright, 1921. Courtesy of Rand, McNally & Co., Chicago.] But the newer methods are suspicious of learning only to forget, and in particular consider that the general principles should be the last things to be forgotten. If principles are taught that are really helpful, that really act in learning and retention, and are taught in the right way, it would seem that, even if certain details of how to compute were forgotten, these vital general principles would not be. 20. Learn One Thing at a Time [THORNDIKE, E. L., The New Methods in Arithmetic, p. 59. Chicago, Rand, McNally & Co., 1921.] If we try to learn all of a game at once, we may learn none of it, and perhaps think it beyond our capacity, or at least take the harmful attitude of expecting to blunder and fail. If we take the same game, one feature at a time, putting each new feature into coöperation with the others until we are playing the whole game as it is really played, we succeed. 21. The Importance of Over-learning [AVERILL, L. A., Elements of Educational Psychology, pp. 323-324. Boston, Houghton Mifflin Co., 1923.] It is an unfortunate tendency of most learners-particularly juvenile to stop the learning process the moment the datum can just be recited from memory. While such a minimum of repetitions may be all that is required, in the case of materials that it is not desired to retain permanently, it is a fact that by far the greater part of the associations that are built up in the schoolroom are supposed to be builded permanently. To guarantee a reasonable perpetuity of such associations it is highly important for the learner to 'over-learn'; otherwise permanence of impressions is extremely dubious. As we have noted in a previous connection, the unfortunate tendency of the quick learner to stop too soon results in his being a rapid forgetter. Through drill and thorough discussion, therefore, the teacher should take constant pains to assure herself that the pupils are thus over-learning, at the same time of course bewaring lest the process become so monotonous that interest lags and attention scatters. 22. Active Connection vs. Passive Learning [THORNDIKE, E. L., The New Methods in Arithmetic, p. 58. Chicago, Rand, McNally & Co., 1921.] The active connection of two things by the person is more potent than the passive hearing or seeing of them in connection. So we have the pupil study part of the table or other facts to be learned, then cover the answers with a card, and give them himself, looking at each to make sure he is right or if he is unable to think of any answer in which he has confidence. This he continues until he can give all correctly and fluently. He thus not only comes to know the facts more quickly, but also to know that he knows them. Cards with the questions on one side and the questions and answers on the other side may be used, especially where it is desirable not to have any help from the printed orders of the facts. 23. Only Correct Practice Makes more Perfect [Book, W. F., "The Psychology of Skill," University of Montana Study in Psychology, 1908, p. 177. Revised and reprinted in Psychology of Skill, p. 245. Gregg Publishing Co., New York, 1925.] Great effort wrongly or carelessly applied is even more detrimental to progress than a simple lapse in attention or effort. . . The tendency to slight the associations in the last stages of their development and to push ahead too fast can, of course, best be overcome, in typewriting, by not always practicing at maximum speed, for the effort for speed usually means that attention deserts the details of the work. To perfect carefully the elemental associations it will therefore be found better, practically, to practice more of the time for accuracy alone and only a small part of the time for speed-a custom generally followed by the best typewriting schools. 24. Daily Fluctuations in Attention and Effort [BOOK, W. F. Psychology of Skill. Copyright, 1925. Courtesy of Gregg Publishing Co., New York.] Variations in attention and effort of still more importance for learning than those just described are the fluctuations which occur from day to day. In our typewriting experiments there 1 These daily fluctations in attention and effort should not be confused with the diurnal changes in efficiency found by Lombard, Kraepelin and Marsh (see especially Archives of Phil., Psy. and Scientific Method, Columbia Contribution to Philosophy and Psychology, |