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diff --git a/76891-0.txt b/76891-0.txt new file mode 100644 index 0000000..73e2be3 --- /dev/null +++ b/76891-0.txt @@ -0,0 +1,2637 @@ + +*** START OF THE PROJECT GUTENBERG EBOOK 76891 *** + + + + + + THE ACCOMPLISHMENT RATIO + + A Treatment of the Inherited Determinants + of Disparity in School Product + + _By_ + RAYMOND FRANZEN + A.B. (Harvard), M.A. (Columbia) + Ph.D. (Columbia) + + Teachers College, Columbia University + Contributions to Education, No. 125 + + Published by + Teachers College, Columbia University + New York City + 1922 + + _Copyright, 1922, by RAYMOND FRANZEN_ + + + + +PREFACE + + +The results of the experiment reported here have become so much a +portion of my process of reasoning that duplication of material +presented elsewhere is unavoidable. I wish in particular to recognize my +indebtedness to the TEACHERS COLLEGE RECORD for permission to reprint +here revised portions of an article which appeared in the November, +1920, number of that journal. I will warn here any reader to whom the +intricacies of a full statistical account are irksome that the logic and +conclusions presented in this study are incorporated in a more palatable +and abbreviated form in Chapter IV of _Intelligence Tests and School +Reorganization_ (World Book Company). + +The work presented here has been made possible by the cooperation +and interest of the two principals of the Garden City public school +during the period of my work there, Miss Gladys Locke and Mrs. Edna +Maule. I also owe any success that this experiment may have had to the +teachers who did the real work of “pushing” abilities to their limit. +My indebtedness to Gladys Locke Franzen for help in expression and +correction is surpassed only by what I credit to her encouragement and +cooperation at its inception. + +During the period in which this experiment was planned and executed it +grew into a real problem through the advice of two of my teachers to whom +I owe all such inspiration and knowledge as I possess—Edward L. Thorndike +and Truman L. Kelley. + + RAYMOND H. FRANZEN + +_Des Moines, Iowa, 1922._ + + + + +CONTENTS + + + I. AN OUTLINE OF THE EXPERIMENT 1 + + The Use of Quotients and Ratios + The Derivation of Age Norms + A Method of Survey of Reading, Language and Arithmetic + + II. STATISTICAL TREATMENT OF THE EXPERIMENT 17 + + The Quotients + The Ratios + Summary + + III. THE PSYCHOLOGICAL CONCLUSIONS OF THE EXPERIMENT 43 + + The Neglect of Genius + Is Genius Specialized? + Current Psychological Opinion + Conclusions + + + + +PART I[1] + +AN OUTLINE OF THE EXPERIMENT + + +THE USE OF QUOTIENTS AND RATIOS + +Standardized measurement of educational product has won its way to a +recognized place in the school life of this country. Many of our larger +cities have research bureaus of tests and measurements, and advanced +private schools have departments of measurement. The logic of the use of +statistically derived evaluations versus the use of opinion, swayed as it +is by the haphazard captions of emotion and condition, has become widely +recognized. The case of scientific measurement in education has been +argued and won. The objections to older forms of measurement have become +the criteria of the value of the new. + +Still administrators, although they have been convinced theoretically of +its importance, find it hard to see just what measurement does for their +schools. They often object that measurements are made, the tests are +carried away by the examiner, and some time later they are presented with +a neat series of distributions and are told where their school stands +in relation to certain other schools or to schools in general. This is +undoubtedly a very important piece of information; since a determination +of the extent to which a goal has been attained forms the basis of the +commendation or condemnation of the methods, curricula, and text-books +employed in the process. But administrators want to know which of the +various elements of school procedure are to be praised and which are to +be blamed. + +We cannot condemn or support a whole school system on the basis of +composite results (unless all possible educational objectives have been +measured, and show one common drift; or unless it is necessary that the +system fall or stand as a whole) since then we should be throwing good +and bad into a common discard. We must measure each thing separately. We +must build our ideal system of education synthetically, taking the best +methods from each of the prevalent groups of theories. There has been +too much absolutism in education, too little of a realism that sees the +good and bad in all and diminishes the bad and augments the good. If +we adopt this point of view we become really empirical in our method, +living through each educational experiment to incorporate it into a +growing treasury of tested theory, not deducing success or failure from +metaphysical or doctrinaire prejudice. In this administrators have been +more scientific than those who measure. They have always objected that +they wanted differential diagnoses. Here the answer to their needs must +come through experimentation and it is only through nation-wide study and +careful comparison and integration of results that methods of teaching +can be scientifically established. + +Three uses of measurement commonly stressed are: (1) Diagnosis of degree +of attainment of goal; (2) selection of method of attainment of goal; +(3) definitive outline of goals. We have seen that the first two are +of little immediate value to the administrator. The first only gives +him an accurate notion of where he stands in any one subject without +pretending to tell him why; the second is a promissory note. Some day +we shall be able to tell him the best methods for the attainment of his +goal. The third has slightly more immediate value. Measurement splits up +the goals of education, gives them concrete formulation, allows teachers +to see an advance in the class in one function as separate from the +rest; allows them, for instance, to distinguish more clearly than they +otherwise would between oral reading and silent reading, or between +addition and division. But this, too, is rather too general to appeal to +administrative economy. One would find it very difficult to sell one’s +services as a measurer to a school board or a superintendent on the basis +of these three values. They answer that universities and scientific +research give them as much as they want of these values. What an expert +on measurement could add in interpretation of results would seem of small +additional value to them. + +Still there is a very marked function that such an expert can perform; +but he must serve a fourth and fifth use of measurement while he serves +a particular school. When he serves the first three he is serving the +science of education and, unfortunately, no one school will pay him to do +that. The uses of measurement that directly benefit any one school are: +(4) Classification by information and intelligence and (5) diagnosis +of individual disability. For the proper prosecution of these aims +individual measurements and age norms are essential. Only with such +equipment can we make the prognoses of future school behavior which the +administrator so urgently needs. + +Grade norms cannot be used to make individual diagnoses. Though we can +see by them which children are below and which above the level that in +their grade they should attain, we cannot see just what administrators +most need to know; namely, whether the retardation and acceleration are +justified or not—how many children are working at maximum. More than +that, computations based on grade norms are very inaccurate in individual +cases because the variability within any grade is so great. As it becomes +necessary to use new norms for such purposes it is important to have them +in terms that are directly comparable to intelligence mensuration.[2] + +First in importance is an interpretation of the meaning of an +Intelligence Quotient. Too often it is stated as a number and left as a +number with the belief that somehow or other that is a tag which carries +its own divine implication. Its importance lies in its diagnosis of power +of adaptation, and it has a high correlation with the maximum possible +rate of school progress. Just as a pure information test diagnoses the +neural bonds that have been formed in any one field, so an intelligence +test diagnoses the ability to form bonds, to meet a new situation and +form satisfactory habits—power to learn. It may be thought of as a +diagnosis of the neural chemistry of the individual. As such it is not +concerned with the connections or quantity, but rather with the quality +of the neural tissue. + +As an intelligence quotient is actual mental age divided by chronological +age—which is the normal mental level of the child’s age-group—so it is +the rate at which the child has progressed to mental maturity. It is his +potential rate of progress. It is a division of what is by what normally +would be. Then, when we use IQ we express the various degrees of power +of adaptation due to various degrees of fitness of neural equipment to +form bonds, by means of a diagnosis of the rate of formation of bonds +which everyone forms sooner or later in an environment such as ours. It +is conceivable that we might test this same power without testing the +presence of such bonds at all. Such a test would detect directly the +quality of the neural equipment irrespective of quantity or conformation. + +A ten-year-old child whose mental age is ten has progressed at the rate +which is normal, and his IQ is 1.00. A very exceptional ten-year-old +child whose mental age is fifteen has progressed just one and one half +times as fast as the former, and his IQ is 1.50. Another exceptional +ten-year-old child whose mental age is five has progressed at just +one-half the rate of the first, and his IQ is .50. What we mean, then, by +an Intelligence Quotient is the rate at which a child grows to the mental +maturity of human beings in the world as it is. + +For purposes of presentation of a problem one can here assume (an +hypothesis the value of which will here be determined) that each child +can attain this rate of progress in each of the elementary school +subjects. The degree to which this is true is the degree to which the +IQ is a valid index of power to deal with school subjects. This assumes +that inherited special disabilities in the school subjects are uncommon, +that school progress is determined by the interplay of intelligence and +environment, and that so-called interest characteristics which aid in +development are the result of an earlier interplay of intelligence and +environment. The degree to which educational product of children can be +made to approach this intelligence will allow us to judge how far these +factors are inherited, since differences that are removable must be +learned, not innate. + +We can the more readily see the significance of viewing a child’s +equipment in terms of educational and mental age, when we conceive of +a Subject Quotient. This is a quotient resulting from the division of +the age level reached in the test in question by the chronological age +of the pupil. It is a measure of the rate of progress of the child in +the school subject under consideration. Thus a ten-year-old child with +ten-year-old ability in Thorndike Reading Scale Alpha 2 would have as +his reading age divided by chronological age, 1.00. This may be called +his Subject Quotient in Reading or his Reading Quotient. The division of +what is by what would be if the child were normal gives the percentage +of normality, the actual rate of progress. Since the IQ is the potential +rate of progress and the SQ the actual rate of progress, the ratio of +SQ to IQ gives the percentage of what that child could do, that he has +actually done. Thus a child with an IQ of 1.32 whose reading quotient +(his RQ) is 1.10, though he is doing work which is above normal, is not +doing work which is above normal for him. His RQ⁄IQ is 1.10⁄1.32, whereas +if he were progressing at his optimum rate it would equal 1.32⁄1.32. This +RQ⁄IQ is the same quantity as RA⁄MA. We may call this a Subject Ratio and +the average of Subject Ratios an Accomplishment Ratio. We could, if the +absolute association between reading age and mental age were perfect, +measure the approximation to ideal educational performance of any one +child in any one elementary school subject through the approximation +of this Subject Ratio to 1.00. As we will see later, Subject Quotients +approach the Intelligence Quotients when special treatment is given; that +is, the correlation of SQ and IQ becomes nearer 1.00 and the difference +between the average IQ and the average SQ approaches zero. It is safe +then to expect these Subject Ratios to be at least 1.00 before we +pronounce satisfaction with the school product. + +There is certainly a significant relation between IQ and SQ, and the +more perfect the educational procedure has been, the more it has called +forth all that the child is capable of, the higher it will be. To +determine whether the quotient in any school subject can be greater than +the Intelligence Quotient in any significant amount, it will only be +necessary after we have perfect age norms by months to get that quotient +amongst enough pupils whom we know to be working at maximum. What is +significant here is that the more nearly any such quotient reaches or +exceeds the Intelligence Quotient the more nearly has the child been +brought up to what he is able to do under the best conditions. The +Accomplishment Ratio is the degree to which his actual progress has +attained to his potential progress by the best possible measures of both. + +This would be a mark of the child’s effort, a mark of the concentration +and interest that the child has in the school work, and as far as no +inherited traits or capacities other than intelligence affect school +work it is a measure of the efficiency of a child’s education thus +far. If there are such other innate bases, it is also a measure of +those inherited traits and capacities or their predisposition, such +as concentration, effort, written expression, etc. At any rate it is +a measure of the child’s accomplishment, and so of the effort and +concentration as they really are at present working under those school +conditions. It is an index of achievement irrespective of intelligence. + +A very convenient graph representing the same facts and easily +interpreted by the teacher may be constructed thus: + +[Illustration: + + Age Scale +------------------------------------------------ Mental Age + | _Reading Age_ + +----------------------------------------- Chronological Age + | _Spelling Age_ + | _Arithmetic Age_ + +---------------------------------------------------------- +] + +Here it can be easily shown that Spelling Age, Reading Age, Arithmetic +Age, etc., are in some definite relation to both Chronological Age and +Mental Age. Using the Mental Age line as a goal, these records may be +kept constantly up to date. Another use of the Accomplishment Ratio is +as the medium in which the children may keep records of their own work. +As it is a mark in terms of intelligence, dull and brilliant children +may compete on a parity to bring their Accomplishment Ratios as high as +possible. + +Mainly we have advanced formal education. We have in many ways promoted +the abilities to read, write, spell and figure. But our philosophy of +education has advanced far beyond that. We have other aims in education, +and consequently other methods and modes, which also must be measured and +judged. We wish to promote such qualities as stability, self-reliance, +concentration, and ambition. It does not necessarily follow that we must +measure these things directly, although every one vitally interested +in measurement cherishes the hope that we may some day measure their +behavioristic correlates,—“For the quality of anything exists in some +quantity, and that quantity can be measured.” + +“Some of us might be entirely willing to rest the case after asking +whether in practical school life anyone ever saw a teacher thoroughly +confident of teaching ideals but neglectful of reading and arithmetic. +The fact is that the conscientious teacher always gives attention to both +and the successful teacher is able, without omitting one, to cultivate +the other. The theoretical possibility of thinking of the two results +separately has little significance in dealing with real teachers and +real schools. Good reading is a school virtue; and when one has measured +good reading he has measured more than the trivial or formal side of +education.”[3] + +This I believe to be true, but I also believe that through measurement +we can actually promote those other more ethical ideals in education. +Through classification by information and by intelligence we gain +a marked increase of attention, concentration, ambition, and other +objectives, measured in part by Accomplishment Ratios. More discussion +due to a greater homogeneity promotes powers of inference and insight; +being only with equals promotes self-confidence and honor, and in many +cases prevents a regrettable conceit among supernormals; having work to +do which is hard enough prevents habits of indolence and carelessness so +commonly found among intelligent children.[4] + +It is a well-known fact that much work must be done in classification to +get homogeneity or real conditions of teaching. As it is, most teachers +are talking to the middle of their classes. When they do they mystify the +lower quarter and bore the upper quarter; they talk to the upper quarter +and mystify the lower three quarters; or they talk to the lower quarter +and bore the upper three quarters. When a child is bored or mystified his +Subject Quotients become less while his Intelligence Quotient remains +constant. Then his Accomplishment Ratios become less as long as he +remains in a position where he is being mistreated educationally. This, +then, is the proper measure to see whether a child is classified properly +or not. At the Garden City public school I changed as far as I was +able the conditions of education of each child in that subject wherein +his Accomplishment Ratio was markedly below 1.00. The concentration +and effort of the child were obviously low and my attempt was to +change conditions and to promote habits of consistent work. When the +Accomplishment Ratio increased I knew that the child was profiting, that +he was working. Our objective was to increase Ratios of all children, not +to attain any set standard. + +This Accomplishment Ratio would, to my mind, be an ideal school mark. +Besides the inaccuracy of marks to-day, which are accurate marks only of +the teacher’s opinion, biased as it is by the personal equation of her +character with that of the pupil, there is another fault of prevalent +school marking. It is based on average work. The mark is the link between +education in the school and education in the home. It gives the parents +an index of the child’s work and allows them to encourage or discourage +the child’s attitudes. Such indices have no real significance when they +are based upon average development, as the parent is generally mistaken +about the ability of the child. + +Marks given by a teacher are satisfactory only for a normal child with +normal age for the grade. Brilliant children are over-praised for work +which, though over the ability for the group, is under their own ability. +Marks given to stupid children are misinterpreted by parents so as +greatly to prejudice the effort of the child. Though his work may be such +as to merit encouragement his mark may be very low. Teachers’ marks are, +aside from their inaccuracy, just, only in a group that is perfectly +classified; just, only when the children are all of the same ability and +all possess the same initial information. So far as they are unjust they +are subversive of our aims, as they then transmit a faulty message to +the home and disrupt the continuity of school and home education.[5] + +Such marks as are here advocated would correct this feature of our +present system, as well as the inaccuracy of our present marks. It is a +mark which evaluates the accomplishment of the child in terms of his own +ability. A brilliant child would no longer be praised for work which in +terms of his own effort is 70 per cent perfect, in terms of the maximum +of the group 90 per cent. The teacher gives him a mark of 90 while we +mark him 70. A stupid child who does work which is marked 70 in terms of +the maximum of the class but 90 in terms of his own, a limited ability, +is no longer discouraged. His effort is evaluated, and the praise which +he receives from home is merited and consequently economical, since the +resultant satisfaction cements the bonds of concentration and attention. +Such a mark is an actual index of the effort that child is making and +consequently forms the proper link between the school and the home. + +Parents would need no great instruction in the interpretation of these +marks, since they have always acted as though the other marks were these, +and since these also are in percentage form. The only kind of mark they +can understand is an Accomplishment Ratio. I found that the parents of +the children at Garden City were more attentive to such marks than to +others, and acted upon them more readily. Of course the parents of the +very intelligent children, who are used to marks above 90, are surprised +at first when you tell them that your mark of the child is 80; but upon +explanation, which should in all cases precede the first report to the +parents, they immediately see the value of such grading. It is fortunate +in this connection that the greatest amount of explanation is necessary +about intelligent children, as one usually deals then with intelligent +parents. + + +THE DERIVATION OF AGE NORMS + +In this study age norms were derived empirically, both regression lines +being taken into consideration. From the point of view of statistics +it becomes imperative, in order to use the technique here advised, to +have the average age of a score—since we are going to predict age from +score—to translate crude scores into indices of maturity in each subject +under consideration. We are in error in the use of grade norms, if we +find the average score of a grade and then, when we obtain that score +in practice, say that the work is of that grade. To be able to say this +we must know the average grade of a score. This takes in an entirely +different cross-section of data. If we get the average score of all +children in grade 6, then we can predict what a 6th grade child is likely +to get, but we can say nothing about a child who is not in grade 6. In +order to decide that a 4th grade child has 6th grade ability, we must +know that he has such ability that all children who share this score make +an average grade of 6.[6] It would be wise then to get the regression +of score on age as well as the regression of age on score, since they +are not identical, the correlation between score and age being less than +unity. + +We will note in passing that the data to establish these norms, except +those of reading, are not as complete as may be desired, inasmuch as +it was difficult to get test scores where the age in months also was +available. However, the general data behind the grade norms could be +used to keep the results from any crude error; and the averages were +obtained for every month from 8 years to 14 years, with a corresponding +refinement in intervals of score, which made still more improbable an +error in the general tendency of the regression lines. Then all the +distributions, when grouped by years, were corrected for truncation; that +is, the tendency for the brighter children of the older group to be in +high school (the data were from elementary schools only) and the duller +children of the younger group to be in the lower grades where they could +not be reached was recognized and corrected by finding the average, +standard deviation, and number of cases which would have existed if these +forces of truncation were not operating. This was done by the use of the +other one half of the figures comprising Table XI of Pearson’s _Tables +for Statisticians and Biometricians_. Dr. Truman L. Kelley pointed the +way to its derivation. + +These norms differ somewhat from those derived from the grade norms by +translation of grade into average age for the grade. This is because the +norm for a grade is the average score for a grade. Hence the norm of age +10 obtained in this way is the average score obtained by a grade whose +average age is 10. Then the data used to obtain this average are made up +of diverse ages, all of one grade, instead of all of one age and diverse +grades. Even then, we would have only an average score of an age which +approximates what we want, but is not as reliable to use as average age +for a score. + + +A METHOD OF SURVEY OF READING, LANGUAGE, AND ARITHMETIC + +The following procedure was employed in the experiment. The experiment +was carried out in the public school at Garden City. Two hundred children +were given the tests. The instructions, shown below, were followed in +November, 1919, and in November, 1918; in June, 1919, and in June, 1920, +with the exception that no arithmetic test was used in November, 1918, +and June, 1919. The Binet tests were given by the author; all of the +others were given either by the author or the principal who was careful +not to deviate from the directions in any way. In June of both years +the author gave instructions for a test in one room, and then left the +teacher in charge and went on to the next. This could be done in June of +each year as the teachers were then fully acquainted with the experiment +and their coöperation was assured. + + DIRECTIONS + + I. Administer and score the following tests according to + standard instructions. Give all tests to grades 3 and above. + + Woody-McCall Mixed Fundamentals in Arithmetic + Thorndike Reading Scale Alpha 2 + Thorndike Visual Vocabulary Scale, A2 + Kelley-Trabue Completion Exercises in Language + Stanford-Binet Tests (given by the author) + + II. Translate the scores into year-month indices of maturity by + means of the following table. (Use Mental Age for the Binet.) + Assume rectilinear development, that is, that the amount of + score which equals the development of one month is the same as + the amount of score which equals the development of any other + month. Then interpolation and extension are allowable. Use the + table in this way: Find in the table the score made by a child + (for instance in the Woody-McCall); find the age to which it + corresponds, then call this age the Arithmetic Age of the + child. For instance, if the score in Woody-McCall is 20, his + Arithmetic Age is about halfway between 10 and 11 or 10 years 6 + months. + + =====+============+=======+=============+============= + Age |Woody-McCall|Alpha 2|Visual Vocab.|Kelley-Trabue + -----+------------+-------+-------------+------------- + 8—0 | 12.00 | 4.50 | 3.60 | 4.30 + 9—0 | 15.16⅔ | 4.98 | 4.32 | 5.00 + 10—0 | 18.33⅓ | 5.46 | 5.04 | 5.65 + 11—0 | 21.50 | 5.94 | 5.76 | 6.35 + 12—0 | 24.66⅔ | 6.42 | 6.48 | 7.05 + 13—0 | 27.83⅓ | 6.90 | 7.20 | 7.70 + -----+------------+-------+-------------+------------- + + III. Arrange these Arithmetic Ages of all the children of your + school in order from high to low with the names opposite the + scores in the extreme left-hand column of the paper. At the + right have parallel columns of the grades. Check the grade of + each child in these columns. You will then have a sheet like + this: + + ================+======+=================== + | | Grade + | +---+---+---+---+--- + Name |Arith.| 4 | 5 | 6 | 7 | 8 + | Age +-+-+-+-+-+-+-+-+-+- + | |B|A|B|A|B|A|B|A|B|A + ----------------+------+-+-+-+-+-+-+-+-+-+- + Gertrude Smith | 180 | | | | | | | | |#| + | +-+-+-+-+-+-+-+-+-+- + Saul Sampson | 176 | | | | |#| | | | | + | +-+-+-+-+-+-+-+-+-+- + Ed Jones | 176 | | | | | | | | |#| + | +-+-+-+-+-+-+-+-+-+- + George Calut | 172 | | | | | | | | | |# + | +-+-+-+-+-+-+-+-+-+- + Ida Henry | 172 | | | | | | | | | |# + | +-+-+-+-+-+-+-+-+-+- + Raymond Teller | 172 | | | | | | | | | |# + | +-+-+-+-+-+-+-+-+-+- + Ed Hoard | 172 | | | | | | |#| | | + + _Etc._ + + Do the same with each of the tests. It is clear that, + independent of the unreliability of the test, if your school + were perfectly classified all the 8th grade children would come + first on each relation sheet and then the 7th grade children, + etc. You have now a picture of the overlapping of your grades. + Regrade in reading and arithmetic. Draw horizontal lines across + these relation sheets at the points of delineation. Divide your + total number of children by the number of teachers available + and then make a class division by the number of pupils, that + is, call the upper one-sixth of the total number of pupils + grade 8 in this subject, the next one-sixth, grade 7, etc. + Teach all grades of arithmetic at the same time and all grades + of reading at the same time. You can now send each pupil to the + grade in which he belongs in each subject. + + IV. Call each derived age a Subject Age (SA). Divide each + subject age by the chronological age of the child. This will + yield what may be called a Subject Quotient (SQ), previously + called an Educational Quotient (EQ).[7] Dividing the Reading + Age by the Chronological Age, you arrive at a Reading Quotient. + This RQ is the rate at which the child has progressed in + reading. We have the same kind of quotient for intelligence + (Stanford-Binet IQ). This IQ is the potential rate of progress + of the child. + + V. The ratio of any Subject Age to Mental Age[8] may be called + a Subject Ratio (SR), previously called an Accomplishment + Quotient (AccQ).[7] This Subject Ratio gives the proportion + that the child has done in that subject of what he actually + could have done, and is a mark of the efficiency of the + education of the child in that subject to date. The goal is + to bring up these Subject Ratios as high as possible. When + they are above .90, the child may be considered as receiving + satisfactory treatment, providing norms for subject ages + are reasonably accurate. (This figure, .90, applies to a + Subject Ratio obtained by using a Stanford-Binet Mental Age.) + An Arithmetic Ratio based on one arithmetic test and one + intelligence test only is not as good as one based on three + arithmetic tests and three intelligence tests. If Subject + Ratios go far over 1.00 the chances are that the Mental Age + diagnosis is too low. The average of the Subject Ratios of a + child may be called his Accomplishment Ratio. + + In the application of the above instructions, whenever + opportunity offers for classification of both subject matter + and intelligence (which means many teachers or a large school), + use a Relation Sheet (for instance for Arithmetic) and then + have additional columns at the extreme right for intelligence + headed _A_, _B_, _C_, and _D_. If a child’s IQ is in the upper + quarter of the IQ’s of your school, check in the column A + opposite his name; if it is in the upper half but not in the + upper quarter check in _B_, and so on with _C_ and _D_. Then + you will be able to split each group; for instance, the one + which is defined as 8th grade in arithmetic ability, into four + sections, each of which progresses at a rate differing from the + others. The _A_ section will progress most rapidly, _B_ next, + _C_ more slowly, and _D_ most slowly. + +As Garden City was a small school, adjustment of procedure to individual +differences in intelligence, besides the grouping for subject matter, +was done mostly by pushing children. Children were advanced whole years +(the grade they “belonged to” was the one in which geography and history +were taught; this was their home grade) besides the readjustment made +by the special regrading in reading and arithmetic. A special treatment +class was formed where pronounced negative deviates were given special +attention. Regrading was also instituted for spelling. Children were +promoted whenever it was considered advisable; teachers were switched +from subject to subject whenever that was considered advisable by the +principal and the author. The Thorndike _Arithmetics_ and other new texts +were introduced to some extent. _Any change possible was made in order +to bring EQ⁄IQ as high as possible._ That was the goal. The purpose +was not to prove that any certain educational procedure would tend to +promote abilities more rapidly than others, but that abilities could be +promoted to the level of intelligence—that intelligence is substantially +the exclusive inherited determinant of variety of product among school +children. (It is to be understood that intelligence may be, and probably +is, the summation of thousands of inherited factors,—neutral elements, +here merged in the broader behavioristic concept of intelligence.) + + +SCIENTIFIC QUESTIONS INVOLVED IN CLASSIFICATION + +If we were able to negate other influences upon disparity of product, +we could conclude that these were not inherited. Hence it would be our +burden as educators so to manipulate education as to prevent their +operation. We will attempt to analyze the determinants of individual +differences in product in these children, to see which influences besides +intelligence are part of the inborn equipment which is not the province +of education, but of eugenics, to correct. No absolute validity is held +for any of the conclusions stated here. The subject is, at best, vague +and complicated; but our conclusions can be used as the basis for a +good guess in school procedure. We can judge general tendencies from the +educational experiences of the two hundred children whose abilities for +two years are here charted. + +The importance to educators of the subject in hand is excuse enough +for its treatment. All educational procedure points a prophetic finger +toward the classification of pupils and a reduction of the individual +differences of product to the inherited bases of these differences. + +Classification, however, needs some more accurate psychological +foundation than the mere awareness of individual variance. We must know: + +1. What tests to use. + +2. How to use them. + +3. Whether abilities in reading, spelling, and arithmetic or their +predispositions exist as special abilities, or whether children differ in +these simply because of their innate differences of intelligence. + +4. Whether individual differences in ambition, interest, and industry, in +so far as they influence accomplishment, are due to special tendencies, +or whether they are learned manifestations of a more general heritage. + +5. How these proclivities, specific or general, are related to +intelligence. + +Points 1 and 2 are problems of procedure which must be evolved from our +existent knowledge of measurements and statistics. Points 3, 4, and +5 are problems which must be solved from the evidence resulting from +an experiment in classification using these methods. Points 4 and 5 +introduce the vexed question of whether there is a “general factor” or +some general inherited cause of disparity in school product other than +intelligence. Should reading ability prove to be the result of certain +inherited abilities, or predisposition to abilities, we could not use +a measure of mental ability alone as the guide to what a child could +attain in reading. If intelligence, however, were the only inherited +prognostic factor of school achievement, we could mark the education +which had functioned in the child’s life by the percentage which the +actual accomplishment of the child was of the maximum accomplishment +of which he was capable at that stage of his mental development. So, +too, if interest in particular subjects and ambition are not mainly the +result of rewards and punishments of early life, but are themselves +significantly rooted in the nature of the child, we could not condemn +or commend curricula and methods upon a basis of the ratio of resultant +accomplishment to mental ability, but must include a measure of this +potentiality. The practical queries whether or not a child can do reading +as well as he does arithmetic, whether his ambition and his honesty have +their origin in the same strength or weakness, can be answered only when +these problems are fully solved. The immediate consequences of knowing +that a child can usually be taught to read if he does other tasks well +is of obvious import. It would be of great service, too, to know whether +lack of application can be corrected so as to bring concentration to the +level of the other traits. If a child is normal in other ways and not in +his tendency to respond to the approval of others by satisfaction, can +this “drive” be increased or reduced to the average, or are individual +differences in specific original tendencies basic to development of +character, and if they are, how much influence do these differences +exert upon school accomplishment? In order to classify children and +comprehendingly watch and control their progress we must know the +relation of achievement to the inherited bases upon which it depends. We +must be able to state a child’s progress in any one school subject in +terms of the potential capacity of the child to progress. We must know +the inherited determinants of disparity in school product. + + + + +PART II + +STATISTICAL TREATMENT OF THE EXPERIMENT + + +In the discussion and tables which follow: + +Q stands for Quotient, which will mean a Subject Age divided by a +Chronological Age. R stands for Ratio, which will mean a Subject Age +divided by a Mental Age. + +AQ means Woody-McCall Arithmetic Age divided by Chronological Age, and AR +means this AA divided by Mental Age. + +VQ means Thorndike Vocabulary Age divided by Chronological Age, and VR +means this VA divided by Mental Age. + +RQ means Alpha 2 Reading Age divided by Chronological Age, and RR means +this RA divided by Mental Age. + +CQ means Kelley-Trabue Completion Age divided by Chronological Age, and +CR means this CA divided by Mental Age. + +SQ means any Subject Quotient, that is, any Subject Age divided by +Chronological Age, and SR means any Subject Ratio, that is, any SA +divided by Mental Age. + +EQ means the average of all Subject Quotients and AccR, the +Accomplishment Ratio, means the average of all Subject Ratios. + +All _r_’s are product-moment correlation coefficients, uncorrected. As +the reliabilities (Table 4) are almost what the other coefficients are +in June, 1920 (Table 5), it is apparent that the corrected coefficients, +when Grade III is excluded, would all be very near unity at that time. + + +THE QUOTIENTS + +In Table 1 are presented all the quotients for all periods of testing, +grouped by children. The table, a sample of which is included here,[9] +shows clearly how all SQ’s approach IQ as special treatment continues. +The grades indicated in this grouping are as of June, 1920. Inasmuch as +many double and triple promotions were made in an effort to get maximum +product for intelligence invested, no conclusion can here be formed of +the grade to which these children belonged at any time except June, 1920. +The correspondence between IQ and the SQ’s in June, 1920 is further +shown in Table 2. In this table the 48 children who took all tests at +all periods are ranked from high to low IQ and their SQ’s are listed +opposite. The high correspondence is readily apparent. + + +TABLE 1[10] + +INTELLIGENCE QUOTIENTS FOR ALL PERIODS GROUPED BY CHILDREN + +The children are arranged by grade as they were in June, 1920, and +alphabetically within the grade. The periods of testing are lettered in +their chronological sequence; _a_ is November, 1918, _b_ is June, 1919, +_c_ is November, 1919 and _d_ is June, 1920. * = Zero Score + + GRADE 3 + + =============+======+==========+==========+========+========== + Intelligence| Test |Arithmetic|Vocabulary|Reading |Completion + Quotient |Period| Quotient | Quotient |Quotient| Quotient + -------------+------+----------+----------+--------+---------- + | _a_ | | | | + 101 | _b_ | | | | + | _c_ | 64 | 58 | | 43 + | _d_ | 106 | 88 | | 93 + | | | | | + | _a_ | | | | + 128 | _b_ | | | | + | _c_ | 80 | 102 | | 81 + | _d_ | | 152 | 124 | 153 + | | | | | + | _a_ | | | | + 116 | _b_ | | | | + | _c_ | 56 | 90 | * | 49 + | _d_ | 94 | 95 | 77 | 89 + | | | | | + | _a_ | | | | + 87 | _b_ | | | | + | _c_ | 90 | 40 | 35 | 54 + | _d_ | 72 | 74 | 61 | 52 + | | | | | + | _a_ | | | | + 112 | _b_ | | | | + | _c_ | 90 | 137 | 133 | 112 + | _d_ | 112 | 113 | 121 | 131 + -------------+------+----------+----------+--------+---------- + + +TABLE 2[11] + +GROUP TAKING ALL TESTS AT ALL PERIODS ARRANGED IN ORDER OF MAGNITUDE OF +INTELLIGENCE QUOTIENTS + + =============+============+==========+==========+=========== + Intelligence | Arithmetic |Vocabulary| Reading |Completion + Quotients | Quotients |Quotients |Quotients |Quotients + -------------+------------+----------+----------+----------- + 146 | 111 | 154 | 164 | 150 + 142 | 129 | 135 | 137 | 136 + 141 | 109 | 118 | 107 | 121 + 139 | 124 | 141 | 124 | 134 + 138 | 101 | 112 | 105 | 106 + | | | | + 138 | 121 | 130 | 110 | 109 + 130 | 107 | 139 | 135 | 136 + 122 | 127 | 130 | 124 | 121 + 122 | 113 | 121 | 117 | 124 + 122 | 112 | 102 | 114 | 129 + | | | | + 121 | 128 | 125 | 128 | 128 + 120 | 100 | 116 | 102 | 119 + 118 | 117 | 123 | 114 | 125 + 117 | 131 | 111 | 118 | 124 + 117 | 106 | 122 | 112 | 111 + | | | | + 114 | 105 | 126 | 110 | 114 + 109 | 83 | 113 | 117 | 103 + 107 | 103 | 112 | 95 | 103 + 107 | 94 | 126 | 94 | 123 + 104 | 99 | 117 | 96 | 104 + | | | | + 104 | 103 | 110 | 94 | 116 + 103 | 108 | 113 | 112 | 106 + 101 | 100 | 114 | 109 | 106 + 100 | 90 | 103 | 92 | 92 + 100 | 109 | 118 | 108 | 113 + | | | | + 99 | 114 | 104 | 106 | 110 + 99 | 114 | 119 | 117 | 115 + 98 | 102 | 101 | 108 | 104 + 98 | 99 | 106 | 107 | 106 + 97 | 95 | 109 | 107 | 105 + | | | | + 97 | 108 | 101 | 102 | 105 + 97 | 95 | 104 | 89 | 110 + 96 | 90 | 104 | 91 | 91 + 95 | 84 | 99 | 93 | 100 + 95 | 90 | 107 | 99 | 105 + | | | | + 95 | 85 | 117 | 114 | 103 + 94 | 106 | 57 | 89 | 108 + 94 | 103 | 103 | 106 | 104 + 92 | 96 | 86 | 94 | 85 + 87 | 83 | 88 | 92 | 87 + | | | | + 87 | 95 | 96 | 94 | 102 + 84 | 85 | 87 | 93 | 87 + 83 | 106 | 91 | 87 | 104 + 80 | 77 | 91 | 80 | 84 + 80 | 84 | 75 | 79 | 84 + | | | | + 80 | 89 | 107 | 88 | 86 + 78 | 87 | 90 | 93 | 85 + 60 | 69 | 56 | 71 | 77 + -------------+------------+----------+----------+----------- + +The intercorrelations of the quotients of these 48 cases for all periods +may be seen in Table 3 (page 21). The correlations with IQ and the +intercorrelations of the SQ’s have increased toward positive unity or +rather toward the limits of a correlation with tools of measurement such +as we have used. This limit is a function of the reliability of the tests +employed. It is customary to use a formula to correct for attenuation in +order to find the percentage which the correlation is of the geometric +mean of the two reliability coefficients. This is tantamount to saying +that any correlation can go no higher than the geometric mean of the +reliability coefficients of the tests used. It is better to assume that +an _r_ can go as high as the ∜(_r_₁₁⋅_r_₂₂) since an _r_ can go as high +as the square root of its reliability coefficient. Dr. Truman L. Kelley +has shown that the correlation of a test with an infinite number of forms +of the same test would be as the square root of its correlation with any +one other form. + +The reliabilities and limits defining a limit as the fourth root of the +multiplied reliability coefficients are in Table 4. + +Correction for attenuation is often ridiculously high because the +reliability coefficient of one of the measures used is so low. If an +element is included in the two tests which are correlated, but not in +the other forms of each test used to get reliability, the “corrected +coefficient” is corrected for an element which is not chance. Whenever +the geometric mean of the reliabilities is less than the obtained _r_, +the corrected _r_ is over 1.00 and hence absurd.[12] + +Therefore we use here instead, a comparison to the maximum possibility in +a true sense. Since a test correlates with the “true ability” √(_r_₁₁), +∜(_r_₁₁⋅_r_₂₂) is the limit of an _r_, its optimum with those tools. +Although these limits apply, strictly speaking, only to the total +correlations, since the reliability correlations are with all the data; +we may assume that the same facts hold with regard to the correlations of +each of the grades, that is, the reliability is a function of the test +not of the data selected. + + +TABLE 3 + +INTERCORRELATION OF ALL QUOTIENTS FOR ALL PERIODS OF THE 48 CHILDREN WHO +TOOK ALL TESTS + + NOVEMBER, 1918 + + IQ VQ RQ S.D. M + + IQ 19.12 105.15 + ±1.32 ±1.86 + + VQ .72 20.54 102.52 + ±.05 ±1.41 ±2.00 + + RQ .64 .64 19.09 95.90 + ±.06 ±.06 ±1.31 ±1.86 + + CQ .63 .71 .77 19.34 99.44 + ±.06 ±.05 ±.04 ±1.33 ±1.88 + + JUNE, 1919 + + IQ VQ RQ S.D. M + + IQ 19.12 105.15 + ±1.32 ±1.86 + + VQ .73 20.80 113.54 + ±.05 ±1.43 ±2.02 + + RQ .65 .58 14.73 101.31 + ±.06 ±.06 ±1.01 ±1.43 + + CQ .62 .68 .77 19.76 101.04 + ±.06 ±.05 +.04 ±1.36 ±1.92 + + NOVEMBER, 1919 + + IQ AQ VQ RQ S.D. M + + IQ 19.12 105.15 + ±1.32 ±1.86 + + AQ .46 14.08 102.90 + ±.08 ±0.97 ±1.37 + + VQ .86 .23 17.07 109.17 + ±.03 ±.09 ±1.18 ±1.66 + + RQ .65 .56 .71 13.91 101.42 + ±.06 ±.07 ±.05 ±0.96 ±1.35 + + CQ .79 .47 .83 .82 17.53 105.21 + ±.04 ±.08 ±.03 ±.03 ±1.21 ±1.71 + + JUNE, 1920 + + IQ AQ VQ RQ S.D. M + + IQ 19.12 105.15 + ±1.32 ±1.86 + + AQ .73 14.10 101.79 + ±.05 ±0.97 ±1.37 + + VQ .81 .60 18.89 108.94 + ±.03 ±.06 ±1.30 ±1.84 + + RQ .79 .68 .87 16.43 104.94 + ±.04 ±.05 ±.02 ±1.13 ±1.60 + + CQ .84 .77 .78 .84 15.87 108.08 + ±.03 ±.04 ±.04 ±.03 ±1.09 ±1.54 + + +TABLE 4 + +RELIABILITY COEFFICIENTS + + One Form Two Forms One Form Two Forms + of Each of Each with an with an + Test Test (by Infinite Infinite + Brown’s Number Number + Formula) of Forms of Forms + + _r_₁₁ _r_₁₁ √_r_₁₁ √_r_₁₁ + + Intelligence Quotient .888 .942 + (by Brown’s Formula)[13] + + Arithmetic Quotient .824 .904 .908 .951 + + Vocabulary Quotient .820 .901 .906 .949 + + Reading Quotient .866 .928 .931 .963 + + Completion Quotient .883 .938 .940 .968 + + Limits of the _r_’s = ∜(_r_₁₁ × _r_₂₂) + + Nov. 1918, + June and Nov. 1919 June 1920 + IQ and AQ .925 .946 + IQ and VQ .924 .946 + IQ and RQ .936 .953 + IQ and CQ .941 .955 + + The limits of the June, 1920 _r_’s are naturally somewhat larger than + the others since two forms of tests (except the Binet) were used; the + unreliability of the quantitative indices is therefore lower and hence + the correlation with IQ may be larger. + +The correlations in 1920 of another group—the whole school except Grade +III—are reproduced in Table 5. Grade III was excluded since here there +had as yet been little chance to push the _r_’s. Partials were obtained +with these data (Table 6). Little faith may be placed in the relative +sizes of these partials, much because the _r__{VQ.RQ} is here only .73 +and, in the data presented in Table 3, it is .87. This is due to the +fact that the data in Table 3 cover all periods (2 years) while those +in Table 5 cover only one. This difference has comparatively slight +influence on our general conclusions; but it makes a huge difference +in the correlation of RQ and VQ when IQ is rendered constant, whether +the one or the other set of data is used. Moreover, the whole logic of +arguing for general factors by reduction of partial correlations from +the original _r_ has been called gravely into question in Godfrey H. +Thomson’s recent work on this subject: “The Proof or Disproof of the +Existence of General Ability.” Thomson shows that partial correlation +gives one possible interpretation of the facts, but not an inevitable +one. Thus we cannot say that because RQ and IQ and RQ and AQ are highly +correlated, correlation of IQ and AQ is dependent upon RQ. We can say, +however, that it is likely to be. IQ and AQ may be correlated by reason +of inclusion of some element not included at all in RQ. The higher the +correlations which we deal with the less we need worry about this, and of +course correlations of unity exclude any such consideration. + + +TABLE 5 + +INTERCORRELATION OF ALL QUOTIENTS IN JUNE, 1920. ALL CHILDREN EXCLUSIVE +OF GRADE 3 ARE HERE REPRESENTED + + The P.E.’s are all less than .05 + _N_ = 81 + + Arithmetic Vocabulary Reading + IQ Quotient Quotient Quotient + + Arithmetic Quotient .733 + + Vocabulary Quotient .837 .628 + + Reading Quotient .758 .694 .734 + + Completion Quotient .821 .770 .825 .801 + +I therefore draw no conclusions from the comparative size of these +partials, nor do I get partials with any of the other data, and rest the +case mainly on the high _r_’s between IQ and SQ’s in 1920; increase in +correspondence of the central tendencies and range of the SQ’s by grade +with the central tendency and range of the IQ’s of the same data; small +intercorrelation of SR’s and negative correlation of AccR with IQ. + +The general lowness of the partials (Table 6) does, however, indicate +the great causative relation between IQ and disparity of product. +The elements still in here are common elements in the tests and the +mistreatment of intelligence. + + +TABLE 6 + +PARTIAL CORRELATIONS OF QUOTIENTS IRRESPECTIVE OF INTELLIGENCE QUOTIENTS + + _N_ = 81 + + Arithmetic Vocabulary Reading + Quotient Quotient Quotient + + Vocabulary Quotient .04 + ±.07 + + Reading Quotient .31 .28 + ±.07 ±.07 + + Completion Quotient .43 .44 .47 + ±.08 ±.06 ±.06 + +What happened by grade in 1918-1919 is summarized in Table 7. What +happened by grade in 1919-1920 is summarized in Table 8. Since there were +many changes in personnel from 1918-1919 to 1919-1920, we need expect no +continuity from Table 7 to Table 8. For the continuous influence of the +two years, see Table 3, which includes 48 children taking all tests at +all periods. + + +TABLE 7 + +ALL CORRELATIONS, MEANS, AND STANDARD DEVIATIONS BY GRADE, SHOWING +PROGRESS FROM NOVEMBER, 1918 TO JUNE, 1919 + + I stands for Intelligence Quotient + V stands for Vocabulary Quotient + R stands for Reading Quotient + C stands for Completion Quotient + + GRADE _r_ M S.D. + + Nov. June Nov. June Nov. June + + I V .467 .633 I 109.89 113.20 I 12.83 15.49 + ±.12 ±.07 ±1.98 ±1.91 ±1.40 ±1.35 + + III I R .541 .492 V 96.11 109.90 V 21.21 18.69 + ±.11 ±.09 ±3.28 ±2.30 ±2.32 ±1.63 + + I C .641 .386 R 82.26 101.40 R 22.58 15.85 + ±.09 ±.11 ±3.49 ±1.95 ±2.47 ±1.38 + + C 86.89 108.40 C 22.76 15.79 + ±3.52 ±1.94 ±2.49 ±1.37 + + _N_ = 19 30 + ----------------------------------------------------------------- + + I V .724 .819 I 105.90 104.82 I 18.08 18.21 + ±.07 ±.05 ±2.73 ±2.98 ±1.93 ±2.11 + + IV I R .665 .845 V 97.20 108.53 V 17.26 24.92 + ±.08 ±.05 ±2.60 ±4.08 ±1.84 ±2.88 + + I C .596 .717 R 91.06 107.82 R 27.85 10.35 + ±.10 ±.08 ±4.20 ±1.69 ±2.97 ±1.20 + + C 101.45 108.12 C 21.53 17.75 + ±3.25 ±2.90 ±2.30 ±2.05 + + _N_ = 20 17 + ----------------------------------------------------------------- + + I V .887 .822 I 101.64 99.42 I 24.76 17.63 + ±.04 ±.05 ±3.56 ±2.73 ±2.52 ±1.93 + + V I R .799 .832 V 100.59 111.58 V 26.71 19.78 + ±.05 ±.05 ±3.84 ±3.06 ±2.72 ±2.16 + + I C .818 .890 R 94.59 101.42 R 22.10 12.56 + ±.05 ±.03 ±3.18 ±1.94 ±2.25 ±1.37 + + C 97.00 102.68 C 22.52 17.71 + ±3.24 ±2.74 ±2.29 ±1.94 + + _N_ = 22 19 + ----------------------------------------------------------------- + I V .793 .772 I 109.90 115.90 I 23.45 24.38 + ±.08 ±.09 ±5.00 ±5.20 ±3.54 ±3.68 + + VI I R .497 .726 V 108.00 126.80 V 30.20 25.25 + ±.16 ±.10 ±6.44 ±5.39 ±4.55 ±3.81 + + I C .798 .891 R 103.10 107.20 R 13.77 20.62 + ±.08 ±.04 ±2.94 ±4.40 ±2.08 ±3.11 + + C 108.90 117.10 C 15.23 18.81 + ±3.25 ±4.01 ±2.30 ±2.84 + + _N_ = 10 10 + ----------------------------------------------------------------- + I V .625 .504 I 99.29 98.92 I 11.11 11.45 + ±.11 ±.14 ±2.00 ±2.14 ±1.42 ±1.51 + + VII I R .622 .709 V 109.43 115.23 V 14.07 17.43 + and ±.11 ±.09 ±2.54 ±2.95 ±1.79 ±2.31 + VIII + I C .782 .730 R 97.00 98.85 R 12.59 15.77 + ±.07 ±.09 ±2.27 ±3.26 ±1.61 ±2.09 + + C 102.43 95.85 C 13.49 17.72 + ±2.43 ±3.31 ±1.72 ±2.34 + + _N_ = 14 13 + ----------------------------------------------------------------- + I V .685 .680 I 105.07 106.88 I 19.34 18.45 + ±.04 ±.04 ±1.41 ±1.32 ±1.00 ±0.93 + + I R .568 .626 V 101.12 112.67 V 22.83 21.58 + TOTAL ±.05 ±.04 ±1.67 ±1.54 ±1.18 ±1.09 + + I C .639 .702 R 92.40 102.91 R 22.65 15.27 + ±.04 ±.04 ±1.66 ±1.09 ±1.17 ±0.77 + + C 98.08 106.27 C 21.48 18.19 + ±1.57 ±1.30 ±1.11 ±0.92 + + _N_ = 85 89 + ----------------------------------------------------------------- + + +TABLE 8 + +ALL CORRELATIONS, MEANS, AND STANDARD DEVIATIONS OF QUOTIENTS BY GRADE, +SHOWING PROGRESS FROM NOVEMBER, 1919 TO JUNE, 1920 + + I stands for Intelligence Quotient + V stands for Vocabulary Quotient + R stands for Reading Quotient + C stands for Completion Quotient + A stands for Arithmetic Quotient + + _r_ M S.D. + + Nov. June Nov. June Nov. June + + I A .413 .709 I 102.00 105.53 I 9.60 10.89 + ±.16 ±.08 ±1.87 ±1.68 ±1.32 ±1.19 + + III I V .649 .667 A 82.75 97.84 A 15.88 18.62 + ±.11 ±.09 ±3.09 ±2.88 ±2.19 ±2.04 + + I R .651 .609 V 94.00 103.47 V 33.44 27.66 + ±.11 ±.10 ±6.51 ±4.28 ±4.60 ±3.03 + I C .612 .719 R 87.59 93.88 R 32.06 19.02 + ±.12 ±.07 ±6.24 ±3.21 ±4.41 ±2.27 + + C 90.17 96.84 C 28.82 25.59 + ±5.58 ±3.96 ±3.95 ±2.80 + + _N_ = 12 19 + ----------------------------------------------------------------- + I A .426 .725 I 111.48 113.00 I 14.73 15.04 + ±.10 ±.06 ±1.85 ±1.93 ±1.30 ±1.36 + + IV I V .635 .772 A 94.07 111.08 A 12.34 15.02 + ±.075 ±.05 ±1.55 ±1.99 ±1.09 ±1.40 + + I R .316 .569 V 109.79 115.61 V 16.97 18.39 + ±.11 ±.09 ±2.13 ±2.34 ±1.50 ±1.66 + + I C .594 .837 R 99.31 110.11 R 17.89 14.67 + ±.08 ±.04 ±3.24 ±1.67 ±1.58 ±1.32 + + C 108.14 118.14 C 15.51 12.70 + ±1.94 ±1.62 ±1.37 ±1.15 + + _N_ = 29 28 + ----------------------------------------------------------------- + I A .698 .713 I 103.72 98.83 I 19.57 18.84 + ±.07 ±.07 ±2.69 ±2.65 ±1.91 ±1.87 + + V I V .881 .908 A 87.58 99.71 A 12.43 16.47 + ±.03 ±.02 ±1.71 ±2.27 ±1.21 ±1.60 + + I R .773 .891 V 109.00 105.17 V 15.58 19.97 + ±.06 ±.03 ±2.14 ±2.81 ±1.52 ±1.99 + + I C .786 .923 R 104.46 103.00 R 16.99 17.07 + ±.05 ±.02 ±2.34 ±2.40 ±1.65 ±1.70 + + C 107.00 103.48 C 16.12 14.51 + ±2.22 ±2.04 ±1.57 ±1.44 + + _N_ = 24 23 + ----------------------------------------------------------------- + I A .533 .805 I 102.43 105.39 I 11.61 13.56 + ±.13 ±.06 ±2.09 ±2.16 ±1.48 ±1.52 + + VI I V .774 .858 A 91.43 104.53 A 11.43 11.31 + ±.07 ±.04 ±2.06 ±1.75 ±1.46 ±1.24 + I R .420 .661 V 106.07 112.94 V 11.93 10.94 + ±.15 ±.09 ±2.15 ±1.74 ±1.52 ±1.23 + + I C .739 .620 R 96.64 106.20 R 12.38 11.88 + ±.08 ±.10 ±2.23 ±1.79 ±1.58 ±1.27 + + C 100.36 107.61 C 13.95 10.55 + ±2.51 ±1.68 ±1.78 ±1.19 + + _N_ = 14 18 + ----------------------------------------------------------------- + I A .740 .795 I 107.27 100.58 I 23.29 19.78 + ±.09 ±.07 ±4.74 ±2.85 ±3.35 ±2.72 + + VII I V .867 .718 A 100.00 99.31 A 9.26 11.00 + ±.05 ±.09 ±1.86 ±2.06 ±1.33 ±1.45 + + I R .862 .799 V 114.36 108.75 V 19.15 14.42 + ±.05 ±.07 ±3.89 ±2.81 ±2.75 ±1.98 + + I C .833 .677 R 101.73 98.58 R 12.28 11.56 + ±.06 ±.11 ±2.50 ±2.25 ±1.77 ±1.59 + + C 105.82 101.42 C 17.41 16.02 + ±3.54 ±3.12 ±2.50 ±2.21 + + _N_ = 11 12 + ----------------------------------------------------------------- + I A .663 .796 I 104.83 108.79 I 15.46 18.25 + ±.11 ±.07 ±3.01 ±3.29 ±2.13 ±2.33 + + VIII I V .828 .750 A 92.92 93.86 A 10.20 9.74 + ±.06 ±.08 ±1.99 ±1.76 ±1.40 ±1.24 + + I R .775 .722 V 111.67 117.21 V 16.44 14.02 + ±.08 ±.08 ±3.20 ±2.53 ±2.26 ±1.79 + + I C .838 .868 R 100.83 104.38 R 11.52 20.62 + ±.06 ±.04 ±2.24 ±3.72 ±1.59 ±2.63 + + C 104.92 109.64 C 18.11 17.41 + ±3.53 ±3.14 ±2.49 ±2.22 + + _N_ = 12 14 + ----------------------------------------------------------------- + + I A .576 .686 I 106.02 105.87 I 16.73 16.87 + ±.05 ±.03 ±1.12 ±1.07 ±0.79 ±0.75 + + TOTAL I V .679 .727 A 91.35 102.01 A 13.22 15.61 + ±.04 ±.03 ±0.88 ±0.98 ±0.62 ±0.69 + + I R .529 .609 V 107.95 110.54 V 19.76 19.57 + ±.05 ±.04 ±1.32 ±1.24 ±0.93 ±0.87 + + I C .678 .731 R 99.22 103.65 R 18.85 17.12 + ±.04 ±.03 ±1.26 ±1.08 ±0.89 ±0.76 + + C 104.06 108.00 C 18.87 18.11 + ±1.26 ±1.14 ±0.89 ±0.81 + + _N_ = 102 114 + ----------------------------------------------------------------- + + NOTE—Totals without Grade III are much higher than these (Table 5). + Grade III has many children in it who have not been long enough in an + academic situation to allow their SQ’s to go as high as they may. + +It is proper to note here that not much can be expected from Grades III +and VIII and from totals including Grade III, since children in Grade III +have not been there long enough to be pushed, and children in Grade VIII +have been pushed beyond the limits which the tests used will register. +Our logic is one of _pushed_ correlations. If the association of IQ and +the SQ’s is what we are attempting to establish, it is necessary to show: + +1. That the _r_ comes near unity; + +2. That the central tendencies come near coincidence; + +3. That the S.D.’s come near coincidence. + +The value of the _r_ is obvious; the value of coincidence of means +becomes clearer if we think of Σ(IQ-EQ)⁄_n_, the average difference of +potential rate of progress and actual rate of progress. This average of +differences is the same as the difference of the averages, which is more +readily calculated. Obviously, if we wish to use an AccR, it is necessary +to show more than correspondence when differences in average and +spread are equated as they are by the correlation coefficient. Besides, +coincidence of M’s, correspondence of S.D.’s is also necessary since a +correlation might be positive unity, the M’s might be equal, and still +the spread of one measure might be more than the spread of the other. If +the spreads are the same and the M’s are the same, and the correlation is +positive unity, each _x_ must equal its corresponding _y_. Then _b_₁₂ = +_b_₂₁ = 1.00; and the M’s being equal, the deviations are from the same +point. Therefore, we will attempt to measure similarity of M’s and S.D.’s +as well as _r_. + +It will be observed that both Tables 7 and 8 give evidence of each +of these tendencies in all grades. In Table 8 marked progress in +arithmetic is apparent. This is due to re-classification in terms of +the Woody-McCall test, which was not done in 1918-1919. In 1918-1919 +no arithmetic test was given and all re-classification was in terms +of reading, being done on the basis of both reading tests. Spelling +re-classification was done each year, but the data were not treated in +this manner. It can be said that wherever re-classification in terms of +intelligence and pedagogical need was undertaken the desired result of +pushing the SQ’s up to IQ was hastened. Of all the remedial procedure, +such as changing teachers and time allotment and books and method, +all of which were employed to some extent, it is my opinion that the +re-classification was more important than everything else combined. + +It is noticeable that when _r_’s approach the limit which the +unreliability of the test allows them, they drop down again. This is +probably due to continued increase of SQ’s over IQ. Of course, for some +SQ’s to be greater than IQ out of proportion to the general amount lowers +the correlation as much as for some to lag behind. When the SQ’s of the +children of lower intelligence reach their IQ they continue above. This, +of course, is due to errors in establishment of the age norms. The norms +are not limits of pushing, though an attempt was made by correction for +truncation to get them as nearly so as possible. It is to be noted, +however, that these norms are up the growth curve, that is, reading +age of 10 means a score such that the average age of those getting it +is 10, not the average score of children whose mental age is 10. The +average reading achievement of children all ten years old chronologically +is _higher_ than that of a group all mentally ten, since many of the +mentally advanced have not been pushed in product. The group used here +to establish norms gives more nearly pushed norms than the others would. + +The tendency of the low IQ’s to go over unity in their SR’s is apparent +in Table 1 and in Table 12 and also in the negative correlation between +AccR and IQ. + +In both years some second grade children were advanced to Grade III +during the year. This accounts for the low _r_’s in June, 1919, but in +1919-1920 the Grade III correlations are raised and the means raised +toward the M_{IQ}, even though some second grade children were put in +this group during the year. + + +TABLE 9 + +SUMMARY OF PROGRESS IN ARITHMETIC BY INCREASE IN _r_, DECREASE IN +M_{IQ}-M_{AQ} AND DECREASE IN DIFFERENCE OF STANDARD DEVIATIONS +IRRESPECTIVE OF DIRECTION + + Average Intelligence Difference of + GRADE _r_ Quotient Minus Standard Deviations + Average Arithmetic Irrespective of + Quotient Sign (of IQ and + Arith. Q) + + Nov. June Nov. June Nov. June + + III .413 .709 19.25 8.16 6.27 6.63 + ±.16 ±.08 ±2.87 ±2.05 ±2.04 ±1.45 + + IV .426 .725 7.41 0.46 2.39 0.47 + ±.10 ±.06 ±1.84 ±1.50 ±1.29 ±1.02 + + V .698 .713 16.14 0.54 7.14 2.06 + ±.07 ±.07 ±1.93 ±1.84 ±1.37 ±1.30 + + VI 5.33 .805 11.00 3.00 0.19 1.63 + ±.13 ±.06 ±2.01 ±1.19 ±1.42 ±0.85 + + VII .740 .795 7.27 0.62 14.03 8.15 + ±.09 ±.07 ±3.58 ±2.33 ±2.53 ±1.63 + + VIII .663 .796 11.92 [14]14.93 5.26 [14]8.53 + ±.11 ±.07 ±2.25 ±2.69 ±1.59 ±1.54 + + Total .576 .686 14.67 3.72 3.51 1.16 + ±.05 ±.03 ±0.94 ±0.81 ±0.67 ±0.57 + + +TABLE 10 + +SUMMARY OF PROGRESS IN READING, NOVEMBER, 1918 TO JUNE, 1919, BY INCREASE +IN _r_, DECREASE IN M_{IQ}-M_{RQ}, AND DECREASE IN DIFFERENCE OF STANDARD +DEVIATIONS IRRESPECTIVE OF SIGN + + Average Intelligence Difference of + GRADE _r_ Quotient Minus Standard Deviations + Average Reading Irrespective of + Quotient Sign (of IQ and RQ) + + Nov. June Nov. June Nov. June + + III .541 .492 27.63 11.80 9.75 0.36 + ±.11 ±.09 + + IV .665 .845 14.84 -3.00 9.77 7.86 + ±.08 ±.05 + + V .799 .832 7.05 -2.00 2.66 5.07 + ±.05 ±.05 + + VI .497 .726 6.80 8.70 9.68 3.76 + ±.16 ±.10 + + VII .622 .709 2.28 0.07 1.48 5.98 + 3 of VIII ±.11 ±.09 + + Total .568 .626 12.67 3.97 3.31 3.18 + ±.05 ±.04 + + +TABLE 11 + +SUMMARY OF PROGRESS IN READING, NOVEMBER, 1919 TO JUNE, 1920, BY INCREASE +IN _r_, DECREASE IN M_{IQ}-M_{RQ}, AND DECREASE IN DIFFERENCE OF STANDARD +DEVIATIONS IRRESPECTIVE OF SIGN + + Average Intelligence Difference of + GRADE _r_ Quotient Minus Standard Deviations + Average Reading Irrespective of + Quotient Sign (of IQ and RQ) + + Nov. June Nov. June Nov. June + + III .651 .609 14.41 11.57 22.46 8.62 + ±.11 ±.10 ±5.22 ±2.55 ±3.69 ±1.81 + + IV .316 .569 12.17 2.43 3.16 0.76 + ±.11 ±.09 ±2.41 ±1.78 ±1.70 ±1.26 + + V .773 .891 -0.74 -4.17 2.58 1.77 + ±.06 ±.03 ±1.72 ±1.20 ±1.22 ±0.85 + + VI .420 .661 5.79 0.90 0.77 0.87 + ±.15 ±.09 ±2.33 ±1.53 ±1.65 ±1.09 + + VII .862 .799 5.54 0.92 11.00 8.31 + ±.05 ±.07 ±2.88 ±2.54 ±2.03 ±1.80 + + VIII .775 .722 4.00 4.43 3.94 2.41 + ±.08 ±.09 ±1.90 ±2.64 ±1.92 ±1.87 + + Total .529 .609 6.80 2.86 2.12 0.06 + ±.05 ±.04 ±1.16 ±0.30 ±0.82 ±0.67 + +The changes in rates of progress are expressed in summaries by subject +matter in Tables 9, 10, and 11. Approach of Arithmetic Quotient to +Intelligence Quotient is measured in Table 9 by: + +1. Comparison of _r_ in June with _r_ in November. + +2. Comparison of M_{IQ}-M_{AQ} in June and M_{IQ}-M_{AQ} in November. + +3. Comparison of S.D.’s of Arithmetic and Intelligence Quotients in June +and November. + +The P.E.’s of each of these differences were obtained by + + P.E._{diff}² = P.E.₁² + P.E.₂² - 2 _r_₁₂ P.E.₁ P.E.₂ + +The only M_{IQ}-M_{SQ} in Table 9 which does not show a decrease at +least two times as large as the P.E. of either of the elements involved, +is the 8th grade; and this is due to the limits of the test used. As +mentioned before, the 8th grade did not register its true abilities in +June since a perfect, or nearly perfect, score in the test was too easy +to obtain. The small arithmetic S.D.’s in Grade 8 and consequent great +S.D._{IQ}-S.D._{SQ} is due to the same cause. + +Tables 10 and 11 present the summary of facts with regard to Thorndike +Reading Quotients, the first and second years respectively. + + +THE RATIOS + +The discussion which follows concerns _Ratios_, not _Quotients_. + + +TABLE 12 + +INTELLIGENCE QUOTIENTS AND SUBJECT RATIOS FOR ALL PERIODS GROUPED BY +CHILD. THE ORDER OF ENTRIES IS JUST AS IN TABLE 1 + +GRADE III + + Intelligence Arithmetic Vocabulary Reading Completion + Quotient Ratio Ratio Ratio Ratio + + _a_ + 101 _b_ + _c_ 63 57 43 + _d_ 105 87 92 + + _a_ + 128 _b_ + _c_ 62 80 63 + _d_ 119 97 120 + + _a_ + 116 _b_ + _c_ 48 78 * 42 + _d_ 81 82 66 77 + + _a_ + 87 _b_ + _c_ 103 46 40 62 + _d_ 83 85 70 60 + + _a_ + 112 _b_ + _c_ 80 122 119 100 + _d_ 100 101 108 117 + + _a_ + 101 _b_ + _c_ 84 93 37 55 + _d_ 90 110 98 92 + + _a_ + 90 _b_ + _c_ 76 58 72 89 + _d_ 68 121 77 102 + + _a_ + 105 _b_ + _c_ 60 43 * 57 + _d_ 104 95 83 66 + +The remainder of this table is filed in Teachers College Library, +Columbia University. + + +TABLE 13 + + Nov., 1918 June, 1919 Nov., 1919 June, 1920 + + MEANS + + Arithmetic Ratio 89.02 97.16 + ±1.05 ±1.07 + + Vocabulary Ratio 98.96 111.44 106.20 107.61 + ±1.48 ±1.61 ±0.90 ±0.93 + + Reading Ratio 96.47 101.96 98.98 100.60 + ±1.19 ±1.18 ±1.03 ±0.97 + + Completion Ratio 99.76 101.83 101.67 103.10 + ±1.11 ±1.23 ±0.93 ±0.85 + + STANDARD DEVIATIONS + + Arithmetic Ratio 12.03 12.53 + ±0.74 ±0.76 + + Vocabulary Ratio 15.71 16.58 10.34 10.84 + ±1.05 ±1.14 ±0.64 ±0.66 + + Reading Ratio 12.63 12.14 11.82 11.36 + ±0.84 ±0.84 ±0.73 ±0.69 + + Completion Ratio 12.34 12.63 10.85 9.90 + ±0.82 ±0.87 ±0.67 ±0.60 + + CORRELATIONS OF RATIOS + + Arithmetic and Vocabulary .60 .30 + ±.06 ±.08 + + Arithmetic and Reading .70 .64 + ±.04 ±.05 + + Arithmetic and Completion .48 .61 + ±.07 ±.05 + + Vocabulary and Reading .34 .32 .57 .47 + ±.08 ±.09 ±.06 ±.07 + + Vocabulary and Completion .45 .36 .53 .54 + ±.07 ±.08 ±.06 ±.06 + + Reading and Completion .61 .65 .67 .67 + ±.06 ±.06 ±.05 ±.05 + +In Table 12 are presented the Subject Ratios in the same order as the +Quotients appear in Table 1.[15] There plainly is a rapid rise of SQ⁄IQ +from period to period, excluding all pupils who did not take all tests +and excluding Grade III; which includes all children taking all tests who +were in school in June, 1920, and were Grade IV and above in November, +1918. The average AccR is 98.24 in November, 1918, and 102.78 in June, +1920. The average IQ for these children is 105.22. The S.D_{AccR₁₉₁₈} is +11.17; the S.D._{AccR₁₉₂₀} is 9.09; the S.D._{IQ} is 19.24. It is obvious +that the average amount of product per intelligence has increased, that +the range of AccR’s has decreased (which means that factors causing +disparities, other than intelligence, have been removed), and that the +S.D. of the AccR’s is about one half the S.D. of the IQ’s. M’s are about +equal so it is not necessary to use coefficients of variability. The +variability of children, intelligence aside, is only one half what the +variability is otherwise. The correlations when IQ = _X_, AccR₁₉₁₈ = _Y_ +and AccR₁₉₂₀ = _S_ and when AccR = average of Vocabulary, Reading and +Completion Ratios, are:[16] + + _r__{X.Y.} = -.602 + _r__{X.S.} = -.493 + _r__{Y.S.} = +.549 + +The remaining disparity is then due to something which is in negative +correlation with intelligence. + +The number of cases here is only 48. + +The P.E.’s are then as follows: + + P.E._{M} P.E._{S.D.} + _X_ 1.91 1.35 + _Y_ 1.11 0.79 + _S_ 0.90 0.64 + P.E._r__{X.Y.} = .06 + P.E._r__{X.S.} = .08 + P.E._r__{Y.S.} = .07 + +The differences between the M’s and between the S.D.’s of our 1918 and +our 1920 AccQ’s; namely, 102.78 - 98.24 = 4.54 and 11.17 - 9.09 = 2.08, +have formed a step in the argument. We must have the P.E.’s of these +amounts in order to establish the reliability of the quantitative indices +we employ: + + P.E._{diff} = √P.E._{X}² + P.E._{Y}² - 2 _r__{XY} P.E._{X} P.E._{Y} + + P.E._{M₂₀-M₁₈} = 0.94 + + P.E._{S.D.₁₈-S.D.₂₀} = 0.47 + +These differences are then reliable. If the same data were accumulated +again in the same way with only 48 cases, the chances are even that the +4.54 would be between 3.50 and 5.48 and the 2.08 between 1.61 and 2.55. +That there would be positive differences is practically certain, since +the difference between the means is over four times as large as its P.E., +and the difference between the S.D.’s over four times as large as its P.E. + +To make still more certain this observation of positive amount in M of +second testing minus M of first testing and in S.D. of first testing +minus S.D. of second testing (AccR), which means an increase in central +tendency of AccR’s and a decrease in spread of AccR’s under special +treatment, we have listed in Table 13 the means and standard deviations +of Subject Ratios of each test for each period and the intercorrelations +of these Subject Ratios. These do not include exactly the same children +in each period but are inclusive of all grades for all periods. They +are a measurement of increased efficiency of the school as a whole, +rather than of any one group of children; though, of course, the bulk +of the children have representation in each of these indices. Too much +continuity is not to be expected from June, 1919, to November, 1919, as +the children are different. Comparison should always be from November to +June. + +These tables bear out the fact presented by AccR. It is clear that +there is a marked development in the S.R.’s, both by increase of M. +and decrease of S.D. The decrease of correlation between S.R.’s is not +so marked, but neither is the negative correlation between AccR and +IQ much less in June, 1920, than in November, 1918. The association +of achievements in terms of intelligence is very probably due to +mistreatment, since it is in negative correlation with IQ, as a general +inherited ethical factor could not be. + +We will note that the Arithmetic Ratios are in as high positive +association with the Reading Ratios as the Vocabulary Ratios are with the +Reading Ratios. This makes it highly improbable that the intercorrelation +of these remnants is due, to any large extent, to common elements in +the test or to specific abilities. The common interassociation of all +Ratios seems to point to the operation of some common factor other than +intelligence as a determinant of disparity in school progress. It would +be easy to identify this as the part of Burt’s “General Educational +Factor” which is not intelligence—that is, industry, general perseverance +and initiative—were it not for the fact that this same influence _stands +in negative association to intelligence_. It is our belief that it is the +influence of a maladjusted system of curricula and methods which accounts +for these rather high interassociations of achievements, irrespective of +intelligence. + + +SUMMARY + +The association of abilities in arithmetic, reading, and completion with +intelligence is markedly raised by special treatment. Disparities of +educational product are therefore to a great extent due to intelligence. +(Tables 2, 3, 5, 7, 8, 9, 10 and 11.) + +The remnants (intelligence being rendered constant by division of each +SQ by IQ) intercorrelate about .5. If there were specialized inherited +abilities, these intercorrelations would not all be positive nor would +they be as uniform. (Tables 6 and 13.) + +The averages of these remnants, for reading, vocabulary, and completion, +correlate -.61 in 1918 and -.49 in 1920 with IQ. These remnants are in +negative association to intelligence. If the intercorrelations of these +remnants were due to a “General Factor,” this correlation would not be +negative. + +Therefore intelligence is far and away the most important determinant of +individual differences in product. + +As part of the relation between tests, irrespective of intelligence, is +due to common elements in the tests, this reasoning becomes still more +probable. + +General factor in education, as distinct from intelligence, has not +been separated here from inherited bases of ambition, concentration, +and industry. It seems out of our province to conjure up some inherited +complex of abilities other than intelligence, specialized inherited +abilities, or proclivities and interests tending to thorough prosecution +of school work. I have therefore meant this last by the general factor. + +McCall has correlations varying continually in size from -.63 to +.98 +between various measurements of a group of 6B children.[17] The abilities +involved were not pushed as are those considered here. Some of the low +correlations are no doubt indications of low association because of the +way children _are_, not the way they _might be_ by heritage; still +others, such as handwriting and cancellation (unless bright children +do badly in cancellation tests because they are _more bored_ than the +others), are correlated low or negatively with intelligence when the +correlation is at its maximum. Such results as those of McCall serve as a +guide not to argue about other tests by analogy. It is necessary to find +which traits and abilities can be pushed to unity in their relation to +intelligence and which, like handwriting, are practically unrelated to +general mental power. + +It is well to know about music tests and such tests as Stenquist’s +mechanical ability test _when the correlation with intelligence is +pushed_, before we decide whether the quality measured is a manifestation +of specific talent or general intelligence. + +Cyril Burt obtained data much like that presented here except that +instead of getting rid of the influence of intelligence and finding +determinants for the remnants of disparity, he built up a hierarchy of +coefficients as they would be if they were due entirely to a common +factor and compared these with his obtained _r_’s. I will present his +conclusions with regard to a general factor which are in substantial +though not complete agreement with those advanced here. + + “Evidence of a Single Common Factor. + + “The correlations thus established between the several school + subjects may legitimately be attributed to the presence of + common factors. Thus, the fact that the test of Arithmetic + (Problems) correlates highly with the test of Arithmetic + (Rules) is most naturally explained by assuming that the same + ability is common to both subjects; similarly, the correlation + of Composition with Arithmetic (Problems) may be regarded as + evidence of a common factor underlying this second pair; and + so with each of the seventy-eight pairs. But is the common + factor one and the same in each case? Or have we to recognise a + multiplicity of common factors, each limited to small groups of + school subjects? + + “To answer this question a simple criterion may be devised. + It is a matter of simple arithmetic to reconstruct a table + of seventy-eight coefficients so calculated that all the + correlations are due to one factor and one only, common to + all subjects, but shared by each in different degrees. Such + a theoretical construction is given in Table XIX. In this + table theoretical values have been calculated so as to give + the best possible fit to the values actually obtained in the + investigation, and printed in Table XVIII. It will be seen that + the theoretical coefficients exhibit a very characteristic + arrangement. The values diminish progressively from above + downwards and from right to left. Such an arrangement is termed + a ‘hierarchy.’ Its presence forms a rough and useful criterion + of the presence of a single general factor. + + “On turning to the values originally obtained (Table XVIII.) + it will be seen that they do, to some extent, conform to this + criterion. In certain cases, however, the correlations are far + too high—for instance, those between Arithmetic (Rules) and + Arithmetic (Problems), and again Drawing and both Handwork and + Writing (Quality). Now these instances are precisely those + where we might anticipate special factors—general arithmetical + ability, general manual dexterity—operating over and above + the universal factor common to all subjects. These apparent + exceptions, therefore, are not inconsistent with the general + rule. Since, then, the chief deviations from the hierarchical + arrangement occur precisely where, on other grounds, we + should expect them to occur, we may accordingly conclude that + performances in all the subjects tested appear to be determined + in varying degrees by a single common factor. + + “Nature of the Common Factor. + + “What, then, is this common factor? The most obvious + suggestions are that it is either (1) General Educational + Ability or (2) General Intelligence. For both these qualities, + marks have been allotted by teachers, quite independently of + the results of the tests. The correlations of these marks with + performances in the tests are given in the last two lines of + Table XVIII. + + “Upon certain assumptions, the correlation of each test with + the Hypothetical Common Factor can readily be deduced from the + coefficients originally observed. These estimates are given in + the last line but two of the table. They agree more closely + with the observed correlations for General Educational Ability, + especially if the latter are first corrected for unreliability. + (Correlations: Hypothetical General Factor coefficients and + General Educational Ability coefficients .86; after correction + .84. Hypothetical General Factor coefficients and General + Intelligence coefficients .84; after correction .77.) We may, + therefore, identify this hypothetical general factor with + General Educational Ability, and conclude provisionally that + this capacity more or less determines prowess in all school + subjects. + + “The high agreement of the estimated coefficients with the + intelligence correlations suggest that General Intelligence is + an important, though not the only factor in General Educational + Ability. Other important factors are probably long-distance + memory, interest and industry. It is doubtless not a pure + intellectual capacity; and, though single, is not simple, but + complex.”[18] + + + + +PART III + +THE PSYCHOLOGICAL CONCLUSIONS OF THE EXPERIMENT + + +THE NEGLECT OF GENIUS + +Schools of to-day are organized and administered so as to yield less +chance to a child to obtain as much information as is possible for him +to have in direct proportion to his mental ability. The correlation +between accomplishment and intelligence (using AccR, the average of +Reading, Vocabulary, and Completion Ratios with IQ) was -.61 in November, +1918, and -.49 in June, 1920, in the Garden City public school. The +regrading and special promotion work from November, 1918, to June, +1920, reduced the handicap of brightness, but could not obliterate the +sparsity of returns per increment of capacity in the upper reaches of the +intelligence. Further, work along this same line done by A. J. Hamilton +in the Washington School, Berkeley, California, indicates that this was +not a peculiarity of the school at Garden City. + +The wide range of abilities which we know exists in pupils of any one age +makes it impossible to adjust our formal education to the extremes. Much +adjustment has been made in favor of the lower extreme, but little has +been done for our genius. Of course the work with extreme subnormals is +conceived and prosecuted more in the sense of clearing them away for the +good of those remaining than of fitting education to their own needs. We +are neglecting, however, our duty to those whom nature has endowed with +the essentials of leadership. They do not interfere quite as much with +ordinary classroom procedure, but they are greater social assets and need +special treatment to develop _them_ rather than to let others develop +better. + +Neither of the extreme groups is certain of getting the normal stamina +necessary for good citizenship. Neither group forms good habits of +study nor accumulates such information as it might. Being aware of this +discrepancy between the gift and the recipient, we have made our lessons +easier and we have segregated the lower percentile. There is much more +to be done. We must adapt education to at least five varying classes +in order to reduce the spread within each to a commodious span. But the +genius is the most important and should have the greatest claim to our +immediate attention. + +First, our social needs demand special attention for the genius in +order that we may better exploit our best nervous resources. Second, +our educational needs demand it since the very bright as well as the +very stupid disrupt calm and cogent classroom procedure. Third, they +themselves demand it in order that they may, even when they do function +as leaders, be happier in that function, since now they often lose much +in social contact by peculiarities which prevent an integration of their +“drives” into a harmonious economy of tendency. These peculiarities come +from their continuous maladjustment, since when they are with children +of their own mental maturity they are physically and physiologically +handicapped; when they are with children of their own size and muscular +equipment they are so far mentally superior that they are unhappily +adjusted. Only classification on a large scale will allow sufficient +numbers of them to congregate to correct this. + +I am reminded of a boy ten years old whose IQ on the Terman test was 172. +He defined a nerve as the “conduction center of sensation” and, when +asked to explain, did so in terms of sensation of heat and motive to +withdraw. He explained the difference between misery and poverty thus: +“Misery is a lack of the things we want; poverty is a lack of the things +we need.” How can we expect a boy like this to grow into a normal citizen +if we do not provide the companionship of peers in mentality and in +physique? + +Fourth, our eugenic needs demand it, since we are not conserving this, +our chiefest asset, genius. Unless we conserve better these rare +products, the standard deviation of the intelligence of humanity will +keep shrinking as we select against imbeciles and against genius as well. +The waste of a genius who becomes an intellectual dilettante, as many now +in fact do, is double. We lose what he might do for society; he does not +marry and we lose the potentiality of his highly endowed germ-plasm. + +And they do become dilettantes when special treatment is not given. I +know of a young man who was first of his high-school class, who got all +A’s his first year in College (at Wisconsin), and all A’s his second year +(at Harvard); and then he began to read all manner of literature with +no schema of expression, no vocation, because, as he said, all college +courses are so stupidly easy. He attended no lectures and read none of +the books in one course, and then two days before the examination he was +taunted with not being able to pass this course. He spent two nights +and two days studying, and he received B in the course. But now he is a +failure because he has no organized, purposive schema of expression; he +was always in classes with people less fortunately endowed than he, and +so he never had a chance. + +On these four counts then we must segregate our genius: (1) Social +exploitation of our resources. (2) Educational procedure for the sake of +other children as well as for them. (3) Happiness for them, organization +of their trends, and formation of social habits. (4) Biologic +conservation of great positive deviation from average human intelligence. + + +IS GENIUS SPECIALIZED? + +This genius is of various kinds, political and business leaders, +scientists and artists. Have they then the same inherited nervous +structure with regard to abilities and capacities as distinct from +interests? We know that they must have something in common, something +that we call intelligence, power of adaptation. Calling this the nervous +chemistry, the way the nervous system acts its quality, we must still +know whether we have also an inherited nervous physics to deal with, +or a further inherited nervous chemistry which predisposes to specific +ability. Are there inherited capacities or predispositions to ability? We +are in a position to answer this question with regard to the elementary +school subjects, and are tempted here into a more general discussion of +the matter in hand. + +The need to clarify our view on what is inherited and what is due to +environment can be clearly envisaged in terms of our teachers. Whatever +psychologists may mean by “predisposition to ability” it is quite certain +that teachers make no distinction between this and the inheritance +of a capacity. They feel that some children figure better than they +read, and others read better than they figure, “by nature,” and there +their obligation ends. If it is a grave matter that we shoulder the +burden of bringing a child to his optimum achievement, then it is an +immediate duty that we find how much of the failure to produce product +of one kind or another is due to unremovable factors, and how much is +due to our inadequacy. So, too, we have much loose discussion about +finding out what children can do and want to do in the way of vocational +diagnosis,—loose because it assumes that children are born with definite +vocational capacities. Certainly we can do much more in the way of +development and much more in the way of preparation for social needs if +we know just how much “predisposition to ability” means. The teacher +interprets it to mean about what was meant by the turtle that held up +Atlas who held up the world. She makes no real distinction between +predisposition to ability and specific ability, just as there was no real +causal distinction between the turtle and Atlas. She then gets at her +conception of intelligence additively,—a summation of school abilities. + +The correlation of teachers’ judgment of “power of adaptation,” carefully +explained, and marks given six months previously by the same teachers +was .82. The correlation of this same average judgment with the average +of thirteen intelligence tests was only .58. These teachers obviously +reached their conclusions of the intelligence of a child in the same +way as they reached their conclusions of what marks he earned in their +subjects. + +The unit characteristics which make up what we describe in terms of gross +behavior as intelligence must of course be many. No one denies that +if we knew just what these units were we could describe two possible +manifestations of what we now call intelligence, of which one person +could do one only and another person could do the other only because of +the particular combinations of the units inherited. This would constitute +inheritance of predisposition to special capacities. But it is not the +same to assume that the vocations and aptitudes desirable in a world such +as ours have specialized inherited bases. It is far more probable that +substantially the same inherited characteristics are necessary to success +in all the gross cross-sections of behavior which we call vocations and +abilities. + +As the unit characteristics are certainly not so closely allied to our +social needs as “mechanical intelligence” and “social intelligence” or +even “rote memory for numbers,” we may not even distinguish presence +of any five hundred elements from presence of any other five hundred +elements in terms of what we now measure as intelligence. It is just as +likely that all the elements of intelligence are necessary for every +vocation and that all contribute to success of any one kind as it is +likely that some are necessary for one vocation and others for another. + +This is a question of more or less. I believe that the amount to which +a person’s specific talents, his vocation as distinct from his general +power, are shaped by the combinations of elements which make up his +inheritance, is much less than believed by Francis Galton, who says: +“There cannot then remain a doubt but that the peculiar type of ability +that is necessary to a judge is often transmitted by descent.” And again: +“In other words, the combination of high intellectual gifts, tact in +dealing with men, power of expression in debate, and ability to endure +exceedingly hard work, is hereditary.”[19] + +I believe that the amount of influence which inheritance has upon the +_kind_ of thing a man does in life has been overestimated; that the +inherited factors influence more the _way_ in which he shall do whatever +the environment influences him to do. This leaves plenty of play for the +close correlation between parents and children in both intelligence and +vocation. The former is the result of inheritance, the latter is the +result of environment. All competent psychologists would agree to-day to +less specific inheritance than a basis, for instance, for the distinction +in vocation of minister and orator; and more specific inheritance than +for such a statement as “We inherit how well we will do, we learn what we +will do.” There would be substantial agreement to the statement that the +inherited nervous bases of a very intelligent plumber are more like those +of a very intelligent statesman than like those of a stupid plumber. This +question is, _how much_ inheritance we can conceive of as being made +up of neuro-chemical elements determining us to do one kind of a thing +rather than another. + +Interpretation statistically of one thousand possible elements, simply +viewed as present or absent, and again simply viewed only as combinations +and not permutations, would mean that the less the intelligence the +more specific the inheritance. The most intelligent man alive could, by +what he is born with, do anything since he has all of the one thousand +factors, all of which help him in the prosecution of any venture. But +the fewer elements he has the less well he does most things, and when +lacking certain elements he has lost the capacity to do some things more +completely than others. (I have neglected physiological characteristics +necessary to an ability. A deaf man certainly is handicapped in music. +I speak of _possible_ mental capacities.) Such a view leaves scope for +some degree of special abilities. It accounts for the idiot-savants, it +accounts for the cases where genius is diverse as well as where it is +not though it would demand that specialized genius be very rare and that +inherited specialization be much rarer in the upper than in the lower +reaches of intelligence. It allows for such cases as Galileo, whose +father was a composer, as well as the cases cited by Galton. Heredity +need not imply the same kind of genius though it does suggest it, whereas +the environment backs up this inherited implication. We further can here +absolutely resent an inheritance of such things as ability in the common +school subjects without being involved in a view to deny the inheritance +of a predisposition to mechanical rather than musical successes. + +Observation of brilliant children would corroborate this view. They can +do anything. Observation of the mentally deficient is equally encouraging +to this view. It has always been puzzling that they seem to do a few +things much better than others. According to this conception there +would be a negative correlation between intelligence and specialized +inheritance. + +We will then consider each inherited element, not as music or as science, +but rather as an element of intelligence which will help in all lines of +work, but which may be a little more necessary for some than others. This +is a predisposition in a true sense. If a man had only one element out +of one thousand, he could do only a few things. If he had all thousand +he could do everything. Inheritance of ability is not in terms of units +valuable to us socially, but only in terms of undefined nervous elements; +and we may conceive of specialization, and still hold that there be less, +the more intelligent a man is. + +To make the matter still more concrete, imagine two men each of whom have +900 of the hypothetical 1000 elements, this being a value of +3 S.D. from +the mean intelligence of the human race. One is a composer, the other +financier. According to this view the greatest number of their inherited +bases on which they could differ would be 100 of the 900 elements. The +other 800 must be alike. Assuming that all of the elements contribute +to all of the activities, but that some of them are more essential to +some activities than to others, we could in this case say that the 100 +which are different decided in some measure the vocation of each man. +But it is much more probable that they overlap in 850 and that each has +only 50 distinct elements, and further that the 50 which are distinct in +each would not all be such as to influence one kind of ability rather +than another. Then these two men, had they interchanged environments, +would probably have interchanged vocations in that transaction. For the +purposes of this discussion we treat physiological inherited features +(such as hearing), as environment, as we are considering the mental +capacity of composer as distinct from the necessary conditions to its +development. According to this view, then, we account easily for the +versatility of genius, which is so apparent in such accounts as Terman’s +_The Intelligence of School Children_.[20] Also, though very infrequent, +we account for the genius who could not have done other things as well as +those he did. + +Let us consider the case of negative deviates, say 3 S.D. from the +mean intelligence of the human race. Two men each have 100 of the 1000 +hypothetical elements. It is much more probable here than not, that an +appreciable amount of the 100 elements would be distinct in each person, +though it is improbable that they would often be such as to form the +basis of an “ability.” This then would account for specific abilities +amongst morons and also for the presence but rarety of idiot-savants. +Also since there are a limited number of such combinations possible and +since many overlap for all practical purposes, we would account for +the common likenesses as well as the relatively more uncommon extreme +differences. This view is consistent with an examination of the data of +this thesis which are contrary to the common belief in special abilities +or to a view of inheritance of units which are actually the goals of +education and the uses of a civilization too recent to leave its imprint +on inheritance. We found no unremovable predispositions to one school +subject more than to the others in any of the children. We would thus +argue that such predispositions as to mathematics or to oratory are +extremely rare and cannot be used as rules by which to interpret human +nature. + +Woodworth says in a criticism of McDougall’s view of instincts: “What +he here overlooks is the fact of native capacities or rather, the fact +that each native capacity is at the same time a drive towards the sort +of activity in question. The native capacity for mathematics is, at the +same time, an interest in things mathematical and in dealing with such +things. This is clearly true in individuals gifted with a great capacity +for mathematics.”[21] + +I do not wish to become involved here in a discussion of the original +nature of man on the instinctive side. I wish merely to rebel at +the assumption of specific inheritance of abilities that are really +sociological units. Mathematics is an ability which is useful to us, +which we have come to encourage in education. But it is a man-made unit. +There is no reason to believe that the inherited components of mentality +are in any direct way related to such talents as mathematics or music. +The units may vaguely predispose, but the units are not mathematics and +music. We may say that the inherited physical and chemical units of +the nervous system may be so distributed as to predispose one man to +mathematics, and another to music, but we must not argue for inherited +interests as correlates. The evidence is all that the inherited nervous +chemistry of the individual is what on the side of behavior, we define +as intelligence—power of adaptation. We may logically fall back on the +inheritance of predisposition to ability, meaning thereby the inheritance +of such nervous qualities as will better fit the individual to cope +with mathematical than with musical situations; but if we adopt this +cautious ground in disputation we cannot argue in another matter for +an inherited interest in mathematics, innate because of the inborn +mathematical talent. If the inherited qualities merely predispose they +merely delimit; just as a man born without arms would probably not become +a great baseball player, nor a deaf man a great musician, nor a man with +poor motor control a skilled mechanic—so we are predisposed nervously +for capacities. Hence can we argue that the inborn root of the interest +is the capacity? Is it not safer to assume that interests in success, +approval of fellowmen and general mental activity led to the development +of the capacity by virtue of a favorable environment, and led by the same +environment to interests centered about its activity? + +It is far from my intention to say that inheritance is not as specific +nervously as it is in matters of blood pressure and texture of skin. +As we, in our limited knowledge, still define abilities in terms +of behaviour and not by nervous elements, my contention is that +intelligence should be regarded as the sum total of this inheritance, +much as general strength is, in terms of the body. We have still to +find the component units of this intelligence. We can then define +predisposition to ability. To split intelligence into inherited units of +mathematics, reading, composition, mechanics, etc., is as unjustifiable +as to split inherited vigor of body into baseball capacity, running +capacity, climbing capacity, etc. Mathematics and music are what we do +with intelligence, not what intelligence is made of. Of course everyone +agrees to this. The lack of emphasis upon the chance that the inherited +units are general in their application, that the same inherited elements +are involved in many of the behavior complexes which we call traits and +abilities, is what confuses the situation. + + +CURRENT PSYCHOLOGICAL OPINION + +We must know what these elements are, and how many contribute to which +capacities. Then we can decide the question of specialized inheritance. +In all crude behavior data it is impossible to separate the influence of +nature and nurture. A theory of specialized inheritance will inevitably +infringe upon common sense in its claims. Of the following statements, it +would be easier for most of us to endorse 1 and 2 than 3 and 4, whereas +few would agree with 5 and 6. + +1. “Unless one is a blind devotee to the irrepressibility and +unmodifiability of original nature, one cannot be contented with +the hypothesis that a boy’s conscientiousness or self-consciousness +is absolutely uninfluenced by the family training given to him. Of +intelligence in the sense of ability to get knowledge rather than +amount of knowledge got, this might be maintained. But to prove that +conscientiousness is irrespective of training is to prove too much.” +(Thorndike, _Educational Psychology_, III, pp. 242.) + +2. “Some attempts have been made to apply these laws to behavior +complexes, but as yet psychology has provided little foundation for such +studies. The most thorough-going attempts have been made with human +mental traits and some evidence has been collected here in favor of the +view that differences in the instinctive behavior of individuals are +inherited according to Mendelian ratios. _But in the field of human +psychology too little is known of the genesis of character, of the +distinction between nature and acquired behaviour to provide a very firm +foundation for the work of the geneticist._” (Watson, _Behaviour_, p. +156. Italics are mine.) + +3. “Even, however, when we omit the trades as well as the cases in +which the fathers were artists, we find a very notable predominance of +craftsmen in the parentage of painters, to such an extent indeed that +while craftsmen only constitute 9.2 per cent among the fathers of our +eminent persons generally, they constitute nearly 35 per cent among the +fathers of the painters and sculptors. It is difficult to avoid the +conclusion that there is a real connection between the father’s aptitude +for craftsmanship and the son’s aptitude for art. + +“To suppose that environment adequately accounts for this relationship +is an inadmissible theory. The association between the craft of builder, +carpenter, tanner, jeweller, watchmaker, wood-carver, rope-maker, +etc., and the painter’s art is small at the best and in the most cases +non-existent.” (Ellis, quoted in Thorndike, _Educational Psychology_, +III, p. 257.) + +4. “—the statesman’s type of ability is largely transmitted or inherited. +It would be tedious to count the instances in favor. Those to the +contrary are Disraeli, Sir P. Francis (who was hardly a statesman, but +rather bitter a controversialist) and Horner. In all the other 35 or 36 +cases in my Appendix, one or more statesmen will be found among their +eminent relations. In other words, the combination of high intellectual +gifts, tact in dealing with men, power of expression in debate and +ability to endure exceedingly hard work, is hereditary.” (Galton, +_Hereditary Genius_, pp. 103, 104.) + +Thorndike comments on this last quotation: “Of course there is, in the +case of all of Galton’s facts the possibility that home surroundings +decided the special direction which genius took, that really original +nature is organized only along broad lines. Moreover, it is difficult to +see just what in the nervous system could correspond to a specialized +original capacity, say, to be a judge. Still the latter matter is a +question of fact, and of the former issue Galton’s studies make him the +best judge. We should note also that it is precisely in the traits the +least amenable to environmental influence such as musical ability, that +the specialization of family resemblance is most marked.” + +This cautious and sagacious commentary is in marked contrast to the +following: + +5. “But no training and no external influence can entirely supersede +the inborn tendencies. They are the product of _inheritance_. Not only +unusual talents like musical or mathematical or linguistic powers can be +traced through family histories, but the subtlest shades of temperament, +character and intelligence can often be recognized as an ancestral gift.” +(Munsterberg: _Psychology, General and Applied_, p. 230.) + +6. “Statistical studies which covered many characteristic opposites like +industrious and lazy, emotional and cool, resolute and undecided, gay +and depressed, fickle and constant, cautious and reckless, brilliant +and stupid, independent and imitative, loquacious and silent, greedy +and lavish, egoistic and altruistic and so on, have indicated clearly +the influence of inheritance on every such mental trait.” (Munsterberg, +_Psychology, General and Applied_, p. 237.) + +Undoubtedly Munsterberg here refers to the data accumulated by Heymans +and Wiersma since they used such opposites as these, and also used what +might be called statistical methods. Speaking of the same data Thorndike +says: + +“In view of the insecurity of their original data it seems best not to +enter upon an explanation of their somewhat awkward method of measuring +the force of heredity, and not to repeat the figures which are got by +this method. Also they do not attempt to estimate an allowance for the +influence of similarity in home training, though they state that some +such allowance must be made.” (_Educational Psychology_, III, p. 262.) + +Hollingworth and Poffenberger, commenting on the data of Galton and Ellis +mentioned in the quotation above, say: + +“Francis Galton has made a statistical study of the inheritance of +_specified_ mental abilities and found that the abilities required +for success as a judge, statesman, minister, commander, poet, artist, +and scientific man, are inherited. But the nature of his data makes +him unable to make exact allowances for influences of training and +environmental influences. Consequently, his figures might really show +general intelligence to be inherited and the form of its expression to be +dependent upon environment. + +“Other investigators, among them F. A. Woods and Havelock Ellis, have +made similar statistical studies and conclude that there is inheritance +of even such qualities as temper, common sense, and the like, but +these reports are also subject to the same complicating influence of +environment.” (_Applied Psychology_, p. 43.) + +It can readily be seen, from these quotations, that there is fundamental +disagreement among psychologists with regard to the inheritance +of specific ability,—fundamental disagreement in three ways: (1) +Interpretation of Galton’s and Ellis’s data. (2) Opinion on the matter. +(3) Degree of precision possible in giving judgment. + +We have noted that it is very difficult to understand what the neural +bases for such special abilities as Galton speaks of could be; that +they are social, not neural or psychological units. A view of a large +number of inherited elements all of which contribute to what we call +general intelligence and each of which is slightly more necessary to +some vocation than others, would account for all the observed facts, is +neurally imaginable, and does not need to view ability to be a “judge” +or “artistic talents” as biological entities. It further explains the +differences in their limited abilities of mentally deficient children. + +Burt says in this connection: “Among children of special (M.D.) schools, +the evidence for a general factor underlying educational abilities and +disabilities of every kind is not so clear. In administrative practice, +‘mental deficiency’ implies among different children deficiencies in +very different capacities, both general and specific.” (Cyril Burt: _The +Distribution and Relation of Educational Abilities_, p. 83.) + +For these reasons it is justifiable to attempt to present evidence +of the inheritance of school abilities with a view to showing that +school abilities are not dependent upon special inherited aptitudes, +as teachers so often assume, but that general intelligence is the only +inherited cause of disparity in product. Investigations where the +correlation between educational product and intelligence, irrespective +of chronological age, was less than around .75, used data where many +removable causes were not removed, and consequently measured results of +the environment as well as heredity. A case such as this follows: + +“The influence of inheritance upon a _very specific_ mental quality, +namely, spelling ability, has been tested experimentally, although here +there is some difficulty in separating the influence of heredity from +that of environment. Earle studied the spelling ability of 180 pairs +of brothers and sisters who had uniform school training and found a +correlation of .50. This means that if one child deviated by a certain +amount from the average child in spelling ability, his brother or sister +would deviate from the average child just half as much; that is, he +would resemble his brother or sister to that extent.” (Hollingworth and +Poffenberger: _Applied Psychology_, p. 44.) + +The data presented in this thesis indicate that that correlation could +have been pushed as high as the _r_ between the intelligence of the +pairs of brothers. In other words, a child could be made to resemble +his brother as nearly in spelling ability as he did in intelligence. +All disparity could be reduced to that of general intelligence. Then +intelligence alone is inherited as far as the data here presented have +any bearing on the matter in hand. The influence of environment is in +this case a matter of no consequence, since the subjects all had the same +schooling, and home influence does not as a rule teach children to spell; +but the data are not irrespective of the influence of intelligence. + + +INDICATIONS OF THE GARDEN CITY DATA + +Table 3 presents intercorrelations between IQ and quotients in the +various subjects. The correlations are in each instance irrespective +of chronological age since all quantitative indices are expressed as +quotients. We have seen that they go up from September, 1918, to June, +1920. Every possible means was used to push these correlations to their +limit, to remove all removable factors. We have seen that the data show +here, as in Tables 7 and 8, that there is little association between +traits which is not a result of differences in intelligence. Table 3 +shows the same 48 children throughout. The _r_’s are not corrected +for attenuation. Though the _r_’s are high throughout and go higher +under special treatment, the association can still be more accurately +registered by some attention to relation of the means and the S.D.’s. Two +traits to be identical must have _r_ = 1.00 S.D._{_x_} = S.D._{_y_} and +M_{_x_} = M_{_y_}. We have seen that the _r_ increases, M-M decreases and +S.D.-S.D. regardless of sign decreases. (Tables 9, 10 and 11.) + +But as the S.D.’s of the Subject Quotients (though they do approach S.D. +of IQ) sometimes go below the S.D. of IQ, we must know why. It is because +the low IQ’s do better per their intelligence than the high IQ’s. We have +seen above that the correlation between IQ and average of the Vocabulary, +Reading, and Completion Subject Ratios is -.61 in November, 1918, and +-.49 in June, 1920. + +Then the ratio of achievement to intelligence is in definite relation +to intelligence—a negative relation. It is this same tendency to adapt +our education to a low level which has prevented a perfect association +between intelligence and the various subjects. The relation of one +subject to another, irrespective of intelligence, would be zero if there +were no other factors except intelligence responsible for the product. +After two years of such attempts as an ordinary public school will +allow, we have removed many of the causes of disparity and increased +the association between potential progress and progress in arithmetic, +reading and language. The correlations, correspondence of S.D.’s, and +Σ(IQ-EQ)⁄_n_ registered in Tables 9, 10, and 11 give evidence of this +as does also the increase in the AccR, an average of the Arithmetic, +Reading, Vocabulary and Completion Ratios. (Table 13.) + +Are the unremoved causes other than intelligence unremovable? These +causes might be, besides the unreliability of tests and the common +elements in the tests, the specialized inheritance we have considered, +ethical qualities of endurance, ambition, initiative and industry or a +general factor. The correlations between Arithmetic Ratios and Reading +Ratios and the other intercorrelations of Subject Ratios will yield us +an index of how much of this remaining disparity is due to specialized +inheritance. These intercorrelations for all years are embodied in Table +13. The partial correlations of quotients when intelligence is rendered +constant will be found in Table 6. These intercorrelations, and the +partials as well, give an indication of some general factor other than +intelligence since the _r_’s irrespective of intelligence are uniform and +all are positive. Only the correlation of arithmetic with vocabulary, +intelligence being rendered constant, goes to zero. Though this might be +due in part to common elements in the tests, it is more likely that there +is another factor in operation. Inheritance of specific abilities could +not have this uniform effect on the correlations. + +These correlations all being positive and the _r_’s being very uniform, +both correlation of ratios and the partials, makes the interpretation of +specialized inheritance of ability extremely unlikely. The correlation +of Arithmetic Ratios with Reading Ratios is higher in 1920 than that of +Vocabulary Ratios with Reading Ratios. It leaves the possibility that +the unremoved factors are inherited ethical differences or that they +are a “general educational factor.” The negative correlation of AccR +with intelligence, however, being as high as these positive remnants of +interrelation, would tend to make more probable an interpretation of this +as a remnant of disparity, intelligence accounted for, which is entirely +due to the organization of our schools. + +All disparity not due to intelligence was worked on as far as it was +possible. Thereupon the association of intelligence and educational +product increased markedly and the negative association of intelligence +with achievement in terms of intelligence decreased somewhat. However, +some association of abilities not due to intelligence remains. Exactly +as much negative association of achievement in terms of intelligence, +with intelligence, remains. So, when some of the disparities due to the +environment have been removed and therefore the correlation of Arithmetic +Ratio with Vocabulary Ratio and Reading Ratio has been decreased, the +causes which contributed to a correlation such as lack of interest having +been removed, there still remains some relation of school qualities. +But there also still remains a negative association between this +accomplishment and intelligence which means that we still have a remnant +of such removable influence as is due to badly adjusted curricula. + +This enables us to interpret our partials. The partials are not nearer +zero because although we have partialed out the effect of intelligence, +we have not partialed out the factor which controls the negative relation +to intelligence of these very partial resultants, since that is the +effect of the methods and curricula. Though we did advance bright pupils +and give them more chance, we have not given them a chance proportionate +to the stupid children. And that is true since we often wanted to advance +pupils and were not allowed to; whereas we were never allowed to demote +pupils except in particular subject matter. The stupid children were +always at the frontier of their intelligence at the educational cost of +the others. + +It is this remnant which has usually been interpreted as “general factor” +or as inherited factors basic to initiative, ambition, and industry. +The fact of importance is that these remnants, these marks of children +independent of their intelligence, are associated negatively with +intelligence to the same degree that they are associated positively to +each other. Unless we wish to assume that the “general factor” or the +inherited bases of initiative and industry are associated negatively +with intelligence we must account for the remnant in some other way. It +seems far more reasonable to attribute this remaining association to the +educational handicaps of intelligence which we were unable to remove. + +The original tendencies of man, as distinct from his original +equipment, have not been considered in this study. If the quantitative +differences in endowment of this kind were added to the denominator of +our accomplishment ratio formula, we would have a better measure and +better results. We share in this investigation a general limitation of +educational psychology—the requisite technique to measure individual +differences of instincts and the ethical traits of which they are the +predisposition. Industry, ambition, and initiative are not inherited +units. They are, however, the rules of an economy of expression and as +such are dependent upon individual differences in strength of instinct. + + +CONCLUSIONS + +1. IQ can be used as a limit of school achievement expressed as SQ. + + _a_ Progress in Σ(IQ-SQ)⁄_n_ may be used as a measure of school + efficiency. + + _b_ SQ⁄IQ may be used as a measure of individual efficiency. + +2. Correlations between intelligence and achievement are very different +before and after the abilities are pushed. + + _a_ Many _r_’s are reported where conclusions are drawn as + though they had been pushed. These conclusions should be + restated. + + _b_ Intelligence and achievement are far more closely + associated than has been assumed to date. + +3. Disparity of school product can be reduced to individual differences +in intelligence. + + _a_ Little specific inheritance of school abilities. + + _b_ Little unremovable difference in industry, + conscientiousness and concentration. + + _c_ Intelligence is the only inherited general factor. + +4. Negative association between AccR and IQ. + + _a_ To-day’s educational procedure involves a handicap to + intelligence. + + _b_ The genius has been neglected. + +[Illustration] + + + + +FOOTNOTES + + +[1] Part of this section is reprinted with revisions from TEACHERS +COLLEGE RECORD, Vol. XXI, No. 5 (November, 1920). + +[2] For scientific purposes we want year-month means and standard +deviations, that we may say that Charlie Jones is 2.1 S.D. above the mean +for his age level, while Harold Smith is .1 S.D. below that mean. It is +in terms such as these that we may be able to compare accomplishment +in one function with accomplishment in another, progress in one +with progress in another. For many of our problems we need a common +denominator of measurement so that we may compare progress between tests +and age-groups. The best common denominator is, I believe, S.D. in an +age-group. Thus we may locate a child in any age-group in any test and +compare that location with the position of any other child in any other +test in his age-group. + +For practical purposes, however, it is for many reasons more convenient +to use quotients in elementary schools. Principals would rather deal with +quotients since it is easier to explain them in terms of attainment and +capacity. It is the use of such quotients that this thesis discusses. + +[3] Judd, C. H., “A Look Forward,” in _Seventeenth Yearbook_, Pt. II, of +the N.S.S.E., 1918. + +[4] When the disadvantages of “pushing” children are discussed, the +disadvantages of keeping children at their chronological age levels +should be considered as well. Although it is true that a supernormal +child placed in that grade for which he is mentally equipped loses +much in social contact, it is also true that he loses a great deal +by remaining in the grade where he physiologically belongs. There he +develops habits of conceit, indolence, and carelessness. It is in all +cases much better to group intelligent children and enrich the curriculum +than to “push” them; but pushing may be better than leaving them where +they belong by age. It is a possibility worth considering that the +explanation of the “peculiarities” of genius lies in the fact that he has +never associated with equals. When his fellows are mentally his equals +they are physically far older and when they are physically his equals +they are mentally inferior. + +[5] Whether only the Accomplishment Ratio as a percentage should be given +the parents, or whether they should know both the IQ and all the SQ’s, +is a question on which I am not prepared to give an opinion. I incline +to believe that the parents should know only the final marks and am sure +that I advise telling the children these only. + +[6] There will be reported elsewhere a fuller consideration of this +aspect of the technique of derivation of norms, together with a complete +presentation of the data used to obtain the age norms herein used. + +[7] “The Accomplishment Quotient,” _Teachers College Record_, November, +1920. + +[8] Or the ratio of the Subject Quotient to the Intelligence Quotient, +which is the same as the ratio of the Subject Age to the Mental Age. + +[9] This table is too bulky for complete publication but may be found on +file in Teachers College Library, Columbia University. + +[10] The remainder of this table is filed in Teachers College Library, +Columbia University. Decimals are dropped in this table. + +[11] Decimals are dropped in this table. + +[12] Truman L. Kelley: _Statistics_, The Macmillan Co. + +[13] This correlation was obtained by correlating one half of the Binet +against the other one half and then using Brown’s Formula to determine +the correlation of a whole Binet against another whole Binet. + +[14] These quantities do not decrease because a perfect score on the +arithmetic test was too easy to obtain at this time. The children had +reached the limits of this test. + +[15] Table 12 is too bulky for complete publication. The first page is +reproduced here and the complete table is filed at the library, Teachers +College, Columbia University. + +[16] No arithmetic was given in 1918, therefore arithmetic was not used +in these averages. + +[17] William Anderson McCall: _Correlations of Some Psychological and +Educational Measurements_, Teachers College Contributions to Education, +No. 79. + +[18] Cyril Burt: _The Distribution and Relations of Educational +Abilities_, pp. 53-56. + +[19] Quotations from Galton: _Hereditary Genius_, ’92, pp. 61-62 and pp. +103-104. + +[20] Terman, Lewis: _The Intelligence of School Children_. Boston: +Houghton Mifflin, 1919. + +[21] Woodworth, R. S.: _Dynamic Psychology_, p. 200. New York: Columbia +University Press, 1918. + + + + +*** END OF THE PROJECT GUTENBERG EBOOK 76891 *** |