,,the ,,accomplishment ,,ratio ,a ,treatment of the ,inherited ,determinants of ,disparity in ,school ,product ,by ,,raymond ,,franzen ,a4,b4 7,harvard71 ,m4,a4 7,columbia7 ,ph4,d4 7,columbia7 ,teachers ,college1 ,columbia ,university ,contributions to ,education1 ,no4 #abe ,published by ,teachers ,college1 ,columbia ,university ,new ,york ,city #aibb ,copyright1 #aibb1 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 unavoidable4 ,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 ,november1 #aibj1 number of that journal4 ,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 7,world ,book ,company74 ,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 there1 ,miss ,gladys ,locke and ,mrs4 ,edna ,maule4 ,i also owe any success that this experiment may have had to the teachers who did the real work of 8pushing0 abilities to their limit4 ,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 inception4 ,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 ,l4 ,thorndike and ,truman ,l4 ,kelley4 ,,raymond ,h4 ,,franzen ,des ,moines1 ,iowa1 #aibb4 ,,contents ,i4 ,,an ,,outline ,,of ,,the ,,experiment #a ,the ,use of ,quotients and ,ratios ,the ,derivation of ,age ,norms ,a ,method of ,survey of ,reading1 ,language and ,arithmetic ,,ii4 ,,statistical ,,treatment ,,of ,,the ,,experiment #ag ,the ,quotients ,the ,ratios ,summary ,,iii4 ,,the ,,psychological ,,conclusions ,,of ,,the ,,experiment #dc ,the ,neglect of ,genius ,is ,genius ,specialized8 ,current ,psychological ,opinion ,conclusions ,,part ,i#a ,,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 country4 ,many of our larger cities have research bureaus of tests and measurements1 and advanced private schools have departments of measurement4 ,the logic of the use of statistically derived evaluations versus the use of opinion1 swayed as it is by the haphazard captions of emotion and condition1 has become widely recognized4 ,the case of scientific measurement in education has been argued and won4 ,the objections to older forms of measurement have become the criteria of the value of the new4 ,still administrators1 although they have been convinced theoretically of its importance1 find it hard to see just what measurement does for their schools4 ,they often object that measurements are made1 the tests are carried away by the examiner1 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 general4 ,this is undoubtedly a very important piece of information2 since a determination of the extent to which a goal has been attained forms the basis of the commendation or condemnation of the methods1 curricula1 and text-books employed in the process4 ,but administrators want to know which of the various elements of school procedure are to be praised and which are to be blamed4 ,we cannot condemn or support a whole school system on the basis of composite results 7unless all possible educational objectives have been measured1 and show one common drift2 or unless it is necessary that the system fall or stand as a whole7 since then we should be throwing good and bad into a common discard4 ,we must measure each thing separately4 ,we must build our ideal system of education synthetically1 taking the best methods from each of the prevalent groups of theories4 ,there has been too much absolutism in education1 too little of a realism that sees the good and bad in all and diminishes the bad and augments the good4 ,if we adopt this point of view we become really empirical in our method1 living through each educational experiment to incorporate it into a growing treasury of tested theory1 not deducing success or failure from metaphysical or doctrinaire prejudice4 ,in this administrators have been more scientific than those who measure4 ,they have always objected that they wanted differential diagnoses4 ,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 established4 ,three uses of measurement commonly stressed are3 7#a7 ,diagnosis of degree of attainment of goal2 7#b7 selection of method of attainment of goal2 7#c7 definitive outline of goals4 ,we have seen that the first two are of little immediate value to the administrator4 ,the first only gives him an accurate notion of where he stands in any one subject without pretending to tell him why2 the second is a promissory note4 ,some day we shall be able to tell him the best methods for the attainment of his goal4 ,the third has slightly more immediate value4 ,measurement splits up the goals of education1 gives them concrete formulation1 allows teachers to see an advance in the class in one function as separate from the rest2 allows them1 for instance1 to distinguish more clearly than they otherwise would between oral reading and silent reading1 or between addition and division4 ,but this1 too1 is rather too general to appeal to administrative economy4 ,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 values4 ,they answer that universities and scientific research give them as much as they want of these values4 ,what an expert on measurement could add in interpretation of results would seem of small additional value to them4 ,still there is a very marked function that such an expert can perform2 but he must serve a fourth and fifth use of measurement while he serves a particular school4 ,when he serves the first three he is serving the science of education and1 unfortunately1 no one school will pay him to do that4 ,the uses of measurement that directly benefit any one school are3 7#d7 ,classification by information and intelligence and 7#e7 diagnosis of individual disability4 ,for the proper prosecution of these aims individual measurements and age norms are essential4 ,only with such equipment can we make the prognoses of future school behavior which the administrator so urgently needs4 ,grade norms cannot be used to make individual diagnoses4 ,though we can see by them which children are below and which above the level that in their grade they should attain1 we cannot see just what administrators most need to know2 namely1 whether the retardation and acceleration are justified or not--how many children are working at maximum4 ,more than that1 computations based on grade norms are very inaccurate in individual cases because the variability within any grade is so great4 ,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 mensuration4#b ,first in importance is an interpretation of the meaning of an ,intelligence ,quotient4 ,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 implication4 ,its importance lies in its diagnosis of power of adaptation1 and it has a high correlation with the maximum possible rate of school progress4 ,just as a pure information test diagnoses the neural bonds that have been formed in any one field1 so an intelligence test diagnoses the ability to form bonds1 to meet a new situation and form satisfactory habits--power to learn4 ,it may be thought of as a diagnosis of the neural chemistry of the individual4 ,as such it is not concerned with the connections or quantity1 but rather with the quality of the neural tissue4 ,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 maturity4 ,it is his potential rate of progress4 ,it is a division of what is by what normally would be4 ,then1 when we use ,,iq we express the various degrees of power of adaptation due to various degrees of fitness of neural equipment to form bonds1 by means of a diagnosis of the rate of formation of bonds which everyone forms sooner or later in an environment such as ours4 ,it is conceivable that we might test this same power without testing the presence of such bonds at all4 ,such a test would detect directly the quality of the neural equipment irrespective of quantity or conformation4 ,a ten-year-old child whose mental age is ten has progressed at the rate which is normal1 and his ,,iq is #a4jj4 ,a very exceptional ten-year-old child whose mental age is fifteen has progressed just one and one half times as fast as the former1 and his ,,iq is #a4ej4 ,another exceptional ten-year-old child whose mental age is five has progressed at just one-half the rate of the first1 and his ,,iq is 4#ej4 ,what we mean1 then1 by an ,intelligence ,quotient is the rate at which a child grows to the mental maturity of human beings in the world as it is4 ,for purposes of presentation of a problem one can here assume 7an hypothesis the value of which will here be determined7 that each child can attain this rate of progress in each of the elementary school subjects4 ,the degree to which this is true is the degree to which the ,,iq is a valid index of power to deal with school subjects4 ,this assumes that inherited special disabilities in the school subjects are uncommon1 that school progress is determined by the interplay of intelligence and environment1 and that so-called interest characteristics which aid in development are the result of an earlier interplay of intelligence and environment4 ,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 inherited1 since differences that are removable must be learned1 not innate4 ,we can the more readily see the significance of viewing a child's equipment in terms of educational and mental age1 when we conceive of a ,subject ,quotient4 ,this is a quotient resulting from the division of the age level reached in the test in question by the chronological age of the pupil4 ,it is a measure of the rate of progress of the child in the school subject under consideration4 ,thus a ten-year-old child with ten-year-old ability in ,thorndike ,reading ,scale ,alpha #b would have as his reading age divided by chronological age1 #a4jj4 ,this may be called his ,subject ,quotient in ,reading or his ,reading ,quotient4 ,the division of what is by what would be if the child were normal gives the percentage of normality1 the actual rate of progress4 ,since the ,,iq is the potential rate of progress and the ,,sq the actual rate of progress1 the ratio of ,,sq to ,,iq gives the percentage of what that child could do1 that he has actually done4 ,thus a child with an ,,iq of #a4cb whose reading quotient 7his ,,rq7 is #a4aj1 though he is doing work which is above normal1 is not doing work which is above normal for him4 ,his ,,rq,,iq is #a4aja4cb1 whereas if he were progressing at his optimum rate it would equal #a4cba4cb4 ,this ,,rq,,iq is the same quantity as ,,ra,,ma4 ,we may call this a ,subject ,ratio and the average of ,subject ,ratios an ,accomplishment ,ratio4 ,we could1 if the absolute association between reading age and mental age were perfect1 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 #a4jj4 ,as we will see later1 ,subject ,quotients approach the ,intelligence ,quotients when special treatment is given2 that is1 the correlation of ,,sq and ,,iq becomes nearer #a4jj and the difference between the average ,,iq and the average ,,sq approaches zero4 ,it is safe then to expect these ,subject ,ratios to be at least #a4jj before we pronounce satisfaction with the school product4 ,there is certainly a significant relation between ,,iq and ,,sq1 and the more perfect the educational procedure has been1 the more it has called forth all that the child is capable of1 the higher it will be4 ,to determine whether the quotient in any school subject can be greater than the ,intelligence ,quotient in any significant amount1 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 maximum4 ,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 conditions4 ,the ,accomplishment ,ratio is the degree to which his actual progress has attained to his potential progress by the best possible measures of both4 ,this would be a mark of the child's effort1 a mark of the concentration and interest that the child has in the school work1 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 far4 ,if there are such other innate bases1 it is also a measure of those inherited traits and capacities or their predisposition1 such as concentration1 effort1 written expression1 etc4 ,at any rate it is a measure of the child's accomplishment1 and so of the effort and concentration as they really are at present working under those school conditions4 ,it is an index of achievement irrespective of intelligence4 ,a very convenient graph representing the same facts and easily interpreted by the teacher may be constructed thus3 ,illustration3 ,age ,scale ---------------------------------------- -------- ,mental ,age ,reading ,age ---------------------------------------- - ,chronological ,age ,spelling ,age ,arithmetic ,age ---------------------------------------- ------------------ ,here it can be easily shown that ,spelling ,age1 ,reading ,age1 ,arithmetic ,age1 etc41 are in some definite relation to both ,chronological ,age and ,mental ,age4 ,using the ,mental ,age line as a goal1 these records may be kept constantly up to date4 ,another use of the ,accomplishment ,ratio is as the medium in which the children may keep records of their own work4 ,as it is a mark in terms of intelligence1 dull and brilliant children may compete on a parity to bring their ,accomplishment ,ratios as high as possible4 ,mainly we have advanced formal education4 ,we have in many ways promoted the abilities to read1 write1 spell and figure4 ,but our philosophy of education has advanced far beyond that4 ,we have other aims in education1 and consequently other methods and modes1 which also must be measured and judged4 ,we wish to promote such qualities as stability1 self-reliance1 concentration1 and ambition4 ,it does not necessarily follow that we must measure these things directly1 although every one vitally interested in measurement cherishes the hope that we may some day measure their behavioristic correlates1--8,for the quality of anything exists in some quantity1 and that quantity can be measured40 8,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 arithmetic4 ,the fact is that the conscientious teacher always gives attention to both and the successful teacher is able1 without omitting one1 to cultivate the other4 ,the theoretical possibility of thinking of the two results separately has little significance in dealing with real teachers and real schools4 ,good reading is a school virtue2 and when one has measured good reading he has measured more than the trivial or formal side of education40#c ,this ,i believe to be true1 but ,i also believe that through measurement we can actually promote those other more ethical ideals in education4 ,through classification by information and by intelligence we gain a marked increase of attention1 concentration1 ambition1 and other objectives1 measured in part by ,accomplishment ,ratios4 ,more discussion due to a greater homogeneity promotes powers of inference and insight2 being only with equals promotes self-confidence and honor1 and in many cases prevents a regrettable conceit among supernormals2 having work to do which is hard enough prevents habits of indolence and carelessness so commonly found among intelligent children4#d ,it is a well-known fact that much work must be done in classification to get homogeneity or real conditions of teaching4 ,as it is1 most teachers are talking to the middle of their classes4 ,when they do they mystify the lower quarter and bore the upper quarter2 they talk to the upper quarter and mystify the lower three quarters2 or they talk to the lower quarter and bore the upper three quarters4 ,when a child is bored or mystified his ,subject ,quotients become less while his ,intelligence ,quotient remains constant4 ,then his ,accomplishment ,ratios become less as long as he remains in a position where he is being mistreated educationally4 ,this1 then1 is the proper measure to see whether a child is classified properly or not4 ,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 #a4jj4 ,the concentration and effort of the child were obviously low and my attempt was to change conditions and to promote habits of consistent work4 ,when the ,accomplishment ,ratio increased ,i knew that the child was profiting1 that he was working4 ,our objective was to increase ,ratios of all children1 not to attain any set standard4 ,this ,accomplishment ,ratio would1 to my mind1 be an ideal school mark4 ,besides the inaccuracy of marks to-day1 which are accurate marks only of the teacher's opinion1 biased as it is by the personal equation of her character with that of the pupil1 there is another fault of prevalent school marking4 ,it is based on average work4 ,the mark is the link between education in the school and education in the home4 ,it gives the parents an index of the child's work and allows them to encourage or discourage the child's attitudes4 ,such indices have no real significance when they are based upon average development1 as the parent is generally mistaken about the ability of the child4 ,marks given by a teacher are satisfactory only for a normal child with normal age for the grade4 ,brilliant children are over-praised for work which1 though over the ability for the group1 is under their own ability4 ,marks given to stupid children are misinterpreted by parents so as greatly to prejudice the effort of the child4 ,though his work may be such as to merit encouragement his mark may be very low4 ,teachers' marks are1 aside from their inaccuracy1 just1 only in a group that is perfectly classified2 just1 only when the children are all of the same ability and all possess the same initial information4 ,so far as they are unjust they are subversive of our aims1 as they then transmit a faulty message to the home and disrupt the continuity of school and home education4#e ,such marks as are here advocated would correct this feature of our present system1 as well as the inaccuracy of our present marks4 ,it is a mark which evaluates the accomplishment of the child in terms of his own ability4 ,a brilliant child would no longer be praised for work which in terms of his own effort is #gj per cent perfect1 in terms of the maximum of the group #ij per cent4 ,the teacher gives him a mark of #ij while we mark him #gj4 ,a stupid child who does work which is marked #gj in terms of the maximum of the class but #ij in terms of his own1 a limited ability1 is no longer discouraged4 ,his effort is evaluated1 and the praise which he receives from home is merited and consequently economical1 since the resultant satisfaction cements the bonds of concentration and attention4 ,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 home4 ,parents would need no great instruction in the interpretation of these marks1 since they have always acted as though the other marks were these1 and since these also are in percentage form4 ,the only kind of mark they can understand is an ,accomplishment ,ratio4 ,i found that the parents of the children at ,garden ,city were more attentive to such marks than to others1 and acted upon them more readily4 ,of course the parents of the very intelligent children1 who are used to marks above #ij1 are surprised at first when you tell them that your mark of the child is #hj2 but upon explanation1 which should in all cases precede the first report to the parents1 they immediately see the value of such grading4 ,it is fortunate in this connection that the greatest amount of explanation is necessary about intelligent children1 as one usually deals then with intelligent parents4 ,,the ,,derivation ,,of ,,age ,,norms ,in this study age norms were derived empirically1 both regression lines being taken into consideration4 ,from the point of view of statistics it becomes imperative1 in order to use the technique here advised1 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 consideration4 ,we are in error in the use of grade norms1 if we find the average score of a grade and then1 when we obtain that score in practice1 say that the work is of that grade4 ,to be able to say this we must know the average grade of a score4 ,this takes in an entirely different cross-section of data4 ,if we get the average score of all children in grade #f1 then we can predict what a #fth grade child is likely to get1 but we can say nothing about a child who is not in grade #f4 ,in order to decide that a #dth grade child has #fth grade ability1 we must know that he has such ability that all children who share this score make an average grade of #f4f ,it would be wise then to get the regression of score on age as well as the regression of age on score1 since they are not identical1 the correlation between score and age being less than unity4 ,we will note in passing that the data to establish these norms1 except those of reading1 are not as complete as may be desired1 inasmuch as it was difficult to get test scores where the age in months also was available4 ,however1 the general data behind the grade norms could be used to keep the results from any crude error2 and the averages were obtained for every month from #h years to #ad years1 with a corresponding refinement in intervals of score1 which made still more improbable an error in the general tendency of the regression lines4 ,then all the distributions1 when grouped by years1 were corrected for truncation2 that is1 the tendency for the brighter children of the older group to be in high school 7the data were from elementary schools only7 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 average1 standard deviation1 and number of cases which would have existed if these forces of truncation were not operating4 ,this was done by the use of the other one half of the figures comprising ,table ,,xi of ,pearson's ,tables for ,statisticians and ,biometricians4 ,dr4 ,truman ,l4 ,kelley pointed the way to its derivation4 ,these norms differ somewhat from those derived from the grade norms by translation of grade into average age for the grade4 ,this is because the norm for a grade is the average score for a grade4 ,hence the norm of age #aj obtained in this way is the average score obtained by a grade whose average age is #aj4 ,then the data used to obtain this average are made up of diverse ages1 all of one grade1 instead of all of one age and diverse grades4 ,even then1 we would have only an average score of an age which approximates what we want1 but is not as reliable to use as average age for a score4 ,a ,,method ,,of ,,survey ,,of ,,reading1 ,,language1 ,,and ,,arithmetic ,the following procedure was employed in the experiment4 ,the experiment was carried out in the public school at ,garden ,city4 ,two hundred children were given the tests4 ,the instructions1 shown below1 were followed in ,november1 #aiai1 and in ,november1 #aiah2 in ,june1 #aiai1 and in ,june1 #aibj1 with the exception that no arithmetic test was used in ,november1 #aiah1 and ,june1 #aiai4 ,the ,binet tests were given by the author2 all of the others were given either by the author or the principal who was careful not to deviate from the directions in any way4 ,in ,june of both years the author gave instructions for a test in one room1 and then left the teacher in charge and went on to the next4 ,this could be done in ,june of each year as the teachers were then fully acquainted with the experiment and their coperation was assured4 ,,directions ,i4 ,administer and score the following tests according to standard instructions4 ,give all tests to grades #c and above4 ,woody-,mc,call ,mixed ,fundamentals in ,arithmetic ,thorndike ,reading ,scale ,alpha #b ,thorndike ,visual ,vocabulary ,scale1 ,a#b ,kelley-,trabue ,completion ,exercises in ,language ,stanford-,binet ,tests 7given by the author7 ,,ii4 ,translate the scores into year-month indices of maturity by means of the following table4 7,use ,mental ,age for the ,binet47 ,assume rectilinear development1 that is1 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 month4 ,then interpolation and extension are allowable4 ,use the table in this way3 ,find in the table the score made by a child 7for instance in the ,woody-,mc,call72 find the age to which it corresponds1 then call this age the ,arithmetic ,age of the child4 ,for instance1 if the score in ,woody-,mc,call is #bj1 his ,arithmetic ,age is about halfway between #aj and #aa or #aj years #f months4 ,age ,woody-,mc,call,alpha #b,visual ,vocab4,kelley-,trabue ---------------------------------------- ---------- #h--j #ab4jj #d4ej #c4fj #d4cj #i--j #ae4af #d4ih #d4cb #e4jj #aj--j #ah4cc #e4df #e4jd #e4fe #aa--j #ba4ej #e4id #e4gf #f4ce #ab--j #bd4ff #f4db #f4dh #g4je #ac--j #bg4hc #f4ij #g4bj #g4gj ---------------------------------------- ---------- ,,iii4 ,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 paper4 ,at the right have parallel columns of the grades4 ,check the grade of each child in these columns4 ,you will then have a sheet like this3 ,grade --------------- ,name ,arith4 #d #e #f #g #h ,age ---------- ,b,a,b,a,b,a,b,a,b,a -------------------------------- ,gertrude ,smith #ahj ---------- ,saul ,sampson #agf ---------- ,ed ,jones #agf ---------- ,george ,calut #agb ---------- ,ida ,henry #agb ---------- ,raymond ,teller #agb ---------- ,ed ,hoard #agb ,etc4 ,do the same with each of the tests4 ,it is clear that1 independent of the unreliability of the test1 if your school were perfectly classified all the #hth grade children would come first on each relation sheet and then the #gth grade children1 etc4 ,you have now a picture of the overlapping of your grades4 ,regrade in reading and arithmetic4 ,draw horizontal lines across these relation sheets at the points of delineation4 ,divide your total number of children by the number of teachers available and then make a class division by the number of pupils1 that is1 call the upper one-sixth of the total number of pupils grade #h in this subject1 the next one-sixth1 grade #g1 etc4 ,teach all grades of arithmetic at the same time and all grades of reading at the same time4 ,you can now send each pupil to the grade in which he belongs in each subject4 ,,iv4 ,call each derived age a ,subject ,age 7,,sa74 ,divide each subject age by the chronological age of the child4 ,this will yield what may be called a ,subject ,quotient 7,,sq71 previously called an ,educational ,quotient 7,,eq74#g ,dividing the ,reading ,age by the ,chronological ,age1 you arrive at a ,reading ,quotient4 ,this ,,rq is the rate at which the child has progressed in reading4 ,we have the same kind of quotient for intelligence 7,stanford-,binet ,,iq74 ,this ,,iq is the potential rate of progress of the child4 ,v4 ,the ratio of any ,subject ,age to ,mental ,age#h may be called a ,subject ,ratio 7,,sr71 previously called an ,accomplishment ,quotient 7,acc,q74#g ,this ,subject ,ratio gives the proportion that the child has done in that subject of what he actually could have done1 and is a mark of the efficiency of the education of the child in that subject to date4 ,the goal is to bring up these ,subject ,ratios as high as possible4 ,when they are above 4#ij1 the child may be considered as receiving satisfactory treatment1 providing norms for subject ages are reasonably accurate4 7,this figure1 4#ij1 applies to a ,subject ,ratio obtained by using a ,stanford-,binet ,mental ,age47 ,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 tests4 ,if ,subject ,ratios go far over #a4jj the chances are that the ,mental ,age diagnosis is too low4 ,the average of the ,subject ,ratios of a child may be called his ,accomplishment ,ratio4 ,in the application of the above instructions1 whenever opportunity offers for classification of both subject matter and intelligence 7which means many teachers or a large school71 use a ,relation ,sheet 7for instance for ,arithmetic7 and then have additional columns at the extreme right for intelligence headed ,a1 ,b1 ,c1 and ,d4 ,if a child's ,,iq is in the upper quarter of the ,,iq's of your school1 check in the column ,a opposite his name2 if it is in the upper half but not in the upper quarter check in ,b1 and so on with ,c and ,d4 ,then you will be able to split each group2 for instance1 the one which is defined as #hth grade in arithmetic ability1 into four sections1 each of which progresses at a rate differing from the others4 ,the ,a section will progress most rapidly1 ,b next1 ,c more slowly1 and ,d most slowly4 ,as ,garden ,city was a small school1 adjustment of procedure to individual differences in intelligence1 besides the grouping for subject matter1 was done mostly by pushing children4 ,children were advanced whole years 7the grade they 8belonged to0 was the one in which geography and history were taught2 this was their home grade7 besides the readjustment made by the special regrading in reading and arithmetic4 ,a special treatment class was formed where pronounced negative deviates were given special attention4 ,regrading was also instituted for spelling4 ,children were promoted whenever it was considered advisable2 teachers were switched from subject to subject whenever that was considered advisable by the principal and the author4 ,the ,thorndike ,arithmetics and other new texts were introduced to some extent4 ,any change possible was made in order to bring ,,eq,,iq as high as possible4 ,that was the goal4 ,the purpose was not to prove that any certain educational procedure would tend to promote abilities more rapidly than others1 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 children4 7,it is to be understood that intelligence may be1 and probably is1 the summation of thousands of inherited factors1--neutral elements1 here merged in the broader behavioristic concept of intelligence47 ,,scientific ,,questions ,,involved ,,in ,,classification ,if we were able to negate other influences upon disparity of product1 we could conclude that these were not inherited4 ,hence it would be our burden as educators so to manipulate education as to prevent their operation4 ,we will attempt to analyze the determinants of individual differences in product in these children1 to see which influences besides intelligence are part of the inborn equipment which is not the province of education1 but of eugenics1 to correct4 ,no absolute validity is held for any of the conclusions stated here4 ,the subject is1 at best1 vague and complicated2 but our conclusions can be used as the basis for a good guess in school procedure4 ,we can judge general tendencies from the educational experiences of the two hundred children whose abilities for two years are here charted4 ,the importance to educators of the subject in hand is excuse enough for its treatment4 ,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 differences4 ,classification1 however1 needs some more accurate psychological foundation than the mere awareness of individual variance4 ,we must know3 #a4 ,what tests to use4 #b4 ,how to use them4 #c4 ,whether abilities in reading1 spelling1 and arithmetic or their predispositions exist as special abilities1 or whether children differ in these simply because of their innate differences of intelligence4 #d4 ,whether individual differences in ambition1 interest1 and industry1 in so far as they influence accomplishment1 are due to special tendencies1 or whether they are learned manifestations of a more general heritage4 #e4 ,how these proclivities1 specific or general1 are related to intelligence4 ,points #a and #b are problems of procedure which must be evolved from our existent knowledge of measurements and statistics4 ,points #c1 #d1 and #e are problems which must be solved from the evidence resulting from an experiment in classification using these methods4 ,points #d and #e introduce the vexed question of whether there is a 8general factor0 or some general inherited cause of disparity in school product other than intelligence4 ,should reading ability prove to be the result of certain inherited abilities1 or predisposition to abilities1 we could not use a measure of mental ability alone as the guide to what a child could attain in reading4 ,if intelligence1 however1 were the only inherited prognostic factor of school achievement1 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 development4 ,so1 too1 if interest in particular subjects and ambition are not mainly the result of rewards and punishments of early life1 but are themselves significantly rooted in the nature of the child1 we could not condemn or commend curricula and methods upon a basis of the ratio of resultant accomplishment to mental ability1 but must include a measure of this potentiality4 ,the practical queries whether or not a child can do reading as well as he does arithmetic1 whether his ambition and his honesty have their origin in the same strength or weakness1 can be answered only when these problems are fully solved4 ,the immediate consequences of knowing that a child can usually be taught to read if he does other tasks well is of obvious import4 ,it would be of great service1 too1 to know whether lack of application can be corrected so as to bring concentration to the level of the other traits4 ,if a child is normal in other ways and not in his tendency to respond to the approval of others by satisfaction1 can this 8drive0 be increased or reduced to the average1 or are individual differences in specific original tendencies basic to development of character1 and if they are1 how much influence do these differences exert upon school accomplishment8 ,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 depends4 ,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 progress4 ,we must know the inherited determinants of disparity in school product4 ,,part ,,ii ,,statistical ,,treatment ,,of ,,the ,,experiment ,in the discussion and tables which follow3 ,q stands for ,quotient1 which will mean a ,subject ,age divided by a ,chronological ,age4 ,r stands for ,ratio1 which will mean a ,subject ,age divided by a ,mental ,age4 ,,aq means ,woody-,mc,call ,arithmetic ,age divided by ,chronological ,age1 and ,,ar means this ,,aa divided by ,mental ,age4 ,,vq means ,thorndike ,vocabulary ,age divided by ,chronological ,age1 and ,,vr means this ,,va divided by ,mental ,age4 ,,rq means ,alpha #b ,reading ,age divided by ,chronological ,age1 and ,,rr means this ,,ra divided by ,mental ,age4 ,,cq means ,kelley-,trabue ,completion ,age divided by ,chronological ,age1 and ,,cr means this ,,ca divided by ,mental ,age4 ,,sq means any ,subject ,quotient1 that is1 any ,subject ,age divided by ,chronological ,age1 and ,,sr means any ,subject ,ratio1 that is1 any ,,sa divided by ,mental ,age4 ,,eq means the average of all ,subject ,quotients and ,acc,r1 the ,accomplishment ,ratio1 means the average of all ,subject ,ratios4 ,all r's are product-moment correlation coefficients1 uncorrected4 ,as the reliabilities 7,table #d7 are almost what the other coefficients are in ,june1 #aibj 7,table #e71 it is apparent that the corrected coefficients1 when ,grade ,,iii is excluded1 would all be very near unity at that time4 ,,the ,,quotients ,in ,table #a are presented all the quotients for all periods of testing1 grouped by children4 ,the table1 a sample of which is included here1#i shows clearly how all ,,sq's approach ,,iq as special treatment continues4 ,the grades indicated in this grouping are as of ,june1 #aibj4 ,inasmuch as many double and triple promotions were made in an effort to get maximum product for intelligence invested1 no conclusion can here be formed of the grade to which these children belonged at any time except ,june1 #aibj4 ,the correspondence between ,,iq and the ,,sq's in ,june1 #aibj is further shown in ,table #b4 ,in this table the #dh children who took all tests at all periods are ranked from high to low ,,iq and their ,,sq's are listed opposite4 ,the high correspondence is readily apparent4 ,,table #aaj ,,intelligence ,,quotients ,,for ,,all ,,periods ,,grouped ,,by ,,children ,the children are arranged by grade as they were in ,june1 #aibj1 and alphabetically within the grade4 ,the periods of testing are lettered in their chronological sequence2 a is ,november1 #aiah1 b is ,june1 #aiai1 c is ,november1 #aiai and d is ,june1 #aibj4 99 ,zero ,score ,,grade #c ,intelligence ,test ,arithmetic,vocabulary,reading ,completion ,quotient ,period ,quotient ,quotient ,quotient ,quotient ---------------------------------------- ----------------- a #aja b c #fd #eh #dc d #ajf #hh #ic a #abh b c #hj #ajb #ha d #aeb #abd #aec a #aaf b c #ef #ij 99 #di d #id #ie #gg #hi a #hg b c #ij #dj #ce #ed d #gb #gd #fa #eb a #aab b c #ij #acg #acc #aab d #aab #aac #aba #aca ---------------------------------------- ----------------- ,,table #baa ,,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 ---------------------------------------- ---------------- #adf #aaa #aed #afd #aej #adb #abi #ace #acg #acf #ada #aji #aah #ajg #aba #aci #abd #ada #abd #acd #ach #aja #aab #aje #ajf #ach #aba #acj #aaj #aji #acj #ajg #aci #ace #acf #abb #abg #acj #abd #aba #abb #aac #aba #aag #abd #abb #aab #ajb #aad #abi #aba #abh #abe #abh #abh #abj #ajj #aaf #ajb #aai #aah #aag #abc #aad #abe #aag #aca #aaa #aah #abd #aag #ajf #abb #aab #aaa #aad #aje #abf #aaj #aad #aji #hc #aac #aag #ajc #ajg #ajc #aab #ie #ajc #ajg #id #abf #id #abc #ajd #ii #aag #if #ajd #ajd #ajc #aaj #id #aaf #ajc #ajh #aac #aab #ajf #aja #ajj #aad #aji #ajf #ajj #ij #ajc #ib #ib #ajj #aji #aah #ajh #aac #ii #aad #ajd #ajf #aaj #ii #aad #aai #aag #aae #ih #ajb #aja #ajh #ajd #ih #ii #ajf #ajg #ajf #ig #ie #aji #ajg #aje #ig #ajh #aja #ajb #aje #ig #ie #ajd #hi #aaj #if #ij #ajd #ia #ia #ie #hd #ii #ic #ajj #ie #ij #ajg #ii #aje #ie #he #aag #aad #ajc #id #ajf #eg #hi #ajh #id #ajc #ajc #ajf #ajd #ib #if #hf #id #he #hg #hc #hh #ib #hg #hg #ie #if #id #ajb #hd #he #hg #ic #hg #hc #ajf #ia #hg #ajd #hj #gg #ia #hj #hd #hj #hd #ge #gi #hd #hj #hi #ajg #hh #hf #gh #hg #ij #ic #he #fj #fi #ef #ga #gg ---------------------------------------- ---------------- ,the intercorrelations of the quotients of these #dh cases for all periods may be seen in ,table #c 7page #ba74 ,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 used4 ,this limit is a function of the reliability of the tests employed4 ,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 coefficients4 ,this is tantamount to saying that any correlation can go no higher than the geometric mean of the reliability coefficients of the tests used4 ,it is better to assume that an r can go as high as the 7rr7 since an r can go as high as the square root of its reliability coefficient4 ,dr4 ,truman ,l4 ,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 form4 ,the reliabilities and limits defining a limit as the fourth root of the multiplied reliability coefficients are in ,table #d4 ,correction for attenuation is often ridiculously high because the reliability coefficient of one of the measures used is so low4 ,if an element is included in the two tests which are correlated1 but not in the other forms of each test used to get reliability1 the 8corrected coefficient0 is corrected for an element which is not chance4 ,whenever the geometric mean of the reliabilities is less than the obtained r1 the corrected r is over #a4jj and hence absurd4#ab ,therefore we use here instead1 a comparison to the maximum possibility in a true sense4 ,since a test correlates with the 8true ability0 7r71 7rr7 is the limit of an r1 its optimum with those tools4 ,although these limits apply1 strictly speaking1 only to the total correlations1 since the reliability correlations are with all the data2 we may assume that the same facts hold with regard to the correlations of each of the grades1 that is1 the reliability is a function of the test not of the data selected4 ,,table #c ,,intercorrelation ,,of ,,all ,,quotients ,,for ,,all ,,periods ,,of ,,the #dh ,,children ,,who ,,took ,,all ,,tests ,,november1 #aiah ,,iq ,,vq ,,rq ,s4,d4 ,m ,,iq #ai4ab #aje4ae #a4cb #a4hf ,,vq 4#gb #bj4ed #ajb4eb 4#je #a4da #b4jj ,,rq 4#fd 4#fd #ai4ji #ie4ij 4#jf 4#jf #a4ca #a4hf ,,cq 4#fc 4#ga 4#gg #ai4cd #ii4dd 4#jf 4#je 4#jd #a4cc #a4hh ,,june1 #aiai ,,iq ,,vq ,,rq ,s4,d4 ,m ,,iq #ai4ab #aje4ae #a4cb #a4hf ,,vq 4#gc #bj4hj #aac4ed 4#je #a4dc #b4jb ,,rq 4#fe 4#eh #ad4gc #aja4ca 4#jf 4#jf #a4ja #a4dc ,,cq 4#fb 4#fh 4#gg #ai4gf #aja4jd 4#jf 4#je 4#jd #a4cf #a4ib ,,november1 #aiai ,,iq ,,aq ,,vq ,,rq ,s4,d4 ,m ,,iq #ai4ab #aje4ae #a4cb #a4hf ,,aq 4#df #ad4jh #ajb4ij 4#jh #j4ig #a4cg ,,vq 4#hf 4#bc #ag4jg #aji4ag 4#jc 4#ji #a4ah #a4ff ,,rq 4#fe 4#ef 4#ga #ac4ia #aja4db 4#jf 4#jg 4#je #j4if #a4ce ,,cq 4#gi 4#dg 4#hc 4#hb #ag4ec #aje4ba 4#jd 4#jh 4#jc 4#jc #a4ba #a4ga ,,june1 #aibj ,,iq ,,aq ,,vq ,,rq ,s4,d4 ,m ,,iq #ai4ab #aje4ae #a4cb #a4hf ,,aq 4#gc #ad4aj #aja4gi 4#je #j4ig #a4cg ,,vq 4#ha 4#fj #ah4hi #ajh4id 4#jc 4#jf #a4cj #a4hd ,,rq 4#gi 4#fh 4#hg #af4dc #ajd4id 4#jd 4#je 4#jb #a4ac #a4fj ,,cq 4#hd 4#gg 4#gh 4#hd #ae4hg #ajh4jh 4#jc 4#jd 4#jd 4#jc #a4ji #a4ed ,,table #d ,,reliability ,,coefficients ,one ,form ,two ,forms ,one ,form ,two ,forms of ,each of ,each with an with an ,test ,test 7by ,infinite ,infinite ,brown's ,number ,number ,formula7 of ,forms of ,forms r r r r ,intelligence ,quotient 4#hhh 4#idb 7by ,brown's ,formula7#ac ,arithmetic ,quotient 4#hbd 4#ijd 4#ijh 4#iea ,vocabulary ,quotient 4#hbj 4#ija 4#ijf 4#idi ,reading ,quotient 4#hff 4#ibh 4#ica 4#ifc ,completion ,quotient 4#hhc 4#ich 4#idj 4#ifh ,limits of the r's 7r r7 ,nov4 #aiah1 ,june and ,nov4 #aiai ,june #aibj ,,iq and ,,aq 4#ibe 4#idf ,,iq and ,,vq 4#ibd 4#idf ,,iq and ,,rq 4#icf 4#iec ,,iq and ,,cq 4#ida 4#iee ,the limits of the ,june1 #aibj r's are naturally somewhat larger than the others since two forms of tests 7except the ,binet7 were used2 the unreliability of the quantitative indices is therefore lower and hence the correlation with ,,iq may be larger4 ,the correlations in #aibj of another group--the whole school except ,grade ,,iii--are reproduced in ,table #e4 ,grade ,,iii was excluded since here there had as yet been little chance to push the r's4 ,partials were obtained with these data 7,table #f74 ,little faith may be placed in the relative sizes of these partials1 much because the r,,vq4,,rq is here only 4#gc and1 in the data presented in ,table #c1 it is 4#hg4 ,this is due to the fact that the data in ,table #c cover all periods 7#b years7 while those in ,table #e cover only one4 ,this difference has comparatively slight influence on our general conclusions2 but it makes a huge difference in the correlation of ,,rq and ,,vq when ,,iq is rendered constant1 whether the one or the other set of data is used4 ,moreover1 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 ,h4 ,thomson's recent work on this subject3 8,the ,proof or ,disproof of the ,existence of ,general ,ability40 ,thomson shows that partial correlation gives one possible interpretation of the facts1 but not an inevitable one4 ,thus we cannot say that because ,,rq and ,,iq and ,,rq and ,,aq are highly correlated1 correlation of ,,iq and ,,aq is dependent upon ,,rq4 ,we can say1 however1 that it is likely to be4 ,,iq and ,,aq may be correlated by reason of inclusion of some element not included at all in ,,rq4 ,the higher the correlations which we deal with the less we need worry about this1 and of course correlations of unity exclude any such consideration4 ,,table #e ,,intercorrelation ,,of ,,all ,,quotients ,,in ,,june1 #aibj4 ,,all ,,children ,,exclusive ,,of ,,grade #c ,,are ,,here ,,represented ,the ,p4,e4's are all less than 4#je ,n #ha ,arithmetic ,vocabulary ,reading ,,iq ,quotient ,quotient ,quotient ,arithmetic ,quotient 4#gcc ,vocabulary ,quotient 4#hcg 4#fbh ,reading ,quotient 4#geh 4#fid 4#gcd ,completion ,quotient 4#hba 4#ggj 4#hbe 4#hja ,i therefore draw no conclusions from the comparative size of these partials1 nor do ,i get partials with any of the other data1 and rest the case mainly on the high r's between ,,iq and ,,sq's in #aibj2 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 data2 small intercorrelation of ,,sr's and negative correlation of ,acc,r with ,,iq4 ,the general lowness of the partials 7,table #f7 does1 however1 indicate the great causative relation between ,,iq and disparity of product4 ,the elements still in here are common elements in the tests and the mistreatment of intelligence4 ,,table #f ,,partial ,,correlations ,,of ,,quotients ,,irrespective ,,of ,,intelligence ,,quotients ,n #ha ,arithmetic ,vocabulary ,reading ,quotient ,quotient ,quotient ,vocabulary ,quotient 4#jd 4#jg ,reading ,quotient 4#ca 4#bh 4#jg 4#jg ,completion ,quotient 4#dc 4#dd 4#dg 4#jh 4#jf 4#jf ,what happened by grade in #aiah-aiai is summarized in ,table #g4 ,what happened by grade in #aiai-aibj is summarized in ,table #h4 ,since there were many changes in personnel from #aiah-aiai to #aiai-aibj1 we need expect no continuity from ,table #g to ,table #h4 ,for the continuous influence of the two years1 see ,table #c1 which includes #dh children taking all tests at all periods4 ,,table #g ,,all ,,correlations1 ,,means1 ,,and ,,standard ,,deviations ,,by ,,grade1 ,,showing ,,progress ,,from ,,november1 #aiah ,,to ,,june1 #aiai ,i stands for ,intelligence ,quotient ,v stands for ,vocabulary ,quotient ,r stands for ,reading ,quotient ,c stands for ,completion ,quotient ,,grade r ,m ,s4,d4 ,nov4 ,june ,nov4 ,june ,nov4 ,june ,i ,v 4#dfg 4#fcc ,i #aji4hi #aac4bj ,i #ab4hc #ae4di 4#ab 4#jg #a4ih #a4ia #a4dj #a4ce ,,iii ,i ,r 4#eda 4#dib ,v #if4aa #aji4ij ,v #ba4ba #ah4fi 4#aa 4#ji #c4bh #b4cj #b4cb #a4fc ,i ,c 4#fda 4#chf ,r #hb4bf #aja4dj ,r #bb4eh #ae4he 4#ji 4#aa #c4di #a4ie #b4dg #a4ch ,c #hf4hi #ajh4dj ,c #bb4gf #ae4gi #c4eb #a4id #b4di #a4cg ,n #ai #cj ---------------------------------------- ------------------------- ,i ,v 4#gbd 4#hai ,i #aje4ij #ajd4hb ,i #ah4jh #ah4ba 4#jg 4#je #b4gc #b4ih #a4ic #b4aa ,,iv ,i ,r 4#ffe 4#hde ,v #ig4bj #ajh4ec ,v #ag4bf #bd4ib 4#jh 4#je #b4fj #d4jh #a4hd #b4hh ,i ,c 4#eif 4#gag ,r #ia4jf #ajg4hb ,r #bg4he #aj4ce 4#aj 4#jh #d4bj #a4fi #b4ig #a4bj ,c #aja4de #ajh4ab ,c #ba4ec #ag4ge #c4be #b4ij #b4cj #b4je ,n #bj #ag ---------------------------------------- ------------------------- ,i ,v 4#hhg 4#hbb ,i #aja4fd #ii4db ,i #bd4gf #ag4fc 4#jd 4#je #c4ef #b4gc #b4eb #a4ic ,v ,i ,r 4#gii 4#hcb ,v #ajj4ei #aaa4eh ,v #bf4ga #ai4gh 4#je 4#je #c4hd #c4jf #b4gb #b4af ,i ,c 4#hah 4#hij ,r #id4ei #aja4db ,r #bb4aj #ab4ef 4#je 4#jc #c4ah #a4id #b4be #a4cg ,c #ig4jj #ajb4fh ,c #bb4eb #ag4ga #c4bd #b4gd #b4bi #a4id ,n #bb #ai ---------------------------------------- ------------------------- ,i ,v 4#gic 4#ggb ,i #aji4ij #aae4ij ,i #bc4de #bd4ch 4#jh 4#ji #e4jj #e4bj #c4ed #c4fh ,,vi ,i ,r 4#dig 4#gbf ,v #ajh4jj #abf4hj ,v #cj4bj #be4be 4#af 4#aj #f4dd #e4ci #d4ee #c4ha ,i ,c 4#gih 4#hia ,r #ajc4aj #ajg4bj ,r #ac4gg #bj4fb 4#jh 4#jd #b4id #d4dj #b4jh #c4aa ,c #ajh4ij #aag4aj ,c #ae4bc #ah4ha #c4be #d4ja #b4cj #b4hd ,n #aj #aj ---------------------------------------- ------------------------- ,i ,v 4#fbe 4#ejd ,i #ii4bi #ih4ib ,i #aa4aa #aa4de 4#aa 4#ad #b4jj #b4ad #a4db #a4ea ,,vii ,i ,r 4#fbb 4#gji ,v #aji4dc #aae4bc ,v #ad4jg #ag4dc and 4#aa 4#ji #b4ed #b4ie #a4gi #b4ca ,,viii ,i ,c 4#ghb 4#gcj ,r #ig4jj #ih4he ,r #ab4ei #ae4gg 4#jg 4#ji #b4bg #c4bf #a4fa #b4ji ,c #ajb4dc #ie4he ,c #ac4di #ag4gb #b4dc #c4ca #a4gb #b4cd ,n #ad #ac ---------------------------------------- ------------------------- ,i ,v 4#fhe 4#fhj ,i #aje4jg #ajf4hh ,i #ai4cd #ah4de 4#jd 4#jd #a4da #a4cb #a4jj #j4ic ,i ,r 4#efh 4#fbf ,v #aja4ab #aab4fg ,v #bb4hc #ba4eh ,,total 4#je 4#jd #a4fg #a4ed #a4ah #a4ji ,i ,c 4#fci 4#gjb ,r #ib4dj #ajb4ia ,r #bb4fe #ae4bg 4#jd 4#jd #a4ff #a4ji #a4ag #j4gg ,c #ih4jh #ajf4bg ,c #ba4dh #ah4ai #a4eg #a4cj #a4aa #j4ib ,n #he #hi ---------------------------------------- ------------------------- ,,table #h ,,all ,,correlations1 ,,means1 ,,and ,,standard ,,deviations ,,of ,,quotients ,,by ,,grade1 ,,showing ,,progress ,,from ,,november1 #aiai ,,to ,,june1 #aibj ,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 ,s4,d4 ,nov4 ,june ,nov4 ,june ,nov4 ,june ,i ,a 4#dac 4#gji ,i #ajb4jj #aje4ec ,i #i4fj #aj4hi 4#af 4#jh #a4hg #a4fh #a4cb #a4ai ,,iii ,i ,v 4#fdi 4#ffg ,a #hb4ge #ig4hd ,a #ae4hh #ah4fb 4#aa 4#ji #c4ji #b4hh #b4ai #b4jd ,i ,r 4#fea 4#fji ,v #id4jj #ajc4dg ,v #cc4dd #bg4ff 4#aa 4#aj #f4ea #d4bh #d4fj #c4jc ,i ,c 4#fab 4#gai ,r #hg4ei #ic4hh ,r #cb4jf #ai4jb 4#ab 4#jg #f4bd #c4ba #d4da #b4bg ,c #ij4ag #if4hd ,c #bh4hb #be4ei #e4eh #c4if #c4ie #b4hj ,n #ab #ai ---------------------------------------- ------------------------- ,i ,a 4#dbf 4#gbe ,i #aaa4dh #aac4jj ,i #ad4gc #ae4jd 4#aj 4#jf #a4he #a4ic #a4cj #a4cf ,,iv ,i ,v 4#fce 4#ggb ,a #id4jg #aaa4jh ,a #ab4cd #ae4jb 4#jge 4#je #a4ee #a4ii #a4ji #a4dj ,i ,r 4#caf 4#efi ,v #aji4gi #aae4fa ,v #af4ig #ah4ci 4#aa 4#ji #b4ac #b4cd #a4ej #a4ff ,i ,c 4#eid 4#hcg ,r #ii4ca #aaj4aa ,r #ag4hi #ad4fg 4#jh 4#jd #c4bd #a4fg #a4eh #a4cb ,c #ajh4ad #aah4ad ,c #ae4ea #ab4gj #a4id #a4fb #a4cg #a4ae ,n #bi #bh ---------------------------------------- ------------------------- ,i ,a 4#fih 4#gac ,i #ajc4gb #ih4hc ,i #ai4eg #ah4hd 4#jg 4#jg #b4fi #b4fe #a4ia #a4hg ,v ,i ,v 4#hha 4#ijh ,a #hg4eh #ii4ga ,a #ab4dc #af4dg 4#jc 4#jb #a4ga #b4bg #a4ba #a4fj ,i ,r 4#ggc 4#hia ,v #aji4jj #aje4ag ,v #ae4eh #ai4ig 4#jf 4#jc #b4ad #b4ha #a4eb #a4ii ,i ,c 4#ghf 4#ibc ,r #ajd4df #ajc4jj ,r #af4ii #ag4jg 4#je 4#jb #b4cd #b4dj #a4fe #a4gj ,c #ajg4jj #ajc4dh ,c #af4ab #ad4ea #b4bb #b4jd #a4eg #a4dd ,n #bd #bc ---------------------------------------- ------------------------- ,i ,a 4#ecc 4#hje ,i #ajb4dc #aje4ci ,i #aa4fa #ac4ef 4#ac 4#jf #b4ji #b4af #a4dh #a4eb ,,vi ,i ,v 4#ggd 4#heh ,a #ia4dc #ajd4ec ,a #aa4dc #aa4ca 4#jg 4#jd #b4jf #a4ge #a4df #a4bd ,i ,r 4#dbj 4#ffa ,v #ajf4jg #aab4id ,v #aa4ic #aj4id 4#ae 4#ji #b4ae #a4gd #a4eb #a4bc ,i ,c 4#gci 4#fbj ,r #if4fd #ajf4bj ,r #ab4ch #aa4hh 4#jh 4#aj #b4bc #a4gi #a4eh #a4bg ,c #ajj4cf #ajg4fa ,c #ac4ie #aj4ee #b4ea #a4fh #a4gh #a4ai ,n #ad #ah ---------------------------------------- ------------------------- ,i ,a 4#gdj 4#gie ,i #ajg4bg #ajj4eh ,i #bc4bi #ai4gh 4#ji 4#jg #d4gd #b4he #c4ce #b4gb ,,vii ,i ,v 4#hfg 4#gah ,a #ajj4jj #ii4ca ,a #i4bf #aa4jj 4#je 4#ji #a4hf #b4jf #a4cc #a4de ,i ,r 4#hfb 4#gii ,v #aad4cf #ajh4ge ,v #ai4ae #ad4db 4#je 4#jg #c4hi #b4ha #b4ge #a4ih ,i ,c 4#hcc 4#fgg ,r #aja4gc #ih4eh ,r #ab4bh #aa4ef 4#jf 4#aa #b4ej #b4be #a4gg #a4ei ,c #aje4hb #aja4db ,c #ag4da #af4jb #c4ed #c4ab #b4ej #b4ba ,n #aa #ab ---------------------------------------- ------------------------- ,i ,a 4#ffc 4#gif ,i #ajd4hc #ajh4gi ,i #ae4df #ah4be 4#aa 4#jg #c4ja #c4bi #b4ac #b4cc ,,viii ,i ,v 4#hbh 4#gej ,a #ib4ib #ic4hf ,a #aj4bj #i4gd 4#jf 4#jh #a4ii #a4gf #a4dj #a4bd ,i ,r 4#gge 4#gbb ,v #aaa4fg #aag4ba ,v #af4dd #ad4jb 4#jh 4#jh #c4bj #b4ec #b4bf #a4gi ,i ,c 4#hch 4#hfh ,r #ajj4hc #ajd4ch ,r #aa4eb #bj4fb 4#jf 4#jd #b4bd #c4gb #a4ei #b4fc ,c #ajd4ib #aji4fd ,c #ah4aa #ag4da #c4ec #c4ad #b4di #b4bb ,n #ab #ad ---------------------------------------- ------------------------- ,i ,a 4#egf 4#fhf ,i #ajf4jb #aje4hg ,i #af4gc #af4hg 4#je 4#jc #a4ab #a4jg #j4gi #j4ge ,,total ,i ,v 4#fgi 4#gbg ,a #ia4ce #ajb4ja ,a #ac4bb #ae4fa 4#jd 4#jc #j4hh #j4ih #j4fb #j4fi ,i ,r 4#ebi 4#fji ,v #ajg4ie #aaj4ed ,v #ai4gf #ai4eg 4#je 4#jd #a4cb #a4bd #j4ic #j4hg ,i ,c 4#fgh 4#gca ,r #ii4bb #ajc4fe ,r #ah4he #ag4ab 4#jd 4#jc #a4bf #a4jh #j4hi #j4gf ,c #ajd4jf #ajh4jj ,c #ah4hg #ah4aa #a4bf #a4ad #j4hi #j4ha ,n #ajb #aad ---------------------------------------- ------------------------- ,,note--,totals without ,grade ,,iii are much higher than these 7,table #e74 ,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 may4 ,it is proper to note here that not much can be expected from ,grades ,,iii and ,,viii and from totals including ,grade ,,iii1 since children in ,grade ,,iii have not been there long enough to be pushed1 and children in ,grade ,,viii have been pushed beyond the limits which the tests used will register4 ,our logic is one of pushed correlations4 ,if the association of ,,iq and the ,,sq's is what we are attempting to establish1 it is necessary to show3 #a4 ,that the r comes near unity2 #b4 ,that the central tendencies come near coincidence2 #c4 ,that the ,s4,d4's come near coincidence4 ,the value of the r is obvious2 the value of coincidence of means becomes clearer if we think of 7,,iq-,,eq7n1 the average difference of potential rate of progress and actual rate of progress4 ,this average of differences is the same as the difference of the averages1 which is more readily calculated4 ,obviously1 if we wish to use an ,acc,r1 it is necessary to show more than correspondence when differences in average and spread are equated as they are by the correlation coefficient4 ,besides1 coincidence of ,m's1 correspondence of ,s4,d4's is also necessary since a correlation might be positive unity1 the ,m's might be equal1 and still the spread of one measure might be more than the spread of the other4 ,if the spreads are the same and the ,m's are the same1 and the correlation is positive unity1 each x must equal its corresponding y4 ,then b b #a4jj2 and the ,m's being equal1 the deviations are from the same point4 ,therefore1 we will attempt to measure similarity of ,m's and ,s4,d4's as well as r4 ,it will be observed that both ,tables #g and #h give evidence of each of these tendencies in all grades4 ,in ,table #h marked progress in arithmetic is apparent4 ,this is due to re-classification in terms of the ,woody-,mc,call test1 which was not done in #aiah-aiai4 ,in #aiah-aiai no arithmetic test was given and all re-classification was in terms of reading1 being done on the basis of both reading tests4 ,spelling re-classification was done each year1 but the data were not treated in this manner4 ,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 hastened4 ,of all the remedial procedure1 such as changing teachers and time allotment and books and method1 all of which were employed to some extent1 it is my opinion that the re-classification was more important than everything else combined4 ,it is noticeable that when r's approach the limit which the unreliability of the test allows them1 they drop down again4 ,this is probably due to continued increase of ,,sq's over ,,iq4 ,of course1 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 behind4 ,when the ,,sq's of the children of lower intelligence reach their ,,iq they continue above4 ,this1 of course1 is due to errors in establishment of the age norms4 ,the norms are not limits of pushing1 though an attempt was made by correction for truncation to get them as nearly so as possible4 ,it is to be noted1 however1 that these norms are up the growth curve1 that is1 reading age of #aj means a score such that the average age of those getting it is #aj1 not the average score of children whose mental age is #aj4 ,the average reading achievement of children all ten years old chronologically is higher than that of a group all mentally ten1 since many of the mentally advanced have not been pushed in product4 ,the group used here to establish norms gives more nearly pushed norms than the others would4 ,the tendency of the low ,,iq's to go over unity in their ,,sr's is apparent in ,table #a and in ,table #ab and also in the negative correlation between ,acc,r and ,,iq4 ,in both years some second grade children were advanced to ,grade ,,iii during the year4 ,this accounts for the low r's in ,june1 #aiai1 but in #aiai-aibj the ,grade ,,iii correlations are raised and the means raised toward the ,m,,iq1 even though some second grade children were put in this group during the year4 ,,table #i ,,summary ,,of ,,progress ,,in ,,arithmetic ,,by ,,increase ,,in r1 ,,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 7of ,,iq and ,arith4 ,q7 ,nov4 ,june ,nov4 ,june ,nov4 ,june ,,iii 4#dac 4#gji #ai4be #h4af #f4bg #f4fc 4#af 4#jh #b4hg #b4je #b4jd #a4de ,,iv 4#dbf 4#gbe #g4da #j4df #b4ci #j4dg 4#aj 4#jf #a4hd #a4ej #a4bi #a4jb ,v 4#fih 4#gac #af4ad #j4ed #g4ad #b4jf 4#jg 4#jg #a4ic #a4hd #a4cg #a4cj ,,vi #e4cc 4#hje #aa4jj #c4jj #j4ai #a4fc 4#ac 4#jf #b4ja #a4ai #a4db #j4he ,,vii 4#gdj 4#gie #g4bg #j4fb #ad4jc #h4ae 4#ji 4#jg #c4eh #b4cc #b4ec #a4fc ,,viii 4#ffc 4#gif #aa4ib #adad4ic #e4bf #adh4ec 4#aa 4#jg #b4be #b4fi #a4ei #a4ed ,total 4#egf 4#fhf #ad4fg #c4gb #c4ea #a4af 4#je 4#jc #j4id #j4ha #j4fg #j4eg ,,table #aj ,,summary ,,of ,,progress ,,in ,,reading1 ,,november1 #aiah ,,to ,,june1 #aiai1 ,,by ,,increase ,,in r1 ,,decrease ,,in ,m,,iq-,m,,rq1 ,,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 7of ,,iq and ,,rq7 ,nov4 ,june ,nov4 ,june ,nov4 ,june ,,iii 4#eda 4#dib #bg4fc #aa4hj #i4ge #j4cf 4#aa 4#ji ,,iv 4#ffe 4#hde #ad4hd -#c4jj #i4gg #g4hf 4#jh 4#je ,v 4#gii 4#hcb #g4je -#b4jj #b4ff #e4jg 4#je 4#je ,,vi 4#dig 4#gbf #f4hj #h4gj #i4fh #c4gf 4#af 4#aj ,,vii 4#fbb 4#gji #b4bh #j4jg #a4dh #e4ih #c of ,,viii 4#aa 4#ji ,total 4#efh 4#fbf #ab4fg #c4ig #c4ca #c4ah 4#je 4#jd ,,table #aa ,,summary ,,of ,,progress ,,in ,,reading1 ,,november1 #aiai ,,to ,,june1 #aibj1 ,,by ,,increase ,,in r1 ,,decrease ,,in ,m,,iq-,m,,rq1 ,,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 7of ,,iq and ,,rq7 ,nov4 ,june ,nov4 ,june ,nov4 ,june ,,iii 4#fea 4#fji #ad4da #aa4eg #bb4df #h4fb 4#aa 4#aj #e4bb #b4ee #c4fi #a4ha ,,iv 4#caf 4#efi #ab4ag #b4dc #c4af #j4gf 4#aa 4#ji #b4da #a4gh #a4gj #a4bf ,v 4#ggc 4#hia -#j4gd -#d4ag #b4eh #a4gg 4#jf 4#jc #a4gb #a4bj #a4bb #j4he ,,vi 4#dbj 4#ffa #e4gi #j4ij #j4gg #j4hg 4#ae 4#ji #b4cc #a4ec #a4fe #a4ji ,,vii 4#hfb 4#gii #e4ed #j4ib #aa4jj #h4ca 4#je 4#jg #b4hh #b4ed #b4jc #a4hj ,,viii 4#gge 4#gbb #d4jj #d4dc #c4id #b4da 4#jh 4#ji #a4ij #b4fd #a4ib #a4hg ,total 4#ebi 4#fji #f4hj #b4hf #b4ab #j4jf 4#je 4#jd #a4af #j4cj #j4hb #j4fg ,the changes in rates of progress are expressed in summaries by subject matter in ,tables #i1 #aj1 and #aa4 ,approach of ,arithmetic ,quotient to ,intelligence ,quotient is measured in ,table #i by3 #a4 ,comparison of r in ,june with r in ,november4 #b4 ,comparison of ,m,,iq-,m,,aq in ,june and ,m,,iq-,m,,aq in ,november4 #c4 ,comparison of ,s4,d4's of ,arithmetic and ,intelligence ,quotients in ,june and ,november4 ,the ,p4,e4's of each of these differences were obtained by ,p4,e4diff ,p4,e4 ,p4,e4 - #b r ,p4,e4 ,p4,e4 ,the only ,m,,iq-,m,,sq in ,table #i which does not show a decrease at least two times as large as the ,p4,e4 of either of the elements involved1 is the #hth grade2 and this is due to the limits of the test used4 ,as mentioned before1 the #hth grade did not register its true abilities in ,june since a perfect1 or nearly perfect1 score in the test was too easy to obtain4 ,the small arithmetic ,s4,d4's in ,grade #h and consequent great ,s4,d4,,iq-,s4,d4,,sq is due to the same cause4 ,tables #aj and #aa present the summary of facts with regard to ,thorndike ,reading ,quotients1 the first and second years respectively4 ,,the ,,ratios ,the discussion which follows concerns ,ratios1 not ,quotients4 ,,table #ab ,,intelligence ,,quotients ,,and ,,subject ,,ratios ,,for ,,all ,,periods ,,grouped ,,by ,,child4 ,,the ,,order ,,of ,,entries ,,is ,,just ,,as ,,in ,,table #a ,,grade ,,iii ,intelligence ,arithmetic ,vocabulary ,reading ,completion ,quotient ,ratio ,ratio ,ratio ,ratio a #aja b c #fc #eg #dc d #aje #hg #ib a #abh b c #fb #hj #fc d #aai #ig #abj a #aaf b c #dh #gh 99 #db d #ha #hb #ff #gg a #hg b c #ajc #df #dj #fb d #hc #he #gj #fj a #aab b c #hj #abb #aai #ajj d #ajj #aja #ajh #aag a #aja b c #hd #ic #cg #ee d #ij #aaj #ih #ib a #ij b c #gf #eh #gb #hi d #fh #aba #gg #ajb a #aje b c #fj #dc 99 #eg d #ajd #ie #hc #ff ,the remainder of this table is filed in ,teachers ,college ,library1 ,columbia ,university4 ,,table #ac ,nov41 #aiah ,june1 #aiai ,nov41 #aiai ,june1 #aibj ,,means ,arithmetic ,ratio #hi4jb #ig4af #a4je #a4jg ,vocabulary ,ratio #ih4if #aaa4dd #ajf4bj #ajg4fa #a4dh #a4fa #j4ij #j4ic ,reading ,ratio #if4dg #aja4if #ih4ih #ajj4fj #a4ai #a4ah #a4jc #j4ig ,completion ,ratio #ii4gf #aja4hc #aja4fg #ajc4aj #a4aa #a4bc #j4ic #j4he ,,standard ,,deviations ,arithmetic ,ratio #ab4jc #ab4ec #j4gd #j4gf ,vocabulary ,ratio #ae4ga #af4eh #aj4cd #aj4hd #a4je #a4ad #j4fd #j4ff ,reading ,ratio #ab4fc #ab4ad #aa4hb #aa4cf #j4hd #j4hd #j4gc #j4fi ,completion ,ratio #ab4cd #ab4fc #aj4he #i4ij #j4hb #j4hg #j4fg #j4fj ,,correlations ,,of ,,ratios ,arithmetic and ,vocabulary 4#fj 4#cj 4#jf 4#jh ,arithmetic and ,reading 4#gj 4#fd 4#jd 4#je ,arithmetic and ,completion 4#dh 4#fa 4#jg 4#je ,vocabulary and ,reading 4#cd 4#cb 4#eg 4#dg 4#jh 4#ji 4#jf 4#jg ,vocabulary and ,completion 4#de 4#cf 4#ec 4#ed 4#jg 4#jh 4#jf 4#jf ,reading and ,completion 4#fa 4#fe 4#fg 4#fg 4#jf 4#jf 4#je 4#je ,in ,table #ab are presented the ,subject ,ratios in the same order as the ,quotients appear in ,table #a4ae ,there plainly is a rapid rise of ,,sq,,iq from period to period1 excluding all pupils who did not take all tests and excluding ,grade ,,iii2 which includes all children taking all tests who were in school in ,june1 #aibj1 and were ,grade ,,iv and above in ,november1 #aiah4 ,the average ,acc,r is #ih4bd in ,november1 #aiah1 and #ajb4gh in ,june1 #aibj4 ,the average ,,iq for these children is #aje4bb4 ,the ,s4,d,acc,r is #aa4ag2 the ,s4,d4,acc,r is #i4ji2 the ,s4,d4,,iq is #ai4bd4 ,it is obvious that the average amount of product per intelligence has increased1 that the range of ,acc,r's has decreased 7which means that factors causing disparities1 other than intelligence1 have been removed71 and that the ,s4,d4 of the ,acc,r's is about one half the ,s4,d4 of the ,,iq's4 ,m's are about equal so it is not necessary to use coefficients of variability4 ,the variability of children1 intelligence aside1 is only one half what the variability is otherwise4 ,the correlations when ,,iq ,x1 ,acc,r ,y and ,acc,r ,s and when ,acc,r average of ,vocabulary1 ,reading and ,completion ,ratios1 are3#af r,x4,y4 -4#fjb r,x4,s4 -4#dic r,y4,s4 4#edi ,the remaining disparity is then due to something which is in negative correlation with intelligence4 ,the number of cases here is only #dh4 ,the ,p4,e4's are then as follows3 ,p4,e4,m ,p4,e4,s4,d4 ,x #a4ia #a4ce ,y #a4aa #j4gi ,s #j4ij #j4fd ,p4,e4r,x4,y4 4#jf ,p4,e4r,x4,s4 4#jh ,p4,e4r,y4,s4 4#jg ,the differences between the ,m's and between the ,s4,d4's of our #aiah and our #aibj ,acc,q's2 namely1 #ajb4gh - #ih4bd #d4ed and #aa4ag - #i4ji #b4jh1 have formed a step in the argument4 ,we must have the ,p4,e4's of these amounts in order to establish the reliability of the quantitative indices we employ3 ,p4,e4diff ,p4,e4,x ,p4,e4,y - #b r,,xy ,p4,e4,x ,p4,e4,y ,p4,e4,m-,m #j4id ,p4,e4,s4,d4-,s4,d4 #j4dg ,these differences are then reliable4 ,if the same data were accumulated again in the same way with only #dh cases1 the chances are even that the #d4ed would be between #c4ej and #e4dh and the #b4jh between #a4fa and #b4ee4 ,that there would be positive differences is practically certain1 since the difference between the means is over four times as large as its ,p4,e41 and the difference between the ,s4,d4's over four times as large as its ,p4,e4 ,to make still more certain this observation of positive amount in ,m of second testing minus ,m of first testing and in ,s4,d4 of first testing minus ,s4,d4 of second testing 7,acc,r71 which means an increase in central tendency of ,acc,r's and a decrease in spread of ,acc,r's under special treatment1 we have listed in ,table #ac the means and standard deviations of ,subject ,ratios of each test for each period and the intercorrelations of these ,subject ,ratios4 ,these do not include exactly the same children in each period but are inclusive of all grades for all periods4 ,they are a measurement of increased efficiency of the school as a whole1 rather than of any one group of children2 though1 of course1 the bulk of the children have representation in each of these indices4 ,too much continuity is not to be expected from ,june1 #aiai1 to ,november1 #aiai1 as the children are different4 ,comparison should always be from ,november to ,june4 ,these tables bear out the fact presented by ,acc,r4 ,it is clear that there is a marked development in the ,s4,r4's1 both by increase of ,m4 and decrease of ,s4,d4 ,the decrease of correlation between ,s4,r4's is not so marked1 but neither is the negative correlation between ,acc,r and ,,iq much less in ,june1 #aibj1 than in ,november1 #aiah4 ,the association of achievements in terms of intelligence is very probably due to mistreatment1 since it is in negative correlation with ,,iq1 as a general inherited ethical factor could not be4 ,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 ,ratios4 ,this makes it highly improbable that the intercorrelation of these remnants is due1 to any large extent1 to common elements in the test or to specific abilities4 ,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 progress4 ,it would be easy to identify this as the part of ,burt's 8,general ,educational ,factor0 which is not intelligence--that is1 industry1 general perseverance and initiative--were it not for the fact that this same influence stands in negative association to intelligence4 ,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 achievements1 irrespective of intelligence4 ,,summary ,the association of abilities in arithmetic1 reading1 and completion with intelligence is markedly raised by special treatment4 ,disparities of educational product are therefore to a great extent due to intelligence4 7,tables #b1 #c1 #e1 #g1 #h1 #i1 #aj and #aa47 ,the remnants 7intelligence being rendered constant by division of each ,,sq by ,,iq7 intercorrelate about 4#e4 ,if there were specialized inherited abilities1 these intercorrelations would not all be positive nor would they be as uniform4 7,tables #f and #ac47 ,the averages of these remnants1 for reading1 vocabulary1 and completion1 correlate -4#fa in #aiah and -4#di in #aibj with ,,iq4 ,these remnants are in negative association to intelligence4 ,if the intercorrelations of these remnants were due to a 8,general ,factor10 this correlation would not be negative4 ,therefore intelligence is far and away the most important determinant of individual differences in product4 ,as part of the relation between tests1 irrespective of intelligence1 is due to common elements in the tests1 this reasoning becomes still more probable4 ,general factor in education1 as distinct from intelligence1 has not been separated here from inherited bases of ambition1 concentration1 and industry4 ,it seems out of our province to conjure up some inherited complex of abilities other than intelligence1 specialized inherited abilities1 or proclivities and interests tending to thorough prosecution of school work4 ,i have therefore meant this last by the general factor4 ,mc,call has correlations varying continually in size from -4#fc to 4#ih between various measurements of a group of #f;,b children4#ag ,the abilities involved were not pushed as are those considered here4 ,some of the low correlations are no doubt indications of low association because of the way children are1 not the way they might be by heritage2 still others1 such as handwriting and cancellation 7unless bright children do badly in cancellation tests because they are more bored than the others71 are correlated low or negatively with intelligence when the correlation is at its maximum4 ,such results as those of ,mc,call serve as a guide not to argue about other tests by analogy4 ,it is necessary to find which traits and abilities can be pushed to unity in their relation to intelligence and which1 like handwriting1 are practically unrelated to general mental power4 ,it is well to know about music tests and such tests as ,stenquist's mechanical ability test when the correlation with intelligence is pushed1 before we decide whether the quality measured is a manifestation of specific talent or general intelligence4 ,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 disparity1 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's4 ,i will present his conclusions with regard to a general factor which are in substantial though not complete agreement with those advanced here4 8,evidence of a ,single ,common ,factor4 8,the correlations thus established between the several school subjects may legitimately be attributed to the presence of common factors4 ,thus1 the fact that the test of ,arithmetic 7,problems7 correlates highly with the test of ,arithmetic 7,rules7 is most naturally explained by assuming that the same ability is common to both subjects2 similarly1 the correlation of ,composition with ,arithmetic 7,problems7 may be regarded as evidence of a common factor underlying this second pair2 and so with each of the seventy-eight pairs4 ,but is the common factor one and the same in each case8 ,or have we to recognise a multiplicity of common factors1 each limited to small groups of school subjects8 8,to answer this question a simple criterion may be devised4 ,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 only1 common to all subjects1 but shared by each in different degrees4 ,such a theoretical construction is given in ,table ,,xix4 ,in this table theoretical values have been calculated so as to give the best possible fit to the values actually obtained in the investigation1 and printed in ,table ,,xviii4 ,it will be seen that the theoretical coefficients exhibit a very characteristic arrangement4 ,the values diminish progressively from above downwards and from right to left4 ,such an arrangement is termed a #8hierarchy4' ,its presence forms a rough and useful criterion of the presence of a single general factor4 8,on turning to the values originally obtained 7,table ,,xviii47 it will be seen that they do1 to some extent1 conform to this criterion4 ,in certain cases1 however1 the correlations are far too high--for instance1 those between ,arithmetic 7,rules7 and ,arithmetic 7,problems71 and again ,drawing and both ,handwork and ,writing 7,quality74 ,now these instances are precisely those where we might anticipate special factors--general arithmetical ability1 general manual dexterity--operating over and above the universal factor common to all subjects4 ,these apparent exceptions1 therefore1 are not inconsistent with the general rule4 ,since1 then1 the chief deviations from the hierarchical arrangement occur precisely where1 on other grounds1 we should expect them to occur1 we may accordingly conclude that performances in all the subjects tested appear to be determined in varying degrees by a single common factor4 8,nature of the ,common ,factor4 8,what1 then1 is this common factor8 ,the most obvious suggestions are that it is either 7#a7 ,general ,educational ,ability or 7#b7 ,general ,intelligence4 ,for both these qualities1 marks have been allotted by teachers1 quite independently of the results of the tests4 ,the correlations of these marks with performances in the tests are given in the last two lines of ,table ,,xviii4 8,upon certain assumptions1 the correlation of each test with the ,hypothetical ,common ,factor can readily be deduced from the coefficients originally observed4 ,these estimates are given in the last line but two of the table4 ,they agree more closely with the observed correlations for ,general ,educational ,ability1 especially if the latter are first corrected for unreliability4 7,correlations3 ,hypothetical ,general ,factor coefficients and ,general ,educational ,ability coefficients 4#hf2 after correction 4#hd4 ,hypothetical ,general ,factor coefficients and ,general ,intelligence coefficients 4#hd2 after correction 4#gg47 ,we may1 therefore1 identify this hypothetical general factor with ,general ,educational ,ability1 and conclude provisionally that this capacity more or less determines prowess in all school subjects4 8,the high agreement of the estimated coefficients with the intelligence correlations suggest that ,general ,intelligence is an important1 though not the only factor in ,general ,educational ,ability4 ,other important factors are probably long-distance memory1 interest and industry4 ,it is doubtless not a pure intellectual capacity2 and1 though single1 is not simple1 but complex40#ah ,,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 ability4 ,the correlation between accomplishment and intelligence 7using ,acc,r1 the average of ,reading1 ,vocabulary1 and ,completion ,ratios with ,,iq7 was -4#fa in ,november1 #aiah1 and -4#di in ,june1 #aibj1 in the ,garden ,city public school4 ,the regrading and special promotion work from ,november1 #aiah1 to ,june1 #aibj1 reduced the handicap of brightness1 but could not obliterate the sparsity of returns per increment of capacity in the upper reaches of the intelligence4 ,further1 work along this same line done by ,a4 ,j4 ,hamilton in the ,washington ,school1 ,berkeley1 ,california1 indicates that this was not a peculiarity of the school at ,garden ,city4 ,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 extremes4 ,much adjustment has been made in favor of the lower extreme1 but little has been done for our genius4 ,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 needs4 ,we are neglecting1 however1 our duty to those whom nature has endowed with the essentials of leadership4 ,they do not interfere quite as much with ordinary classroom procedure1 but they are greater social assets and need special treatment to develop them rather than to let others develop better4 ,neither of the extreme groups is certain of getting the normal stamina necessary for good citizenship4 ,neither group forms good habits of study nor accumulates such information as it might4 ,being aware of this discrepancy between the gift and the recipient1 we have made our lessons easier and we have segregated the lower percentile4 ,there is much more to be done4 ,we must adapt education to at least five varying classes in order to reduce the spread within each to a commodious span4 ,but the genius is the most important and should have the greatest claim to our immediate attention4 ,first1 our social needs demand special attention for the genius in order that we may better exploit our best nervous resources4 ,second1 our educational needs demand it since the very bright as well as the very stupid disrupt calm and cogent classroom procedure4 ,third1 they themselves demand it in order that they may1 even when they do function as leaders1 be happier in that function1 since now they often lose much in social contact by peculiarities which prevent an integration of their 8drives0 into a harmonious economy of tendency4 ,these peculiarities come from their continuous maladjustment1 since when they are with children of their own mental maturity they are physically and physiologically handicapped2 when they are with children of their own size and muscular equipment they are so far mentally superior that they are unhappily adjusted4 ,only classification on a large scale will allow sufficient numbers of them to congregate to correct this4 ,i am reminded of a boy ten years old whose ,,iq on the ,terman test was #agb4 ,he defined a nerve as the 8conduction center of sensation0 and1 when asked to explain1 did so in terms of sensation of heat and motive to withdraw4 ,he explained the difference between misery and poverty thus3 8,misery is a lack of the things we want2 poverty is a lack of the things we need40 ,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 physique8 ,fourth1 our eugenic needs demand it1 since we are not conserving this1 our chiefest asset1 genius4 ,unless we conserve better these rare products1 the standard deviation of the intelligence of humanity will keep shrinking as we select against imbeciles and against genius as well4 ,the waste of a genius who becomes an intellectual dilettante1 as many now in fact do1 is double4 ,we lose what he might do for society2 he does not marry and we lose the potentiality of his highly endowed germ-plasm4 ,and they do become dilettantes when special treatment is not given4 ,i know of a young man who was first of his high-school class1 who got all ,a's his first year in ,college 7at ,wisconsin71 and all ,a's his second year 7at ,harvard72 and then he began to read all manner of literature with no schema of expression1 no vocation1 because1 as he said1 all college courses are so stupidly easy4 ,he attended no lectures and read none of the books in one course1 and then two days before the examination he was taunted with not being able to pass this course4 ,he spent two nights and two days studying1 and he received ,b in the course4 ,but now he is a failure because he has no organized1 purposive schema of expression2 he was always in classes with people less fortunately endowed than he1 and so he never had a chance4 ,on these four counts then we must segregate our genius3 7#a7 ,social exploitation of our resources4 7#b7 ,educational procedure for the sake of other children as well as for them4 7#c7 ,happiness for them1 organization of their trends1 and formation of social habits4 7#d7 ,biologic conservation of great positive deviation from average human intelligence4 ,,is ,,genius ,,specialized8 ,this genius is of various kinds1 political and business leaders1 scientists and artists4 ,have they then the same inherited nervous structure with regard to abilities and capacities as distinct from interests8 ,we know that they must have something in common1 something that we call intelligence1 power of adaptation4 ,calling this the nervous chemistry1 the way the nervous system acts its quality1 we must still know whether we have also an inherited nervous physics to deal with1 or a further inherited nervous chemistry which predisposes to specific ability4 ,are there inherited capacities or predispositions to ability8 ,we are in a position to answer this question with regard to the elementary school subjects1 and are tempted here into a more general discussion of the matter in hand4 ,the need to clarify our view on what is inherited and what is due to environment can be clearly envisaged in terms of our teachers4 ,whatever psychologists may mean by 8predisposition to ability0 it is quite certain that teachers make no distinction between this and the inheritance of a capacity4 ,they feel that some children figure better than they read1 and others read better than they figure1 8by nature10 and there their obligation ends4 ,if it is a grave matter that we shoulder the burden of bringing a child to his optimum achievement1 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 factors1 and how much is due to our inadequacy4 ,so1 too1 we have much loose discussion about finding out what children can do and want to do in the way of vocational diagnosis1--loose because it assumes that children are born with definite vocational capacities4 ,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 8predisposition to ability0 means4 ,the teacher interprets it to mean about what was meant by the turtle that held up ,atlas who held up the world4 ,she makes no real distinction between predisposition to ability and specific ability1 just as there was no real causal distinction between the turtle and ,atlas4 ,she then gets at her conception of intelligence additively1--a summation of school abilities4 ,the correlation of teachers' judgment of 8power of adaptation10 carefully explained1 and marks given six months previously by the same teachers was 4#hb4 ,the correlation of this same average judgment with the average of thirteen intelligence tests was only 4#eh4 ,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 subjects4 ,the unit characteristics which make up what we describe in terms of gross behavior as intelligence must of course be many4 ,no one denies that if we knew just what these units were we could describe two possible manifestations of what we now call intelligence1 of which one person could do one only and another person could do the other only because of the particular combinations of the units inherited4 ,this would constitute inheritance of predisposition to special capacities4 ,but it is not the same to assume that the vocations and aptitudes desirable in a world such as ours have specialized inherited bases4 ,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 abilities4 ,as the unit characteristics are certainly not so closely allied to our social needs as 8mechanical intelligence0 and 8social intelligence0 or even 8rote memory for numbers10 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 intelligence4 ,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 another4 ,this is a question of more or less4 ,i believe that the amount to which a person's specific talents1 his vocation as distinct from his general power1 are shaped by the combinations of elements which make up his inheritance1 is much less than believed by ,francis ,galton1 who says3 8,there cannot then remain a doubt but that the peculiar type of ability that is necessary to a judge is often transmitted by descent40 ,and again3 8,in other words1 the combination of high intellectual gifts1 tact in dealing with men1 power of expression in debate1 and ability to endure exceedingly hard work1 is hereditary40#ai ,i believe that the amount of influence which inheritance has upon the kind of thing a man does in life has been overestimated2 that the inherited factors influence more the way in which he shall do whatever the environment influences him to do4 ,this leaves plenty of play for the close correlation between parents and children in both intelligence and vocation4 ,the former is the result of inheritance1 the latter is the result of environment4 ,all competent psychologists would agree to-day to less specific inheritance than a basis1 for instance1 for the distinction in vocation of minister and orator2 and more specific inheritance than for such a statement as 8,we inherit how well we will do1 we learn what we will do40 ,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 plumber4 ,this question is1 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 another4 ,interpretation statistically of one thousand possible elements1 simply viewed as present or absent1 and again simply viewed only as combinations and not permutations1 would mean that the less the intelligence the more specific the inheritance4 ,the most intelligent man alive could1 by what he is born with1 do anything since he has all of the one thousand factors1 all of which help him in the prosecution of any venture4 ,but the fewer elements he has the less well he does most things1 and when lacking certain elements he has lost the capacity to do some things more completely than others4 7,i have neglected physiological characteristics necessary to an ability4 ,a deaf man certainly is handicapped in music4 ,i speak of possible mental capacities47 ,such a view leaves scope for some degree of special abilities4 ,it accounts for the idiot-savants1 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 intelligence4 ,it allows for such cases as ,galileo1 whose father was a composer1 as well as the cases cited by ,galton4 ,heredity need not imply the same kind of genius though it does suggest it1 whereas the environment backs up this inherited implication4 ,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 successes4 ,observation of brilliant children would corroborate this view4 ,they can do anything4 ,observation of the mentally deficient is equally encouraging to this view4 ,it has always been puzzling that they seem to do a few things much better than others4 ,according to this conception there would be a negative correlation between intelligence and specialized inheritance4 ,we will then consider each inherited element1 not as music or as science1 but rather as an element of intelligence which will help in all lines of work1 but which may be a little more necessary for some than others4 ,this is a predisposition in a true sense4 ,if a man had only one element out of one thousand1 he could do only a few things4 ,if he had all thousand he could do everything4 ,inheritance of ability is not in terms of units valuable to us socially1 but only in terms of undefined nervous elements2 and we may conceive of specialization1 and still hold that there be less1 the more intelligent a man is4 ,to make the matter still more concrete1 imagine two men each of whom have #ijj of the hypothetical #ajjj elements1 this being a value of #c ,s4,d4 from the mean intelligence of the human race4 ,one is a composer1 the other financier4 ,according to this view the greatest number of their inherited bases on which they could differ would be #ajj of the #ijj elements4 ,the other #hjj must be alike4 ,assuming that all of the elements contribute to all of the activities1 but that some of them are more essential to some activities than to others1 we could in this case say that the #ajj which are different decided in some measure the vocation of each man4 ,but it is much more probable that they overlap in #hej and that each has only #ej distinct elements1 and further that the #ej which are distinct in each would not all be such as to influence one kind of ability rather than another4 ,then these two men1 had they interchanged environments1 would probably have interchanged vocations in that transaction4 ,for the purposes of this discussion we treat physiological inherited features 7such as hearing71 as environment1 as we are considering the mental capacity of composer as distinct from the necessary conditions to its development4 ,according to this view1 then1 we account easily for the versatility of genius1 which is so apparent in such accounts as ,terman's ,the ,intelligence of ,school ,children4#bj ,also1 though very infrequent1 we account for the genius who could not have done other things as well as those he did4 ,let us consider the case of negative deviates1 say #c ,s4,d4 from the mean intelligence of the human race4 ,two men each have #ajj of the #ajjj hypothetical elements4 ,it is much more probable here than not1 that an appreciable amount of the #ajj elements would be distinct in each person1 though it is improbable that they would often be such as to form the basis of an 8ability40 ,this then would account for specific abilities amongst morons and also for the presence but rarety of idiot-savants4 ,also since there are a limited number of such combinations possible and since many overlap for all practical purposes1 we would account for the common likenesses as well as the relatively more uncommon extreme differences4 ,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 inheritance4 ,we found no unremovable predispositions to one school subject more than to the others in any of the children4 ,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 nature4 ,woodworth says in a criticism of ,mc,dougall's view of instincts3 8,what he here overlooks is the fact of native capacities or rather1 the fact that each native capacity is at the same time a drive towards the sort of activity in question4 ,the native capacity for mathematics is1 at the same time1 an interest in things mathematical and in dealing with such things4 ,this is clearly true in individuals gifted with a great capacity for mathematics40#ba ,i do not wish to become involved here in a discussion of the original nature of man on the instinctive side4 ,i wish merely to rebel at the assumption of specific inheritance of abilities that are really sociological units4 ,mathematics is an ability which is useful to us1 which we have come to encourage in education4 ,but it is a man-made unit4 ,there is no reason to believe that the inherited components of mentality are in any direct way related to such talents as mathematics or music4 ,the units may vaguely predispose1 but the units are not mathematics and music4 ,we may say that the inherited physical and chemical units of the nervous system may be so distributed as to predispose one man to mathematics1 and another to music1 but we must not argue for inherited interests as correlates4 ,the evidence is all that the inherited nervous chemistry of the individual is what on the side of behavior1 we define as intelligence--power of adaptation4 ,we may logically fall back on the inheritance of predisposition to ability1 meaning thereby the inheritance of such nervous qualities as will better fit the individual to cope with mathematical than with musical situations2 but if we adopt this cautious ground in disputation we cannot argue in another matter for an inherited interest in mathematics1 innate because of the inborn mathematical talent4 ,if the inherited qualities merely predispose they merely delimit2 just as a man born without arms would probably not become a great baseball player1 nor a deaf man a great musician1 nor a man with poor motor control a skilled mechanic--so we are predisposed nervously for capacities4 ,hence can we argue that the inborn root of the interest is the capacity8 ,is it not safer to assume that interests in success1 approval of fellowmen and general mental activity led to the development of the capacity by virtue of a favorable environment1 and led by the same environment to interests centered about its activity8 ,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 skin4 ,as we1 in our limited knowledge1 still define abilities in terms of behaviour and not by nervous elements1 my contention is that intelligence should be regarded as the sum total of this inheritance1 much as general strength is1 in terms of the body4 ,we have still to find the component units of this intelligence4 ,we can then define predisposition to ability4 ,to split intelligence into inherited units of mathematics1 reading1 composition1 mechanics1 etc41 is as unjustifiable as to split inherited vigor of body into baseball capacity1 running capacity1 climbing capacity1 etc4 ,mathematics and music are what we do with intelligence1 not what intelligence is made of4 ,of course everyone agrees to this4 ,the lack of emphasis upon the chance that the inherited units are general in their application1 that the same inherited elements are involved in many of the behavior complexes which we call traits and abilities1 is what confuses the situation4 ,,current ,,psychological ,,opinion ,we must know what these elements are1 and how many contribute to which capacities4 ,then we can decide the question of specialized inheritance4 ,in all crude behavior data it is impossible to separate the influence of nature and nurture4 ,a theory of specialized inheritance will inevitably infringe upon common sense in its claims4 ,of the following statements1 it would be easier for most of us to endorse #a and #b than #c and #d1 whereas few would agree with #e and #f4 #a4 8,unless one is a blind devotee to the irrepressibility and unmodifiability of original nature1 one cannot be contented with the hypothesis that a boy's conscientiousness or self-consciousness is absolutely uninfluenced by the family training given to him4 ,of intelligence in the sense of ability to get knowledge rather than amount of knowledge got1 this might be maintained4 ,but to prove that conscientiousness is irrespective of training is to prove too much40 7,thorndike1 ,educational ,psychology1 ,,iii1 pp4 #bdb47 #b4 8,some attempts have been made to apply these laws to behavior complexes1 but as yet psychology has provided little foundation for such studies4 ,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 ratios4 ,but in the field of human psychology too little is known of the genesis of character1 of the distinction between nature and acquired behaviour to provide a very firm foundation for the work of the geneticist40 7,watson1 ,behaviour1 p4 #aef4 ,italics are mine47 #c4 8,even1 however1 when we omit the trades as well as the cases in which the fathers were artists1 we find a very notable predominance of craftsmen in the parentage of painters1 to such an extent indeed that while craftsmen only constitute #i4b per cent among the fathers of our eminent persons generally1 they constitute nearly #ce per cent among the fathers of the painters and sculptors4 ,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 art4 8,to suppose that environment adequately accounts for this relationship is an inadmissible theory4 ,the association between the craft of builder1 carpenter1 tanner1 jeweller1 watchmaker1 wood-carver1 rope-maker1 etc41 and the painter's art is small at the best and in the most cases non-existent40 7,ellis1 quoted in ,thorndike1 ,educational ,psychology1 ,,iii1 p4 #beg47 #d4 8--the statesman's type of ability is largely transmitted or inherited4 ,it would be tedious to count the instances in favor4 ,those to the contrary are ,disraeli1 ,sir ,p4 ,francis 7who was hardly a statesman1 but rather bitter a controversialist7 and ,horner4 ,in all the other #ce or #cf cases in my ,appendix1 one or more statesmen will be found among their eminent relations4 ,in other words1 the combination of high intellectual gifts1 tact in dealing with men1 power of expression in debate and ability to endure exceedingly hard work1 is hereditary40 7,galton1 ,hereditary ,genius1 pp4 #ajc1 #ajd47 ,thorndike comments on this last quotation3 8,of course there is1 in the case of all of ,galton's facts the possibility that home surroundings decided the special direction which genius took1 that really original nature is organized only along broad lines4 ,moreover1 it is difficult to see just what in the nervous system could correspond to a specialized original capacity1 say1 to be a judge4 ,still the latter matter is a question of fact1 and of the former issue ,galton's studies make him the best judge4 ,we should note also that it is precisely in the traits the least amenable to environmental influence such as musical ability1 that the specialization of family resemblance is most marked40 ,this cautious and sagacious commentary is in marked contrast to the following3 #e4 8,but no training and no external influence can entirely supersede the inborn tendencies4 ,they are the product of inheritance4 ,not only unusual talents like musical or mathematical or linguistic powers can be traced through family histories1 but the subtlest shades of temperament1 character and intelligence can often be recognized as an ancestral gift40 7,munsterberg3 ,psychology1 ,general and ,applied1 p4 #bcj47 #f4 8,statistical studies which covered many characteristic opposites like industrious and lazy1 emotional and cool1 resolute and undecided1 gay and depressed1 fickle and constant1 cautious and reckless1 brilliant and stupid1 independent and imitative1 loquacious and silent1 greedy and lavish1 egoistic and altruistic and so on1 have indicated clearly the influence of inheritance on every such mental trait40 7,munsterberg1 ,psychology1 ,general and ,applied1 p4 #bcg47 ,undoubtedly ,munsterberg here refers to the data accumulated by ,heymans and ,wiersma since they used such opposites as these1 and also used what might be called statistical methods4 ,speaking of the same data ,thorndike says3 8,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 heredity1 and not to repeat the figures which are got by this method4 ,also they do not attempt to estimate an allowance for the influence of similarity in home training1 though they state that some such allowance must be made40 7,educational ,psychology1 ,,iii1 p4 #bfb47 ,hollingworth and ,poffenberger1 commenting on the data of ,galton and ,ellis mentioned in the quotation above1 say3 8,francis ,galton has made a statistical study of the inheritance of specified mental abilities and found that the abilities required for success as a judge1 statesman1 minister1 commander1 poet1 artist1 and scientific man1 are inherited4 ,but the nature of his data makes him unable to make exact allowances for influences of training and environmental influences4 ,consequently1 his figures might really show general intelligence to be inherited and the form of its expression to be dependent upon environment4 8,other investigators1 among them ,f4 ,a4 ,woods and ,havelock ,ellis1 have made similar statistical studies and conclude that there is inheritance of even such qualities as temper1 common sense1 and the like1 but these reports are also subject to the same complicating influence of environment40 7,applied ,psychology1 p4 #dc47 ,it can readily be seen1 from these quotations1 that there is fundamental disagreement among psychologists with regard to the inheritance of specific ability1--fundamental disagreement in three ways3 7#a7 ,interpretation of ,galton's and ,ellis's data4 7#b7 ,opinion on the matter4 7#c7 ,degree of precision possible in giving judgment4 ,we have noted that it is very difficult to understand what the neural bases for such special abilities as ,galton speaks of could be2 that they are social1 not neural or psychological units4 ,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 others1 would account for all the observed facts1 is neurally imaginable1 and does not need to view ability to be a 8judge0 or 8artistic talents0 as biological entities4 ,it further explains the differences in their limited abilities of mentally deficient children4 ,burt says in this connection3 8,among children of special 7,m4,d47 schools1 the evidence for a general factor underlying educational abilities and disabilities of every kind is not so clear4 ,in administrative practice1 #8mental deficiency' implies among different children deficiencies in very different capacities1 both general and specific40 7,cyril ,burt3 ,the ,distribution and ,relation of ,educational ,abilities1 p4 #hc47 ,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 aptitudes1 as teachers so often assume1 but that general intelligence is the only inherited cause of disparity in product4 ,investigations where the correlation between educational product and intelligence1 irrespective of chronological age1 was less than around 4#ge1 used data where many removable causes were not removed1 and consequently measured results of the environment as well as heredity4 ,a case such as this follows3 8,the influence of inheritance upon a very specific mental quality1 namely1 spelling ability1 has been tested experimentally1 although here there is some difficulty in separating the influence of heredity from that of environment4 ,earle studied the spelling ability of #ahj pairs of brothers and sisters who had uniform school training and found a correlation of 4#ej4 ,this means that if one child deviated by a certain amount from the average child in spelling ability1 his brother or sister would deviate from the average child just half as much2 that is1 he would resemble his brother or sister to that extent40 7,hollingworth and ,poffenberger3 ,applied ,psychology1 p4 #dd47 ,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 brothers4 ,in other words1 a child could be made to resemble his brother as nearly in spelling ability as he did in intelligence4 ,all disparity could be reduced to that of general intelligence4 ,then intelligence alone is inherited as far as the data here presented have any bearing on the matter in hand4 ,the influence of environment is in this case a matter of no consequence1 since the subjects all had the same schooling1 and home influence does not as a rule teach children to spell2 but the data are not irrespective of the influence of intelligence4 ,,indications ,,of ,,the ,,garden ,,city ,,data ,table #c presents intercorrelations between ,,iq and quotients in the various subjects4 ,the correlations are in each instance irrespective of chronological age since all quantitative indices are expressed as quotients4 ,we have seen that they go up from ,september1 #aiah1 to ,june1 #aibj4 ,every possible means was used to push these correlations to their limit1 to remove all removable factors4 ,we have seen that the data show here1 as in ,tables #g and #h1 that there is little association between traits which is not a result of differences in intelligence4 ,table #c shows the same #dh children throughout4 ,the r's are not corrected for attenuation4 ,though the r's are high throughout and go higher under special treatment1 the association can still be more accurately registered by some attention to relation of the means and the ,s4,d4's4 ,two traits to be identical must have r #a4jj ,s4,d4x ,s4,d4y and ,mx ,my4 ,we have seen that the r increases1 ,m-,m decreases and ,s4,d4-,s4,d4 regardless of sign decreases4 7,tables #i1 #aj and #aa47 ,but as the ,s4,d4's of the ,subject ,quotients 7though they do approach ,s4,d4 of ,,iq7 sometimes go below the ,s4,d4 of ,,iq1 we must know why4 ,it is because the low ,,iq's do better per their intelligence than the high ,,iq's4 ,we have seen above that the correlation between ,,iq and average of the ,vocabulary1 ,reading1 and ,completion ,subject ,ratios is -4#fa in ,november1 #aiah1 and -4#di in ,june1 #aibj4 ,then the ratio of achievement to intelligence is in definite relation to intelligence--a negative relation4 ,it is this same tendency to adapt our education to a low level which has prevented a perfect association between intelligence and the various subjects4 ,the relation of one subject to another1 irrespective of intelligence1 would be zero if there were no other factors except intelligence responsible for the product4 ,after two years of such attempts as an ordinary public school will allow1 we have removed many of the causes of disparity and increased the association between potential progress and progress in arithmetic1 reading and language4 ,the correlations1 correspondence of ,s4,d4's1 and 7,,iq-,,eq7n registered in ,tables #i1 #aj1 and #aa give evidence of this as does also the increase in the ,acc,r1 an average of the ,arithmetic1 ,reading1 ,vocabulary and ,completion ,ratios4 7,table #ac47 ,are the unremoved causes other than intelligence unremovable8 ,these causes might be1 besides the unreliability of tests and the common elements in the tests1 the specialized inheritance we have considered1 ethical qualities of endurance1 ambition1 initiative and industry or a general factor4 ,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 inheritance4 ,these intercorrelations for all years are embodied in ,table #ac4 ,the partial correlations of quotients when intelligence is rendered constant will be found in ,table #f4 ,these intercorrelations1 and the partials as well1 give an indication of some general factor other than intelligence since the r's irrespective of intelligence are uniform and all are positive4 ,only the correlation of arithmetic with vocabulary1 intelligence being rendered constant1 goes to zero4 ,though this might be due in part to common elements in the tests1 it is more likely that there is another factor in operation4 ,inheritance of specific abilities could not have this uniform effect on the correlations4 ,these correlations all being positive and the r's being very uniform1 both correlation of ratios and the partials1 makes the interpretation of specialized inheritance of ability extremely unlikely4 ,the correlation of ,arithmetic ,ratios with ,reading ,ratios is higher in #aibj than that of ,vocabulary ,ratios with ,reading ,ratios4 ,it leaves the possibility that the unremoved factors are inherited ethical differences or that they are a 8general educational factor40 ,the negative correlation of ,acc,r with intelligence1 however1 being as high as these positive remnants of interrelation1 would tend to make more probable an interpretation of this as a remnant of disparity1 intelligence accounted for1 which is entirely due to the organization of our schools4 ,all disparity not due to intelligence was worked on as far as it was possible4 ,thereupon the association of intelligence and educational product increased markedly and the negative association of intelligence with achievement in terms of intelligence decreased somewhat4 ,however1 some association of abilities not due to intelligence remains4 ,exactly as much negative association of achievement in terms of intelligence1 with intelligence1 remains4 ,so1 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 decreased1 the causes which contributed to a correlation such as lack of interest having been removed1 there still remains some relation of school qualities4 ,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 curricula4 ,this enables us to interpret our partials4 ,the partials are not nearer zero because although we have partialed out the effect of intelligence1 we have not partialed out the factor which controls the negative relation to intelligence of these very partial resultants1 since that is the effect of the methods and curricula4 ,though we did advance bright pupils and give them more chance1 we have not given them a chance proportionate to the stupid children4 ,and that is true since we often wanted to advance pupils and were not allowed to2 whereas we were never allowed to demote pupils except in particular subject matter4 ,the stupid children were always at the frontier of their intelligence at the educational cost of the others4 ,it is this remnant which has usually been interpreted as 8general factor0 or as inherited factors basic to initiative1 ambition1 and industry4 ,the fact of importance is that these remnants1 these marks of children independent of their intelligence1 are associated negatively with intelligence to the same degree that they are associated positively to each other4 ,unless we wish to assume that the 8general factor0 or the inherited bases of initiative and industry are associated negatively with intelligence we must account for the remnant in some other way4 ,it seems far more reasonable to attribute this remaining association to the educational handicaps of intelligence which we were unable to remove4 ,the original tendencies of man1 as distinct from his original equipment1 have not been considered in this study4 ,if the quantitative differences in endowment of this kind were added to the denominator of our accomplishment ratio formula1 we would have a better measure and better results4 ,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 predisposition4 ,industry1 ambition1 and initiative are not inherited units4 ,they are1 however1 the rules of an economy of expression and as such are dependent upon individual differences in strength of instinct4 ,,conclusions #a4 ,,iq can be used as a limit of school achievement expressed as ,,sq4 a ,progress in 7,,iq-,,sq7n may be used as a measure of school efficiency4 b ,,sq,,iq may be used as a measure of individual efficiency4 #b4 ,correlations between intelligence and achievement are very different before and after the abilities are pushed4 a ,many r's are reported where conclusions are drawn as though they had been pushed4 ,these conclusions should be restated4 b ,intelligence and achievement are far more closely associated than has been assumed to date4 #c4 ,disparity of school product can be reduced to individual differences in intelligence4 a ,little specific inheritance of school abilities4 b ,little unremovable difference in industry1 conscientiousness and concentration4 c ,intelligence is the only inherited general factor4 #d4 ,negative association between ,acc,r and ,,iq4 a ,to-day's educational procedure involves a handicap to intelligence4 b ,the genius has been neglected4 ,illustration ,,footnotes #a ,part of this section is reprinted with revisions from ,,teachers ,,college ,,record1 ,vol4 ,,xxi1 ,no4 #e 7,november1 #aibj74 #b ,for scientific purposes we want year-month means and standard deviations1 that we may say that ,charlie ,jones is #b4a ,s4,d4 above the mean for his age level1 while ,harold ,smith is 4#a ,s4,d4 below that mean4 ,it is in terms such as these that we may be able to compare accomplishment in one function with accomplishment in another1 progress in one with progress in another4 ,for many of our problems we need a common denominator of measurement so that we may compare progress between tests and age-groups4 ,the best common denominator is1 ,i believe1 ,s4,d4 in an age-group4 ,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-group4 ,for practical purposes1 however1 it is for many reasons more convenient to use quotients in elementary schools4 ,principals would rather deal with quotients since it is easier to explain them in terms of attainment and capacity4 ,it is the use of such quotients that this thesis discusses4 #c ,judd1 ,c4 ,h41 8,a ,look ,forward10 in ,seventeenth ,yearbook1 ,pt4 ,,ii1 of the ,n4,s4,s4,e41 #aiah4 #d ,when the disadvantages of 8pushing0 children are discussed1 the disadvantages of keeping children at their chronological age levels should be considered as well4 ,although it is true that a supernormal child placed in that grade for which he is mentally equipped loses much in social contact1 it is also true that he loses a great deal by remaining in the grade where he physiologically belongs4 ,there he develops habits of conceit1 indolence1 and carelessness4 ,it is in all cases much better to group intelligent children and enrich the curriculum than to 8push0 them2 but pushing may be better than leaving them where they belong by age4 ,it is a possibility worth considering that the explanation of the 8peculiarities0 of genius lies in the fact that he has never associated with equals4 ,when his fellows are mentally his equals they are physically far older and when they are physically his equals they are mentally inferior4 #e ,whether only the ,accomplishment ,ratio as a percentage should be given the parents1 or whether they should know both the ,,iq and all the ,,sq's1 is a question on which ,i am not prepared to give an opinion4 ,i incline to believe that the parents should know only the final marks and am sure that ,i advise telling the children these only4 #f ,there will be reported elsewhere a fuller consideration of this aspect of the technique of derivation of norms1 together with a complete presentation of the data used to obtain the age norms herein used4 #g 8,the ,accomplishment ,quotient10 ,teachers ,college ,record1 ,november1 #aibj4 #h ,or the ratio of the ,subject ,quotient to the ,intelligence ,quotient1 which is the same as the ratio of the ,subject ,age to the ,mental ,age4 #i ,this table is too bulky for complete publication but may be found on file in ,teachers ,college ,library1 ,columbia ,university4 #aj ,the remainder of this table is filed in ,teachers ,college ,library1 ,columbia ,university4 ,decimals are dropped in this table4 #aa ,decimals are dropped in this table4 #ab ,truman ,l4 ,kelley3 ,statistics1 ,the ,macmillan ,co4 #ac ,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 ,binet4 #ad ,these quantities do not decrease because a perfect score on the arithmetic test was too easy to obtain at this time4 ,the children had reached the limits of this test4 #ae ,table #ab is too bulky for complete publication4 ,the first page is reproduced here and the complete table is filed at the library1 ,teachers ,college1 ,columbia ,university4 #af ,no arithmetic was given in #aiah1 therefore arithmetic was not used in these averages4 #ag ,william ,anderson ,mc,call3 ,correlations of ,some ,psychological and ,educational ,measurements1 ,teachers ,college ,contributions to ,education1 ,no4 #gi4 #ah ,cyril ,burt3 ,the ,distribution and ,relations of ,educational ,abilities1 pp4 #ec-ef4 #ai ,quotations from ,galton3 ,hereditary ,genius1 '#ib1 pp4 #fa-fb and pp4 #ajc-ajd4 #bj ,terman1 ,lewis3 ,the ,intelligence of ,school ,children4 ,boston3 ,houghton ,mifflin1 #aiai4 #ba ,woodworth1 ,r4 ,s43 ,dynamic ,psychology1 p4 #bjj4 ,new ,york3 ,columbia ,university ,press1 #aiah4