When should a child begin school? An inquiry into the relation between the age of entry and school progress

Front matter

LB 1133 .M5 Copy 1

Class.

Book li JC^

Prefatory Note

The results of this inquiry are now to be published for the first time. Some of them have been privately circulated, and a few of the tables, together with the methods employed, were discussed at a meeting of the Inspectors of the Education Committee for London in the Autumn of 1905.

I tender my thanks to Sir Francis Galton and Professor Karl Pearson, who, some years ago, kindly considered this research in its statistical aspects; but I hasten to say that the responsibility for all error, both of method and calculation, is wholly mine.

I wish also to express my indebtedness to the teachers who helped me in this inquiry, especially to those who assisted me in preparing the tables and working out the coefficients of correlation.

I started the inquiry with an opinion in favour of early entry; but my only regret at the conclusion arrived at is due to the pain, as of wasted effort, felt by more thaii one excellent Infants' Mistress to whom the full force of the figures came home.

W. H. W.

London, August, 1910.

STATISTICAL NOTE.

The formula for correlation which is used throughout the following research is the well-known Pearson formula :

2xy

r=r

Its meaning and application will become clearer to the non-statistical if it is considered in relation to one or two examples.

Let us suppose that we have seven boys who receive marks for Arithmetic and marks for English Composition; and let us suppose, for illustrative purposes, that the marks are as given in the following table :

:a

S m O s

MS3

S'

M a ly a

CO

^ a cc n est:

m w r1

A. B.

+3

+ 6

4-18

C. D.

+2

+4

+8

E. F.

+ 1

+ 2

+ 2

G. H.

I. J.

+2

K. L.

+8

M. N.

+ 18

Dtal=

AV.:

Av.=

=A

A casual glance will show us that there is a perfect positive correlation between the marks for the two subjects, arithmetic and composition. The boys strong in one subject are proportionately strong in the other, and the weak boys in one subject are proportionately weak in the other. Perfect positive correlation is expressed by unity or, more exactly, by +1. Let us see how this value would be obtained by means of the calculations required for the given formula.

First find the average mark in the first series of marks, namely, those for Arithmetic. This is seen to be 4. Now find the deviation from the average of each individual mark in the first series, of A. B's mark, of C. D's mark, and so on. These deviations are shown in the second column of figures starting from the left, and constitute the ''x's" of the Pearson Formula. The x's are now squared, as given in the next column of figures to the right. These squares are added up and their average found, which in this case =4. Finally, the square root of the average of the squares is found (=2) and this figure is the **(Ti" (standard deviation), of the given formula. Corresponding operations with the marks for Composition enable us to find the y's and "a--" required by the formula — a glance at the table will show what these are. The last column of figures to the right shows the xy's required. These are obtained by the multiplication of the first series of deviations (x's) into the second series of deviations (y's), and the "^ xy" of the formula is the sum of these x y's, which, in this case, =56. The ''n" of the formula is the number of cases, in this instance =7. Substituting the numerical values found we have

Coefficient of correlation or "r" = = -= ^ — ; = -|- 1.

n<T,ff2 7 X 2 X4

Now let us imagine that the marks were quite otherwise related than as shown in the above table. Let us suppose that the boys who were strongest in

AGE OF ENTRY AND SCHOOL PEOGRESS. 5

Arithmetic were weakest in Composition, and that those who were strongest in Composition were weakest in Arithmetic in such wise as is represented by the next table. It is still obvious that we have perfect correlation, but this time of a negative kind. After the preceding explanations, it will be quite clear from a mere inspection of the table how the coefficient of correlation, namely — 1, is arrived at.

ll to

CO

OD O in s

to

A. B.

+3

C. D.

+2

E. F.

+ 1

G. H.

I. J.

+2

K. L.

+4

M. X.

Av

—3 1

Av

.=8

.=4

^otal=

^56

Av.=

Av.= i2

Coefficient of correlation

I or

Sxy

But, of course, the relationships between the marks for Arithmetic and for Composition are never in actuality like those of either of the above tables. If they were usually of such forms as these, common sense would be adequate to discover the correlation without appeal to formulae. But let me now give a case, still artificially simplified, but such as might be more likely to occur in actual practice.

I ask my reader to look first at the marks for Arithmetic and those for Composition in the next table and guess the correlation between them. It is b WHEN SHOULD A CHILD BEGIN SCHOOL.

obviously positive ; that is, the good boys in one subject are, generally speaking, good in another; but there are some irregularities. The correlation is not perfect, but it seems rather nearer to perfect correlation than to the absence of all correlation, which would be expressed by 0. The table with the working out of the formula shown below gives us a definite value for this correlation, namely, +.75.

a es 1 m o

BJ a*

CO to

X

A. B.

+3

+4

+ 12

C. D.

+2

+2

+4

E. F.

+ 1

+6

+6

G. H.

I. J.

+6

K. L.

+8

M. N.

+6

=+42

Av.=

Av.=

Coefficient of correlation or "r" =: = - — ^ — j^ = + '75

One word of caution — these tables are merely illustrative. The marks are not actual, and moreover, the formula is not generally suitable for application to series containing such a small number of cases as seven.

One further word — correlation coefficients are not reliable unless they are two or three times as large as the "probable error." In the following research the probable error has been found from the formula where 'n,' as in the previous formula, is the number of cases in the series, and 'r' is the coefficient of correlation.

Introduction

Few educational questions have excited more general interest in recent years than that of the age at which children should commence their attendance at school. On the one side we have had the rule-of-three conclusion, felt rather than expressed as an inference, that the more teaching the child gets and the sooner he begins school, the more progress he is sure to make. On the other side we have had a strong feeling, now, I think, growing in intensity and range, that attendance at school in England begins too early and that there is an educational disadvantage in commencing so soon. I am not aware that any inquiry has been undertaken, the facts and conclusions of which would be logically acceptable to both parties in the dispute. An English educationist turns naturally to Germany and America to see if any scientific inquiry has been made on this question in either of those countries. So far as I know, no such research has been made. There are, however, causes for this in addition to those operative in England. In the first place, school atendance is compulsory in Germany at six years of age, not, as with us, at five; and there are no municipal infant schools or kindergartens. In the United States, even in those most progressive educationally, six years is ^he usual compulsory school age. In some of the New England States, five is the lower limit; but both this 'five' and the previous 'six' represent regulations rather than facts; the average Grade I (about half a year's work below our Standard I.) in America being decidedly old. It is true that some of the States have kindergartens which are not compulsory, but attendance therein is not usual before five years of age. An admirable opportunity exists for measuring the advantages of kindergarten training in the States just now, since, at present, the Grade I children in many schools are about equally divided between those who have and those who have not received it. The application of proper psychological exercises would help to solve this important question, but the work has not yet been done.

In England, attendance is optional at three years of age, and does not become compulsory till five. A considerable number of children do not begin to attend until some months after five, but, after that age, the numbers entering are so small in most cases that they are hardly worth tabulating. But between three and five we have children entering at all ages, and it seemed to me that this elasticity gave an excellent opportunity for valuable research. Do those who enter early make more progress than those who enter late I

II. Age Of Entry And Subsequent Progress In Senior Schools

In Age of Entry we have an independent variable of great accuracy and of easy ascertainment. But how shall we measure school progress? Schools are divided into classes and standards, and, provided that we do not lump together the results from different schools, we shall find the school standards a most valuable aid in our inquiry. This statement needs some explanation. Schools differ so much in neighbourhood and in the standard of work demanded by their Head Teachers that it would not be wise straightwfiy to assume that Standard I. or II. or any other standard in one school, indicated the same mental proficiency or attainments as in another school. But in any one school, particularly where great care is exercised in the classification of the children, it would be correct to suppose that the vast bulk of, say, Standard IV. children are more developed mentally than those of Standard III., Standard III. than Standard II., and so on. But what is meant by great care? On the one hand, that clever children are promoted though they may be young, and on the other hand, that very dull children are not put into classes where the work is beyond their power even if they make due effort.

There is a tendency in some cases to put a child up because, though not fit, he has already been * through,' as it is called, a previous class or standard. The expert in school organization will see at once that that tendency works against the conclusion which I believe my figures will establish.

This short discussion will have already shown that progress cannot be considered apart from age; a boy of 10 in Standard VI. has obviously made more school progress than one of 14 in Standard VII. Somehow we must allow for both age and standard. There are numerous and complicated and somewhat elastic rules governing the question of classification by age and standard, and promotion from infants' departments to boys' and girls' departments. This is not the place for a detailed discussion of these rules. Their upshot is that a sort of ideal age for each standard emerges on which teachers and inspectors roughly base their judgments. Children are supposed to commence their Standard I. work at an average age of 6 years 6 months, their Standard II. work at 7 years 6 months, their Standard III. work at 8 years 6 months, and so on; thus they should commence the work of Standard VII. at 12 years 6 months. This is probably somewhat too high a standard for schools in poor or inferior neighbourhoods. Only one of the schools (all good ones) in which my investigations were made — a school long established in a good neighbourhood with a firstrate staff — attained it. But it was useful as a sort of guide which teachers well understood. Now, of course, some children reached these standards at earlier ages than those given above, and some later.

Very few were more than two years behind; so I took the pupil who was two years behind as being accredited with o progress marks, and those who were more than two years behind received a negative mark. The ages of the children were calculated in months, so that a boy two years and one month behind would receive a negative mark of one. If he were 1 year and 11 months behind he would of course receive a positive mark of one ; if he were just right his mark would be 24; and if he were one year ahead of the normative age — a by no means unusual thing — he would receive a positive mark of 36. Take one case in illustration. Alfred Brown enters Standard IV. when he is 9 years 9 months old; the normative age is 9 years 6 months; Brown's progress mark is 24 — 3, that is 21.

We can obviously, with no difficulty except the laborious nature of the undertaking, assign a progress mark to every child in any school at any time. We have merely to take the age in years and months when he entered his present standard, and add to, or subtract from 24, the months by which he is in advance of, or behind, the normative age. It would be better to have a normative which was a little more normal, but obviously that will not affect our figures, which are used only for purposes of comparison within the same school. They are not valid for comparison between one school and another, since, as I have said above, the standards in one school differ from those in another. We have in England no Lehrplane as in Germany, nor official courses of study as in America; the standards in different schools would not be really 'standards'

in the scientific sense, if we had ; though there might be more uniformity between schools of the same type ; for our Lehrplane, if we ever have them again, will, I hope, unlike those of America, discriminate between schools of different types.

So far there is little difficulty; but when we set out to get the figures which we wish to compare with these progress marks, those, namely, relating to age of entry, we find that, in whatever school we choose, we have a number of children who did not commence their school life in that school, but somewhere else. If in private schools, it would be difficult, if not impossible, to get reliable statistics; and if in other municipal schools, much correspondence would have been involved; and, even if this difficulty had been surmounted, there would, probably, in many cases, have been awkward breaks in the school lives of such children that would have rendered their cases abnormal. One Head Master wrote to me thus — "The difficulty of obtaining reliable facts relating to children who have previously attended private or other elementary schools makes it necessary to ignore those who did not begin instruction in these buildings. The statistics concerning the latter are absolutely reliable." We, therefore, excluded every child who had at any time attended any other school.

In the first school for which the results of this inquiry are given, we tabulated the name of every child who was on the roll for August 1st, 1905 — the first day of the educational year 1905 to 1906 — with two exceptions, (1) of children who had at any time attended any other school, (2) of one boy

AGE OF ENTRY AND SCHOOL PROGRESS. lo

who was subsequently sent to a school for mentally defective children. The list appeared thus:

Standard Age on Progress-

Name. Age of Entry, on 1, 8, '05. 1, 8, '05. mark.

Holloway, William, 3 yrs. 1 mth. I

Mitchell, Richard, 3 yrs. 3 mths. I

Friend, Victor, 3 yrs. 7 mths. I

Shillings, Albert, 3 yrs. 5 mths. II

Moog, Philip, 5 yrs. 4 mths.

8 yrs. 1 mth. 5 7 yrs. 6 mths. 24

If now we collect the progress marks of all children who entered between 3 and 314 years of age, and of all those who entered between 31/0 and 4, and so on, we ought to see at a glance whether there is any marked correlation between the age of entry and subsequent progress in school; provided, of course, that the influence of age of entry is not obscured by that of any other relevant factor than the increased length of school life at any given subsequent age. Whether there is another factor depressing or raising the position of those who entered early as compared with those who entered late is a question I will discuss subsequently. For the present, I shall suppose that the groups entering at different ages between 3 and 5 are of approximately equal natural ability tcitJiin the same school. The last limitation is important, for I am well aware that, in London, the age of entry in some suburban schools is very late, and it would be unfair to compare these children with the early groups of poor neighbourhoods. This school for which the figures are now to be given, was rather a new one; consequently, we were compelled to cross out a very large number of children who had been to other schools;

but I selected it because the Head Master, I knew, took very great care in classification and neither under nor over promoted. The progress marks are indeed very satisfactory for a new school containing this type of child. I ought perhaps to mention that the classification was not made in view of this inquiry, which was not begun until November, four months after the school had been organized for the educational year.

The results follow:

I.

K.

Boys.

Age of entry.

No,

. of boys.

mark per boy.

3—31/2

14.2

6.2

31/2—4

15.3

5.9

14.1

6.8

15.0

6.3

16.3

5.7

Boys who entered after 51/2 years, very few in number, were excluded; they were boys who were feeble or in ill-health: the large number entering after 5 is due, not to the character of the neighbourhood but, partly at least, to the comparative lack of school accommodation before this school was opened.

My reader will see how very close these groups are in average progress if he remembers that each unit stands for a month only. Thus the 23 boys who began school from 3 to 31/2 years of age are 9.8 months on the average behind the ideal standard

* M. V. (Mean Variation) is the average deviation of the individual progress marks from the average of the group. The highest mean variation differs from the lowest only 'by .6 of a month.

for their ages ; the next group is 8.7 months behind, and so on. But our interest just now is in the comparative results ; and it is very hard to believe that, in this school, the age of entry has been an operative factor at all so far as the child's subsequent progress is concerned.

This method of grouped averages, though excellent for obtaining a general notion of correlation, is not adequate to show small amounts of correlation. This has, however, been worked out from the individual cases by the Pearson formula, and gives a coefficient of +.07 with a probable error of .07. One cannot draw an inference either way from this result, except that no correlation exists ; one may, however, remember that, as we are correlating age of entry and progress marks, a positive coefficient is against early entry.

I have given the results of the above boys' school first, because the numbers were small and easy to manipulate; it was not, however, the one in which my first investigation was made. That was also a boys' school, one situated in a good neighbourhood, long established and popular, though not very large.

The inquiry was commenced in June, 1905. All the boys in the school were placed on our list, except those who had previously attended any other school, public or private. Every boy included, therefore, had attended the corresponding infants ' department, the very few who had commenced their school attendance at a very late age in the boys' department itself being excluded.

WHEN SHOULD A CHILD BEGIN SCHOOL.

As before, certain particulars were supplied for each pupil, and were set out as follows:

Name.

Age of admission to Infants' dept.

3 yrs. 2 mths. 3 yrs. 3 mths.

Ward, Charles, 5 yrs. 5 mths.

Total, 195 boys.

Present standard.

II.

II.

vii.'

8 yrs. 8 mths. 8 yrs. I mth.

Each boy then received a progress mark calculated in the way previously explained. The pupils had worked for 11 months in their present standards, and this, of course, had to be allowed for. Thus 11 months were deducted from the present age of each pupil if, as was almost invariably the case, he had been placed in his present standard at the commencement of the current educational year.

I propose to present first the final summary of the results..

TABLE II.

School "L." Boys.

Lge of entry.

No. of children.

mark per boy.

M. V.

3—31/2

23.4

5.3

3^2—4

21.9

7.8

23.0

8.6

41/2—5

22.5

4.3

5—51/3

22.1

7.6

It will help us clearly to comprehend the great similarity between the progress of these five groups if we remember that this table means that the first group (those that enter from 3 to Syo years of age) are, on the average, .6 months below the normative standard for their age: the second group, on the average, 2.1 months below: the third group, 1 month below: the fourth, 1.5 months below: and the fifth,

1.9 months below. The differences in the progress of the various groups are extremely small. It is not, however, unreasonable to suggest that the earlier entering groups may show more advance in the lower standards than those entering later, and that this difference gradually disappears ; or perhaps, as would be necessary if the average progress mark for the various groups of all standards together remains approximately the same, that a reverse difference appears in the upper standards. The following classification will help us to test this supposition.

TABLE III.

School "L." Boys.

mark to

Age of entry.

No. of boys.

standard.

nearest unit.

3—31/2

II.

31/2—4

II.

4—41/2

II.

41/.— 5

II.

5—51/2

II.

3—31/2

31/0—4

VI.

4—41/2

VI.

41/2—5

VI.

5—51/2

VI.

VII. 31/2-^

VII.

VII.

41/2—5

VII.

VII.

A comparison of the progress marks of the earlyentering groups with those of the later entering groups in each standard separately (the school contained no Standard I. children) will show that this supposition is untenable. Teachers will note the low progress marks of Standard VI., but will at once understand when I tell them that there were two divisions of Standard VII.

But a still further issue may be legitimately raised. It may be fairly urged that the early groups, though not in a higher standard for their age than the groups who entered late, are yet decidedly superior within those standards. To test this question would, under ordinary circumstances, have been a task of extreme difficulty ; but the Head Master of this school was one who kept the records of his terminal examinations with exceptional care and conducted his tests with exceptional thoroughness. He had, moreover, in each standard, given 25 marks for each subject, so that there was plenty of room for variation ; and, further, it was easily possible to find for every boy an average mark per subject. It would be quite impossible without enormously swelling the contents of this monograph, to give all the exercises set. Suffice it to say that they ranged from Reading, Writing, Spelling, Arithmetic and Drawing in Standard II. to Reading, Spelling, Composition, Arithmetic (Rule Sums and Problems) Mental Arithmetic, Arithmetical Computation, Algebra, and Drawing in Standard VII. The examination had been conducted some months before and was not undertaken for the purpose, or with the knowledge, of this approaching inquiry.

I append the final summary of the marks gained :

AGE OF ENTRY AND SCHOOL PEOGRESS. 19

TABLE IV.

School "L." Boys.

Age of entry.

No. of children.

Average mark pe boy per subject.

38 40 47 28 39

21.5 21.5 20.5 21.9

21.2

It is, I think, fair to conclude from this table that the children had not been classified on an age basis, but on an ability basis ; for if old children, entering school late, had been put forward simply because they were old, we should have discovered it by a rapidly decreasing examination mark for the late entering groups. The outstanding result is the extraordinary closeness of the progress and class proficiency of these five groups. These results give no countenance to the view that early entry into school results, later on, in greater proficiency and progress. I was not prepared for such a result, for I certainly expected that the grouj^ which entered after 5 would show an appreciable falling off, either in their progress in the standards or in their comparative proficiency within their standards.

That these tabulated results are not adventitious ones may be shown in a variety of ways, of which the subjoined analysis is one:

:U WHEN

SHOULD A

CHILD BEGIN

SCHOOL.

V.

School ''L."

Boys.

Average marl

per boy

per subject.

Age of entry.

standard.

ir.

22.1

III.

22.0

IV.

20.6

V.

21.0

VI.

21.8

VII.

21.3

II.

22.3

III.

22.0

IV.

21.0

V.

23.0

VI.

21.7

VII.

21.0

II.

17.3

III.

22.2

IV.

20.4

V.

20.2

VI.

20.8

VII.

22.2

4^2—5

II.

21.6

III.

22.3

IV.

21.1

V.

22.6

VI.

20.6

VII.

22.3

5—51/0

II.

21.1

III.

21.6

IV.

20.8

V.

20.8

VI.

19.7

VII.

22.0

The earliest entering groups have a slightly higher mark in Standard II. than the later entering groups : in III. the mark is practically identical for all ages of entry: in IV. it is practically identical throughout : in V. the 314 — 4 and 4i/4 — 5 groups are the best : in VI. the early entering groups are better than the later ones : in VII. VIII. the later entering groups are better than the earlier entering ones. Our only conclusion can be that early or late entry is an unimportant factor within each class.

We have now a mark for each child called the progress mark, which depends on the standard he has reached at his present age : we have also a terminal examination mark, which shows how he stands within that standard. We can see, by referring to our tables, that the group entering from 3 — 3i/^ years have a progress mark of 23.4 with an examination mark of 21.5, and so on.

It will be of service if I give the two sets of results side by side.

TABLE VI.

''L." Boys.

Ago of entry.

No. of boys.

Average progress mark.

examlnatioii

mark.

38 40

47 28 39

21.5 21.5

20.5 21.9 21.2

Considering both these values it will be seen that the 3 to 31/2 group and the 41/. to 5 group are the most proficient, while the three remaining groups are practically identical.

But, after all, these are results for one school only, and one well situated in a good neighbourhood. We have, however, to remember that they correspond, so far as the relative progress of the different groups within the same school is concerned, with those of the former school "0. K.", which was situated in a neighborhood very different from that of the school just referred to.

Perhaps I may say a word here as to the lumping together of results which I deprecated in the explanation of my method. If we had put these two schools together let us see what would have happened. I pass over, for a moment, the consideration that the "standards" of work were not likely to be the same; they did, as a fact, closely approximate.

TABLE VII.

, School "O. K." , , School "L." , progress Average progress

Age of entry. No. of boys. mark. No. of boys. mark.

3—31/2 23 14.2 38 23.4

4—41/2 17 14.1 47 23.0

5—51/2 23 16.3 39 22.1

Obviously the results from the second school, with its larger numbers and higher progress marks, would, if we had combined the results, have swamped those from the first school. Whereas, by taking them separately, we find that quite a different rate of progress per age is, nevertheless, accompanied by the same steady resemblance between the groups entering early and those entering late.

One word to teachers. The school "0. K." was just as good a school as School ''L.," its lower progress marks depended (1) on the fact that it was relatively new, (2) on the fact that it was in a different neighbourhood and was attended by children of different birth and social environment. (On this latter question I hope to publish some definite work in the near future.)

I now pass from these schools to another, which was nearer in social type to School "L.," but shared with School "0. K." the disadvantage of being somewhat new. Teachers will understand without argument that, in a new school, if anywhere, the ages of the children, in the lower standards at least, are apt to be high; and progress, measured by age and standard, is apt to be low. But, as before, we are concerned, not with the general progress of the school, but with the comparative progress of the children entering early and those entering late. As on the previous occasion, every child was excluded whose whole school life was not passed within the school itself. The cordial co-operation of the three head teachers — the Infants' Mistress, the Girls' Mistress, and the Head Master of the Boys' School working together — made the investigation easy and rapid. The name of every child on the roll on the 31st of July preceding the investigation (which took place some months later) was placed on a list, together with the following particulars collected from the school registers. It was not known beforehand that such an investigation would be made.