A Tentative Inventory of the Habits of Children From Two to Four Years of Age

In this study of children it is important not only to discover as far as possible the original tendencies and capacities

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A Tentative Inventory of the Habits of Children From Two to Four Years of Age

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A TENTATIVE INVENTORY OF THE HABITS OF CHILDREN FROM TWO TO FOUR YEARS OF AGE

By RUTH ANDRUS

SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY, I N THE FACULTY OF PHILOSOPHY COLUMBIA UNIVERSITY

Published by

^satifsra (Hatlsqs. (SLalumbm lUnivsreits New York City .

1924

Copyright, 1924, by Teachers College, Columbia University

ACKNOWLEDGMENTS The writer is deeply indebted to Professor Patty Smith Hill for her unfailing interest and inspiration, and also for the opportunity to train a class in Kindergarten-Primary Education in observation of young children. Without-Professor Hill's interest and the opportunities offered by her, this study could not have been completed. The members of the class in Kindergarten-Primary Education contributed many hours of hard work and for this the writer is •very grateful.' This occasion is taken tp express gratitude to Dr. Agnes Rogers, whose friendly interest and advice in the preliminary experiment made the present experiment possible. To the heads of the nursery schools in which the experiment was carried on, the writer .wishes to express her appreciation of their kindly and helpful cooperation. The writer acknowledges her indebtedness to the other members of the dissertation committee, Professor Gates, Professor Thomson, and Professor Pintner for their advice and aid, and is also grateful to Professor McCall who, in an unofficial capacity, rendered assistance. R. A.

CONTENTS CHAPTER I

PAGE

INTRODUCTION

i

T H E PRELIMINARY EXPERIMENT

c

III

T H E PRESENT EXPERIMENT...

8

IV

TRAINING I N OBSERVATION.

II

V VI VII

lo

T H E CHILD FROM TWO TO FOUR YEARS OF AGE

19

T H E FINAL REVISION OP THE INVENTORY

25

SUMMARY OF ACHIEVEMENTS AND CONCLUSIONS

27

APPENDIX: INVENTORY I I A N INVENTORY OF THE HABITS OF CHILDREN FROM . Two

TO FOUR YEARS OF AGE

35

TABLES AND FIGURES TABLE I

PAGE

METHOD OF COMPUTING VARIATIONS AND CHILDREN'S SCORES

II

13

M E A N VARIATION FOR 69 STUDENTS

14

III

M E A N SCORES AND SIGMA OF INVENTORY SCORES FOR Two AGE-GROUPS

15

IV

M E A N VARIATIONS FOR 25 STUDENTS OBSERVING FOR FIVE WEEKS

V

16

M E A N VARIATIONS FOR "DOCUMENTARY EVIDENCE" EXPERIMENT

VI

16

INTERCORRELATIONS FOR INVENTORY SCORES FOR TWO AGE-GROUPS

21

FIGURE

1

PROFILES FOR

2

PROFILES FOR 3 CHILDREN I N GROUP I I

23

3

PROFILE FOR BOYS AND GIRLS I N GROUP 1

23

4

PROFILE FOR BOYS AND GIRLS I N GROUP I I

24

5

PROFILES FOR GROUP I I N 4 NURSERY SCHOOLS

24

6

PROFILES FOR GROUP I I I N 4 NURSERY SCHOOLS

24

7

CURVES SHOWING EFFECT OF DIRECTED PRACTICE ON ABILITY TO F I L L OUT AN INVENTORY...

29

8

3

CHILDREN I N GROUP

CURVE SHOWING EFFECT

I

'.....

OF DIRECTED PRACTICE ON

T I M E CONSUMED I N FILLING OUT INVENTORIES 9

23

29

CURVES SHOWING THE EFFECT OF N O PRACTICE, U N D I RECTED,

AND

DIRECTED

PRACTICE

ON ABILITY

TO

F I L L OUT AN INVENTORY ON THE BASIS OF DIARY RECORDS

30

^

'

CHAPTER I INTRODUCTION

. *

Since the time of Rousseau and Pestalozzi, the child, his original tendencies and capacities, has become more and rriore the center around which our educational theories and, of late to an increasing extent, our practice have developed. In this country, the child study movement was initiated by G. Stanley Hall. Decided impetus has beeri given to the scientific pursuit of child study by E. L . Thorndike and John B. Watson; by the former in his emphasis on the importance of original tendencies for any theory of education, and by the latter in his experiments to determine the instinctive reactions of infarits especially in the field of emotions. The necessity for careful study of the child as a basis for curriculum-making has always been a fundamental tenet of the philosophy of education advocated by Patty S. Hill. The method of child study suggested and employed by Thorndike and Watson is the laboratory method of animal psychology. Various other methods have been used in the study of children such as: I . The questionnaire method— a. in which the answers depend on observation directed in a general way to some one subject. b. in which the answers depend on reminiscence and anecdote. G. Stanley Hall is probably responsible for the first method and, in this way, vast amounts of data were amassed by him and his students. The second means of collecting data was employed by many' too enthusiastic followers of Hall who so deluged the country with more or less pointless questionnaires that James says, " I t will be well for us if in the next generation such circulars be not ranked among the common pests of life." There are two chief faults to be found with the method used

2

Habits of Children from Two to Four Years

by Hall: one, that no means were employed by which reliable interpretation is given the data; the other, that the results of the interpretation are not given statistical treatment (E. L . Thorndike, £dMca/ioMo/ Psychology, 1920, pp. 29-37). 2. The method of observation, which may be: a. "intensive," i.e., observation of one child. b. "extensive," i.e., observation of many children. (Norsworthy and Whitley, The Psychology of Childhood.) c. for a long period of time to determine growth. d. for a short period to determine specific achievement or for the purpose of diagnosis. e. active or participating when questions are put to the child by the observer and the answers recorded. f. passive or non-participating when the observer as unobtrusively as possible records the activities observed. g. carried on in controlled or uncontrolled situations, ranging from such controlled situations as those of a standardized intelligence test through such semi-controlled situations as are found in school to the relatively uncontrolled situations of entirely unsupervised play. . h. directed or undirected, i.e., directed by lists of objective questions; undirected because the observation is carried on merely for its own sake. Since Tiedemann in 1787 noted from day to day and month to month the activities of his son (Essay on Infancy trans, by Perez), there have been many such diaries of children's growth. Among these are Preyer's The Infant Mind, Darwin's The Expression of Emotion in Man and Animals, Shinn's The Biography of a Baby, and Rasmussen's Child Psyclwlogy. In "The Story of a Sand-Pile" by G. Stanley Hall (Aspects of Child Life and Education), we' have an example of the observation of several children for a short period. The accumulation of data in regard to school grades, and the general and specific condition of the health of children when such data are collected by the census method, is the result of extensive observation. In Rowe's "The Vocabulary of a Child at Four and Six," we find observation carried on for a short period to determine specific achievement (Rowe, E. C. Pedagogical Sennnary, 1913). Such an inventory as that of Taylor's, An Inventory of the Minds of Individuals

Introduction

3

from Five to Six Years Mental Age (Teachers College Contributions to Education, No. 134), is based on active or participating observation, direct questions being put to the individual and the answers recorded. These various types of observation are not mutually exclusive. Indeed, there is great overlapping among them. No one study based on observation will'illustrate one type and only one. The method used in the present experiment is intensive as well as extensive since, while orily one child is observed by one person, fifty-two children are observed by as many individuals. I t is also observation carried* on for a short period to determine achievement; it is non-participating since the observer does not add any stimulus to that offered by the environment of such a controlled situation as that afforded by the nursery school; it is undirected in that the observer is to record every activity of the child, but directed also since the observation is guided and interpreted by a list of objective questions. "Child study," then, to quote Cyril Burt ("Experimental Psychology and Child Study," 1922), "is objective and its data are found in the conduct of children." In-this study of children it is important not only to discover as far as possible the original tendencies and capacities of the infant and young child but also how far these may be subject to training and in what lines, and at what ages such training may be given with a maximum of profit. That educators as well as psychologists and psychiatrists are beginning tb appreciate the iniportance of habit formation in this early period is evidenced by the present movement to extend our educational system downward in the establishment, of nursery schools or educational centers for children from two to four years of age. Since the child is taken as the starting point for curriculummaking, it is very important to have an inventory or list of the abilities of children at various ages that the best curriculum may be developed. Up to this time, no such inventory has been made for children from two to four years of age. The "Tentative Inventory of Habits of Children from Four to Six" (Teachers CoUege Bulletin, Fourteenth Series, No. 4, 1922), by Rogers, applies only to children of kindergarten age. The present study was originally undertaken to discover what abilities children of nursery school age could be expected to possess. With this object in view, the preliminary experiment was

4

Habits of Children from Two to Four Years

undertaken in the summer of 1923 with the Manhattanville Nursery School as a laboratory, with the result that, a tentative list of habits was formed. As the experiment progressed, a twofold use for the inventory became evident,—^as an instrument for the appraisal of the abilities of children from' two to four with possible diagnostic and prognostic value, and also as a means of training teachers in more accurate observation of children and in knowledge of the habits and educability of children of these ages. The objects, then, of the present experiment are: 1. To put in the hands of a group of kindergarten-primary teachers the tentative inventory of specific habits or abilities of children from two. to four to be used in classifying and evaluating such activities. 2. To ascertain the reliability of the results obtained from the use of the inventory by observers of several types. 3. To ascertain the influence of different amounts and types of training on ability to fill out inventories on the basis of diary records. 4. To study the amount and, to some extent, the significance of individual differences among children observed and classified by means of the inventory. 5. To ascertain the merits and defects of the tentative inventory for the purpose of constructing an improved instrument.

CHAPTER I I T H E P R E L I M I N A R Y EXPERIMENT METHOD OF CONSTRUCTING T H E INVENTORY

A preliminary inventory of the abilities of children from two to three was constructed by the four members of a class in kindergarten-primary research. This inventory consisted of four divisions made up of the following number of subheadings and items: PRELIMINARY INVENTORY

Divisions Emotional Mental Motor Social-Moral

Subheadings II

5 4 8

Items 59 41 42 38

The subheadings and items were selected as follows: 1. Items suggested by the "Tentative Inventory of Habits of Children from Four to Six" by Rogers, the Woodworth-Mathews "Study of the Emotional Instability of Children by Means of a Questionnaire," and other unpublished data collected by the kindergarten department of Teachers College. 2. Items suggested by descriptions of observed behavior recorded in some one hundred and more books and articles. 3. Items suggested by actual activities of children observed by the members of the research class. These children were in the Manhattanville Nursery School. This preliminary inventory was then used as the basis of the preliminary experiment and as a result it was revised and enlarged by means of data of the following types: I . Data secured by means of the recorded observations of activities of children. For this purpose, four children from two to three years of age were observed for eight hours each week for four weeks by twenty-four observers. One child was assigned to each observer. Since there were twenty-four observers, during every one of the eight hours of observation at least two people 5

6

Habits of Children from Two to Four Years

were recording the activities of each child. The activities observed were recorded as they occurred and there was no collaboration between observers. 2. Data secured by the further study and analysis of books and articles. REVISION AND EXTENSION OF T H E INVENTORY

That this first inventory might be used as the basis of the present experiment, it was necessary to extend it to include the abilities of the child from three to four since in the present experiment the range of ages found in the usual nursery school was to be covered. The items for this revision and extension were secured as follows: 1. Items suggested by the experimenter's observation of chiU dren from three to four. 2. Data secured from the study and analysis of books and articles. 3. Items suggested by various psychologists and those interested in child study.. In the case of the tentative inventory used in the preliminary experiment, the only method of scoring employed was the tabulation of the number of times in each week any activity occurred. A graph was made for each child for each subheading with a week for the unit of time. The subheadings were not weighted, so the graphs were not comparable, and it was, therefore, impossible to get a profile or graphic picture for each child for each division of the inventory. In the revised form used in the present experiment, a definite method of scoring was devised, space was left before each question for the answer, and to this answer a score was assigned. A scoring key was made by which each division of the inventory was scored and checked three times. The revised form of the inventory consisted of four divisions made up of the following number of subheadings and items: INVENTORY I

Divisions Emotional Mental Motor Social-Moral

Subheadings 14 6 4 ID

Items 144 . Ill

"7 . 75

The subheadings of Inventory I were not used in the revised form, Inventory I I .

The Preliminary Experiment

7

METHOD OF TRAINING OBSERVERS I N T H E PRELIMINARY EXPERIMENT

At the time this experiment was undertaken, opportunity was given to train a class in Nursery School Organization in detailed and accurate observation of children's activities. I t was then possible to have twenty-four trained observers to collect data. The training was conducted in the following manner: During the first week, the members of the class took notes on the activities of the children and classified them according to the divisions and subheadings of the inventory. Because these records were not sufficiently detailed or accurate, it was necessary to present a sample of the type of observing and recording desired. For the remaining period of the experiment, a minute record made during the observation period of every activity of each child was handed in each week. No attempt was made in the preliminary experiment to have the members of the observation class fill out inventories, i.e., answer the questions in the inventory on the basis of the recorded observations.. RESULTS OF T H E PRELIMINARY EXPERIMENT

In the preliminary experiment, in addition to securing data in accordance with which the inventory was revised, two main uses for the inventory became evident: 1. As an instrument for appraising at one time four phases of children's abilities, Emotional, Mental, Motor, and Social-Moral. The possibility of using the results of such appraisal, first, for the diagnosis of general abilities and disabilities, as. well as for the discovery of the growth of children over a longer or shorter period, and second, for the prognosis of the progress and success of the individual child. 2. As a method of training teachers in the knowledge of the habits and abilities of young children, and of how and when these habits may be formed; and also in more accurate observation of the children in their charge. Teachers trained in this way become aware of the importance of details of activity.

CHAPTER I I I T H E PRESENT EXPERIMENT Since such a small group of children with an age range of but twelve months was studied in the preliminary experiment, and since the data secured seemed to indicate the value of attempting to develop and standardize the inventory as well as to test its worth in the hands of a larger group of students of education, the present experiment was undertaken with the following purposes in view: 1. To test the value of the inventory in the hands of such practical workers as a class in Kindergarten-Primary Education in Teachers College; to discover how intelligently and with what ease the questions in the inventory could be answered by such an unselected group. 2. To test the reliability of the results obtained from inventories filled out by such a group, and for this purpose to devise some objective measure of their ability to observe and record. 3. To ascertain individual differences in ability to fill out inventories on the basis of diary records and to what extent such use of the inventory is, conditioned by (o) previous general,experience and training, (b) directed or undirected practice, and to what extent either is desirable. 4. To discover the value of the inventory in estimating individual differences among young children and between groups. 5. To ascertain how many hours of observation are necessary to obtain a reliable score on the inventory. 6. To further revise and extend the inventory on the basis of the data obtained from observing a larger group of children, and to make the method of scoring automatic and simple enough to enable teachers of average training to obtain reliable results. The present experiment was begun in September, 1923, when a class in Kindergarten-Primary Education was given the experi-'. menter that all phases of the problem might be developed. A t , this time, permission was obtained to use four nursery schools in various parts of New York City as laboratories. These were the 8

The Present Experiment

'

9

Manhattanville, Horace Mann, Greenwich House, and Judson Health Center nursery schools. These were chosen, first, because, in addition to their being under the direct supervision of Teachers College, they are all conducted on the same general plan, and second, because they draw their pupils from such different parts of the city that a distribution giving a random sampling of children . from two to four years of age might be obtained. The children of the Manhattanville Nursery" School are predominantly poor American, of mixed parentage, Scotch, Irish, English and German, with one Italian and one Jew. The children in the Horace Mann School are well-to-do American, of mixed' parentage, with one Jew. Those in Greenwich House are poor American, of mixed parentage, with some Italian and Greek children, American born of foreign-born parents. Judson Health Center draws from a foreign quarter, predominantly Italian, but the children are all American born. There are five colored-children in the entire group of fifty-two children. (For discussion of nationality, see Chap. V, p. 20.) Because the children of the Manhattanville Nursery School who were studied in the .preliminary experiment were two to three years of age, not two to four, the inventory was revised and extended to include the abilities of'children from three to four as described in the previous chapter. The revised form, which was used as the basis of the present experiment, is Inventory I,^ "A Tentative Inventory of Habits of Children Two Years Old," Teachers College Bulletin, Fifteenth Series, No. 3. Since there are two distinct phases of this experiment, each will be treated separately in Chapters I V and V under the followimg heads: I . Training in Observation. I I . The Child from Two to Four Years of Age.'' • Inventory I is not included in the present study. I t appears only in the Teachers CoUege Bulletin mentioned above. • • Prom "two to four " includes from 3 years and o months through 3 years and 11 months.

CHAPTER I V T R A I N I N G I N OBSERVATION DEFINITION OF TERMS

1. Diary Record. A detailed account of a child's activities written during the period of observation by the person observing. These records, written as the activities were observed, were required that evidence not affected by memory might be obtained, and on the basis of this evidence the questions in the inventory were answered by both the observer and the experimenter. 2. Inventory. A list of objective questions in regard to the abilities of children from two to four, arranged with space for answers to which a score is assigned. 3. Criterion. The students in the class in KindergartenPrimary Education filled out inventories on the basis of each diary record. The experimenter filled out inventories on the basis of the same diary records. The scores obtained from the experimenter's inventories are used for two purposes: (o) to check the scores obtained from the students' inventories and thus to estimate their ability to answer the questions in the inventory; (b) to obtain scores for the children, and on the basis of these scores to estimate the worth of the diary records.^ 4. Division. One section of the inventory, e.g., Emotional. 5. Variation. The .difference between the scores obtained from the students' inventories and those obtained from experimenter's inventories. 6. X . The letter X refers to the situations which have not arisen during the periods covered by the diary records. (See Directions, Inventory I I , p. 37.) METHOD OF CONDUCTING THE

EXPERIMENT

There were sixty-nine students in the class in KindergartenPrimary Education. In order to ascertain in a general way the ' The reliability of the criterion was tested, and inventories filled out after an interval of two months were found to vary on the average from the original inventories not more than five points for any one division of the inventory.. The maximum score for each division is loo. 10

Training in Observation

ii

relative standing of the class, the Otis Self-Adminstering Test of Mental Ability, Advanced, Form A, was given before the experiment began. Under the circumstances, a more comprehensive intelligence test was deemed inadvisable. The scores obtained showed a range of 13—61, and a median of 41. The median score for 524 college students is 47. ("Otis Self-Administering Tests of Mental Ability," Manucd of Directions, p. 6.) The median score for the class in Kindergarten-Primary Education is, therefore, slightly below the median for college students and the class may be assumed to 'be a somewhat less selected group. The class was divided into two groups, one to observe one child each in one nursery school for 3 weeks for 5 hours a week, the other to observe one child each in one nursery school over a period of 5 weeks for 3 hours a week. The hours of observation were assigned definitely by the experimenter that a distribution of hours giving a random sampling of a child's activities might be assured. For example, in the case of the 3-h6ur-a-week observation group, an hour in the early part of the day embracing meal time, one of free play later in the morning, and one directly after the afternoon nap were chosen. In the case of the group observing 5 hours a week, the same hours as those assigned the 3-hour-group were included and 2 additional hours. Except in rare cases, where the schedule precluded any other arrangement, only one hour was assigned on any one day. There were twentyseven students in the 5-week-group and thirty-two in the other group. No student observed more than one child during the period of observation unless it was necessary to choose a substitute child because of the absence of the child originally assigned. When this was necessary, diary records and inventories covering those diary records were required from each student. The group of. students observing 3 hours a week for 5 weeks handed in 5 inventories, or one inventory for. every 3 hours of observation. Those who observed 5 hours a week for 3 weeks handed in 3 inventories, or one for every 5 hours of observation. At the beginning of the experiment, there was a week of training in making diary records. During this week, each student observed the child assigned her for 3 hours and for each hour of observation handed in a diary record or minute account of a child's activities written at the time of the observation. These

12

Habits of Children from Two to Four Years .

diary i-ecords were carefully criticised and annotated by the experimenter and handed back to the students before the periods of observation used in the main body of the experiment began. This was done to remove the effect of practice during the experiment proper, and also to obtain reliable data. It was decided to have two students who did not take part in the observation experiment, make out inventories on the basis of a certain number of diary records made by'Others in order that some indication might .be obtained of the value of such diary records as documentary evidence in the hands of those not familiar with the child. To obtain additional information on this point, thirteen members of the Psychology Seminar were given diary records to use as a basis for filling out an inventory. The terms,. Group I , I I , and I I I , will be used to refer to the observation class, the two students in the documentary evidence experiment, and the seminar, respectively. It was not possible to give Group I a week of training in filling out the inventory before beginning the experiment. Therefore, any improvement which occurred in Groups I and I I was due to the undirected practice which resulted from filling out several inventories. In order that there might be a further check on the use of diary records as documentary evidence and an indication of the effect of directed practice on ability to fill out an inventory, the following experiment was carried on with ten students, Group. I V , who had had no part in the main experiment. These ten filled out ten inventories, one on each of ten diary records. These diary records were the same as those used by one of the students in Group I I . Each of these students was given one half hour's training every day for eight days. Each diary record was assigned to each of ten different people in rotating order. This was done in order that any difference in the difficulty among the diary records might have no effect upon the average variation for any one day. TREATMENT OF DATA

The students' variations, i.e., the difference between their inventory scores and those obtained by the experimenter, were computed thus (see Table I , p. 13) : The total variation for each subheading under each division of the inventory (e.g., Memory

Training

in

Observation

13

TABLE I M E N T A L D I V I S I O N OF INVENTORY I Week

Obs.* Sc.. Exp.f Sc. Obs. Sc... Exp. Sc... Obs. Sc... Exp. Sc., Obs. Sc... Exp. Sc... Obs. Sc... Exp. Sc.,

I I II II III III IV IV V V

4 6 4 3 4 4 3 4 5 6

o

II X S U I X S I V X S V X S V I X S

5 6 25 2

o o o

4 29 7 5 24 13 4 28 12

o

7 23

I O I O I O 2 O I O

ID IQ. 10 ID ID

5 o 23 19,129 26 5 10 15 5 15 8 I I 17 18 6 50 o

Variation.

V Total.

1 X 5

•51

X

5

221

90

* Observer's score. tExperimenter's score.

51 = the total variation for the division 221 = total number of X's 555 = the maximum score times the number of weeks 51 = the percentage of variation per week 555-22I 51 = .1497, .1497 times 100 = 14.97 555-221 Therefore, the variation for the division is 14.97. 90 = the total score for the division By the same process as that used above 90 = the percentage of score per week 555-221 90 = .2691, .2691 times ICQ = 26.91 555-221 Therefore, 26.91 is the score for this division.

under Mental, in Inventory I ) , was computed for the period of observation. These totals were added to get the entire variation for the division.. This last total was used as the numerator,

14

Habits of Children from Two to Four Years

and the maximum score for the division minus the number of X's for that division was used as the denominator of the ratio. This ratio gives the percentage of variation per division for each inventory or for each week of observation. In estimating the students' variations as well as the child's score, one inventory or one week of observation is used as the unit. Since the observers did not all observe the same child, and since the amount of stimulus afforded by the nursery schools differed somewhat, the X's (situations which did not occur) were subtracted from the maximum score in order that the variations might be comparable. Thus four variations, one for each division of the inventory, were obtained for each student. The mean of the variations and the root mean square deviation were found for each division. (See Table I I . ) TABLE I I VARIATIONS FOR 69 STUDENTS

Division

Mean

15.64 Mental Motor Social-Moral

22.19 20.93 22.98

Root Mean Square Deviation

5.9 7.0 10.0

7.0

The method of dealing with the variations by the Pearson Mean Square Cpntingency Coefficient (Yule, Introduction to the Theory of Statistics, pp. 63-65, 1922) was tried and discarded as being unnecessarily cumbersome in this particular case. In order that the effect of student variation might be stated in terms of the sigma position of the child's score, the score for the children was computed thus (see Table I , p. 13): The scores for each division of the inventory were obtained by adding the scores of the subheadings. These ^sums were used as the numerators of the ratio of which the maximum scores for each division multiplied by the number of inventories minus the number of X's were the denominators. Thus these scores were computed by the same method as the variations. There were fifty-two children used in the experiment. Sixty were originally included but eight were absent the greater part of

Training in Observation

15

the time so their scores were discarded. These fifty-two children were divided into two groups: Group I included all children from 2 years and o months through 2 years and 11 months. Group I I , all children from 3 years and o months through 3 years and I I months. I n Group I there were twenty children, 10 boys and 10 girls; in Group I I there were thirty-two children, 18 girls and 14 boys. (For root mean square deviation of scores for each group, see Table I I I . ) TABLE I I I GROUP I 2 : 0 - 2 : 11Division

Mental

Mean Score

26.4 48.8 71.4 53.1

GROUP I I 3 : 0 - 3 : I I

Sigma

4-7 15-4 15.8 9.23

.

Mean Score

Sigma

28.8 66.2

5-35 13.08 II.81 12.03

79.2 59.0

The student variation may also be stated in terms of the maximum score for each division, which is the same as the maximum variation for the division. The maximum possible score is 100. In each case, for convenience the variations and the scores are multiplied by 100, since, otherwise, they are all unity or below. RESULTS

Twenty-five of th