Improvement and the distribution of practice

Front matter

Class LJ3 /OCo I

Copyright In .

COPYRIGHT OEPOSm

Section II. The Lyndhurst Experiments with Grade Pupils 11 Description 11

Character of the School Population 1 1

Subjects used in the Experiment 1 1

Content-material used 12

Plan of the Experiment 15

Administration of the Experiment J 8

Scoring and Tabulating the Results 20

Results of the Lyndhurst Experiments 23

Tables of Frequencies 23

Comparison of the Two Sorts of Distribution 29

Geography and History 29

Single-column Addition 34

Short Division 38

Section III. The Ohio Experiments with Grade Pupils . . 41 Description 41

Character of the School Population 41

Subjects used in the Experiment 41

Content-material used 42

Plan of the Experiment 42

Administration of the Experiment 45

Scoring and Tabulating the Results 46

Results of the Experiments 46

Tables of Frequencies 46

Factors Conditioning Improvement 5 1

Initial Ability . 66

Amount of Gross Gain 66

Relation of Initial Score to Gross Gain 68

Introduction

It is the purpose of this monograph to report measurements of learning, especially by school children under ordinary classroom conditions, and with special reference to the distribution of time given to practice. The particular comparison made is between (i) a series of practice-periods approximately equal in length, and (2) a series of practice-periods decreasing progressively in length.

Some results obtained by Ebbinghaus ('85, pp. no ff.) and Jost's ('97) conclusions that "in the case of two associations of equal strength, but of different ages, a new repetition has a greater value for the older of the two, and that the older association weakens less with disuse in a given time," suggest that the second form of distribution may be the more favorable in the case of forming serial connections with senseless material. General theory also suggests that such a distribution might prevent wasteful overlearning in both initial practice and reviews in the case of a group of bonds which form a limited unit of instruction, as, for example, learning a new word in spelling, a vocabulary in a foreign language, or the anatomy of an animal. Whether such a distribution would prove essentially more favorable in such miscellaneous work as improving penmanship, oral speech, computations of various kinds, and the like, is more problematical.

The experiments to be reported here concern :

A. The learning of French vocabularies by adults.

B. The learning of geographical and historical facts by school children, after the following manner: A brief condensed summary of the facts was studied. The knowledge thus gained was measured by giving the summary, with certain important words omitted, as a completion test.

C. Improvement in single-column addition by school children and by adults.

D. Improvement in short division by school children.

2 Introduction

There is thus a range from the definite formation of new bonds from zero strength as in A, to the vague general improvement of a function already fairly well established, as in C and D.

Besides the comparison of the two sorts of distribution of time the experiments with school children furnish valuable data concerning the use of the practice method as a means of instruction, and concerning the relation of initial achievement to improvement.

Section I Learning French Vocabularies By Adults

The first study presented, though the last one completed, has to do with the formation of new bonds from zero strength, i. e., the learning of a relatively new thing, as, for example, a new word or object.

THE NATURE OF THE EXPERIMENT

The experiment reported in this chapter was carried out in the fall of 1917, with five graduate students in Teachers College acting as subjects. The group was composed of two women and three men, including the author himself. Three of the subjects (2, 4, and 5) were beginning students in French, and the other two (1 and 3) had studied some French several years ago. These facts will be given due consideration later.

The material learned consisted of French words which were prepared as follows : first, 1 ,200 ordinary French words were selected and written, together with their English equivalents, on separate slips of paper. These slips were placed in a box and shuffled. The words were then drawn out by chance, arranged in groups of ten, and rewritten. From the entire list thus formed two smaller lists of 150 words each were selected by chance. We first eliminated, however, all those words which were the same in English, or which were suggestive of the English meaning. Each list of 150 words was subdivided into five groups, since by trial it was found that approximately thirty French-English words could be read over in one minute, reading at a convenient rate. Thus it would require just five minutes to read over once an entire list of 150 words.

The following set of instructions, a copy of which was given to each of the subjects, will make clear the conditions of the experiment.

EXPERIMENT IN LEARNING

FRENCH VOCABULARIES

The purpose of the experiment is to compare two different distributions of time in the learning of the vocabulary of a foreign language: A — a schedule in which the study- periods are of equal length, and B — a schedule in which the study-periods decrease progressively in length.

DIRECTIONS

i. Be sure you understand all the following directions before beginning the learning of the words.

2. Select a time of the day that is least likely to be interrupted for the next

sixteen days, and use the same time of day throughout.

3. Note that there are two separate lists, each containing 150 French-English

words, and each having its own time-schedule.

4. It should require just five minutes to read over one entire list of 150

French-English words, i. e., at the rate of thirty words per minute.

5. When ready to begin, place a timepiece, having a seconds hand, within

easy view. Begin, when the seconds hand is at zero, and read over the French-English words, glancing at the timepiece at the end of every group of thirty words, in order to regulate the rate of reading so as to cover just thirty words per minute.

6. Articulate the words under the breath, pronouncing the French words as

best you can without undue waste of time.

7. At the end of each five minutes (which should also be at the end of the

list of 150 words, if you have properly timed the rate), allow a rest of one minute, then proceed to go over the entire list again, and so on, until the required amount of time has been put in for that practice-period according to the time-schedule.

8. Having put in the required amount of time with list No. 1, allow two or

three minutes' intermission, and then proceed with list No. 2, if the time-schedule calls for any practice on that day, following the same general instructions.

9. In case it should be found absolutely necessary to deviate from the above

directions, always do the next best thing possible, making note of such deviation on the blank provided. 10. Come to room 300 T. C. on the day after the experiment is finished for the purpose of taking the test.

All necessary materials for the test will be provided.

Note. Keep a daily record as called for on the blank provided.

The daily blank mentioned on the instruction sheet provided for a record of the hour when the study was done, the general conditions, i. e., physical, mental, etc., whether poor, good, or excellent, and whether or not there were any interruptions or other irregularities in the work.

Learning French Vocabularies by Adults 5

Table 1 gives the exact date of each practice, the amount of time spent, and the number of repetitions of the bonds.

TABLE I

Date of Each

Equal Schedule

Reducing Schedule

Study- Period

Time Spent

No. of Repet.

Time Spent

No. of Repet.

Mon. Oct. 29

20 min.

Tues. Oct. 30

40 min.

Wed. Oct. 31

30 min.

Thurs. Nov. 1

20 min.

Fri. Nov. 2

20 min.

Sat. Nov. 3

Sun. Nov. 4

20 min.

Mon. Nov. 5

15 min.

Tues. Nov. 6

Wed. Nov. 7

20 min.

Thurs. Nov. 8

Fri. Nov. 9

10 min.

Sat. Nov. 10

20 min.

Sun. Nov. 11

Mon. Nov. 12

Tues. Nov. 13

20 min.

5 min.

Totals

Thus we have, according to the plan of the experiment, an equal number of practice-periods spread over approximately (Reducing schedule one day shorter) the same total length of time. The total amount of time spent (120 min.), the average length of the study-periods (20 min.), and the total number of repetitions of the bonds (24) were the same for both schedules.

RESULTS OF THE EXPERIMENT

Two tests were given, the first on the day following the completion of the practice, and the second one week later. None of the subjects except the author, however, knew that a second test was to be given.

The order of the words in each list was rearranged for the purpose of the first test. List No. I, which was studied according to the Equal schedule, was given first, and after a few minutes intermission list No. 2, which was studied according to the Reducing schedule, was given. In the second test, the words were presented in the original order in which they were studied, but the order of giving the two lists was reversed, i. e., list No. 2 was given first, and after a few minutes' intermission list No. I was given.

Three of the five subjects did better with the Reducing list in both tests; the other two consistently did better with the Equal list. The number of words attempted and the number recalled correctly by each of the subjects in both tests were as follows:

FIRST

TEST

SECOND TEST

Subject

No. Attempted

No. R

^called

No. Att empted

No. Recalled

Reduc.

Reduc.

Reduc.

Reduc.

1— Alb.

H5

2 — Bar.

H3

H5

3 — Cum.

4 — Sen.

5— Coo.

in

Totals

112. 4

112 .2

107.6

112. 2

P. E.

14.8

27.9

16.0

21.8

The small amount of forgetting during the interval of one week between the first and the second tests, as shown by the above figures, may be partly accounted for by reference to three facts: (1) three of the subjects were studying beginning French at the time of the experiment; (2) one of the subjects (the author) had the advantage of going over both lists of words several times during the interim between the tests, in scoring the results of the first test; (3) the rearranging of the order of the words in the first test caused a lower score than otherwise might have been made, and the presenting of the words in their original order in the second test tended to give

Learning French Vocabularies by Adults 7

a somewhat higher score than otherwise. Hence the amount of forgetting appears less than would have been the case had the conditions just described been reversed in the two tests, or even had they been made equal in both tests.

The influence of these factors does not, of course, in any way invalidate the comparison of the two schedules of distribution of practice, as both lists of words were influenced alike. The only effect would be to reduce the amount of forgetting shown during the interim between the two tests.

Combining the results of the two tests we have, for the five subjects, an average of no words recalled correctly for the Equal list and an average of 1 1 1 .7 words recalled correctly for the Reducing list. Thus there is an average difference of 1.7 words in favor of the Reducing list. Owing to the large variability in the differences between the results of the two lists for the different subjects and the small number of subjects, the unreliability of this difference of 1.7 is very high. The P.E. of the t. — obt. Diff. is 3.56. This means that the chances are about even that the true difference with a large number of subjects will lie between 1.86, or about two per cent, in favor of the Equal schedule, and 5.26, or about six per cent, in favor of the Reducing schedule.

DISCUSSION OF THE TWO SORTS OF DISTRIBUTION

In general, the differences between these two sorts of distribution are as follows: (1) In respect to the length of the practice-period, the Reducing schedule has a larger number of repetitions occurring in the early part of the experiment, while with the Equal schedule the number of repetitions remains uniform for each practice-period throughout the experiment. (2) The length of the time 7 interval between periods gradually increases in the case of the Reducing schedule, while with the Equal schedule it remains constant.

The actual differences between the two schedules in our experiment, together with certain suggestions as to the possible influence of same upon the results, appear as follows: (1) The total length of time covered by the experiment was substantially the same {Reducing schedule one day shorter) for both schedules. (2) The number of practice-periods (six) was the same in both cases. (3) The number of repetitions of the bonds (twenty-four) was the same. (4) The length of the practice-periods was uniform (twenty minutes)

throughout for the Equal schedule, but for the Reducing schedule the length varied from forty minutes at the beginning of the experiment to five minutes at the close. (5) The time-interval between periods was uniform (three days) for the Equal schedule, while for the Reducing schedule it varied from one day at the beginning to four days at the close. In all other respects the conditions were substantially the same for both schedules. (

Referring to the length of the practice-period it might be argued by some that a forty-minute period is too long for grade pupils r especially for the lower grades, as fatigue may set in, or the pupils become bored by so long a period of intensive work. So, also, it might be argued that a five-minute period is too short to allow for a proper 'warming up'. If these suppositions be true, then our Reducing group suffered a disadvantage.

On the other hand, the knowledge of a shorter practice-period at each succeeding time might, conceivably, serve as a stimulant. Moreover, the gradually decreasing length of the practice-period, together with an increasing interval between may be said to approximate more nearly the curve of forgetting; hence the Reducing schedule may, after all, be a more favorable arrangement.

With regard to the time-interval between periods, it would seem fair to conclude that neither schedule had any very great advantage, as no interval was shorter than twenty-four hours and none was longer than four days.

The optimum distribution of time has not, as yet, been determined in a sufficient number of cases to enable one to formulate any general rule that might be calculated to hold true for all situations. The whole matter is summed up by Thorndike in the following words :

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.

What period-length shall be considered 'very long' depends on the amount of variety and satisfyingness the function shows. Two hours is, thus, a very long period for adding or learning 32-syllable nonsense series, but perhaps not for playing golf or chess.

Learning French Vocabularies by Adults 9

What interval between periods shall be considered 'very short' depends on the length of the periods themselves, and also on the character of the function. For adding practised in twenty-minute periods, an interval of five minutes would be very short, and probably also one of five hours. The knowledge that would enable one to define the statement made in the text is lacking.

In a more recent work Hollingworth and Poffenberger confirm the above summary with the following statement :

The conclusion which has been drawn from experiments of this type is that too great concentration or distribution of time is not economical. The learning periods should be short enough to avoid the onset of fatigue, and long enough not to cause the loss of too much time in getting warmed up to the task at the beginning of the learning period.

According to Jost's law, stated in the Introduction, one would expect our Reducing schedule to show better results than the Equal, because of the piling up of repetitions in the earlier part of the experiment, which in turn would mean a larger number of bonds that were older when the same were exercised again later on in the experiment. Just how to equate this fact against the further fact that these older bonds would necessarily receive a fewer number of repetitions as compared with bonds of equal age in the Equal schedule, however, is a problem yet unsolved. It should, at least, be remembered that Jost's main argument was based upon the relearning of associations which had been formed up to a given strength — that of producing one correct recall — and subsequently dropping below the limen through disuse, while most of the experimental work bearing upon the question of length of practice-period and time-interval between has been done by the exercising of subliminal bonds.

The results of our experiment showed a small difference in favor of the Reducing schedule. The large variability amongst individuals in the differences between the two schedules, as shown by the results obtained, together with the small number of subjects, gives the very high unreliability index of 3.56. This means that the chances are about four to one that the true difference with a large number of subjects will lie between 5.42 in favor of the Equal schedule and 8.82 in favor of the Reducing. The chances are about twenty-four to one that the true difference will lie between 8.98 in favor of the Equal schedule, and 12.38 in favor of the Reducing, or about ninety-nine to one that the true difference will lie between

I o Improvement and the Distribution of Practice

12.54 i n favor of the Equal schedule and 15.94 in favor of the Reducing schedule.

In the succeeding chapters will be found a report of an attempt to further answer this same question through a series of experiments with public school children working under ordinary everyday conditions. The same problem was also studied with a group of 157 normal school students acting as subjects. On account of certain difficulties arising from the attempt to use entirely new material in the experiment with school children, it was necessary to adapt material from that which is regularly used in the schools. This was done by making use of material taken from geography, history, addition, and division. A part of this same material was also used in the experiment with normal school students.