LANGE LIBRARY C EDUCATION UNIVERSITY OF CAL.IPORNIA BERKELEY. CAUFORNiA. UC-NRUF ,b5 as 1, Another use of Van wageKen's Table I: to coTioute spelling ages from the Buckingham .^Jxtension of the Ayres Spelling Scale By Walter S. Morgan A. a. 1919 'i'HiSlS Submitted in partial satisfaction of the requirements for the degree of IjIAoTiJR OF Ai\T3 in ■Education in the ^'■AmkT'^ Division T. w . H ftri of the UlilV^iiyiTY OF OALiFOKNiA ^\i ^C-'-y-^ \0\S: z^^-JcXf^AM] LTTb The Par OPS e of the St;ad.v Mucators havo be«J. oonoorned for some time to know jast vhat roiationship exists between the general mental ability and the spelling ability of sohooi children, ^e norms have been availsole for some time nov. for scores on such tests as the Woody-UcCall Mixed Fuiidamentals, the Trabae- ifelley Completion Test Mxeroisos, the Ihorndilce Handwri tiT-g Bcale, tl-ie Thorndike-McCail Silent lieading Scales, aa* the Thorndike Visual Vocabulary Scales, fferetofore, however, there have been no sige norms set up for performance in soellirg. As a result, it has been impossib e to determine accurately Just vrhat relationship the spellinii ability of school children bears to their general intelligence. The purpose of this study is to set forth a method of determining the amount of eo-relationship - or correlation - existing betv-eer these two functions. Oeneral atethod, of the Stady The method followed in this study v.as (1), to determine by an adequate group test of morital ability the Group Intelli- gence Qaotientt of the pupili> to be tested; (2), to obtain by a method to be estjblishou, the SfXJlling quotients of the same 665:^83 Digitized by the Internet Archive in 2008 with funding from IVIicrosoft Corporation http://www.archive.org/details/anotheruseofvanwOOmorgrich ;)ii;)ila; (a), t.» ooraoato tiic oorrel.-itljr coeffJOloVt of tris tv-o sets ui' qautiorits* u!ne jaiiit^ r .ieotea tor teatinf vero tnu..e i« e;ifiUos 6-A to Q-fl. i»,C4.aBive (A ir;4laati>.i; t>© Itr. ar half of tho ►irade, ants 3 iuf^iciuti}^; ti»o uripei nai-r)« in Uie j>a.)iiE! tested vas 203« Of thtise, hov^Ttir, somo missed osjo oj* the othei of the teste, ;ior©ov!!j-, a nurauci of tho tosts had to be throv?n oat foi^ lack of information, such a,s Urn ©hrunoiotiicai a«e of tno pupil. 2he result was tfe^t hoth nentr-X tests ajisi soellls^; tests wero fl>,aliy availatilo for only 182 of the totRl 203 juplls. !i?he Uriti^Q L^t^lllc^cnoe ^aotlen^ s !a»e ment«i t«st solect-eu was the ^rmatj dtoiia Test of ife&tal Ability, uf thich Porra 4 Y;a9 namir-^istered to tr>e -junils* I'hci Sroap tnteili^wiooe quotients (a.I.\i.*s) were outainsd by the method pro>usau by IXx, t?, Q, Keatoj , Aj?8ist.-i:.t liiroctsa- of lesearoh, in a report to ur, Virgil B. JJickBov., li rector of '' esearcii ar.d Ouid^noe, OaklwMi (CkI.) >aolic Sohools, in Uay, 1921. The raentsal t%^ normc far scores on tho 7nrman liroun Tost vhich were t»ed iii this staay voro those estHbllsheci by ]>r. Termai., not those actnpted therefVcm by Sir. • ector. The nonie u8om follow. Table I ItoKtai A^e Equivalentc for Tcoros on tho !7Brman droi^) Vest of Mental Ability Tears : 4 . .o . n t h s - 5 ) i 2 2 4 5 6 7 8 9 ^ } Ai 1! 9 il 12 14 15 17 18 2' 21 23 24 iiS il 27 29 30 32 33 35 38 ZQ 39 41 42 44 12 45 47 48 SQ 51 b^ 64 56 57 59 60 52 17. 6.-> 55 66 6B o9 71 7fe 74 7 b 77 70 80 -14 01 63 84 6o ti7 89 90 9ii 93 95 So 96 lb 99 101 102 104 106 107 1»8 ll.i 111 113 114 116 16 117 119 121) 122 123 125 12S ISS 129 1^1 132 134 17 135 1;57 137 i;:9 140 143 143 145 146 1^ 149 151 10 15. 155 15i 158 159 131 lo2 154 165 137 166 17U 19 171 17a 174 176 177 179 lis' 182 183 185 186 188 2U 1B9 191 192 194 195 197 198 2'0 201 2U3 20A 2.>6 21 207 ,i09 210 21ii 213 215 216 218 gl9 221 222 224 The method of oalcul .ting Crrau7 Intelil^ence t^uotiente on th« basis of DcoreQ mado on the Tensnin (iroap Test nay be exemplified b^ the foiIov>lng case* Pupil X made a score of 90 on tho test. The mentai age equivalent for a score of 90 on the Teman Groar) Test is 14 years, 6 mont'is. This mental a^e reuuced to months Is 174 months. The pupil's chronolOi,icai age at the tinie of tnkini; tho test v.as 13 years, 7 months, or 163 months. !Ihe Group Int&iligeiioe 4uotiont, like the I. Q. derivod from the Binet-Bimon individoal test is tho quotient obfiinsd by dividing the mntal a^ by the chronologioul a^e. In this case tho mental a^;e is 174 months, the ohronolotj;loal •(£« 1S3 months. !&o quo- tient obtsiinod by dlvidirsg 174 by 163 is 1.J7, a fi. I. Q. of 107. Using this process aau tiie norms ^'ivor. in Table I, the suores astue by tije pupils vjom oonverted into raoKtai ages, uonsldering only tlie 182 cases for '^hich both >i. I. 4»*b and Spelling ^uotisnts v.ere obtained, tha following rasalta were 1. ITotal r:ai4;e of G. I. 4. *s "^ 70 . 166 2. Iksim Gr. I. ;i, =. Iij5.51 3. ntaad*rd.©BTlaUoR of Q. l. 4.*s= i.i.:'4 + .S'JSe since there *i re available na smo norma for achievement In spelll!<^« it V/8S neoossary either to establish suc-h norms, or to adopt soiofj other ^oce&ore r^h^ch vsould be equally Talid for obtain, ing; spellinci SkCf'S. It wsic the sug^restion of Lr. '"aymoriO frai.aen, of the Des Moinos ( Ia« } ;iaroaa of 'osearch, that tJie ^raue norms fai tJ«e 50^ lists of the tJuckirvjham extension of the Ayres Speillni; Ecalo bo convertoo -i ?ns, aiai t > 's Table I (Teachers* Ooiiege ficoid, iivowbor, 192u) b.i aaa^itea to detemise, from the pupils* scoros on these lists, the exact point of 50% soocess and failure* The first taslc Ir. this connection vr:.s to Ueolda apoti aga norms for the grnde*;^. Aft» s«ne search and communication soae fifty thousauii (5u,4&6} caaos were locatad, di3trii>ateu by half- year of age in half.year of gtaiie» In each case tho term '*year'* sl^^tified between nine mt.d three months, while "half- year" meant betv«en three ar.d nine months. Thus, in each c^se, the six year group incXoded nil impils betveen flvo years nine months and six years three months of age} while the six and one-half year ^oup included all piv^ils between six jfeare three months and six -6- years nine mmthe of &«;»• The nombor of nuplls its eacii half-year oV gr^de is as follows t Table H iiisirioatloTi of 50,456 "a|>iis, Grruios 1-b to 3-a« iy.clasive. ^^MO , Wf 1"^, -'-^ a-a ^-b ''^'^ M.^ ^a ».p i^^->. ^h, >-a 7-b 7-q U^^,ot^ jaa -s ^bS? ...^^^ Sdc^^^^v ^'^^A ^^>-H .>.>57 1:^7^ 3^o7 a^?u ai70 ;^>^ 2Vwo ^^4, ^o. v>f Cases 240S fi.l3u 50,49^^ . 7Jie aKj-Ji at:«s for liiilf-yBar of gratia obtainaa frors iha above cas<.j? . iiiiici o500 4535 3i? asing the meat. IncroraHj-.t of itgOt 1.0357, v.hich L Vie numijrtr of years r«qaired b^' the av<.*rajj'3 of tho 50,456 chlldran t^ co^solete one year of grade* the above norno ^^ere ex tended tos fable V A^Q norms fOT Chrades 9-12 inol. ■'xtenuotl by Use of Jfeai. Increraert of %e 3et\.een Ctr»-d«s. ^£2M 2 i^ .-U ia- A saiaraary of tho abovs d3ta Is b^V'' iw "able VI. ?flehitiiqae for Otjtair.in<: S;j^l,llT;g Arq Aftor having eEtablishGd. a^-o norras for the grades, the next atop vae %> evolvo (or adait ) a techniqoe of testing and scorLr^i which woald res-ilt Ir, fspellint< age. The followint^ is the orocess v.hlch t.as ased. GiviriK %l\B 7 , f>s , ts , The first teT> v;orde vere Sdlocted tram aach of the 5J% lists 1-., T. 7, X aid Z, and t^ the first eie^nt varus in list a b T.'ere added oriO vtord of appruxias&teiy equal dlffio^lt^ fron each of lists a and c. Ordlr&ry B;iJeiliE« (>^pdr v is distri- 'oated, tlie ;mpils lioing giver, detailed InstruotiOKS for platoiag at the top of the fihaet the follovlng Iteme of inforicationi name, grade (for aoroosss of identifteation)* date, and age In years ariA mouths (to the nearest fifteen days.) The fordr. verQ dictated cloari:/, each bolr^g retreated in a sentence or definition, so that there sh/uid be no aimacos- sary confusion of similar frords. The panlls v.roto the words In ink. ??aeh list was diot»trK> setxiratniy, the pupils being instroc. ted to place at the itesA of each list of ten veords the proifisr literal designatioa, ifuiieatlng the SOjK list f*om ^ifhich they were tajces. i^io dictation vas as raoid as -«as felt to be eonei8-> tent witli fairnoss to the [juoII, caro beln^ taken that the r^apils -9- shoaid not copy from one ai:jthQr. "ho pFipais v.bo oolleoted as soon na the diet ti jn was completed, h^i. c-.iLiQGtQdt the >awrE wore rnarked by the examiner. Aii voras act*»il:y mlBspellou or omitted vore marked by a check {w^, the namlior of saan ml«enallea or omitted rord« boisig (jlacQd lit tiia head of each list. Ai ■ words *ero con- Biderod oorreat unless manifestly incorrect or owittmi, erasores or char,g«s -;^ sor.sidpad errors If the words Trejrs clearly correct. Cqra)>tttinK; 3:?:dlvi<.V<&l t^pelling A^Tee In order tj dotenaine vhich isrs.6 the more eeonomlcal administratively, two methods of scoring the tests and of Computing the Individuai spelling fgos were assdj (i), that i2£ed wi th the Traboa-Eelley Can >lation ?est ?hcercisee for determining individual nerforasar.oe levels, and (2), the laetto- od proposed by Tan Tageaeii, «*klch ie based on th© former method. -10- For obtaining indlvidaal soorus on the TrauiM-Kelloy Cors'iletion T»to(i or, tho rovorso of oaoh Coraolet Lor. %8t blar.k* This shdot consists in a tablo of six oolmris, rosoeotiToly as follomt I* droui of "ontenooBj H, Av !43oros; 7 !Jld.poii.t 'tetv-esn Uroa>s; and 71, ProdaotB, Iv X 7. ?h« Porforrnanoo Level or Boore is then ob- tained by alvidir^; by 1' the sum of the /jroduots obtait.ad by raaiiiplvin^ eaoh Seorease in ?.av; Hoors by tb« oorrespocdl ng ini.u, fui In aroter to asi^ tills method In computing s;)nllin£ agfi, it rna neacssaiv to uoterniir.a the mio-points of ?i<5« boi*e«»?; tho graded!. Theer.- mid-noints, basud on the mean a^^'us ir. Tables 17 and 7, aret 5?able 711 'Ud^oointr. of At^o 15etwe Grade 12 Graues 1-2 2-3 3-4 4-5 5-S ;i-7 7-8 8-9 -r) 10-11 11-12 rirSr^ 1..4' i..4I 15,4. 1^.48 17.52 !0)en, to ootain sjielllif^, agos, a t/iblo vas oonstrueted b7)8od on thnt tt^ .)d with the (^ari;)letion Tost iSxeroisoB, In this -11- OH. '-: the "Groao of .ehtanttos" cola ^ 'je«cirn« ;. jwia^nn h-^- ■ '' List"; the ♦•Average liffioulty" colmm. becaac u ooiotm Age"; th« cola?«m of "Raw Looro" vvaa n '^heet. Ui , . iiy . "* ~~ V vi 5U5 Uet -.rvoj^s . .;;^vi T, »S»'T .•io-?ai„ &.1'6 9.52 r- il.^>5 ii.51 V 12 .-iS 11.57 .:>.5:j 13.89 1..4v a-b-3 ..x-i.?^ . Hi^^ , Totai 10 10 "'*"* In the above tabiR itea I Inclaaes th« letters given by AyrMi and Baojcinghan to the lists of v. or da from v-hioh those oset ■ ;, i . , aeie of ouplls at ths grade for wiicn 6»J/c is tiio avorajja score on the ll9t» Irsdioated In Itera I. (fee arables Vf a\.d V.) Iter, HI la the nitmhht of Kords «tlssi«ll«6 1» each list of ten, Itom 17 Is the differenuo between the number of erxors in efi ...» .wuaot of Itaas IV and 7« l*e*, deviation ti es mld»!JOint* l^e epellin^- age is obtal7.ed by dlvidi'^j tho sum of itens anuer VI by the total aaiount of deviation* which is aiv.&yg 10 (sinao the deviritions are it. errors, yOiitSn r^.^i from I to 10}* ^09, the rjapii*s speliir^g a^e Is found by dividing by ten the sura of the Proauct Sosi&r.ts ob^ineil by mttlti plying the mid->polnts in ai;':^ Setv«<2n grrtdes oy the asioant of deviation in errors betveen gr-*de lists of v.ards. 13io svtn of the Prodaai Uaments is divided by ten beo^ use ten is the stiro of tiie deviations and therefore' the number of cascst the q^otler.t is then the true weighted mann or av»rai^« The follovin^c exi:im<)le givjs a concrete iilostiatlon of the method usedt -13- fable Til r II lU :i V VI 50^ List J^y.: Mid-DQlnt ^ev» .35 • idoo'rt (iv«.y) B 9.- 6 0. 9.52 11,05 2 z 2i.Ui. V 12.09 3 1 11.57 il.57 % i-":-. b> 5 2 12.50 r;5. -0 U-,o9rformQRoe Levels Adantad X , o onoat'^ ; >elXli 414. Aftfir sonKi ©X£XJi Imentatlun vlth a nanbsr of oases it vtits foanti that BpelllBf: a^eB ooalci ba oomnated wi Vs ooneiderable facility by ada»tiiK-r Ver, vsgon^n's Tabio I a^ 's Tribl© II. Van 'vagat.en's "able I ie si ' ily a tabi .i nance Levels or ^cores 'wihiah -.uald correi -KiJid to rtny number of errors tram one to tei; raaae at anj? scnie sto;) frcKi or.e to fifteen on an eAuoaticmal scale, fince the table is oonstruoted on the basis of a River, number of errors at a giver scale step» oorrec- tlon mast be oaao for the nombrtr of errors Bade at l^s difficalt scale stO;>s. Tbie is dose by Siibtractir^ from the score obtained in the above a&m^er one-tentii the sum of the errors made at the Icjss difficult scale steps. Table tl is correctlo- ■ v lues to be added to the aooimt i,u u=. cv^i -tracted frj «...■. -..-.., - ar, the least diffioait scale Vjilao has tv^o or more errors* Since fai; "agenen's •«>»1«» I Is in terna of whole-number Sc il© sterns, it v-as f uond necessary to interpolat declsial :jart r - for grades, nvhen the iat'. - - -■■ --- - ru-j.'B. ;jf v!*i£s :>aroose an extension of ..^o VIS for the i^urjoae of this stody, iping interpolated -15- Table IX Excerpt from Yan "agenan's table I, for Coraputing Merm Indivirtual Tcorea in idacational 'Jcales , (Ida ted to Compate -oelling Ai^cs. Scale Staos — — — — ikrors 9 10 11 12 13 14 15 X 11.5 12.5 13.5 14.5 13.5 17.5 16.6 2 10.5 11.6 12.6 13.6 14.6 15,6 3 10.2 a.2 U.2 13.2 14.2 15t2 x^.z 4 «.6 lu.S 11.8 12.8 1-3,8 14.8 15.5 5 9.5 10.5 11.5 12.5 15.5 14.5 6 iO.2 11. ii 12. £ ;3.2 14,2 15.2 7 9.0 10.0 11,0 12.0 13,0 14.0 15.0 8 8.8 9.8 10.8 11.8 12.8 13.8 14,8 9 _.8.6 9.6 .10,6 11.6 12.6 1^.6 14.6 ™^.^ ,9»5 Jgs^ 11.5 J^h^ IS. 5 Jd&L. Interpolation can be made on the above table by adding to each V. \7. Value the correction necessary, the correction in each case being the difference between the V. T.'. Scale Ctep and the E»an Age used in its place. iHias the following table «a£ obtained* -IS- Table X TablQ of Interpolations for GomaatiKi,' Bpelling Ages Adapted from Vmr, v,'agenen*s Table I Grade 4 i: 6 . 7 B 9 10 Mean Aee 9.96 ii.u5 xr..09 12.90 13.69 14.95 15.96 "Errors 1 12. 4S ia.05 14.59 15.40 16.39 17.43 ie.4S 2 11.5b lil.cif. i:>.69 14.50 15.49 16.3b 17.56 il.lb iii.^S, 12,29 16.13 17.16 4 , 10.76 ll.oS 12.8; 13.70 14.6- 16. 7£. 16.76 5 10.46 11.55 lii.5v 13.40 14.39 ],5.45 i6.46 6 10.15 11.25 L':.29 13.10 14.09 15.13 16.15 7 9.yu 11.05 12.09 12.9U 13.69 14.93 15.96 8 9.76 10.85 11.89 12.70 13.69 14.73 15.76 9 9.56 10.65 U.69 12.50 13.49 ,A,9.,.. „-. 5,»i^-iO,a55J1.^2, ,A.^iii,k2aat .14^43 15.45 Var. Wagenen's Table II, rearranged, is as foliowe: Table XI Table of Corrections to Scores on Elducational Scales for errors oi TiOv^est values in Fcale irr ors 9 8 7 o ""E 4 3 2 Ada to Amount to be " ubtr acte d 2.1 1 t5__l.RQ_^.X..— «5_ -•? -^ .,,_,:l^ ^ ©lis table should be readt viisn the lo^'est v' lue (list of •words) has 9 errors, add 2.1 to tho amount to be subtracted (from value obtairied from Table X); vtoen it has 8 errors, add 1.3 to the amount to be subtracted, etc. -17- By usiag the tvo table above (Tables X ami XI), the process of obtaining siJelling ages was reuderecl extremely simple* Steps ir^ Obtaining Sp . e^inK Age Tj8i ,nK Van , "^^agenen's Table i., adapted , and gable , IJ, !rhe entire prooess was reduced to a maximum uf fire- a rainimom of four - simple steps. 1. Ada the number of errors rnsde above the last list of words attempted. 2» Diviae this sura by ten. 3. Ii: case two or moi-e errors ai'e made on the easiest list attetopted, find in Table XI the amount to be adaed to the quotient obtained in 2* 4. Find in Table X the interpolated Van 'Vagenen 7alue corresi>ondir,g to the number of errors made on the last (most difficult) list of v ords attempted. 5. Subtract from the interpolated ?. V/, Value obtained in 4 either the quotient obtained in 2, or the sum obtained in 3, THE SUM. IE TH3 SP6a[.LIl«J A{}£. -18- Tii exemplify th:^ method usud, tv.o cases will be cited: (l), that of a pupil v.ho inade no errors on the ep-siest list of v.'ords ; ai.d (2), that of a japil vlio made two or moreerrors oq the easiest list attoiriptud. Exainple 1 List fitean A^e Errors R 9.9u T 11.05 2 V 12.09 3 X 12.90 5 z i3.se 8 16 1.8 a-b-c 14. 9E lu 10 Ir ExaiTiple 1, tiie pupil raatie 18 errors above the last list attempted. One-tenth of 18 is 1.8. Loolting for 14.93 (the mean age for the last list attempted}, in the Mean Age colujnn at tha top of iTable X and foilov.'ing ^vn the c olaan until 0;?posite 10 (the nisnber of errors made in the last list attempted) in the Error c^iMiim, gives us tha interpolated V. '\7. V^lue, 14.43. ?ab- tracting from lle 2» y.cj ,i_i,__ . . list attesipted, On»>testh of 20 iE 2»0» fat t«« ^aoll ?^ 2 errors or; t. !« ttaai^st list attempted. of •1 to toe ad-oui to tHe e-mount ta Mdisg th«8a gtvcs a,l. Laaklr^ fOi 14.':'., lAst list attt«!tpt9ii) iB the mm\ Age oolomu^ -. ^ X n:-t. frsllowir^: Sm^.n wttii on/KWite 10 fthn n*^">nr o 15 isffit list Of vAwdf. otiftw> . OB ths ralae i4«4i>. r«&tri«tiag from U.-i."^ t . ., givoi 12*33* tiif? BjeiliKg iHj« af ti«B yjipii. laa ^n^AJt^tf sH9^i»n^^ i^oW.^.^. B;^ ti^ ttSQ of thltB adaptatian of Var. >>ai;r:i^R*s Table I Spellixii; itae-s WW® comrmted for "j"*^ ^ .,.«tii tHr<>«igh the at ' ' 2o8t of mant&i ability* Those siKtlliRK; agf^e iHir« ooTtverted i&td Sgelllsg Hoatieate Isy dividing 9<*eii by ti^e chraniloir riapil at t^)«» tins of takint? lJfi«) test* with ^le follow >^ut^ 4^«ii«ti,tss -20- 1. Total Bajage of Spelllniii Quotients ... 61 - 137 2. Mean Spelling Quotient 98.01 3. Standard Iteviation of Spelling Q'a... 12,86 _ .4876 Cornoaris m ^ 0. I. Q. *a and Sp . Q.*b . A comparison of the results may be given briefly. Nomber of Cases 182 Kanges Bg. G. I. Q.= 70 - 166 Hg. Sp. q,. - 61 - 137 Standard S. ^' G.I.Qf 1^.94 ± .5938 £. D.gp.^^ ^ ^^^^^ ^ ^^^^ Standard DeYiati,on Pi f fere 71,06 S.D.p . „ - r.I>. = 3.08 Ifeans K. . = 105.51 M. = 98.01 ^•I.Q. Sp.Q. Maar Difference M.^ - M. — 7-. 50 OorreJAion betTJeer. Geno^s^L Mental Ability And Spelling Ability Apply-^ng the Bearson product-moment formula for computing -21- the oorrelatiJu coefficient to the two series of 182 quotients resulted in a correlation coefficient oi+»7515 jt.0218« Significance of, % h.e > . Correlation A positive correlation so high as .TS. x^lth so lov. a ftrobahle Error as .02, based upon n arly 200 cases, and with a standard deviation difference of only three points (3,08}, is very highly significant indeed* The low Probable iilrror and the slight difference between the T^tandard Dev Ja ti ois mean that the correlation itself is valid. IDhe high degree of correlation here shown indicates a very close, positive relationship between general mental ability and ability tu sj>ell. Sie fact of such a close relationship should be taloen into account in teaching practise, aisL no teacher should rest content until the pupi]*iF ' aoconiplishment in spelling closely approximates his niental aocom> plishmentt that is, imtil his Accomplishment Quotient for spelling (Intelligence Quotient divided by Spelling Quotient) aporoximates 100. Until this is the case, the pupil is not loarning to spell as well as he is capable of learning. For the inevitable corrol^y of low accomplishment quotients is inade- quate teaching. ~Z2- Farther Uorrelatijii. Between S.I.d.*s and So.Q. *s In order tj carry the investigation a littie faj-ther an atteraut vas maiie to measarR the increase, if any, in the correl- ation bott.'ecn the general mental ability and the soelling ability of a graduating clasB. Of this class, 34 pupils vere given a secoud spelliiig test. The F-pelling Quotiests were coniijuted, and the correlations botwesn CJ.I.Q. and the Spelling iuotientK de- rived from the tvo spelling tests 7;ore caicalated. It was found that the correlation on the first set of r;p, ij, 's vjas .67, while that on the second set of If). Q. 's was .S9, the latter oeing an increase of .02 over the former. The results are as follows j Number of Gases = 54 ;es Hg. = 70 - 141 -ig. = 70-116 Vg. = 70 - 130 G.I.Q. Sp.q; Sp.Q^ Standard Ijeviatioits n.J)._ ^ = 16.18+1.87 S.D.^ .,1-12.19+1.40 Ci^ 2=12.26^.41 S.D, — S.D. ,= 3.99 S.D. — S.D. G.I.q. Sjj.a.l G.I.Q. To. Sp.ti 2 Sp.Q. «-G, .1.^. -109.20 ^•G. ,I.Q- - ^-Sp.Q. ,1=11.0 L^^j^. ^Sp.^.2=58.7 •Sn.Q.2=10.50 Correlations betvjeen Geaeral Lleataj, Ability and Spelling Ability r, - r,= .02 1 a '2he iacreasa in correlation is proably due to the fact that the class lisas stadyia^^ lists of words in vbich were included sobs of the ivords also incladed in the Buclcingham-Ayres lists. !!!h@ text being used «as Peao'sou and Suzzalo*s '^Essentials of C pel- ling." Undoubtedly the increase in the amount of correlation wooid have been greater, had it not been for the unfaTorablo conditions under iidiich the tests were given the second tisrie. Pressure of •erorlc caused the givir^g of the x ists to be delayed until close to the graduation period (tlure* mod >- iio\: the date of the first teste). Che pupil? were of course exyitcu and nervous, their attention and concentration dissipated. Under noi-: j ooKditions the correlation would therefore pirobably have been increosed considerably more than it actually was. Correlations ie^ween S.I.Q . , Aritimetic. aaotler.ts . g jellii. -, ^aotients , a.rd Conpletion Q,aQtients . Another short study, not es.ooci'-illy oertiKent perhaps to this satdy, out of allied interest, was made to determive the difference aetv.een correlations oetweon general mental ability and soellinr. aoility, gener a mental ability and ability to uer- forra in the Bslley-Trabue Completion Test lixercise alpha, and Senerai mental ability aiA ability in arithmetic as measured by the Woody-lfcCall mixed Pundaraentals test. ^e following- figures give the facts discovtjred* ijomber of C^ses 77 r.anKes Hg. =^ 62 -155 Rg. = 35 - 138 Compl.Q Arith.Q. Standard Deviations S.D. =18.4a-*-1.004 ' S.D,„ „ 15.197:^.826 G.I.Q. - So. Q. - S.Da , ,= 16.5(>+.903 S.D., . ^^ ^ 14.257^.775 Comol.Q. - ATith.Q. - £ tandard Deviation Differences S.D.^ -.F.D.^ ,=-3.263 S.D.^ r-S.D._ , =1.406 S.D. — S. D. =1.857 S, D. — S. D. - .840 G.I Q. CJom,)i. Q.. Sp.. Q. Arith.... 3.D. — S. D. =4.203 S. D. - E. D. = 2.346 G. I.Q. Arith.a. Compl. Q. Arith. Q. -25- ^ans M. =109.13 M. =101. 42 G.I.Q. Sp. Q. M. =105.13 M., .^. ^, =93.65 Ooraple.Q. Aritti.Q. Mean Di f ferenees M. — -.U =7.71 :i. — :i. = 3.71 G.r.Q. Sp. Q.i Sp. Q. Compi. Q. ^•S. I.Q.- "'•Oompl.f.^-'^" ^-Sp. Q.--^-Arith. Q.= ^'^ II.G.I.Q. — :i. =15.48 I,!. -M. ^11.48 Arith Q. Comol.Q. Ar.th. 0.. Gorrelation Coefficients 'G. I.Q. - G,).r^-«113i-°26 r 5^ i.Q..,omnl.Q.= +.8417+.022 rG.I.Q.-^ritir.i^020J:.063 The abovo data present facts of considerable signifiCince. All three of the correlations are extremely high, witla extremely low Probable .irrors. And yet the :,feaji differences are so great as to seem to indicate, if they stood alone, that there vas no great roli tionshi^:! aetv.eevi the fanctions iv.volved in the four types of activity hero called for. This is, of cowse, in viev; of the correlations obtaii.ed, a clear case of inadequate teachivg. Especially so is this true in the case of arithmetic. That all the oapils of the group should be so far below their mental acoom- plishraent in their arxthmetioal achievemeit, aii^ht be explicable ■26- on the grounds that the abilities iy.volved aro not related, ;3at the hi^h correlation shown - much higher even than in the case of Spellir,g or Comolstion >taotients - obviates this bolief. It is sim^ily a case v.heroin the iustructiju is at faalt, co grievoasly at faalt that not oven the brightest ouoils in the grjap ar« get- ting therefrom nearly ^ 1 of vahat should be exnected of them. It is evident that the jupils are learning in direct ratio to their ability - but the toDrtally 15-year-old is or.iy about 12 years old in aritiunetic. 1 ability, vhile the mentally 1)- year-old is only about 8 years old in terms of aritiunetical ao^oraolishmeiit. In the situation here deolcted is alearly represented the need for a close study of instructional methods, in all of the subjects involved, but more soecifically in arithmetic and Boelling, A. study of the marlcs recejived oy these 77 ouoils shows that approximately one- third (31%) are ohroi-ic failures in s.)oliing, while over one-half (53%) consister.tiy fail in arithmetic. It is the puroose of such studies as this to ooint out the defects in the instructional methods. It is the duty of the school administrator to determine just wherein instruction is at fault: whether the fault lies with the text-book, the te . ;her, or the phj^Blcal plant of the school. Hear A^-os of 50,456 Mi>iis. Crrades 1-8 UOx pf ^as s Grrade :fear. Age Butte 1914 Des .'.ioines 'Ta^ja 1921 1921 "jslcford 15-16 ■^t. Paul 1917 Total 1 - n i.24 8-8 Ifx? 133 709 1410 4687 1 - A 7.04 3::8 867 57 1851 3516 2-3 7.47 5,Q§ 1290 84 523 1284 3689 2 - A 8.12 ^90 739 55 1696 3289 3 - 3 5.60 5o6 1251 33 510 1291 3641 3 - A 9.35 Zii7 608 90 1528 3214 4-3 9.73 444 1140 77 505 1191 3357 4 - A 10.18 346 822 50 416 1239 2873 5 - B 10.69 443 114^; 95 562 1?19 3467 5 - A 11.41 346 78'^ 50 3^4 1321 2870 o - 3 11.81 586 lv;5& 90 478 1155 3170 5 - A 12.36 3;il 661 57 313 1286 2648 7 - 3 12.78 3:^8 l^oj 78 396 1014 2906 13.01 213 702 38 320 1321 2594 8-3 13.66 209 921 59 341 675 2405 14.12 159 611 50 258 1052 2130 Total 6232 15.434 ijy6 6928 ZO. 766 50^ 456 Uean Age per jji-ade:- ffi-ade, 1 2 3 4 5 6 7 8 Age 11.05 12. 09 12. 91 13.89 S!id- 7.22 6.435 9 '.515 10> ,505 11.57 i,:.395 iSean Increnent 1.0357 Ifi at of Be fere noes 1. iJutte, ilontana, Survey CJommissioR F;e,30rt, 1914} -ioard of i^ohool Trustees, Butte, -Montana. 2. Ifepa, California, ^Kshool building Hurvey, 1921» University of California, lienartment of Education, Suraaa of "esearch in .^duoation: Study number 2 3. l^ockford, Illinois, Feview of Public fichools, 1915 -1916» OSae 3oard of Sduoation, Eockford, Illinois. 4. St. Paul, Hinr.esota, Harvey 'vioaaiisaion i;eport, 1915: City Oounoil, '^t. Paul, Llinnesota. 5. Franzen, Haymond, "She -^oomplishment Quotient," Teachers College T;ecord, November, 1920: aureau o:? Publications, Teashei's College, *-^olumbia University, Hew York. 6. HiBlley, Trumari Lee, "A ilethod of ^cale Construction," n«hool and Tociety, Tol, lY, (pa^-es 34 - 37, 71 )j Science Press, Qanason^on^Hudson, H. T. 7. Keiley, Truman Lee, "Individual Testing with Completion T«8t Sxercises," i-eachers Golleiie Record, September, 1918: Bureau of Publicatiojis, 'i^eachers College, Columbia University, Hev.' 7or&. ^1 Division, 0!3>)aflnK (Calif.) ^blio I'choola, Boreaa of ""esearoh i:^' .". Zg, 7irgil :s. Dj-OJksoc,* ?4rwtor. 9. Var. -sagenen, Uarvln J«, "A "T^olt? far --^ompatlrii; Moark i,v,4i'vldtt.-jl reores in ^ducat I onai Posies,'* Terrohors ooll«^:tt K»cord, 30¥'*ia^r I920» isar. Bib** ?. C, Rol. ftsiT., "?. T. i 665283 a. ,-.// UNIVERSITY OF CALIFORNIA UBRARY LANGE LIBRARY OI tDUCATION UNIVERSITY OF CAl.1FORN:a BERKELEY. CALIFORNIA.