Post on 08-Mar-2023
AN EXPERII1:Bl'NT
WITH
DIAGNOSTIC Am> RE:M3DIAL WOJUC
Ilr
DllOll1AI.S
BJ llARL S. GRIEWSKl, B ,Ail
A the.ta *ubmitie4 to 'he JaQQlty .t \he Ora4uat. Sqhool, Xa:rqu."". ValTer.itT. til
Partlal Jul'111men\ 01 thet R.quh'.~ ment to*, the Detar •• ot JIa.'el'
ot E4uoatlluh
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KILWA't:JJClm, WISC{)BSI'J
Ap~11. 191'
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ACkno.ledaemeUt
Due acknowledgement 1, here siTen to'll' the
c1irectlon of thi. \heai, to Prot ••• or J'o)ul P.
T"eaoy; Depar tment of Eduoation; lIarquette Uni.
Tersity, Milwauk.~. W1SCODStD.
This study in d1agnost, and remedia1 teach.
ing 'nelooi-.1s walt cortducted with the aPllro'Y81
S7~,8'"
ot Aseiatant Superintendent. Paul B. Clemena anel
Dr. w. w. Thet:len of the til..-auke. PUblic School;
the O<,opera 'UO~'l of the principal a 01 two f.lj11ld,e
aohoola of the q1t:rJ and the participation of the
aeTenth and eighth grade pupil. of the two aohoole.
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TI'1'LEPAGE to .. to ..
ACIQTOVILEDGEMEN'l:' •
TABLE OF OONTENTS
1:A134E 01 QOJ'!'lU1TS
. .. . .. . !II -t .. ~ it . .. . . . .. it • • •• • • • .. , j , j • . .. " . . ,. • • • • • to . j . .. .. • : . ,4i • " "
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Ill.
LIST Oll' TABLES.. .. .. II •• II II /I .. i • 11 .~ • .. , . ' V 1}
LIst OF' INDIVIDUAL REOOIUlS ,AND T.A1IDLA'1'IONa. , "to . t VI.
LIST OF GRAPHS.. ,lI' " •• .I., '. •• i • .. • .. t i' • VII.
SEO'1'iPN I.. It .. • • Ii • " • .. .. • • •• " • .• ••
1.e Introduotion and ObJect.ive, i , ••• i •• . .,
2,1 Current Thought In Educe. tlona1 Dtagnoa,.. * 3,. Pl-evlou8 InT'8tt8a~h. , • t .• II •• " "
SROTIO. U: i Dtagtto8tlc ActiTt ty ~ , ,. ,'tII .. ,; ~ . 1. Soope and Proc,dureot ne8la ... lI' ..... 2. Rel1ab1U. ty ot te.t \18e and ProgJ'Qm
s. 4. 5.
6.
7. S. 9.
Activity_ • ~ ..... ,. .' . ~ '\' ... .. Ba.ia tor Anal".1. of Teet :ReBulta
Pre U.m1na 17 , statemon'''; • .. .• • .. " •• Amt.lya1. or D1ff10ult1e. " • , oj ' . ti ,. •• •
TABU X. Table . Qt lJitttcul,tl freqUen01 • • ,. ••
TAl3LE U;. summar., ~f Detailed A~~781' ot Dlf.
ficultiea, , ;; , t ... ~ •••• , •
General An.lyai8 ot Error, • • • , • .. .. • Specltic D'tttou1"~'. ;; ~ .. • .. • .. , • • Test ~lts18 of: Eri""~
~lanl,'Uon of Jlall'ldN" ...... , ,. • Sampl, Natk ... TeBt.. .• • " • ~ \I , , ..
SECTIO)J III. Rem.dial Program. " • ;; •• i it "
1. Jrajor Rem'd.ial Attacks , ;; . ' • " ;; • .. .. • 2. Student t e RemecAtal W~~ltbook.. • • • it •
3. Teaeher Helps and IDstructl'Ol1$ • , •• If •
" OOPl of Wo~k'book in ~Gu.al. .t , • • • .. :aea.lng .",4 Wrl"l'lS D.ota1,. , .. ,. •• Deoimal. and )lrae'tonlJ t j , • • • " • ,. 41
Addl tien of Deoimal.;; i '. • • " • Ii • •
Subtraotion of neoba18., • " If 110 • , •
1m~'1pU.c.at,len of Declmal ....... .- • 1'>1. visionot Deol-.lth • • \I • • •• .. 'iI
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1 2 4 6
a 9
11
1:5 16
1'1
21 22 27
28 IQ
32 33 36 3' 39
'0 41 42 •• 45 46
XII.
SECTION IV' D1agnOiJt10-:iem.di.1.'i"es' nata • ~ • 1 ~'l'abula t1.ns and. Graphs. In~):'od.uc~lon • • • 2~. l:ncUv1dual RecOrdS u4- (Jl'aphs
J:ndtvldua.l 'Recor4 ,J 'Twellt,.-s,.,.nth st. Individual Record. 'B Wisoonsln ATen\te •
7.:a,. Graph I. 1ea~ Co.pa"1'C)J~. " • • Indh"t4\la1 Record. 'A fWen"1-"Venth s.t. 1.d.lvf.dll&1 Reoo'l"d '1A .'.6qnein 'Avenue • 'A. <:J",pb 11.1'8:.' Ofmpe.l"i.Cfn. it _ •
IntU.i4ual 'R.ool'd. 8:1 'Tjent7 ... ~.'f.nth a,~ Ind~v'4ual ReeoX'd. 1:15 Wlee.onsln AveB'" 41
. 8). al'llph III ~ '.t •• , ¢lompar'aop . _ ; . ; I»d1 "i4ual a,oord. SA Tw.ntY ..... vonth at ~ lI141v1clua.l. 'Reccl'd. SA wi.eon.~n · Atenu, ~
8A.Q .... ph. IV- TeBt Comparllon_ II • iI
e.mpOeilte SoO.;r. h"n'\-y-'."'nth S\~ ~. Oomposi'. Soore Wl"t)nsUl Aven'!l:',.' • it ~
Oompo,lI.1 'e Gra;ph V .Com~;r:l.on. • _ ; All Grade Twenty.s'''en1t;h $\.
Graph Vi. Te •• Comp .. ri.orh , Ii • ~ I. Graphlnte,pret .. 't.ion &rut $~" . " " " ~
SBO'1'leil VII C.... S\u4.,. ii' .. •• .. II • .. . ' " "
li at_v of a.,..ntl J?alr .. 06~pa!'i~ot.\ .•• i • . ,
'1'QIJj Xll ,1i Ta)1,a.le.t~'.Jl of ",tohlns., eA .• TAllLi IV. ot .. bula'UOJl ,t · Jfatchina. 8D , 't.ABI..1'i V. ~ab\lUto1.fm otvatohl ••• 'A •• TABlJil V:J:. Ta)Ula\1CtJ'1 ,of lfatClhlns;; '13 i
'tABLE VII'. S\UIIIIl.$.J7 total Ali Sect.$"onl_, Graph VII. PrO$l" .••• -Go.pa.tl'on ,I. ~
l.Bp.ctal S'~4¥ 8e"',nt1.-'. 1. v. oa.... ,.. .. , TAltLB VIIJ.: i 'rab'ul"'~OBt S."el1t1 .. ·tlye Ca.... ~ , . , 1/ .. ' '. • II " it • , "
'.U,,;x.:m IX.S\UJJQLiQ' Se.entf.t~T. ea ••• 1/
'tABIJD X. Sta\l.t~o. S."en1l,..th'. Ca •••• S\Ulllllil:1'f and Sonelu.ion.. ~ • it ij • to • •
011.Lph 'flit!" Value Co~parl.611 • « ;, ~
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SECtION Vi. s'~tion '0, 'th4uai .... " • i .iI " •
. 1. Theal. Llml\e,iU,oilu. • • It .i " • • • i , • " e. SlImIJII.i'y ap4 00nolu840n,. • •• • • " i , •
S'QJDInI.."" •• Ii . ' ,. Ii .• • • • ., t . , , • 00no1 •• 10n8 • • • • • _ • • ,. ill. , ,
'.Bt'b11~gl',apb3' It • " " • • • _ • . ' • I! • .. •
'1' "lit" •• . • • io • .• • • • • • • • • , ; ,
llIag •• 1.'.8 .' . t • t ,; ~ • • • • •• .. ~.
48 49 _1 52 54 155 5'1 ~$ 15, ~O 6l. 62 63 64 65 86 8'1
68 69
V2 73 '11 7'7 '1& $0 82 &$ 84
8'7 89 90 92 94
96 96 tv,
I' 99 102 102 l(;)V
SJC,?IO' VII. Appen~(iXi It ;0 • ~ • .~ " It. • • •• If lQ$ 1.. Sup), .• Tea'.. ij" • , , • • • • • • " • t 10' 2. '1'1.\ Soore She.''-" 1/ II .". II •• • t • • . 111,
The::,h .s u l)'Cl l ement 115 ~ - .
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IV.
LIS'!' OF TABLES
hge
1, Table of DiffioultY' Fr.quency Detailed Analyst" ' •••• iIi........... 17
Ii. Summary of De~ail$4 Analysis of Difficulti es " Major Dl"'18i~fts ••• e. ... 21
III" TAbulation ot Matching or seventy P"lrst S .. A Seotl.OIl ' ••• I •• iii •• ~, " , • • • ?6
IV. 'T"bula1;ion of ifatehlnsof Seventy Pairs, 8 ... B s ection " •• , •••• iii .. ........ ' '7
V. Te.bule.ttGn of Matohing of Seventy Fairs, ? ."A Seotion ............. .,. 78
VI. Tabulation of .tohtng of SeYen~1 Paj.rs, 7'.'B Section ." ••• '" .. .. ....... '. ' 80
VII. Tabulation of 1~.tc:hlng of Sey,en',. Pail's, All Section. SlIJIIIM'l7 •• , ... ". 82
VItI. Tabulation for Sp.olal st~dy Thre. Te~ts, All Sections ., •• ~ •• •••• i.t. 87
IX. Speoial study Summary Three ~a9ts All Sect!l.ons l!.,"".: •• li!" •••• ' ••• ,i • It • • 89
X. Speolal study Three Teat S"atlat!1'ce.l SU!IlJnI),ry by Grades •••• if ••• <. . .. . .. . . . . 90
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LIst OF INDIVIDUAL RECORDS
AND TABULATIONS
Pag.
1. 'rwentY .... ·.Tenth Stl',.t SOhool 7.B 01as8 Ii'. 51
2. W1scon8lfl Avenue School '.B 01a"8' .. . ..... "., ~2,
S. Tw.ntY"8ev~ilth Street Sch~ol 'I.A 01a88 ., ', <t 56
4. Wl '8Qonsin ATenue School 7 .. 11. 01aell' ......... .. . fS'
~. '!t'wenty-eeventh Street Sohool 8 ... :8 elaee ••• 59
th Wisoonsin Avenue School 8 .. :8 Claet; ........ II" 60
7. Twenty-sevent.h Streetl SenoolS ... A Class .. p .62
8 .. Wisconsin AvenUE! SchQol 8 ... 1. Cltuts ... ~., ,, .... 6S
9. Twenty-seventh s treet School All 01a ••
Compos! t e ... ... . ~ ........ . ... ,. it . • ,.ii .......... 65
10. Wisoonsin Avenall SQh~ol All Clas8
6omp0l!"t ~e /I ...... II .... " •• " . ' ••• ., " It it • ., .... 0) ". ee
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VI1.
V:UI.
LIST 0' GRkPBS
'1'~st COJlparleon, Twen1,.,.eTsn\h. Wis~(ilnsl~ Aven\le,. 7 .... :5 CIa!! •• Diagnoa,ttQ anci Remedia! Ch.clfl BOGres ••••••••• , ••• ~ •••••••••• ~~
Test Comparison., ·.rw.mty.Ii&T$n~h ... WisQOn$1h Avenue. ",.A Gla"a. Diagnost,ie and l1emed1al Cha9k Booroe •• t~.~, ••••• t."'.".f".'
Tes\O(:nnparlQon. 'T.en~y.j."'.n'h .. W;lSQonsin Avenu,o. 8;jj,B Ola.aa. D~ag1'l • .,t~e ~u14 Remedial Check Scores .'~t,* ••• • ••••• • t'i"-'~_'
Test CCllTt;pa):'lson, Twenty"'$e"err~h ... Wlsoonldn~-ven~e. 8-AOJ.al •• Dl.a.gpoGti~ and Remedial Oh~ek Sco,es ' ~' • • ~' •• i"'."' . '.'.' •• ~
'1'estOOmpaf1sol1; 1'wenty ••• .,enth. 'iflS(tQus1n Avenu,e, Co.posi'.;: Dle,gnost1cand Remec1ia,l Cheek Seowes ." ...... . ... II! •• 'I!., ·~t: ••• : •••• •
t eet C~miatlaon, tw.~t7·&e~en$h St:r •• ~ SobOQ.l ., ~11 q.las.e •• !>iEloenQ$thl s,nd RPledlal Ohe~k Scoree •• ,~.j~._.W' ••••• i.'.j •• '.
'l"e,,,,t Coxnparisc)!\. i'went.y.sev6J'}\h. Whoonllln A~enue a 1>rQ·gI'8a8'" .e'IllP'orta.Q1'l t$1' Seyent,. hh" tJiagnoetic a.nd Remedial. check aoo~ ••••••••••••••••• i.4t ••• *t~,
Value eQmp~r1eOll, 'tw'nty ..... ., .. tb street. s Chool" SplH>lill study. Se.ven~y-t1ve ea".' t Three t·,."., SUrvel, Dia~nQ.tlc, and Remed!J1l GheQk ScOre. • ... f •••• 41 ... ,u ••••••
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VII.
Fage
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68
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64
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SECTION %.
Pl'el1mtJ1t.17 Stuq
1" lntX'E)duQ\l()ft a.nd Ob"~oUTe
2. Cut-rent 'i'h:ought ill Educa~!.Q1'le.l
:P~8;p •• h
~. Prev!llltus Invelit!gaU.I,)tl
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Introduction
'.018 object ~t thl.s investigation 'a to locate more ape'"
011'1c&11y, by diagnosis, thoa' factors in decimals which bear
causal relation to the progress 1n learning of the individual
.r gl"OllPJ t. preparQ 'a remedial '.o~rse of .tud.y 1n de01mals
'b.se4 \ipon the tlnc1!ngoof the dlagnol1e' and to effect by
analyst, of individual errOr8 and remedial ~eachll18. a. stuc:l1
of an .. d.equat. prooedure, and lit learning Or understanding of
the tunelalnentals 0:£ declmal.. Upon thi. 8tUdy is to be de~
'ermined, as aocuratelY' as po081ble, tile Talue ot d1agnosis
and remedial teaohing 1n 4ec1mal.~
In recent years more and mc!!"e J.'ecognltion 1s 'be1nggi ... en
to the tact that the teacher. 1f her ln8'truQtion i8 to be
really eftecUve, illU8t supplement her cla80 teaching by a
more speoific treatmen\ of individual pttpila. To do this In
telltsentl.,-, the teacher requirea detaU.ad information as to
the etreJ)gths and weaknesse:s 01 the indt"'~dual or olaSI. The
,so-oalled diagnoetlc proo,dure .111 gl .... 8 her such information.
Thtoup d1asnostto proQedure the teaoher will r,oognize
.xllt~n8 8k1,11s, <Uffiqult1e., and weaknosses the ohi14 has
4eY810pe4, It 18 upon such knQwledge that .ttecttve correo.
'U..,e m,th()d. are oaused to t~ot1on,. Thit intOl'J.l&tton 8,"e .. '-11
help. the teacher itl her pte.,.enttTe work whioh 1, more valu
able in many re.pects than the ,u.b.equent ,oorreotlye work.
The '.aohe, !nUB' lm ... of the tctndeno1e. tewal"d ert-or aDd the.
pittalls to avoid. and ot the habits to deyo10p in order to ~ .
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become a more effective t eacher.
Various r esearch studies into t he genera l field of
arithmet19 and i nto somo specifio branches have been made.
Leo J. Brueckner, Professor of Elementary Educa tion, Unive~-
sHy of Minnesota; G. T. Buswell, Professor of Element a ry
Psychology, School of ]ldl)"ca tion, University Of Chicago; and
c. E. Green, Director of Research, Denver Public SOhools are
among the leadera of present da.y resea.rch in t he field of
diagnosis and remedial teaching in deciools t - It i s upon
Brueckner's study in this field and with t he use of his test
and tabulation of errora in decimals that the prelimina ry
activity in diagnosis in t h is experiment was based. A r eme ..
dial and ac tiv.ity progr am, a step beyond Brueckner ' s diag-
noeis study a.nd analysis is, however, t he major a.ctiv-ity of
this experiment and t he basis for conclusions regarding t he
apparent v~lue of diagnosis and remedial study i n decimals .
Remedial work in this study was undertaken as definite
program, :carried on wi th a. purpose of giving the class,
small group, or individua l remedial instruction during the
regular class period . An a ttempt was de with the a i d of
a wo rkbook, des i gned for the purpose, to replace aimless
nd mi scellaneous drills by
to the needs of the pupil .
sys tematic procedur~ directed
A complete diagnosis, analysis, and the remedial progr am ,
wi th an experimental group i s the theme of this projeot. The.
check and comparison of results wi th a control group 1s the ~
basis fo~ the conclusions on the apparent value of diagnosis
and remedia l work in decimals.
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CUl"rent~hought tn Educ3.tional Diagnosis
The gl'oV11ng need for diagnQsIs is l'eceiv1ng more and
more reoogn1 'Uon daily . Heili'etotore t only the ~la.dJuated,
tll&mantallyd.ef~c1ent . the physically handicapped. and t be
aoeta.l deltnqnant were the ob,J ects Qf dlagnostiQ trea t men·t,
Throughaut the na. tion everywhere the handicapped l'eo~ive
attention,. Today the program 01 d1a.gnoois and r~medlal
study has been enlarged so as to inolude not only tho~e hera.
toto"t trea ted but al so the chlld wb.o 3u!ters no aetnill phy
"le.a l 0:1:' menb.l ha,ndiOo.p but who tor some rea-Bon is per:f'o'lt'l'll"
' tie beloW' the level of non.na.l exp"e~ancy.·
ft]Jd.u~e:. tf()nal d:i.e.gnos.ie :'rQb.tee to the t eohniques by
which one dieoovara and e~.lu~tes bothatrengtha and w6a,k ..
n8aaes of the individus,l as a basis for roqre ettectlV'e gu14-
ance . Diagnosis 113 a. log ical pl"oces$ baaed ,t)n a ccma1d.cra.
iion of v.ll the available data conoerning a particular in"
dividual or group cf indfv1dtUlls.'l'he ana,lysis ot these data
and. their interpretation in the light Qf knowledge gained
from pas t eXperienoe enables the diagnostioian to IJuggest
naoessar;y doYelopmenial or remedia l meaaures. Dtagnoels lea.d.
to vrognoa it el that ie, to the predlct1~n of' the probable out
oome of the cond1tlQn.-l
1. The liattonal SooietY' tcu' t,he Study of Education, ~4th . bat Book, Introduotlon~ P. 2.
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In l1ke menner as a physician needs an aec~lated
hj.stOl·Y of h is pat1en.tts a.ilments, physica l and ment al so too
t he teacher nn.1St have "s. syate:rr..a. tie knowledge of the types of
d,fff1cul tics ::tnd their symptoms in ord,e,t to rna.ke a T3.11d
dia.gI1(>sill fit the pupi ls f a ilure to grow in dealretl ways a t
e. aatiefttctory t'a.te."2
2. lo,S-, p. '1
Knowladge of th(i mans- s ld.edfunot1onEl of the human ani ...
m."!,l is impo:r1iant to a.doqun teo dia.gnosis in erder to, pvo'V'ld.e
a basis to!' eonstruotiTe remedial attaOks f whlch J in tu.rn,
i s to promote permanent re(ml ts Ii Muoh of our remedia l work
i .e tnef'factl va becal.1se we know s o 11 ttle eonctl:t'nlng causes
of' fe.flure <I
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Pl-eyiQu8 :tnyest'ga~lQD
A few prellmtne.;fy rQmarks ' rep;rdtng the previoUe tnv.,·
tigations .of the subject matter Qf thia theets aire made in
the ,ntrO(iuo'lon. We may hare "(Speat for emphasia that L$G
1. ;Brueokner, l'rtJte~80l"Cr Elementary Ed.ucation; University
of lltnn •• cta; (h 1'. Buswell ot the Un! vel's! ty cf Ohicago.;
and C. E. ~reene of the Denver Publio Sohools are among the
leaders in ~he field 0.'1 diagnoSis and remedial work ' in dec!
-.11 a8 it ooncet'DS this stu47,.
LeO J j Bi"UeokneJl' in 'hi. _&1'11 4180u8810.8 en the Oaueea
ot I".rel" iit the uee 01 d,01_1a. 'by a moat oaretul 8tUdy aftd
det .. ll.d analY8'8, brlrJge Qut the _jor .au.see ot la11ure in
deo1mal u.,. This i8 an ea."ly 8tUdy, and it precedCfs the
surT'" which 1',.,u1,.4 1n the preduotion of the Brueokner
DlagJ'i98t'~ Teet tn Deo:1l118.1a, whlCi;h. lad,dent,all,.. is used; 1n
the test1l1S' pregrrunof this thea!,. Ria attempt with deci
mal. was to pte4uoe a test that wou14 "check the examples
that were1nQ"rreOtand detenn1ne the, cauee of erro~ by ex
amlna\1onof the written wQ!l9k ot the pupil., It shOUld be
pOint"d out tha;t the oOIllputatlons 1n the test wet'e kept as
elmple as' possible $0 'that errQl'B due to taUl'y bandl1ng ot
the deoimal, would be rev<taled l'ath~r than the erre1"s due
to Caul t1 oOlllpUta:Uonef "1
1. BWeClcner. Leo J., "Analysis ot Dlttloultl.s in Decimals,· :glemen:tari SOlul,l JQuma&. VOl. 29. pp. 32.44,
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A. survey ot aucceecUng articles and. texts by B:rueckner
reTeale a modification of earlier t.eats and projects so as
to realize this purpe;,ae.
A .u.rvey of the yearly bulletin~ of the Untied s tates
effie. of Education tor the pe,st tive years; with l1ts U,st.
ing ot rtseafoll theses 1n partioular fielde, shows no re ..
sea);"ch dealing dl1?6ctly with the plul's. ot decimals and 1'e ..
media.l study. Seve:ral afa listed a& research 1ndb.gnoetic
and relled-tal teaching in the ys,riou8 ' tUnd&rnente.ls.' One
wh1chcom.es more ne8.r1y being ellmlla.:J' in contents though thl.
thesis doee not mention a palr'UoUlar tree,tment (;)1 deOima.:a.s
i.e "){aat,era 1933. No. it$JRpshl,re" Need and Value of Reme
dial Ar1thmetio . Foote, Lew!. )'."2
2,. Oftice of EdUoa\lon •. "Rea."rob, Theaea, II Special SubJeot. ,t Curriculum" ft"l,tln ':al. the . uut\!8 S,at,I , Ott;ce tt .Educa .. ·Uop. Vol. -4. 13~. TheIrs number 11 2.
B~eo:knetll as mentioned a~ove.he.B to the 8uthtf',
knowledge tnftde the most e;xteneive treatment 01 d~oimals in
d! .. gnOel& and remedial tee.ching. IUs actiT1ty 1. frequently
mentipned !n this connection.
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SEO'tIOll II.
Diagnostl0 ActtTt~Y
1.500»8 and Procedure ot Th •• i,
~. Reliabillty ot teet 1,1" and P~ogr$:Dl
AQt.1Tlty
3. :saeie foJ' AnalY8180t Tes'\ ae.u1tl
4. Analy.,18 or DltfloUlt1e8
G. Ta~l. of D'ttlcu1~y Frequency
g. summary of Detaile(1 Analy,". of Dlt-
11,1,11'18'
'1. Genera1 Ana178ia o.t Er:rOl"1
8. Speolt1o Dlttloultl ••
9.. Teet Anal,s!. of Errol'''. Explana'Uon
.f :Markin'if Salnpl.e ¥arked Te8~
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SOQpe a,nd Procedure of Thesis
PrelQ1inary tlteps we;re ts.ken to provide an ~xperlmental,
e.nd a control. group tor the project lndia.gno~tlc and lI:'emo
dial teaching 1n decimals. These provided, ~ full test.!ng
program was put, u,nder way. The Brueckner Diagnost1c Teet in
DecimAls was used to determine, tor both gl'OUpS, db,gnoais
and zoemecUal cheCkeeOl'ee . (See appendix tot ,sampl.c;t ot test
and lieOre shee'b j) Jour grades '.B" " ... At 8..,B, and a-A. 135
pupils from Twenty.seventh street Sc>hool were used as the
experimental gxooup, while tour grades 7-13, '1 .. A, a-B. and a-A, 129 pupils from wtaconein Avenue Schoo1 comprise the control
group.
The lir.t cU"p,oetl.e teet we.. l\@1nlstered ttl both group ••
The 1n1t.1a1 testing program gtven .1n Deoember 19!6 .."a8 ex ....
puted in lts entirety by the authOl? 'l'he telits were sOored_
the errot's e;ru9.1Ylled. the tesul ts tal)ula:ted, 8.nd the d1tti
oulties U .$'!fed. A care.tul study of all maJor errors was made
to proTide a basie tor ~ remedial workbook. A rem$d1e.l work ...
book c,onetruotQd fQr ,he needs of the pupl1eaB 'based on tlte
findings "8$ prope.red. 'the remedial program was then put in
to 'operation w1 th the use restrIcted to the eXpeJ'imental
group.. The control group was not informed or the procedure.
Upon the complet~on of the remedial program early in
Maresh 193'7, accomplished entirely as a cllaes projeot and
without tlOme"ork assignment. a ascond.. Or remedle.l check test ., .~ . prop-am _a's eet up. Both groups were again 1ieetecl by the
~ -
author', tests were scored, errors were te.bulatect, graphs were'
r
9
oon.'b'uotl,d,., and 1'o.8u1 t,s were $\UIIJII&l:'ized.
It Je UP(i)Jl thil!l p~£)c.duJ'e that daU ~ ace~latecl
Pl"ol'id'inE1J a ~1!t8le tot tho. rea:U.~at1on .o·f t.h~ s.i.1n Qt' this
th(:ls!', Illl.Ji'lely. ~he d5.$COV~UfY of aCO\1l'ate tntQi"):na:Uon ~b de.
termlne withln the scope Q:f thl,$ thell$ the ttlattve value
of d..:tagnolrth: and wemedial tea¢htll$ In d.e,,~1ma.l~H
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10
Reliabilit.y p! Teet. Uee and PrOgram A..,t4.v1ty
There are many tests in the fteld of arithmetio which
luA.ve appeaJ'ed up to the p,eeent time that are generally of
a survey natul'e designed to pleture a general Crose seotion
rath.,:r than to give an analysis of speoif10 dift,"culties and
skill.. b"'ew tests ha.ve been 4 •• 18.,d that may be classed 88
truly diapostio in nature. Br'U.e~n.r· s Diagno., -tic Teet in
DecUla18. and the Compass l)iagno8tl~ Tests in Arithmetio
b'orm IX. and X. which deai with decimals are among the best.
The former was seleoted and. used as t he te"ting JDaterial tor
t he diagnostic and remedial check teets of this til.si .. _
An atithmetic tes~ , in order to be genuinely diagnostio.
must m4et a nwnbet of important. r(,qu1rementa l
1. It must have currloular validity. :It must cover all
the separate skill. ot the field i t is designed to test.
2. It must be rel iable. I t must moasure, .accura tely
11
eaoh phase of skill tea t ed so as to furnish a d.ependable index
tor 1nd1T1dual measurement.
3. I~ mus t ~$ simple yet progressively difficult. It
i s pa~unt tha~ It bo easy andconvenJ.ent t .o aclmJ.n1eter,
and obJective in $coll'tng,
4. It must provide an acourato ~as1s tOl' anallsis.
Tbe test mus~ picture the strengths and weaknesses 01 the in
dividual pupil.
In the s-eleotion of the Bwueokner DiflgrlOet 1o Test in
Deoimals tOJ' use as the basic tes' material in this expert .. ~
Inent it 1s the author's opinion that tho test measures up to
~
r
all the foregoing requirements as a. valid and reliable teet.
this 1V8.S de'.Ulonetratad 'by the effectiveneea of the remed1al
Pl'ogrrun ba.sed directly ul'on the diagnot)ia resulting from the
USe of this test.
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12
Baets for AU-lysis o:tTes~ :a"su1t,
;fre,.1mlnaJ7 Stat.ments
Owlns to the wide divergence-ot op1nl(!)n rega.rdLng what
JDAycons,1tute e. oorrect answer the marldng 61 tests wU.l
cUtter with this dltte;nnce of vie,. pof.nt!i A rew 111ustJ"&
tlona in tiUs regaiJj'd w111 setve to t'],;t:.ullItrate this pc1n1h
1. Part. V""a. In changing ., as t4 a oommon :f'ra~tlc. 1/2 . .
is the 8.ceep\al)le answet. The tracrUtSn 5,/l0 was g1 ven ttl 22
per cent of the papers wnich with 26 per cent actual errors
and: 21 pel' cent oxn1s$10n$ ¢onst.1 tl;l\e a 69 per cent 'total
wrong; Tho~lt~itY'ot an alternative aniJWerseems necessanr
boC)a~,e of' the me .. ~cn· e~lanat1.ono.r the aSB'Wnpt1on that the
wOrda ·cownon trs:ct.to,ft It would imply a reduction to the lowest
terms.
2. Pal"t V+bi' JIe:;oe aleo as In the ·'.14lld1a.te1y above m.en
t""ned ¢$..,e .'5 to It ¢oJDlDOn fract1Q. ls5/4, and the porcent""
a.ge "nng tQ'tallns '10 per' cent include$ ~e per cen' unreduced
tl' .. ctlo~. '15/100, 1.e pel' cent omtee1ons .) and ,2e percent
erl'o1",.
1.3
~l'l pll'Ob18l11 12 of' a.dd! t10n,. an all t ,ern$. tlve aDswer ls per
mitted, l/~ or '.6,. the reason 'being the po,elbl.11ty 01 working
the p",'l)lem eit-her as a. traction by conversation qf the dec! ...
mal or villi.$. VeJ;'ealii In this case e1ther an$weJ;' wou.l.(i be c()r;rect.
;Based 011 thte aesuznption lt would be equally 10g1ca.l to P:fO.
:pQ8e the acoe.ptance ot an unreduced fte,ction euoh as 5/10 or .
7e/lOo tor the· fe4uced tracttoB8 1/2 and S/4 reepectlTe17. in
the prob~.ma a and b of Part v.
f
:3. Part IV- a produces e. similar aituation in grading
results . The frac tion 7/8 i s to be changed to a dec i mal.
o ~875 is the acceptable answer showing an 85 per cen'c errer.
Of this 40 per cent i s due t o emission and 45 per cent to
ac t ual err ors .
4 . Pa.rt IV .. d changing? 8/ 9 te a decimal inv.olves e,
new problem i n addit ion to the .one mentioned abcve . The
nswer is 7 .889 . 7 . 88 8/9 would be permissaole considering
8/9 a circu1a 'ting fra ction and being t ha t it 1s not con-
vertable . Based en the sco re sheet t here i s an errer of 96
per cent, 65 per cent due to erre re of .omi ss ion and :31 per
cent 9,c tual errers.
5 . Division Problems 14 and 22 involve a ls.o the type
.o f a.nower mentioned i mmedi a tely above in number 4, the cir
cula ting fract ion . The acceptabl e quot i ent i s 2 . 636 4/ 11
fer problem 14 and 5 . 71 3/7 fer pr.oblem 22 . In the above
citatien, number 4, t he 8/9 bei ng nearly e full . 001 i s
merely added t o the numbe r as full .001 t hus elimi nat ing
tho ci rcula ting fraction. In problems 14 and 22 the quo ..
tient r.etaine t he sma.l1er cirou1a ting fraction, as a frac
tion . Thie procedure involves in one case t he appl i ca tion
of a rule whereby a ix'a otion wi th Ita value grea t er, than one ...
half 1s made equal to one and fra ction les s t han one -half
is dropped " a.tJ.d the utte r disrega r d for the rule .in the
second case. The situa tion ra ises the ques tions of t he num-
'ber .o f places to Whi ch ~
division mus t be ca rri ed in .order
to be correct, and whether or not to ca rry or drop a frao t ion . ,
~ y
14
6. In mu l t i plica.ti on the s tudent is me rely £l sked, "Can
you do t hese mul tipl i oa tion pr oblema co)"rec t ly 'l" E:x.ample~
31 &,nd 32 i nvo l ve problems i n whi ch f ractions , cie c i mal s a nd
whol e numbers a re used. Wh en t he pupil i s more f smilie.I' w;i. th
t he f r actions than with the decim!".l s , i t i s only r eas onable
t o expect t he che ng ing of the decimal s t .o t he f r a c t ions to
f acilita t e working t he probl em. The logical pr odu.c t t o ex
pect mi ght be expressed as a fra c tion i n t hi s ca se . In pr o
blem 31 i n mul tiplica.tion 12 per cent, scored wrong , since
2 . 4 mus t be expressed i n dec i mal f orm. Of t he number wrong
15 per cent mi ght have received credit fo r the ir answers ex
cept for t he r eason t hn t their answers were gi ven i n a mixed
f rfl.ction r a t her t han t he deoi w..al fo rro .
7. In pr oblem 11 of di vis ion still another quotient ,
when sta t ed a s fraot ion 3/ 4 ins t ead of .?5 t he ~ core shee t
newer, pro ved l oss of 31 per cent. The problem of 6
di vided by 8 , long divis i on needed only mental a rithme tic
in its solution and resulted i n t he sta t ement of t he quotient
s a common fraction 3/4.
The.se s even c1 t 'a tions will pos s ibly serve a.s suffi c ient
illus tra tion of t he involvement of tea ching pr aotices i n pr o
ducing results i n ma t hematica l oa lcula tions . These r esults
woul d be correct i n l i ght of a particula r cla ss pro cedu. r e to
which t he class 1s a. ccus tomed, yet they a re no t co rrec t i n
t his s coring .
Th is study s erves a lso to cite the need fo r a definite ~
prooedure regarding the aocept able results in speoific
ins t Rnoes.
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15
nalysia of Difficulties
Difficul ti (M3 , whether in t he fundamenta l processes,
their applice.tion , or both, are hindrances to progress in
1'1 t hme,tic. Correction of these difficulties augment the
chances for be tter work. critical analysis in system ..
a tic manner leads to the root difficulties .
Finding the source of trouble and pl anning a program of
reconstruction based on t hese fao ts i s the underlying prin-
ciple of remedial study .
The following analysis of errors upon which the course
of remedial study was instituted points out the roots of
trouble .
Based upon t hese tabula tions a workbook was constructed
to assist the program of remedial study . The types of study,
t he number of examples, a.nd the amount of exerc i se i n the
workbook was controlled by the number and caus es of error a s
shown in t he table of difficulty frequency . These errors a re
grouped into five major divisions namely:
1. General Difficulties . 2. Addition Difficulties . 3. Subtraction Difficulties. 4. Multiplica tion Difficulties. 5 . Divi s ion Difficul ties .
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TABLE I . Table of Diffi culty Fr equency
De t a iled Ana lys i s
• Genera l Difficulties Pa rt I . to V. i nclusive
1. Lack of compr ehens ion of
27 t h. St~ 1st. 2nd . Tes t Tes t
decima l value 187 67 2 . Lnck of fundamental knowledge 162 89 3 . Spelling errors 138 53 4. . Not att empted 106 6 5 . Inability - write fra ctions
as dec imals 78 36 6 . Ca relessness in r eading 75 30 7. Failure to r educe frac tions to
lowes t t erms 47 9 8 . I ncompl e t e 47 11 9. Inabil i ty to expres a mi xed
numbers as decimal s 32 22 10 . Inability to Vlri te decima.l
fractions as words 25 18 11. Mi spla oed decima l points 23 4 12 . Fai l u r e t o follow d i reo t i ons 22 10 13 . Writing a s part fraction and
decimal 19 16 14. Inability to exp r ess a,s fra ctions 14 10 15. Unknown 10 7 16. Omitting zero 7 0 17. Us ing per oent s i gn a s hundredths 7 0 18 . Omiss ion Of essentia l words 6 1 19. Us ing extra zero s 6 0 20 . Mispl a ced c i phers 4 1 21. Us ing ext ra VTo,rds 4 0 22 . Multiplying nume r a tor by
denollline. to r 3 0 23 . WrIting decima,l s as dolla r s
a nd cen ts 2 0 24 . Ex tra points and extra zeroes 0 1 25. Decimal poin t i n numer ator of
fra ction 0 0 26. Di s regard f o r dec i mal whole
number 0 0
Tots,l
II . Addition Difficulties ~
1. Weakness in number comb i nations
~
t
1029 391
46 29
Wi s. Av e • 1st . 2nd . Test Test
301 286 239 253 157 145 159 132
173 169 40 21
64 60 l Q2 108
73 61
27 29 59 60 8 2 83
14 7 62 71 83 87 21 16 12 15 14 12 19 17 12 6
2 0
12 15
2 9 17 15
2 4
8 3
1756 1684
70 76
17
TABLE :t. CO}TTI NUED
2 ~ Error in pl acing the deeimal point
3. Mispl acing t he whple number 4 . Addi tion of fractione with
decimal s 5. Not at tempt ed 6 •. Carrying difficulties '7. Adding fra,ottons to d.ecimals s. MUltiplying instead of adding 9. Spelling "dt hs" as "nds" .
1 0 .. FailUre to follow direction 11,. . Carelessness with zero 12 . Dec1mal po1nt ·omitted 13 . Incompleted problems 14. Decimal po i nt mispl aced
To t e1 .. - .. - .... - -
III. Subtra ction Difficulties
2?th. s t .. 1st. 2nd . Test Test
I
41 27
20 19 13
5 5 4 2 2 2 o o
185
2 3
8 4 8 4 o o 1 1 o o o
60
1, Borrowing difficulties 66 27 2 . Weakness in sUbtraction f acts 30 14 3 . Misplacing decimal ntunbers 1n
subtrahend . 22 10 4 , Confusing subt r ac tion and
add ! tioD 1 2 8 5 . Cause~ unknown 6 2 6. Decimal point omitted or :miS ..
pl a ced 4 0 '7. Zero dl:fficu1 ty 4 2 8 . Reversed minuend and subtrahend . 3 1 9 ., Incompleted problems 2 0
10 . Disrega rd for dec1mal poin.t 2 0 11. Not at t empted 1 0 12. Decimal .. who1enumber dist inction 1 0
Tota l - - - - - - - - - 153 64 .
IV. Multiplica tion Difficulties
1 . lU s p.1a ein.g deoimal point 2 . Error i n multiplication 3 . Not attempted 4. Unknown ~ 5. Failure to prefix zero
k r
131 45 82 67 :6:3 23 54 43 43 7
Wis. Ave. 1s t. 2nd . Tes t Tes t
52 76 31 32
24 29 9 13
26 18 9 14 9 ? 7 10 1 8 2 7 4 9 8 6 6 9
254 285
135 130 63 72
34 30
19 8 12 6
19 23 6 12 4 2
12 15 2 9
12 15 6 4
524 526
193 207 174 161 147 137
83 64 62 69
18
TABloE t. CONTINUED
27th. st. 1s t. 2nd. Test Test
6 . Omitting decimal pOint 17 11 7. Incompleted problem 14 7 8 . Inability to mult i ply decimals
and fractions 12 10 9 . Carrying difficulties 11 6
10. Writing answers in fraction form 11 0 11. Errors in addition 9 2 l2w Prefixing unnecessa r y zero 6 6 1 :3 . Jil eplacing zerO 4 1 14" Add-1ng instead of roul tiplylng 2 1 15 . Lack comprehens ion of process in-
volved 2 2 16. Jmnexin~ unnecessary zero 1 0 17. Ine..b!li 'ty to multiply by zero 1 0 18. Failure to use all digits 1 0 19 . Failure to plaee zero i n product 0 0 20. Separated whole numbers from
decimals 0 0
Total ~ - - - - ~ • - -463 231
v. n1viaion Difficulties
1. Decimal point mispl aced 347 93 2 . Errors in division 132 141 3 . I~ot attempted 99 73 4. Decimal polnt omitted 97 21 5 . Incompleted problem 56 17 6 . Error in roul tiplica tioD 47 39 7. Failure to prefix zero in
quotient 39 10 8. Lacks knowledge 36 40 9. Difficulty with trial divis ion 35 10
10 . Fai lure to reduce rema inder to decimal 31 20
11. Failure to annex zero to quotient 22 17
12 . Failure to annex zero to dividend 21 13 13 . No zero annexed to divi dend and
quotient 15 6 14 . Ex.tra zero in quotient 12 2 15. Ertor with remainder 12 16 16. Oarrying difficulty 9 9 17. Prefixed z~o, wrong decimal
point resulted 7 1 18 . Confusing dlv~aion and percentage 4 2
r. r
\l1 i8 . Ave. 1s t . 2nd . Test Test
24 37 102 121
51 53 62 47 12 16 49 12 14 16
2 0 2 8
28 32 10 6 11 6
2 1 2 1
6 4
1035 998
493 422 381 401 103 101
89 97 105 94
92 102
85 72 67 93 56 27
62 60
27 21 31 16
22 12 44 40 15 27 23 29
9 4 10 16
19
19" 20. 21. 22.
TABLE I . CONTI1nrED
27th. st . lat . 2nd. Test Test
Mispl a ced zero i n quotient 4 2 Errors in subtra ction 4 9 Confusing dividend with divisor 4 1 Unknown 2 12
Total - - - - - - - - 1036 554
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20
\ilis . Ave. lat. 2nd. Tes t Test
4 2 4 12
12 4 10 12
1'(44 1684
TABLE II.
Sunanary of Det ailed Analysis of Difficulties
Ma jor Divi s ions of Difficulties
General
Addi tion
Subtraction
Multiplication
Div1eion
27th. st. 1st. 2nd. Test Test
1029 391
185 60
153 64
463 231
1035 554 --,,-, ,~
Total - - - - - - - - 2856 1300
WiSe Ave. 1s t. 2nd. Test Teat
1756 1684
254 285
324 326
1035 998
1'744 1684
--5113 4977
A study of the t abul at ions just presented 1s a l most
sufficient for genera l purposes. The ma jor difficulties a re
expressed. in order of i mportance in t he diff i culty fre quency
t able; t he first test in Twenty-seventh Stree t School serv
ing as t he gui de fo r the order of arrangement.
In t he following analysis more specific trea t ment is
given. Specific difficulties are discussed wi th particula r
reference to their pl ace in the importance in t h is study, and
in t he assembling of the remedia l workbook .
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21
General .Analys is of Errors
Pa,rt I and II. Where one proces s i s t he reversal of
the other , tha t is t h e changing of t he written words to 'I;he
decimal form and visa versa, it was easie s t to write the
words fer t h e dacimnl fo r m, vlhile greater dift'icul ty vias en-
countered in writing the decimal numbers for the written
words . In the former 15.7 per cent errors occurred while in
the latter 5.3 per cent errOI'D were Ina de, ratio of approx-
i ma te ly three to one. The -v-isuali zation of the deci~ll num
ber in t h e Vlri tten form pres ented the obs t·s,cle .
Part I .II. The process Invo1 ving the eve.l uG. t ionof
decima l numbers presented problems to 27.4 per cent of the
s tudents. In each of the 5 problems the f a ilure exoeeded
25 per cent, problem 4 and 5 caused class failures to 52
nd 55 pe r cent r espect ively. The specific diffi culty in
the l a tter case being tho obvious la.ck of knowl edge e s to
the relationship of decin~l numbers to t he whole number.
2 . 303 was given a greater va lue t han 2 . 33 . The conflicting
idea being t he rela tionshi p of 303 t o 33 when written as
decima1 .number. Approximat ely 27 per cent of the pupils
omitted t he problem, and 26 per c ent worked t he problems 4
a.nd 5 i ncorrectly .
Par t IV. This section has only 4 probl ems , changing
fracti ons to decimals, and he,s an error r a te of 62 . 5 per cent"
with 85, 45, 28, and 96 per cent respectively for the 4 pro
b1ema . In pl'oblom a ,; cha,nging 7/8 to a decimal, 87 1/2 was ~
given a s a. mixed number .in 12 per cent of the pape r s r a ther
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22
t han es decimal fract ion of . 875. The possible associat ion
with t he t ab l e of fract iona l equiva l ents 7/8 equals 87 1/2
per cent may be t he cause i n B. numbe r 01 cases . Problem a .
had 22 per cent omi ss ions , 45 per cen t errors, a.nd 18 per
cent wr itten as 81 1/2 or 87 1/2 per cent.
Problem I V- b . The fraction 1 1/4 being changed to a
decime l was correct 57 per cent, wrong 30 per cent and omit-
t ed 13 per cent. The i n troduction of mi xed number, a s in
the case of IV. d followi ng , a few cases showed t he l ack of a
clea r concept ion of the rela t ionshi p be t ween decimal num-
bel' and its equi val ent common fra ction .
Problem IV- c . Cha.nging 9/100 to decimal had fewer
diffi culties be i ng 72 per cent correct, 7 per cent omitted ,
and 21 per cent wrong . Problem V-c pr e s ented t he rever se of
thi s aitua tion, . 09 to a common fra ction , a.nd i nvolving no
reduction, was 52 per cent correct , 14 pe r cent omitted , and
34 per cent wr ong . Thi s shows knowl edge of the el ement ary
proces ses but a gene r a l l e cking in t he epnlica t ion of new
f ea tures such as circula ting fra.ctions , r educ tions , etc .
Problem IV- d . The changing of mi xed number 7 8/9
to a. decimal has s ever a.l s itua tions of diffi culty. t hat of
mi xed numb er, a sel dom us ed fra ct ion , and f raction of a cir-
cul a ting va riety. The l as t ment ioned fea t ure caus ed t he
great es t difficul t y . Four per cent of t he problems were cor~
rect, 34 per cent were wrong , and 62 per cent wer e omitted
entirely. The pl a cement of t he decime l to t he right of the ~
7 revea l ed the presence of fundamenta l knowl edge , but
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25
specific l a cking in the process of changing the fra ction to
a. dec i mal, and the working process of t he circulat ing fra c-
tion .
Problem V- a . Difficulties tote,led 26 per cent wrong ,
21 per cent omi tted end 31 per cent correct with 22 pe r cent
of the f ractions not reduced to the lowest terms. Problem
V- b totaled 30 per cent wrong, 17 per cent omitted , and 30
per cent c orrect 110'1 th 23 per cent of the fractions not re-
duoed to lowest terms . In each ca.se the high tote,l percent-
age wrong wa.s due t o t he reduction of common fra ction as
expl a ined above in the first part of t he prelimina ry state-
ment e
In both s ections IV and V the omissions r an high there
by bringing the error,a high, 62 . 5 per cent and 56.2 per cent
respeotively. Thi s appa r ent l a ck ing may be due to either i n
structional diff iculti es , poss ibly i nsufficient dri ll .
In addition there a re , a long with process errors, :3
fundamental general commi ssions , examples 2, 4, and 12, wi t h
37 , 13 , and 34 per cent r espectively . The peculia rity of .
t he error in 18 per cent of the cases i s quite noticeable .
In addition of the decima l fractions where no whole numbers
were present, t he s t udents fai l to see the possibility of
whole number appearing in the sum as 10/10 end equal to 1.
The one to carry i nto t he whole number column wa s therefore
squeezed i nto t he right a i de of the decimal point.
Problem 12 i n addition was 66 pe r cent correct with 26 ~
per cent wrong, 7 per cent omitted , end 34 per cent tota l
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24
errors. The analys i s shows that the i ntroduction of the com-
b ination of a common f r a ction with dec i m81 caused much con-
cern. Thi s is also true in problems 31 and 32 of t he multi-
plica tion and i s a lso true of several problems of divi sion .
Subtract ion appear ed to be the simpl est of the four
f undamental l)rocesses in t hat the errors averaged only 6 . 5
per cent. Only one ma jor difficulty occurred , namel y , the
process i n which the minuend contained fewer di gito than the
subtrahend, as . 4 minus . 375 or .36 minus . 002 . The borrow
i ng process involving the annexa tion of one or more zeroes
proved difficult . The i dea of pl acing the decimal point
di rectly in line wee accurately worked, the diffi cul t y com-
ing i n t he fundamental proces s -. borrowing , not i n the
decimal s . Problems 7, 8, 9 , 10, 13, 14, 15, 16, and 17
pre sented thi s particula r form of difficulty. Pr oblems were
mi ssed in pr a ctically all cases where t he s tudent had this
difficulty.
Multiplication, like addition and subtraction, with an
verage error of 10.6 per cent preserited gener a l d i fflcul·
ties to minor degree in t he pl acement of t he decimal point
in t he product . As mentioned above the complica tions in
volved by t he i ntroduction of a mixGd problem of f raot i ons ,
whole numb ers, and dec i mal s provided cause for a number ot
errors . Problems 31 and 32 are the best exampl es f or this
s ituation.
Di vi s ion r a,nked a long wi t h Group III , IV, and V wi th ~
7 . 6 average error out of 30 problems or 25 . 3 per cent . Only
r
25
problems 1, 3, 4, 5 , 0, and 8 had fewer than 10 per cent
error .
Thi s divis ion aection i s difficult to analyze and be
caus e of the high gene r a l percentage of error, it mi ght bet
t er be r e-taught with general ins tructions being carefully
given. There i s tota l of 74.7 per cent correct, 2 . 7 per
cent omit t ed f.j,nd 22 .6 per cent wrong . No defect of i mport ..
ance could be detected other than those mentioned above in
connection w1thaddition , subtraction, and multiplica tion.
The defects would be hard to s ingle out because of the total
errors and t he r ange of problems, t he chief offense being
t he mispl acement of the decimal point to 8 .6 per cent. The
suggestion in t h i s case is, however, t he complete re-teaching
of the division of decimal numbers, gua r d ing with ca re
against t he corruption in pr actices ana lyzed in errore found
i n t h e three other fundament&l processes a s mentioned above.
This should be proceeded by a review of Si mple d ivi s ion of
numbers followed by an injection; in fI, very car ef u l manne r,
of the deoimal lde~ .
~
r
26
27
Spec ific Difficulties
The specific difficulties m.entioned 'below are of r a. ther
general commiss ion a.nd these errors may "nell be the banis for
remedia.1 instruction. Omi ssions form a. greater part of the
errors namely 3. 9 per cent and could well be included in the
class of remedia l study_ This survey of 15,795 problems
shows 2. total error of 2 1 865 problema or 18.1 per cent, ornis -
sions to ta.1ing ~ . 9 per cent, actual errors 14.2 per cent .
Because the errors we re gener a l t hroughout the four gr8dee
of t he school in which the test Vfas g iven, the assumption is
t hat either the method of teaohing or t he intensity of drill
is at fault . Upon this oalcu1a tion, it is a t least correct
to a large degree to assume tha t future errors may be cor-
rec t ed by remedial work in a1 ther or both ph..'1.ses of peda.go
gica.l practiceo e It is f a i r to concl ud.e tha.1~ reraedie,l work
should follow t w.o lines of a ttack, corrected pedaGogical
or instructional pr actices, and r emedial ad justmenta .
~
k Y
Test Analysis of Error
Explanati on of Tes t Ma r king
Sample Test.
Score ••••••••••• 117 minua number wrong.
Er ro r t abulation • •• t ally of number wrong, listing by divi
s ion or classificption.
o - 0 - 1 - 1 - 0 - 0 - 0 - 4 - 4 • 10 wrong .
Notation on errora .
Part III. Number 2.
Error listed as ca relessness . Failure due to co pying
numbers i ncorrectly 200 .3 f or 200 . 33.
Pa rt IV. Number (d).
l:ult.
Failure due t o circulating fra ction. In changing
mixed fract ion to a decimal. ? 8/ 9 was g iven a s
7.88 8/9. The correct answe r as a dec i mal i s 7.889 .
Either of course i s correct.
Numbers 2 and 3.
Failure is due to carelessness . Here the pupil mul-
tipl ied the problem number a s a part of the multipli -
oand . The problem as wo rked i s correot.
Mult . Number 16.
Mult .
Fa ilure i s due multiplicat ion of 32 by 1 r esulting in
33 as product or it y be classed as car'elessness.
Number 23 .
Decimal point was omitted .
~
~
t
28
Test Analys i s of Error
Division . Number 9.
Error due to f a i lure to supply t he neoessary zero
quotient.
Division. Numbers 14 and 22 .
Error due to f a ilure to complete example and a ccount
for t he remainder.
Division. Number 24.
Error caused by fa,ilure to provide
the quotient.
~
~
decimal point in
29
~ ' °7 30
BRUECKNER DIAGNOSTIC TEST IN DECIMALS G.M..4-V ~ .•..• 0 - 0 - 1 - / - 0 - 0 - 0- "-I- ~.. 10
NAME ..... ..... .. .. ;B.W;ll.t .... :fui.*.Q;I,4 .................... ... ................ .......... _ ................................... GRADE.._ .. ~A ......... AGE._ ...... ;I,.3 .. _ .. .
SCHOOL ......... )~J.t.h ... ~:t..r.~.~t ... ~.g.h.9..Q_;!,_ ... _ ... _ ........ _ ..... .. .......... .................... ...................... DATE. .. _.¥..~1?! .... J.:.~.! .... .J.~.~.?
I. Below are numbers written as words. Write each in decimal form.
o a. Five tenth,"-s __ ·-=5~_. ___ _ d . Three thousandth .... s ____..-"'o-"'o""3'--_ ____ _
b. Four hundredths. _____ . ~0""'4'--. __ _ e. Forty six thousandths_..!.·..!!O..::;!4~6~ ___ _
c. Sixteen hundredthl'),-...::·~1~6~ _ _ f. One hundred seven thousandths .107
g. Forty nine and eighty four hundredths 49.84
II. Write the numbers below as words.
0 a. .65 Sixty-five hundredths
b. 1.4 One and four ~, tenths
c. 3.75 Three and seventy-five hundredths
d. .146 One hundred fort~-six thousandths
e. 1.09 One and nine hundredths
f. 20.056 Twenty and fifty-six thousandths
III. Arrange the following numbers in order of their size. Write the number of greatest value first.
Write here a. 23.3 b. 2.33 1. 233 c. 233.0 Vi. 200.3@ d. 2.303 e. 200.33
3. 23.3
4. 2.33
5. 2.303
IV. Express as decimals: (a) 7 8 ,
9 (c) 100
, V. Express as common fractions: (a)
(c) o
.875 (b) 1 .!. 4
1.25
.09 ./(d) 7 ~ 9 7.8~
.5 1/2 , (b) .75 3/4
.09 9/100 (d) .149 149/1000
--- -----.. - ------------------------------------Published by
EDUCATIONAL :rEST BUREAU, Inc •. • Minneapolis - NashvillE! C Philad€lphia X . _ __ ____________ ~ ________________ ~
ADDITION -0
Can you find the following sums correctly?
1. .'4 2. , .3 3. .1 .5 .3 .8
.8 1.6 "
6. . 05 7 . 1.06 .09 2.08 .08 3.04
.22 6.18
10. Find the sum of9.65 + 8 .375 + 6.4
11. Find the sum of . 8 + 3 + . 125
12. i + .25 = .5
.16 '
.25 ' .37
.78
~
4 • .28 A3 .95 ._-
1.66
8. 1. 75 2 . 125 3.8 7.675
VVork No. 10-here
9.65 8.375 6.4
24.425
~,
,
5. .02 .03 .04
.09
9. 2.75 4.
16.375 23.125
VVork No. 11 here , ,
.8 3.
.125
3.925
MULTIPLICATION - ~
i 4 Can you do these multiplica~ion examples correctly? ~ ~ tog ,()O
.048 ~ .002-1. 4 X .2 =
4. · 5 X .3 =
7. 8 X .5 =
10. 2.6 4
f0.4
14. 85 .4
34.0
18 • . 4 X .2 =
21. 7.8 6.4
312 468
49.92
25. 10 X 8.5 =
.8
1.5
4.0
,08
(r·02~
5. 6 X .04 = • 24 6. 7 X .008 =
"8. 6 X .05 = ~ 9. 4 X .005 =
11. 3.5 8
28.0
15. 20 .6
12.0
12. 3 . 28 4'
13.12
~ffl lji/ I ~
.OO~A
.056
.020
13. 4.647 5
23.235
17. 2.5 48
200 100 120.0
19. .. 5 X .03 = .015 20. .8 X . 25 = .200
22. 6.5 ~ 18.4 24. 8.04 4.8 .26 .03 --
520 1104 .2412 260 W 31.20
85.0 26. 10 X .96 = ~.6Q 27. 100 ·x .14 = 14..00
28. 100 X 8.5 = 85Q.0 29. 100 X 8.65 = 865.00 30. 200 X 9.4 = 1880'.0
31. ~ of6.4 = 8
~
2.4 1 32. .08 X 25 X ~ =
k J
+"
1
31
DIVISION - ~
Can you work all these division examples?
2.J 1. 4) 8.4
!4 . 4. 2) .8
.03 7. 4) .12
.........!..O 10. 8) 4
2.Q6 13. 25) 64.00
50 14 0 150 12 5 ' 150
~ 16. .3) 3'.'6
20 19. .3) 6
~ ~ 5.~ 1 1 22. • 7) ~. 0 ()
35 11 '~ 50 1-"'3 ~ - 1
~6. 25 .. 11) 3.3
28. 1. 25) --6----..5..aA .75,
~
2.49 2. 3) '.41"
.l9 5. 4) .76
.007 8. 6) .042
.75 11. 8) 6., 0 0
56 ---:r 0 4 0 1/
' ' ~ 2.63 0 It 14. 33) 81.0 V
66 /IY' 210 ,Y,o 198 ~ J./
621~ 120 ~ I I - ,~
17. .3) 18 .63
50 20. .2) lO
11. 23 . . 11) 1. 21
50 26 •. 12) 6
1.1 29. 6 .48) 7.128
648 648
6'48
2.112 3. 8) 16 .896
.162 6. 6) .972
~ ~ .0' 9. 24) 1.2
120
.08 12. 25) 2
.349 15. 25) 8.725
75 225 122 225 100
3. 18 . .40.2
7.5 21. .4) 3 ft
~ ~ .. 11rw.
75 27 .• 12) 9.00
84 60
60
110 30. .834~ 91T4
834 834 834
SECTION lIt •
. Remedlai Program
1. UnJor Remedial Attacke
2. Studentie ltemedial Wc>rkbook
3, Teaoher H,lp, and Inetru.o~iol1e
4, Copy o{ Workbook
~
trIO jor Remedi a l Atta cks
The followi ng sugges tions, be,sed on the diagnost ic t est
revealing general weaknesses, may supply a s eries of leasons
of a remedia l nature. Specific or individual i nstances can-
not be trea ted hera, as s tudents would necessarily need in.
dividual analysis . The policy of dealing only wi t h major
problems i n t he anal ysis i s t he ba s i s for t hese suggestions .
Il.emedh,l class teaohing a l ong t hese lines for upper grades,
nd peda.gogi ca l 'reconstruction of teaching pr actices where
decimal s a r e taught would well be worth the trial. Review
nd drill should form t he technique for t he former, and r e.
adjustment of t eaching methods , time a llocat ion, and quality
and quantity drill t he t echn ique in the l a tter.
For ei t he r class remedi al wo~k or pedagogical analysis
t he fo llowing lis t of sugges tions fo r t he major corrections
is suggested:
1. Giving t he numerica l equiva lent for the vrr itten or
spoken decimal number .
----Teach the reading of decimal numbers and t he value
of the decimal pl a ce. PrOVoke mechB,nice.1 visualiza tion
of decimal pl aces . Drill .
2 . Evalua tion of the decimal fraction.
----Tea ch t he va.l ue of t he decimal pl ace as disassociated
from the whole number , and as related to t he common fra c-
t 10n. This should be followed by
number s of s i mila r digi t s . ~
3. Decimal and fracti ona l equiva lents.
~ '(
comparison with whole
33
----Tea ch clear conception of the r el a tionshi p bet-
ween the common fraot i on and the decimal equivalent.
Show the rel~ tionship between t he numerator of the
common fraction and the di gits of the decimal, and bet
ween t he denomi nator of the common fraction and t he
decimal plaoe name .
4 . Circulat i ng fraotions and decima1s e
----Provide problems wi t h circula ting fractions i nvolved
with decimal s, carrying t he decimal pl a ces 2, 3, or more
pl aces as provided for in t h e pr actice of the s chool.
Tea ch t he subsequent elimination of t he circula ting f r ac
tion 1n t he second, t hird, or fourth pl ace by t he addi~
tion of one to t he l as t pl ace or by dropping t he fra c
tion should it be lesB t han half.
5 . Mixed numbers and decimals.
----Tea ch t he relationship of the whole number of a
mixed number to a whole number in any other ins t anoe,
nd t he common fraction to the decimal placement a t the
right of the decimal. Correlate study of t he simple
f.r action being changed to a deoima1 with the rela tion
ship of whole numbers and fractions.
6. The 10/10 ooncept and t he unit digit.
----Teach t he orea tion of a whole number when t he sum
of 10tha are equal to 10/10 thus providing a whole num-
bel" in t he sum.
7. Combina tiol)s of common fractions and decima.1s.
k r
34
---- ~ each by review the relationship of the common
frac tion to t he decimal equivalent, and intorduce t he
idea of the necess ity for the conversion of one or the
other thus providing but one common name or denomina
tion either decimal or common fra ction.
8 . The borrowing prooess .
----Teach the use and the necessity of the annexed
cipher to provide sufficient pl aces to a llow for the
borrowing process. Illustra te that the annexation of
the cipher to a decimal number does not change the
value. Compare this wi th the a,nnexation of a cipher
to a whole number .
~
k r
35
Student's Remedial ',Vorkbook
Twenty- seventh Street School. 1937
Thi s workbook is constructed to supply mater i a l for re
medi a l study in decima.ls as indica ted by a testing progr am
s.urvey conducted at Twenty- seventh Street and Wisconsin Ave
nue Schools .
It is intended to supply. i n proportiona te degree, such
instructions and examples as the critica l analysis of the
survey test indicated necessary.
The book is used i n all experi ment a l classes at the
Twenty- seventh Stree t School during regula r class periods .
Each pupil is supplied with a wor kbook. No work is completed
outside of claas study. Workbooks are retained by the pupil
with one r es t rict ion s tressed , namely, t hat no work in the
workbook be comple t ed outside of class room study . This does
not exclude the study or aotual wo r king of the same or s im~
ila r exampl es away from the cla.ss room. There i s no homework
as i gnment.
~
36
Tea cher Helps and Instructions
The only knowledge in a rithmetio the tea cher of reme
dia l work as sumes i s t he fundamental processes in addition,
subtraction, multiplica tion and division.
The purpose of t h i s s tudy i s to acquire t he ability to
manipulate the deoimal point when a s socia ted with t he four
fundamenta l proces ses.
Proceed as f or r egula r cla ss work.
1. Pr ovide on t he boa rd examples of an ea sy nature
similar te t he examples supplied in t he illustr a tions.
2 . Supply all information for the illustrations in
the workbook, a nd complete a ll examples. Exhaust a ll
questions before t he pupils a re assigned to begin an
exercis e.
3. Assign the exercise. Work with t he individual
pupil a,s he needs a ssistance . (Al ways motiva te t he de
sire in t he pupil to a sk for needed help by sta tements
preceedlng each as signment such as this one: "Rai ae
your hand as soon a s you have a.ny dlfficul ty. I may be
Qle to help you over Bome troublesome spot t hat will
possibly help you in your future work. 1I Follow through
every reques t . )
4. Pupils will finish a t different times , urge check~
Ing and re-check ing results to avoid needless errors .
5 . Check t he results with the class; each pupil will .
oorrect his own paper. (Suggest that t his is not ~
test;
tha t no score will be t a.ken. and t ha.t every error should
be encircled and e.ne.lyzed t o determine t he caus e of the
~ y
37
Teacher Helps and Instruct ions
errGr. Corrections are not to be n4~de by eras i ng t he
mi s t ake but by r e- worki ng t he exampl e on t he bl ank page
to t he l eft.) Ane.lyze ea ch error wi t h the i ndividual
pupil who fai l s t o f i nd his O\vn cause of error. Have
all pupils make corrections on t he page to t he left be
fore beginning new work . Look fo r additional questions
a lso.
6 . The next lesson will follow in aimilar f ashion.
here is no r equired order in proceeding t hrough t he
workbook. I t i s sugges ted tha t pages A. and B. be com
pleted fir s t, however ., t his i s not obligatory.
~
38
...
0 z
(j)
Fi
P'
8 P'
S
c:::
p,
(D
Q
CD
a ~ '-
':il'
@
0 0 :;>
;:
!D
0 H
0
Z
S
tJ
trJ
0 H
,~ >
t-i
(j)
VIORK SHEEl' IN REJ.DING j,:rn '\lRIl'In~ m~G nJLLS 40
( Illustr2.tion) ( Gtudy Ln1 exple.nation)
3467 • 29851
3000 • 400 •
60 • 7 •
• 2 • 09 • 008 • 0005 -• 00001
Three thousc..nd f our hundred sixty (six tens) seven (seven units) and (Decinal Point)
t wo tenths nine hundredths eiGht thous2.ndths five ten-thousandths one hundred-thousandths
3467 • 29851 Three thousand four hundred sixty-seven c..nd
t wenty-nine thous2.nd ei~ht hundred fifty- one hundred thous['.ndths.
The illustration at the l eft is to help you see the rel2.tionship between who le nunbers [>.nd decinc,l nunbers. Each diGit in the nunber 3467.29851 is taken sepBrately and its place naDed a t the right of it . Study the illustration. Take p2.rticular not ice t @ the spelling of the plac e naDCS. Study the endingf , Can you m['.ke a rule for spelling?
Note the last wo rd in the decinal part of the nunber. note the spellinK
I. Below arc numbers written BS words. Ur itc each in decinal f or:r:l: ' a. Four tenths b. Eight thousandths ______ _
c. s even hundredths d. Fifty-thre e thoUsandth s ______ _
e . twelve hundred ths __ "__ f. On. hundred nine thousandths
g . Forty end sixteen thous['.ndths ______ _
h . Ei Ght hundred £'.nel f our tenths
i. Fifty-nine e nd sixty-four hundredths, ____ ___
II. Ylri te t he deciD['.l nt.lGOe rS be l on in vlo r ds:
a) .7 5
b) 4.008
c) .3 2 7
d) 30.072
e ) 120.1
1110 l.rro.nge these groups of numbers in order of their siz e . ·.lri t o the GRJ:J.l':J:ST value on the first line . Uork cech c r oup s cp['.r2.tely.
2. ) 46.2 , d 41.302
b ) 4 . 62 b) .3214
c) 462 ,.0 c) 43 .1 02
d) 400 .62 d ) 132.4
e) 4062 e) 2.4301
~
r
(1)
(2)
~
j'OW;;: E'7'"ITT I N DBCn~A u,r" T.''-' A.Cr:~I ONS
Change the following fraction s to de ci~als :
1 2
_lL = 6
1 8
l:::: 10
1
3 ::::
_Q.- :::: '7
Change the following decimals to fractions : (Reduce to lowest terms if possible.)
2 3
C)
~ = 25
(1) .25 = .'75 = .4 = .125 = .625 = .48 =
(2 ) 1.25 = 6.125 = 3.24 = 9.8'75 ::::
The following are problems in which ther ", are decim81s, fractions, and whole numbers. IJIla tch the decimal point, and reduce all fr actions to the lowest terms.
(1)
(2)
(3)
~~ul tiply:
!L X 4.8 ... 3
1 4
X 10 X .4 =<
-LX 3
2 3
X .36 =
~
l X 24 = 8
3 5 X - X 1.6 4
1.6 X -L -4 -
-L X ,50 X 6 = 2
3 -'7 X .14 X l 2
/ 4_,.16 X 1 2
X 3 4
::::
~
r
41
42 WORK SHIT:ET I N ADDI'rICr CF DECII1.LS
A fe ,/ sinp1e problems in ~he T.ddi tion of deciG2.1s £',re [;i ven below. TIoti c e th2.t in e2.ch probleD the decimBl points Bre kept in line one belo" the other . In lJrobleD ( B) vrhi ch is completed the deci:ra2.1 point in the SUD is a lso in this line. Vlork a ll pr oblems belovl 2.nd be sure you w2.tch the Deci:ma1 Point .
(a) (b) ( c)
2 • 5 7 . 36 • 9 9 • 0 9 4 • 1 5 • 3 7 '
1. 9 • 3 .32 o 1 37 . • 1 7 • 0 9 5 8 • 9 6 4
( e) (f) ( G)
1 .07 2 • 0 9 6 3 . 74 2 .22 1 • 446 5 • 8 1 . 45 2 • 9 3 6 8 . 04 2 5 .82 4 . 25 2 6 .25 3 .11 3 • 755 1 • 5 5 9
(i) ( j) (k)
4 3 • 099 7 9 0 9 • 5 548 • 9 300 _ 1 3 9 1. 5 5 • 8 8 9 446 • 003 7 7 • 7 7 1 1 34.
.30 1 8 0 0 0 .03 6 5 .03 • 005 9 .0 4 4 1 • 005
5 4 • 1 550 • 8 1 . 09 0 222 .02 4852. 6 73 • 0 9
. 8 • 0 0 9 2 2 . 02 ---
I n the spa c es t o the right b) c oPY the f ollowing problens 2.nd I :.:'ind the s um. ~i12.t ch the D~CHILL FO IF~' ,
( :-:1 ) Find '~he sun of 3.693, 54 . 7, : .754. 33.691, 4.43
( d)
• 002 • 007 • 9 0 1 • 0 9 0
( h)
3 • gOg 1 0 • 002
305 • 9 9 71.
5 • 50 1
( 1)
356 • 78.
7 • 9 . 08 • 1 08
6 • 9 101 •
• 9 9 9
( n ) :B'ind t h e sun of 709.076 , 4 . 0098 , 365, 1.4001, 256.7
~
'-------~, , ---'j
y
43
nORK SHE~l.' I N 1 ... DDI7101 ')£ DE SII:l.IS
In 2.dd i tion of deciD2.1s be sur e co l; l2..ce the dec if:1a1 p oint one be l ow the oth er in the prob1er 2,DO be sure to place the deciLla 1 po int directly below in trle ,J ' ;lG .,
Copy the nUr.1bers in the proper d::n\ ce be l ow and find the PUBS . WATCH THE ])ECH.iJ.L P011J1' •
1.) 7.5, 4 .67 2.) 4 . 8 , 5 .4, 6.2 3. ) 7.78, 6.48,9.63 4 . ~ 2 .7 56, 3.897 5 .) 9 . 86, 2.7 6 .) 8 .9, 3.725 7. ) 3.25,8.0,24,465 8. ) . 6,4, .325
1.) 2. )
, 5.) 6. )
'- -9 • ) 10. )
1 3 . ) 14. )
~
9.) 5 . 65, 9 . 375, 6.8 1 0 .) 9.7, 8 . 65, 3.0, 5.8 11.) 8.67, 9.18, .375 ,9. 4 12.) 12.67, 97.846, 375.2, 47 .8 13.) 68.5 , 3.72, 483, .3 75 14.) 94, . 86, 7.2, .875 15.) 3.420, 1.486, 97.84 16.) .8, . 005, 974
3. ) 4 • )
7. ) 8. )
To) 12 . )
15. ) 1 6 . )
I
YIORK SREET IN SUJ3TRl,CTIOU CF ~)j~CHJ,.LS
Carefully study the prob1eDs work~d bel ow. See if you can tell how the difference or answer is founrt. Th~y arc c orrect .
3.600 .75 2.475 .375 1.125 .375
SUBTRJ.CT. (. " .
( 1 ) 4.820 3.796
( 2) 4 1 .33
(3) .974 • 268
3. 6.1 1.46 1.48 1.541 4.62
9 6
9 4
b.
• 1 • 4 0 2
• 7 .23
2 • 9 7 8 1 • 489
9 :~ ,~ o
.068 2.475 8.932 1.125
c.
5 2 • 7 5
8 • • 002
2 7 • 4 9 .86
(4) • 8 0 3 9 • 4 701 • 004
5 • 001 2 • 666
(5) \7ork subtraction 2,t right ~d r. Subtract 5.835 fron 41
b . FroD 2.75 subtn'.. ct .4
4.68 .746
3.934
d.
8 • 4 2 .43
9 • 7 .00 3
9 .46 1 • 8
2 • 7 8 • 9
bJ
4. 1.1118 2.8882
e •
.46 • 028
2 7 • 1 4 .68
3 4 028 2 • 3
7 8 . 08 8 • 9
C o ~y the following (r, j 9.8 - 2.6
in the proper sp8.ce ( e) 12.1 - 3.04 (f) 6.74 - 2.375 (g) 4 .25 - .065 (h) 15 - 8.75
be l ow r,nd subtrGct. 3 - .125
(b) .976 - . 065 (c) 19.467 - 12.3 (d) 65.87 - 12
a) b)
e) f)
~
i) j )
----- --
"
c)
C;)
k)
~
r
,
( i) ( j) (k) ( 1)
.375 - .37
.166 - .133 2.1 - 2.099
d )
h )
1)
-
i
44
VIORK SHE~T I N 11;LTIrLICl.~ I ClJ 0]' DECH'J.LS
RULE : In nultiplyinc; deciD[',ls :i.)o i nt off 2,S nany :vle.,ces in the pro duct as there are deciDe.,l places in the multi plier and the
mult i plicand. Count fr oD the right . ?rcv i do ~xtra ple.,ces with zeros~ ·
Study the oxanples Ywrkod bolow:
.37 !2 placos) ~ 1 :place
.185 3 l)l[1,COS~ .25 !2 Placosl .25 2 pl aces
.0023 4 pl aces
.011 ! ____ P1EtCOS) .07 placos)
---;:pf ==places)
Eul ti111y . '}["t ch tho Docir.l[",l Point in the product.
1,) 3 . 4 • 0 7
• 97 8 803 __ --'-7 .0 0 9
4 7 • 3 .09
9 • 0 8 o • 6
6 0 .04 • 002
B) 9 • 2 7 5 • 6
7 6 • 9 . 89
6 . 87 .87
• 9 2 5 .23
• 023 4 9
Tho following problens are all worked c orroctly f or you with tho oxcopti on that tho docina l point has been onittod . Can yo u place it?
3 .06 2 16 9 2 4 6 200 • 1 • 329 7 • 0 2 1 • 222 • 00 1 2 2 0 • 2 311 6 4 2 6 4 7952 1 1 0 9 5 2 404202 1 025 367
Copy the f oll ow ing prob1ens in tho spaces provided bolow and find tho i)roduct in o2"ch C2..se . \72..tch the decin[',l po int.
d 327.4 X 4.32
c) 30. 07 X 295
0 ) t X .5 X 24
[" )
d)
b)
e)
~
'.
-
r
b) 9.206 X 70.01
d) 8886 X .904
f) t X 9.287
h)
f)
,
.
..
F ORK SHt:i'>(T IN ~mLTIPPCj\'1:'I ()TT OF D>(CP~j\ L8
Instructions and examples : To multip ly a numb c·, r by 10, wrj.te a zero (0) aft c) r t he
numb ,;r. If the number is a do cim81, move th e::: decimp.l point one place to tho right. 36 X 10 = 360 , or 42 .6 X 10 = 426 •
.' To multiply a numb ,; r by 100, vrri t \.: t FO zeros (00) 8.ft cr the numb~r. If the numbe r is Fl d eCimal, move tho decima. l point t wo plac e to the ri ght. 33 X 100 = 3300, or .87 X 100 = 87.
To multiply by 1000 -- Can you maIn) the rule for 1000 ?
nuickly plac e th( corr ect answer following each problem.
1. 10 X 45 = 35 X 100 = 1000 X 60 = 2 . 1.7 X 10 - 100 X 3 .5 = 1000 X 1. 5 = -3 , 1. 45 X 10 = 2 .006 X 100 = . 275 X 1000 = 4 . 10 X .189 = 100 X 20.01 = 1000 X 460
WORK SHP.~T IN DIVI SION 0'" D~CIHP.LS
Instructions and examplos: To divid u a number by 10, move th~ dcc i m2 l point one
p l ace to the l eft. 46 ~ 10 = 4 . 6 To di vid o [', numb " r by 100, move the; a.ecim[' 1 [.J oint t wo
plac os to tho l oft. 37 ~ 100 = .37 To divid e by 1000 -- Can you make thu rule f or 1000 ?
=
Ciuickly plac o th, corr c:ct ansvIcr follov ing the, problem.
1. 3 .5 + 10 = 3.5 '1- 100 = 250 ~ 1000 = 2 . 35 + 10 = 489 + 100 = .25 + 1000 =
3. 40 + 10 = .27 + 100 - 2 .7 5 '1- 1000 = -
4. . 65 ~ 10 = 3000 ~ 100 :;: 8000 + 1000 =
De: cima 1 point pla c l:mcnt in division of d ecimp l nu.rnb crs . Fh~;n the: divisor i s a whole:· numb er, ple.co the doel l'l[' l point in tho 0uoti unt dir ~ etly over tho deciM21 point in the divi~ en'. Study thu oxamp l e s ,72 .326 19 3 3 a nd 2.p[J ly th:..: rul o . 9)6.48 12) 3 . 912 4).76 3)9,9
V~on the divisor is 8 decimal move the dec ima l pOint to th(! right of the number mc:: king the di vi sor a whole number.
Next shift or mov(~ tht~ d C' cimrl poi n t to the right in the cU vid end £'.s many plac es a s you s hif t ed tho d ecimal point in the divisor. Us a zoros to fill tho empty plpces if n0c c ssary.
The d oc 1;'118. 1 }loint in the (l uoti ent should th,:m be plElc cd directly abov e:: the; n ow decimn l point y (m hav e: loc I" t ed in the dividend, Study the examples a nd Hop ly the rul e .
2.5 1 i\5 • ) 3 A? . 5
~
r
2 5 2,,5 .)62,-\5._
25 .37)925
46
WORK SHH'BT IN DI"lTl: SI 'J ,'1 !)Y i>~\~ Pr.Px
StudY' the examples below and :~j l~ . :·_r. l:h,~ missing decimal point in the 0.uotient. The 1"hole examp::,,, 1 s p) , ' :~ecl, supply only the decimal point and the necessClry ZE'::i'O ,j '}'h::: no.mbers a re correct.
2 2 7 2 2 :s 326 3)6 . 6 9)6.4 8 5)1.2 5 12)3.9 1 2
o 4 3 3 ~ 6 L"!
3) . 1 2 5) . 1 6 5 7) .0 2 1 6) .0 3 6
4 428 418 5.96 ) 2.3 8 4 . 036 ) 1 5 4 0.8 3 . 6 ) 1 5 0 4 .8
Divide the foll01~ng. '~Tatch the decimal point:
1. 2 ) 7 8 . 4 8 . 25 ) 6 .2 7 5 .036 ) 1 5 3.7 2
Divic e the fol10 p ing:
5 . 8 )9 . 7 6 8 CLl 'i ~'9 11 2 . 0 .... I . 0 ~ ::: 6.43 )1 2 3 6 . 8
Copy the probl ems in the proper space below ano divide. Carry the quoti ent to t hree decima l plac e s if n eces s ary .
(1) 1.4}3 2 3 .4 (2) 9)8 . 7 (3) .834}9 1.7 4 (4) .25}6 7 5
11 ) 8) 3) 4) I ,
..
I ~
I I "
! r
<
47
•
SICTloN IV;
D!9.gn~Elt1c .. ~emed1.al 'reat Data
1, tabUlation. and Graph.
2. In(11'9'14\$1 Reootda 8llQ.Gifapha
7.~. Gbph I. 1ee" OOJllP.t'llon "I .. A, Graph II , Test eoJltPe.t'1'loft 8 .. B, GJ'B.ph Itl:. teat Co.pari'OJ! S. A, Graph IV. 'rest eompar~Bon OompoIU.t. Graph V. Compar'aOP Ali. Gr ad.e '!'''el1~Y''8QV"Gn'~h s treet
S(!hoolG",;Ph~ VI, Qompa:rl ... n
3 \0 Gn.ph 11'l\eJ,!'pr.tatton 8<b4 SUJ!II'laJ'Y
~
~
r
Tabulations and Graphs
The f ol lowing t abul at i ons and gr aphs a re a series of
listings of test results by gr ades, and by groups; t he ex-
perimental group, Twenty-seventh s treet School, and t he oon-
trol group , Wisoonsin Avenue School.
49
"Individual Record Sheets" paired by gr ades a r e a ccom
panied by a gr aphic iilus t rat ion of t he results tabula ted
t hereon. Ea ch shee t has an a lphabetica l listing of t he pupils.
Ea ch. name on t he experimental group lis t, Twen ty- seventh Street
School, i s followed by number composed of nine di gits . The
f irs t t hree digits represent the pupil's age, t he second
t hree the pupil' s I . Q. and the third t hree his diagnostic
tes t score. The control group has only a six digit number .
The firs t three r epresent t he age and the l ast three the first
tes t score. The I . Q.. was omitted i n the control group beca.use
of t he ina va ilability of t hie mat erial. 'l'hese series of digits ,
used for grouping purposes , a re f ollowed by the error score ,
for each class ification of error i n decimal s, and the tota l
erro r. In red , d following t he tota l error scora, i s t he
total ~rror s core of the remedia l check tes t. In all in
stance.s t he bla ck figure s repres ent the fir s t or diagnos tic
tes t score, while t he red figures give t he tota l s for t he
second or remedial check tes t s core.
The a ccompanying gr aph f or each gr ade r epresent s a pic-
ture oftha results by compari son of the t wo t es t s cores .
In addition it compa r es i n like manner t he experimenta l and ~
control groupe for t hat grade .
r
"
Graph I. i s e. chax'ting of the 7 .. B grade , Gr aph n . the
7,..A, Graph III . t he 8- B, and Graph IV. 8- A gr ade . Following
t he 8. A charting i s Graph V. t he composite score sheet and
acoompanying gr aph of t he two tests for the experimental and
control groups. Gr aph VI. shows the relat ive placement of
t he grades of the experiment a.l group i n both the initia l and
check teats .
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50
1,100 Series 7-B Twent~=seventh Street School
INDIVIDUAL RECORD Black - Test 1 Red - Test 2
51
lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
Barth, Edwa.rd 011,095,088 .;1... .0.. .~ .. . .~ . .;3.. . ~ . 1 2 11 2918
Behrens, Phyllis 012,134,092 1 o 3 3 2 o 1 3 12 25 9
Bowen,Anita 013,089,092.;1. .. .:I .... ~ ... .4; . . ~ .. 2 1 4 14 25 24
Clasen, June 011,123,084 . ;1... .0.. 2 .. ..3 . . ~.. .+.. .. 2 . ..3. . ;J.'~33 24
Degner,Robert 012, ,093 .0. . . Z .. .0 .. .. 4 . . ~ ... + .. .. 0 . .. Q. .~ ~21
Domrose,Betty 011,126,113 .0.. 0 .0 .... ~ . . 0 ... 0 . . .. 0 ... J, ... . J, __ 4_ 0
Dra.11e,Herbert 012,110,093 .0 .. o .0 .. ..4. .~.. .0 .. 1 .. ~. . ;J.. ~ ~4
Emmrj oh,Wm. 012,119,087 . ;1, . 0 .5 ....3 .. g. .?.. 1 .. J, . .1.~ ~14
Genrich,Gerald 012,119,084 . ;1,. 0 .4 .. .. ~ .. g .. ? .. ? .. ~ .. ;1,J, 3314 \.\.
Gregor,He1en 013,096,064 .7 ... 6 ... 3 .... 3 . 4 .0 .. .. 0 . .. 8 .. g2 5315
Hintz,Hilda. 012,108,079 .1 .. 0 ... 4 .. .... 4 . A. :9 .. · .. ~ . .. J: . ". ;1,8 3816
Jungbauer, Isabel 012,094,090 . ;1, . ).... 2 ... 3. 4 1 1 1 13 2711 ,
Kaemmerer,Robt, 013,114,086 . ~. .9.. .? .. ..3 . .~.. .1.. 1 4 13 3117
Kahn,Pea.rl 012, ,076 . 2 . .l .. .4 . . .4 . . ~ . ) .... 1 9 15 4124
Kletzke, Miriam... 012,118,099 . g . .9. . 0 2 2 ° Koch,Marian 011,122,084 . 0 . o o 4 . 4, . 1
T.andman,Katbl een 011,113,084 .. 1 . .0.. .3 . ..4. 4.. . ~ ..
Leavenworth,Joan 012,098,069 5 0 2 ~ .3 . 3 4
° 2 19
2 6 16
1 .. 2 . ..19
19
18 5
3314
3318
4821
Lewin,Do1ores 013,088,076 .? . . l .. ? . : ~ . , 2 3
L1sherQn,Frank 013. .083 020 2
4
3
1
4
1
" ° 1
4
1
° 1
8
6
6
o
15 41 21
23 ~10
Mensing,Ruth 011,120,097
Micha1,George 013,095,083 ° 1
1
° 2
5
7
1 ... 3 ·1 ' 19
Rauk,Gile 013,092,083 .. ~ . ,;J ..... ~ .. .. 4: . 4 1 '1 1 14
Romoser,Betty 012,129,087 2 1 7 o 18
20 6
34 27
34 14
3010
Rust.Mary 012,104,081 ° ° 7
° o
° 2 ·
2
4
4
.. 4 . . 2.. .. 1 .. 4. ..l~ ~16
Stanfor~,Patsy Dl1,118,089 ° o 4
Trean ts, Paul 014~ 089, Q9JL . 0.. . .Q . . . p. . 4 4
2
° 1
o ~
Va 1 oq ,Norman 013,095,098.!3....0.. 0. . ..' ;2. ..0. ..J, . . .. . ~
3
3
6
7
4
6
28 5
18 8
1914
Watry, June 013,091,0'64 . 0 .... Q. .~.. .. p. ..4:. ..~. 4 13 20 53 30
Williams. James 013,103,087 .;2....Q. ..~. ..~. .. 4:. .~~. . .. Q 1 8 3010
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BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL Twenty-seventh street GRADE 7-B ROOM ___ _
CITY Mi1wa.ukee STATE Wisconsin DATE, ___ _
Directions for tabulating: Indicateforeacn-item the number of pupils who omitted or made .an error. The~ dat a will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
Fractions as Decimals
Addition Subtraction Multiplication Divisio:
I II IV [ t ... 5 .. .. . .. . 5 . . . a . . 29 . . . b . . . 3 . . . . . ... 4 . . . b . . 23 .. . c ... 8 .. .. . . , .3 . . . c . . l5 .. . d .. . 6 .. .. .... 0 .. . d . . 3.Q .. .
7 e ... .... . .. .. ? .. Total 97 5 5
f ... ~ . .. . .. .. 4: .. . . Average 3.2 1.8
g . . 13 . . . . 2.L.1 Total 49 22
Average. 1.6 .7 23 % 10%
_ _ __ 8_ . 23
13. 6% 3. 2%
Value of Decimals
III
a . .. ~ .. ..
b .. . 6 .. .. c . . 11 . .. . d .. J,f~ .. ..
e .. J,~ .. .. Total 63 17
Average_ 2.1~ 56
4 2%' 11%
REMARKS :
80% 45%
Decimals as Fractions
V
a .. ?S .. .. b .. 26 .. .. c . . 18 .. .
d .. 19 .. .. Total 91 41
Average 3 .0 ~.3
75% 3 2%
Averages b a sed on 3 0 c ases . % Avera ges b a sed on 117 s ituatiGns.
Bla ck figur es indica te t a bula tions f or fir s t . te s t.
Red figures i ndic a t e t a b ul a tions , t ota ls, a n d pepcent a ge s f o r
1 0 . .. ... . . . . .. l .. . 2 . .1 .0 ... .. .. 0 .. .
3 ... 1 .. . . .. . 0 .. . 4 .. . 2 ... . . . .. 0 .. . 5 . .. 0 .. . . ... . 1 .. . 6 ... P ... . . . .. 1 .. . 7 ... ~ ... .. .. Q .. . 8 ... 1 ... . . . . 4 . . . 9 .. . 2 .. . . . .. 4 . . .
10 .. . 3 .. .. . '- .. 4 .. . 11 ... 3. ... .. .. 0 . . . 12 . . 15 . . . . .. . . 3 .. . 13 . .. . :? .. . 14 .. . .4: .. . 15 .. .. ~ ... 16 .. .. 9 . . . 17 . ... 5 . . . 18
19
20
21
22
23
24
25
26
27
28
29
30
31 6.9% 10%
32 Total~7 25 47 28
second t e st. Average_ 1.2.83 1.6 .93
Total all Errors 934 4 47 9. 4%
Average all Errors 31.1 14. 9 . 5.4% 26 . 5% 12.7%
. 11> ... .. . .. 0.
.1 . . . .. .. .5
.1 . . . .. . .. Q
.5 . .. .. . .. a
.2 . . . .. .. .2 , .1 . .. · ... .2 ,
9 . .. .. ... q .2 . .. .. . .. 5.
.2 ... . . . 1~
.1 .. . · .. ll
.1 . .. . · ·13
.3 ... . . . 12 ~ ... · .. ?~ ~ .. . · . . 30
. ~ ... . . . 1l
.4 ... · . . 11
.5 . . . · . . 15-
.8 .. . · . . 12
.8 . . . · . . 22 Q ... .. .19.
.5 ... . . . 21
.4: . .. .. .26. 4 .. . · .. l3. ~ .. . · .. ?P. + .. . · .. 14. .3 . .. · .. 18. ·1 ... · . ·20-.4 .. . · . ·26-.4: ... ... 18. .7 ... . . . 21
.... 8 .. . ·
... 11 .. . -.119 81 40~
3.9 2 .7 13.5
1 2 . 2% 4 5%
8.8% 19%
P"b1ished by EDUCATIONAL TEST BUREALf. INC. Minneapolis - Nashville - Philadelphia
7-B Wisconsin Avenue School 52 INDIVIDUAL RECORD Black - Test 1
Red - Test 2 lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number
of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
Ad~m, .Tohn 013,104 0 .. 9 . .. 0 ... ~ .. 2 . . 0 ... 0 .. 3 .. 5 .. ~18
Anoyich, Ani1 012,046 .2 .... P ... Q .. 4 .. 4: ... 6 . . . . 7. :)-4 . :?4: . . -.1..L7l
Antzack, Shirley 011,068 .1.. . .P. . .:? . 4 ... 3.. .:?. . .J,.. 1.l . :?9 .. ~43
Bogie, Robert 012,055p .... P ... Q .. :4 ... 4:: .. 0 . . .. ~ .. ~ .. ~?. ~54
Bottoni, Russell 012,069 .7... . ~ . . .5 . 4 4 1 0 7 15 48 40
~3 Burze1ich, Mike 012:':058 .9. . . .9. ..5 . 4. .4:.. .4: .. . .0. :J.Q. ~9 ..
De Buono, .Toe 012,083 .0 .. .. 3 . .. 5 . .4. .. 4 ... 4 .... 1. . l. 12 .. ~27
Dorn, Robert 012,079 .0 .. .. l .. J~. 4 .4 ... 0 .. . . 0. 'J .. l7 .. ~3l
Drown, Bobby 011,077 .0 . 6 .. 0 .. ~ ... 3 ... 0 . . 0 . l~ . . . 9 .. _~0_37
~ste1e, Clifton 012,097
Fitch. Ralph 012.082
Gabrielson, Benj. 014,046
G11bertson,DoloreW Q11,081
~O'''HHl~' _ no'1v 0'1_08.1 ~~~~~-----.,
.0 .. - .. 1 . ..5 . .4.. .4 .. .0 .. . .1 . 19 .. 20 .. ---M-43
.0 .... 9 . . . l.~ ... 4 .. .0 .. : .7. .. P .. 1,3 .. _~44
.3 .... t? .P . . ~ ... 4 .. 4 .... ~ . ),,7 .. 2~ .. ~64
.0. . . .3. .2. .3. . .3.. 6 .. ..0. .4 .. 15.. -3.6-30
.0 . . .0. . 2 . .4.. .4 . . 1 .. . 3 . .5 .. 14 .. :33 28
Hauge, Mildred 012,070 ~ .... 5 . . A . . 3 .. 2 .. 1 .. . 8. 11. 13 .. 47 39
Herro, Betty .Tane 012,054 .7. .. .. :? . 3 .. 4 ... :? . 4 ... $ . 13 . . ~O .. ~69
Howe, Roy 014,060 .5... .3 . . 5 . .4.. .4. . 1 .. .:3. 14 .. 18 .. ~_49
Ka1im1ch, Mildred 012,070 .2 .... 5 . .. 5 .. 4 .. ' .4 . . 3 ... . 1 .. 6 .. 17. .. ~43
Ks.pke , Raymond 01~.063
Koepp, Walter 012,057
Kot1arek, Robeit 012,071
Kreger,Marguerite 011,070
MOffat, Pearl 012,059
Mn,.n lnL _ _ .T l'!JTlA ~ 012,081
P~nos, .Tames 012,085
Picbettj, illlne 011,064
.6 .. . . . 6 . . 5.. .4.. .4 .. 2 .. . 3. . .2.. .3.. ---5.L62
.J, .. ..fi . . P.. .4.. .4: .. 2. . . . ;L .. ll . . 2.7. .. ~51
.l . ..0 .. 0 ... 4 .. 4 .. 1 . . .. 8 . . 16 .. 1.2 . . ~34
.3 .... 6 .. 5 ... 4 .. 4 .. 1 ... 1 .. 3 .. 2.0 . . 3L46
4 . . 3 .. 4.. .4.. 4 . . P ... ~ . . . ],4 . . 1.~ .. ~53
o 0 ) ..... 3 . . g . . l .... ;L .. 1:1. . . 1.7. .. ~46
0 ... 6.. .1 ... 3 .. :3 . . 2 ... . 1 ... 2 .. 14 .. ~18
Q.. . g. . ~.. .4:.. ~ .. . ? .. . ~. . .4 .. 24 .. ~54
Rediake, Dolores 013,079 6 . ... . 6 .. ~ ... 4 .. :4 . . 2 ... 1 . . 6 . . 7 .... ~40
~ ". 47 Roth, Kathleen 012,06L 0 . ... . 1 . . P . . . 4 .. :4 .. 2 ... a. 19 .. 1.6 .. ~
Salk. Fred 012.069
Segneri, Sy1vjo 013,057
0 . .. . . 0 . . 4 . . 2 .. :4 . . Q .. . .5 . 14 .. 1.7 .. ~47
0 ..... 2. A.. .3.. 2.. 5. . .2 . 19 .. 23 .. ---filL 46
k r
BRUECKNER DIAGNOSTIC TEST IN DECIMALS Class Summary Sheet
SCHOOL Wisconsin Avenue GRADE 7B ROOM ___ _
CITY Milwaukee STATE_ hscons1n DATE, ____ _
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. Thef data will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
Fractions as becimals
Addition , Subtraction Multiplication Divisio
I
" .. . 3 ... . b ... ~ . .. .
c . )·P ... .
d .. 12 ... . e .. 12 .. . . f .. 16 ... . g .. le ... .
Total 80 85
II
. . . 21 . . . · .. l2 . . . · .. 22 .. . · .. :::4: ' .. . · .. 22.; . .. 27 . ..
128101 Average 2.1 2 . 3 ~ 2 .7
30% 56% 32. 9% 4 5%
Value of
Decimals
III
a . .. 21. .. b ... le .. . c .. . 24: .. . d .. 27 .. . e ... ~$ .. .
Total 118 III Average 3.2 ;3 .0
64% 60%
REMARKS :
IV
a . . ~.7. . ,. b . . ~P ... . c .. 30 .. . d . . 3!7 . . ,.
Total 1:39 143
Average 3.7 3 . 8
92% 95%
Decimals as
Fractions
1 ... 0 .. .. · 2 .. 21 .. .. 3 .. . 2 .. . 4 .. 13 .. .
5 ... 1 .. . .
6 ... 3 .. ..
7 ... 0 . . ..
8 ... 3 .. .. ' 9 . .. 5 .... ,
10 ... 6 ... . 11 . ),.~ .. . .
12 .. ~? .. .. 13
14 15 16
V 17 a . .. 36. . 18
b ... 3p.. . 19
c .. . 31 . . . 20
d ... 33... 21
Total 135 124 22
Average :3.rJ 3.3 23
92% 82 .5% 24
· 25
26
27
Averages ba sed on 37 cases Average ; per centage based on
117 test situations.
28
29
30
31
32
Black figures indicate tabulations for first test. 21.6%
19%
.. .. 0 .. . . ... 3 .. .
. ... 0 .. . .. .. 9 .. .
. ... Q .. . .. .. 9 .. .
. ... 0 . . . · .. 17 .. .
.. .. 1 .. . . . . 10 . . .
.. .. 2 .. . · .. 13 .. .
.. 13 .. . . . . 17 .. .
.. 1.2 .. . . .. 10 . . .
.. l.3 .. . ... 15 .. .
.. 1.3 .. . . . .. 5 .. .
.. .. l .. . . .. . 4 . . .
.. .. ~ .. . . . . . 5 .. .
.... Q . . . · ... $ .. . .. :Ll. .. . · ... 4: .. . . . Hi. .. .., .5 .. . .. :L!i .. .. · .10 .. . .. 13 .. . · .10 ...
.. ~.Q .. .
· ~ 17. .. . .. 15 . ..
· .. .6 .. . .... 6 . .. .
· . 1.6 .. . · . 1.2 .. . · .1:4 . .. · . 3..7. .. . .. ;1.2 .. . · .3.5 .. . .. 3.6. .. . .. 22 .. . · .25 ... , · .2~ ... .
. . . 1 .. .
.. .6 .. . · .. 3 . . . . .. 3 .. .
. .. 3. · · · .10 . . ,
· .17· · · .12 .. ' · .24 .. 1
· .17 ..
· .23 . . · .23 .. · .30: . · .37 .. · .34 ..
· .l6 . . · ~9 .. , .15 .. .20 .. .23 ..
.26 ..
.31 . .
.24 ..
.28 ..
.23 . .
.2.9. ..
.2.e ..
.3.1 . .
.3.Q ..
· :3.l ..
Red fi gur e s indicate t abulations; total s, and p~rcentage s for second test. Total 85 99 122_13 1...Q95361 619 E
Average 2.32 , 6 3.;L3 . 5
Total all Errors...lfi2LJ. 791 Average all Errors 49.2 4.8.4
429b. 41.3%
19.2% 20 . 9%
Pllbli,hed by EDUCATIONAL TEST BUREAt? INC. Minneapolis - Nashville - Philadelphia
10.79 . 7 16.7i
33.1% 55.E 30.3% Q7. i
7-B Wis consin Avenue School 53 INDIVIDUAL RECORD Black - Test 1
( continued ) Red - Test 2. lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number
Name of Pupil
Shadid, Dorothy
Smith. Aud.r.ey
Stefanovich.Jesse
Triyer. Robert
Voss, Otis
Vuk. Anna
Wp.t.7.Al, Wp] tel'
of examples wrong or omitted.
I II
012,062 . . 2 . .. 5 .
0012,056 .. 1 . .. 3 .
014.054 . ... 4. .. 2.
012 1 105 2 2
012 , 076 4 6
011;029 7 6
0]2,Q58 .. 1 . .. 6 .
~
~ y
III
. 3.
. ;3 ..
. P . 0
3
5
. 0 ..
IV
. 4 ..
. 4 ..
.4 .. 2
4
4
.4 ..
V Add Sub Multi Div Total
.. 4 . .. 3 . .~ .. .1.0 .l.P . ~46
.. 4 . .. 4 . . ~ . )"'~ .$? ~65
4 4 . 0. . .2_~ 17 ~51
2 2 0 0 2 12 15
4 2 0 5 13 41 44
4 6 1;1. .. 17 28 88 71
.. 4. .. 2 . . 5 .. 29 .. .. 8. --.5..9_45
BRUECKNER DIAGNOSTIC TEST IN DECIMALS . Class Summary Sheet
SCHOOL Wi sconsi n Avenue GRADE 7-B ROOM ______ ~
CITY STATE DATE ____ _
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. The, datll will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
I II
:1 .... . ..•
b ...... ..
c .... ... .
d .. ..... .
e ........
f ....... .
g ....... .
TotalL-__ _
.\ verage _ __ _
Fractions as Decimals
IV
a , ... " ..
b ....... .
c ....... .
d ........ Total __ _
Average ___ _
Addit ion Subtraction Multiplication Divisio:
1 . .. " ...
2 ....... ,
3
4 " .,' ,. ,.
5
6
7 ........
8
9 .... .. ..
10 ", . . '. ' ,
11 . ', ." '"
12 .,".".
(Summary on first page) 13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
III
Value of
Decimals
a ........
b ........
c ....... .
d ....... .
e ....... . Total __ _
AveragiL __ _
REMARKS:
~
Decimals as
Fractions
V
a ........
b ... .... '
c ..... . ..
d ....... .
Total __ _
Average ___ _
Total, ___ __
A verage: ____ _
Total all Errors;---
Average all Errol's----
Published by EDUCATIONAL TEST BUREA\f INC Minneapolis - ·Nashville - Philadelphia
'1 e "
GRAPH I.
Test Comparison Graph
N. 27th Street School
7-B Class
Brueckner Diagnostic Test In Decimals
1st. test Diagnostic
2nd. test Remedi a l Check
Experimental Group
N. 27th Stree t
Control Group Wisconsin Ave .
1 9 3 7
54
~
713 f r :t~ IJ:'i1= ~:f± trt± * i-t . t-+Ll-rffitl n t~ 1 i~ + --++:- ~:t±:± lfr-~ II-!-tt~ ·,
tttt irt-F ~-;:J:t:J ,*~ -ltJ:.' T .I;:: r+=::m-f1 ~
tm ,d f+t-t+$ih~!t 1+ ti+ * ::;:l:;: ±p: ~-T"+'-' I itR: f:H-t 11-""' :j::j: It-C-c-I- H-;-' -j-~~.::j7T 11 + +tt! t .-;1 -H=!+ ~- ' ~'.
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LEGEND
Graph I.
'1-B Class 27th st. - Wis. ATe.
Comparison - Using Brueckner Diagnostic Test in Decimals
Experimental Group Red Line N. 27th street School
Control Group Green Line W.isconsin Ave. School
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Solid Line
Broken Line
1st. Test Diagnostic
2nd. Test Following Remedial Work
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I ~ Reading and Writing Dec 1ms.l.s 'r . : II. Writing and Reading Decimals If ' III. Value of Decimals 11#+#]0 IV. Cbangil'.l.gFractions to Decimals ,
++ C,.,- + .1" t- I ; + /'_ ' -H+ +tc 1 ; ,~ I· +I CT- +H-!-;-t---,- '. +-t--+--'-"-±lttl-= 7,7--i++-r-+ '-tt- , ~'Z-j- -itt+ f ,' --+ -+-t- " 'tt'-+rt+ ,': • :, -I-i--W+t+ J+ 110 -'--~ -1" ¥l+T ~-W '+- r '-t- . " --.. '-+- C't ~--++l-+ t;::T , , ~- - ,+-'+~ ~ -' : ~ +--- T- -t ~ . ----'-i ',.'tt- -, TT \ ::w.. lL1 ~. r +t-H-. "";''''' '. +.-'-;:I~liL 'J7, ~ 1-1+- ,~~ ., _ t ~=+Iit1:itT' ~ ,+-+ ~ p,+ ' 1-4 + • .i, 'b~:1-j~-
V. Changing De·cimals . to Fract1o.ns \ ADD. Addition of Decimals Il-I-SUB. Subtraction of Decimals ~ ltULT.. )luI t ,iplica tion oC Decimals DIV. Division of Decimal.
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-H-tt-I+ ; tt- IHt+ rw ~c~ fflIBi ffi . : . t:;:ti ~j:j:rl-+h=f- I :.j:+ . th ' -\-++I ,. It: tttlt;:j:;: wlET IT+4 , cti 1=. - I I- , 1+.J....ttl- p Hr+I=!±-+-+--,- R+ W++t-'-'++- Jm+ 1 -tt++ 1 ~tt+' , . ,1-1+ 1++ + It+~4. n "j:1-:-I±'tt i-,-'t-~,'i
,~ ";:j::;:r ;t~ rifl '-H+-+++ !::L. i . , 'fT-4tr'- ,+tt- I@ntlttt-t- . ,-; H-t.t H- I-t-+-<+ '±.T tf-M-t-t -;:t-;-t- .-->-r+-'. H-.- -:- ++ 1l+-.-t~'1=I=- +41: ~HTH -,-<-j- d!t:~'t . ".' ' F' ,.~, ~.~+--i-'- dtl -+t.;-'-I f-l--<- . hili-!±!: :-'-t :t:;:: h-c-l+ . -+
v l:±±±I-: F-t---1'tT f-t -h--T , . , ~ ~ I -i-i---+ ;:r ';..,-- .,~, '. ':, f ,. 1 "-+IWt--;1 ... i+'+t - +:::;. ~ , , . . . .,.., ,',' ~-= _ ''''''' "t +l+r =~ ....-t .. ' ~ 1101--+;-=;' "rH t±!:. .,-I+- EE:!: ..;:;;.. :t;ir+-'-I-h-!± f+T" I~I ~rc, ' ':± ' 0.....;.. ..... !-j-:- -W-f--l--' • -H ~ ..i-4-
PR I NTED IN U .S .A . EUGENE DIETZGEN CO" CH ICAGO -NEW .. YORK NO.346 C
-'
BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL N. 27th Street GRADE 7-A ROOML-___ _
CITY Mjlwaukee STATE-----'lliacenajn DATE, ____ ---<
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. The~ dat a will reveal the types of examples in which the class , is weak.
Reading and Writing of Decimals
Fractions as Decimals
L ddition Subtraction Multiplication Divisio'
I
" . . . 2 ... . b ... 1 . .. . c ... 0 . .. . d ... 2 ... .
e ... 4 . . . . f .. J.3 .. .. g .. J.~ .. ..
Total 4'1 19 :\ vel' age 1 • 4
14.2% 5.7%
II
.. . 4 .. ... 0 .. .. .. . 1 ... . .. ~ .. .. .. . 1 ... . ...3. .. ..
1.0..-1----.2_-.15
3.3% . 2 . 5 %
Value of
Decimals
III
a .11 ... . b ... 8 .. .. c .. 11 .. . . d .21 .. .. e .22 .. ..
Total 73 17 Average 1.5 ~37
30% 7.5%
REMARKS:
IV
a .. 42 .. . b .. 22 .. . c . . ~Q .. .
d .. 45 . . . . Total124 66
Average 2.7 1.4
67.5% 3 5%
Decimals as
Fractions
V . a .. 33 . ... . b .. 30, ... .
c .. 10 .... . d . . 22 ... .
Total106 53 Average~J .1
57.5% 27.5%
Averages based on 46 Cases. % Averages based on 117 situations
Black figures indicate t abula tions for first test.
Red fi gures indicate t abulations, totals, and percentages for second test. ~
1 ... 0 . .. 2 .. 19 .... 3 .. . 4 .. . 4 ... S .... 5 ... 0 . ... 6 ... 4 .... 7 ... 3 .. . . 8 .. . ~ ... .
9 .. . 6 . ... 10 .. . 3 . . ..
11 . . . 7 ... . 12 .. 1.9 .... 13 14
15
16
17
18
19
20
21
22
23
24
25
,26
27
28
29
30
31 4.1% 32 ' 13.3%
Total 74 24
.. .. 2 .. .
. ... 0 .. .
. ... 0 .. .
. ... 0 .. .
. ... 0 .. .
.... 2 .. .
.. .. 4 . . .
...B .. .
. .. . 6 . . . · . 1.0 .. . .. .. 0 .. . .. . 1 .. . · ... 7. . . . .. , P. .. . ... ~ ... · . lQ ... ... 3 . ..
~S
. .. 0 ... .
. .. 1 ... .
.. .1 .. ..
· .. 6 ... . . . . 5 ... .
· .. 2 .... . . . . Q ... .
... 2 . . ..
...4 .. ..
.. ~ .. ..
.. .5 .. .. · ... 3. ... . .. .3 .. ..
.. .5 .. ..
...~ .. ..
. l.Q ... ..
.. , .... .
.12 . .. .
.. 5 .... .
..P . ... .
.11. ... .
.. 4 .... .
· '. 5 .... . .. 2 .. . . . .10 .. . ..
· .7 .... . .. 9: .. .. .11 .. : . . .1.9 .... . .13 .... . .10 .... , .14 .... . 2.Q.~1
· .. 2 .. ~ ., .9 . . . . .. 0 . . .
. . . 0 .. .
. .. 3 .. .
... 3 .. ,
.. .4 . .. : .. 3 ..
f
· .. 6 .. (
· .13" j
· .15 . . · .l2 . . '
· .22··1 · .46 . . . .. ~ .. . .. 6 .. · ~O" , · .. 6 . . . . . 5 .. .. .5 . .
· ~:3 . .
. 35 . .
.. . 7 .. f
.16 ..
.11 . , · ;L.Q . ~ .12 ..
. 19 ..
.. .7. .. · ;L.~ ..
3231 Average 1.6 .5 1.4 ____ 39 4.3 2 .2 ~
Total all Errors '022 525 11. 6 %
Average all Errors 22.2 li.4 2 .2% _ . . __ __ _ IS. 9~ 9.7 9&
Published by EDUCATIONAL TEST BUREAl(, INC. Minneapolis - Nashville - Philadelphia
13.4%
6.S%
23.;
169&
7 -A mYifViBlflt sit~edi{~ol Black _ Test 1. 56 (continuation) Red - Test 2 .
lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
Pape, Howard 012.109,096 1 0 o 3 4 o 2 4 7 2113
Peterson,Corne1ia 012,136,106 . 0 .0.. .0 .. . .~ . ~ . ..;J., .. :,.. . .~ . . ~ . ~ 5 ,
Petri, Arlene · 012,129,096 . ;1,. 0 .0 .. .. 3 .. ~ . . . ;J., .. 0 . .. 7. .. ~ .. ~ 5
Pfeiffer, Anne 01~,104,096 . 1 . .0. . .3.. . .3 . . 2. . . ;1, . . l. . .3. . 'J .. ~ 9
Powell, Ada 013,111,088 . l. .. 0 ... 0 .. .. ~ .. l .... ~ .. ~ . l .l .. a .. ~10 Q.uarton, Bill 013,093,100 . . ;J., . 0 .. .0 ... 3 . . ~ ... . :a .. 6. 2 . ;t .. ~17
.Beinold, Harold 013,100,102 . 0 ... 0 .. 0 .... 2 .. 4. ... 1 .. 0 ... 1 .. 5 .. ~ 4
Roge, Dorothy 012,1] 9,103 . 1. . . 0. .0 .. ..2 . .2.. . .l. .. 2. ..3. .3.. --.JA... 7
SanFiJippo, .Tohn OJ3,097,083 .. 1. . 0 .. . 2 .. .. 3 ... 4 . .. 2 .1 .. 6 . 15. _ .3.4.J.4
Sander, lnga 012,121,111 .. 0 ... 0 .. .0 ... 1 .. 0 .... 0 .. 0 .. 1 .. 4 . ~ 2
.. 0 .. 0 . . . 2 .. 1. . .. 0 .. . 0 ·. 4 .. 4. -l..2- 6
.. 2 . . 0 . .. 2 . .4. . .. 3 .. . 1 .. 8 .. 6. -.2L12
Schroeder, Eileen 012,104,097 .. 2 . . . 0 .. 0 .... 2 .. 2 .... 0 . . . 1 .. 2 .11. ~10
Schwartz, "R1fri e da OJ2,321,106 .. 1 ... 0 .. 0 . .. 0 · ·4· ··· 1 ... 0 ··1 · .2. ---9-- 9
strauss, Jean 012,124,075 . . 1 ... 0 .. 4. · . 3 · ·1· ·· ·2 ···7 ·13 ·11· 42 ]9
Zerza, Margie 012,136,101 .. 1 . . . 0 . . 0 . . .. 2 .. 2 . ··· 2 · ··0 ··1 ·· 8 · -J..9- 9
~
~
r
BRUECKNER DIAGNOSTIC TEST IN DECIMALS Class Summary Sheet
Milwaukee STATE W1SC0nSln DATE, ____ ,
Directions for tabulating : Indicate for each item the number of pupils who omitted or made an error. Thef data will reveal the types of examples iri which the class is weak.
Reading and Writing of Decimals
Fractions as Decimals
Addit ion Subtraction Multiplication Divisio~
I TT H IV 1
,1 ... . ... . a ...... .. 2
b .. ..... . b ........ 3
c ........ c .. .. .... 4
d ........ d .. .. .. .. 5
e .. .. .... Total __ _ 6
f ........ Average ___ _ 7
g .. . ... . . 8 TotaIL __ _ 9
.\ verage _ __ _ 10
11
12 ... . . .. .
13 (( For tabulations see fLll:ft page »
III
Value of
Decimals
a .. .. ....
b ........
c .... ... .
d .. .. ....
. e ..... ...
Total __ _
Average ___ _
REMARKS:
~
Decimals as
Fractions
V .
a .. .. ....
b ........
c ........
d .. ......
TotaLI __ _
A verage: ___ _
15 16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32 Tota,-l _--,-_
Average. ___ _
Total all Errors---
Average all Errors----
Publjshed by EDUCATIONAL T EST BUREAlf'. INC. Minneapolis - Nashville - P hiladelphia
...... (
( • • ••• ' 1
· .. . . "
• ••• • "l
. .. . . . . \.
7-~~Wlfconsin Avenue School. INU VIDUAL RECORD Black - Test 1
Red - Test 2
57
lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
A11a, Joseph 015,088 .. 0 .. P . ... 4 .. 2 ... 2 .. 1. .. 2 .. 3 .. . 10-.2.9...28
Asti, Ted 012,097 .. 1 .. 0. . .. .0 .. 2 ... 2 .. 3 .... 2 .. 1 . . . . 9 ~4
Behling, Elizabeth 012,t)89 .. 2 .. 15 .... 0 .. . ~ .. 9 .. 9 .... 0 . . . 4: .. . ],:). 28 28
Bond1er. Richard 013,096 .0 . .3.. .. 1 .. 3 . . .2 . .1.. . .0. . . 3. . .. 8 21 26
Buech. Edith 013,070 .. 2 .. 1. .. 0 . .. 4 ... 4 .. 1 . ... 2 .23 . . 10 47 45
Cata, Steve OJ 2,074 .. 2 . . 5. . .. 4 .. 3. . .2 . . 3. . .. O. .1:3. . .11 ~5
Copou1os. Bessi. 012,085 . . 0. .~. . .. :2. . .2. ..2 . . 0.. .. 1 14. . .. 6 ~6
Davis, Patricia 013,080 . .0 .. l. ... 15 ... 2 ... 2 .. 3 ... 1 .... 7 .. 16 ~7
Daw, Dorothy 0]2,]06 . 0 .. 1 . . . . 0 ... 2 .. .0 .. 1 .. . 0 .... 2 . ... 6 ....l2~6
Dexter, Fred 01 2,087 .0. .2.. . .0. . .2. . 2 . .1.. . .1. 17 · ·· ·5 30 43
. 21 Fergllson , Virginia 012,095 . 0 . .0. . . ·0. .2. .1. .0.. . .0. . ·5 · ·14 --22-1
Go111beff, Geo. OJ 3,069 . 4 . . 5. . .. 4. . .4 . . 2 . .2. . : .1. ..9 . . 17 --4.a-.BO
. 0. .. 5 . . .. 2 ... 4 .. .0 .. 0 .. . . 0 ... 4 .... 6 ~O Guerndt. Doris 012.096
Ho~ Jane 012,084 .1. .0 .... 3 .. .3 .. 2 .. 1 .... 2 .. . 1 . . 11 ~2
Ja,mes, Betty 012,069 .4.. ) ... .. 0 . ..4. .2. .4.. .. 7. . 8. . 1.8 --4a..-J)9
Kraus, Rita 012,09L . 0 .. . 1 .... 2 . . .3 .. 2 .. 0 .... 2 . · 4· . 1.2 --2e---26
Ledin, Donald 012,097. 0.. .0.. . .0. 2 . :2. . .0.. . .2. . .4 . .1Q ~l
MagJio, Caroline 012,072 . 2 . . 6 .. .. :3 ... 4 .. 4 ... 2 .... 3 ... 8 .. 13 ~49
.McGregor. Stuart 013,088 .2 .. . 2 .... 0 . .. 3 . . 2 ... 1 .... 2 ... 3 .. 14 ~_30
. 30 Meriwea ther, Eugene 013,087 .1. .0 .... 5 .. 3 .. 2 ... 2 .... 1 ... 4 .. 1.2 ....:3.!LJ
~o11ak, C1ar~nCe 013,071 .1. . 4 5 .. 4 . .4.. .2.. ..1. l.Q . .15 -.4.L53
Rose. Gerald 011,083 .1 ... f? .... 3 . ... 4 .. 4 ... 3 .... 3 ... 5 . .. . 6 ~34
Salamone, Saverio 013,082 .3 ... 4 .. .. 0 .. 4 . .4 ... 2 .. .. 0 ... 3 .. 15 ~35
Sanford, Annabelle 012,108 . 0.. .0.. . .2. ..2. .2.. .0.. . .0. . .2. . .. 1 ~18
-.Qekeres, Helen 013,]06 .1.. .0 .... 0 .. 2 . . 2 .. . 0 .... 0 . . 4 .... 3 ~20
Serio, Florence 012,098 .1 ... 0 .... 0 ... 4 .. 4 ... 2 .... 0 ... 4 . ... 4 ...19J7
. 32 Smith, Dean _~.oB.5- .1 ... 5 . ... 0 ... 4 .. l. .2. ... 4 ... 7 .... 8 ~
~ling, Jean ~
013,078 .2 .. . 5 .... 0 ... 3 .. 2 .. 2 .. . . 1. 11 ... 13 ~46
Spero, V..a rion 012,076 .:J: .. . 0 .... 9 ... 4 .. g .. 9 .... ~ .. . ~ ... l,~ ~4l
Wright, Robert 012,081 .2 ... 2 . ... 2 ... 4 .. 2 . . 1 .... 3 ... 7 .. 13 ~42
~
BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL Wisconsin Avenue GRADE 7-A ROOM ______ __
CITY .IIU.LWaU.Kee, STATE Wisoensin DATE, ____ _
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. The> data will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals .
Fractions as Decimals
Addition Subtraction Multiplication Divisim
I .) 2 l ~ •••• ••••
b .. ~ ..... c 8 . . . . . . ,. d .. 8 .... . e .10 .... . f .12 .. . .. g ).3 .... .
Total 5137
II
. . ~7 .. . ... 9 ... . .. ~9 .. . .. 24 ... ... ;J...~ .. . .. 22 ..
lQ9127
Average 1.7 1. 2 ~ __ ~. 2
24% 60%
IV
a . .. 36 . . .
b .. .21 .. . c ... 22 .. . d . . .a7 .. .
Total 116 97
Average 3.9 3.2 97~ 80~ , I
1 ... ~ .. ..
2 . 1.7 . .. .
3 .. l. .. ..
4 . 1l. ... .
5 .. 0 .... . 6 .. ~ ... . .
7 .. 1 .. .. 8 1 · .. .... . 9 .. ~ ..... -
10 3 · ... .. . .
11 5 · . . .... .
. .. 0 ....
: . ·0···· . . . 1 ... . · . . 0 ... . . ' . . 0 ... .
2 · ...... . . . . 0 ... . ... t? .. . · .. 4 ... . . . . 5 ... . .. . q ... .
. . . 5 ... .
... ~ . . . . · .. 5 .. ..
· ·15···· . .. ~ ....
11
· ),.:) ...... !f · . ..... . 8 · .... " .
... 4 .. .. · .. !;i ... .
.. 3 .. ..
.:J.P .. ..
..1 .. ..
.. 1 .. ..
..6 .. .. · .3 . .. . ).0 .. ..
2
.+~ .. .
.16 . . .
.21 . . . 17% 70.5%
12 .13 ... . . · .. 3 ... . • . , .4 .. . . .19 .. .
III
Value of
Decimals
a .. 12 .. .. b .. 11 . .. .
c .. 13 ... . d .. 20 .. .. e .. 20 ... .
Total 76 77 A verage-2.....5..-.2~ 5
50% 50%
REMARKS:
Decimals as
Fractions
V
a . . 3.Q .. . b .. 26 .. .
c .. 14 .. . d .. l.5 .. .
Total 85 73 Average 2.8 2 .4
70% 60%
Averages based on 30 cases. Average percentage based on 117
test situations. Black figures indicate tabulations
for first test. Red figures indicate tabulations,
totals, a.nd percentages for second test. '
13
14
15 16
17 18
19
20
21
22
23
24
25
26
27
28
29
30
31 1 5<11, 32 16.6%
Total 60 55
Average
. . . 4 .. . .
.. . ~ .. . .
. ),,3 .. ..
· ~6 .. .. · .. 7. . .. .
69 56
Total all Errors
Average all Errors
2.0 ].8 2.3 1.9
1309 1207 13.5%
43.6 40. 2 11% 37.2% 34.3%
Published by EDUCATIONAL TEST BUREA~. INC. Minneapolis - Nashville - Philadelphia ---
... ~ .. ..
... 9 ... .
... 2 ... . · .13 .. .. ... ~ .. .. · .21 ... . · .14 ... . · .12 ... . .~O .. ..
... 6 .. ..
.. . 6 ... .
... 7 .. ..
... ~ .. ..
.11 .. ..
.. . 8 . . . .
. .. 8 ... .
. . . 8 ... . 14 · ... .. . .
.25 ...•
.23 . . . . 304 287
. ~;J.. .. .
. ~7 .. .
.26 .. .
· .6 .. . ..~ .. . · .3 . . . .15 ... .~l .. .
.18 .. .
.3l. ..
..9 .. .
.l3 .. .
.lO .. .
.l6 .. .
.20 .. .
.31 .. .
.18 .. . 24
439 :
10.1 9.6 14 .6 ' ", 31. 5 /0
30%
48.7
44%
~C'.\' u
GRAPH II.
Test Comparison Graph
N. 27th Street School
7-A Cla ss
Brueckner Diagnostic Test In Decimals
ist. test Diagnostic
2nd. test Remedial Check
Experimental Group
N. 27th Str eet
Control Group Wisconsin Ave.
193 7
58
. .e:t.1!.
LEGEND
Graph II.
27th St. - Wis ,. Ave.
Comparison - Using Brueckner Diagnos:tic Test in Decimal'S
Experill'lental Group Red L111-e N. 27th street School
Control Group Green Line Wisconsin Ave,. School
Solid Line
Broken Line
Base L1ne
1st. Test, Dlagno,stic
2nd. Test Following Remedial Work
. (Brueclcner)
I. Reading and Wr1 ting Decimals 11 .• · Wrl ting and Baading DeCimals 111. - Value of Decimals IV. ' ChangIng Fractions to· Decimals V. ' Changing Dectmals to FractIons ADD. ' Addition ot DeOimals SUB.. Subtraction ot Decimals lIDLT. MultiplicatIon 'of Decimals DIV.. Division of Decimals
PRINTED IN U.S _A
8-B Twenty-seventh Street Scnool 1-300 series . INDIVIDUAL RECORD Black - Test 1
Red - Test 2 59
lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
An~erson, Ernest 012,109,095
. Beyer,Beatrice 013,117,101
Byrd, Jack 013,120,106
. Co1e,Shir1ey 012,112,101
o o
.0 ... 0 .
o 0
o
2 3 4
o . ;2.. 1
201
,Drake, Marion 913,092,096 1
o
o 2
2
2
3
2
2
Thldovjc,E1iz. 012,097,104
Duehring,C1arence013,108,105
.Eisenach. Rob. 013,119,109
.0
o
o
o 0
o 2
o 0
. ~ .. 0
2 0
1 1
o o 2
.. ~. 0 3
002
o 4
11
9
6
5 1
2 3 1 7
o 4
o
2 3
1 0 .. . ..
1 2
. \ .
6
:3
3
22 6
16 9
11 2
16 1
21 10
13 6 '
12 8
8 3
' HjJmers ,Barbera 013,119,1030.. .. 0. . Q . . 3. . . ~ .. . .3. .:1.. 0 .. ~ 14 7
,Kurtz, Harry 013,100,101
Lahmayer,Lorraine013,117,105
. Landisch,Jaanette013,105,099
1 0
1 0
1
Lewis. William 013,107,102 .1 ..
o
o
o Liebherr, Marce11a013,104,100 0
o
o
o
o
2
2
2
2
2
2
1
Q
o
4
2
2 1
0 ' 1
1
1
1
o
o
o
5
3
2
3
6
4 16 3
5 12 12
12
4
4
. I.indow, Ruth 012,131,104 .1 .... 0 . .0 . 1 1 .. + ... 1 .. 3 .. 5
1812
15 8
17 7
13 5
Matoushek,Y~rtin 012.121,110 o 2
Moll, Dorothy 013,109,097
o
o
1
1
2 1 7 5
20 7
,Raley, Vivian 013,093,099
.0
7
o
o o
1
2
1
2
2 1 2
o
o
o
1
3
2
2
6
9
4
2
1815
18 2
12 O'
Rosentha1,A1vin 013,102,099 .0 .. .. + . . .0 .. 3 . . 4 .... 2
She.de, LaVaJJgbn 013,130,105 .0 .... 0 .. .0 .. 3 .. 2 005
Smith, Dorothy ' 012,122,102 2 o o 2 2 1 o 3 . , ~. ~3
Smith, Helen 013,110,101 .1 . 1 .. 3 . . ~ . )'" .. +. ..Q. .3.. .. ~. ~ 3
Snead, Sue 013,118,106~ ... . 0 . . .0 .. ~ . 0 o 0 5 3 11 4
Wa11ner,E1izA 014,099,098 1 0 0 2 4 3 t 2 6 19 14
,Watson, Jessie 012,117,108 0 .. 0. 0 2 2 o . 0 0 5 9 14
Wegner. Robert 012,135,113 .0.. 0 0 1 0 o 0 1 2 · 4 1
weissenfluh,G1en 013J-124Q'IL .1, ... . 0 .. . ? .. ~ . . ;2 .. ),9 . .. ~. 4
,J,Vith, Shirley 013,120",105 1 .. ~. 1 ~ 0 3 0 1
12 43 19
5 12 6
·1
BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL N. 27th street
CITY Milwaukee,
GRADE 8-B ROOM ______ __
STATE Wisconsin DATE, ____ ~.
Directions for tabulating : Indicate for each item the number of pupils who omitted or made an error. The~ dabol will rev'eal the types of examples in which the class is weak.
Reading and Writing of Def!imals
Fractions as Decimals
Addition Subtraction Multiplication
I II
n . .. ~.. . . . . .. 0 .
b .. . 1.. .. .. .. 1 . . . c .. . Z.. .. .. .. 1 .. . d . .. 1. ... . ... 0 . . . e ... 1.... . .. . 0 .. . f ... 4.... . ... Q .. .
g . :LO .. ,. Total 20 21
Average • 7 .7 10~ 10%
~ __ ·9.1. 25
1% 4~
Value of
Decimals
III
a . .. 4 ... . b .. . q .. . . c ... 1, . .. . d ... q ... . e ... q. ' .. .
Total 23 2
Average_ .82 ..b7 16.4% 1.4%
REMARKS:
IV
a . . . 25 .. b .. ... Q . . c .... 1, ...
d ... 2.4 .. Total
Average
55 25 L}
50% 25%
Decimals as
Fractions
V
a ... 13 .. . b ... ~P .. . c .... P .. . d . .. . ~
Total
Average
42 10 1.5 . 36
37.5% 9%
Averages based on 28 cases. % Averages based on 117 situations.
Black figures indicate tabulations for first test.
Red figures indicate tabula tions, totals, and percentages f or
1 .. . 0 .. .. 2 .. 11 .... 3 ... O ... . 4 ... 0. 5 ... I .... 6 . .. :J. . .. 7 ... O .... 8 .. . 1 .... 9 ... ? ...
10 2 . ... . ... 11 .. . 2 .. .. 12 .. . 5 .... 13 14 15 16
17 18
19
20
21
22
23
24
25
26
27
28
29
30
31 1. 7~ 32 8.3%
Total 30 6 second test.
Average 1 .21
Total all Errors 414 192
· . .' .J, ...
· .. .Q ...
· .. .0 .. . · . .. J, .. . .. . .0 .. . · .. ;I, .. . .. . ;I, .. .
. .. 2 .. .
. .. . ~ . .. 2
... Q . ..
· .. Q .. . · .. .:3 . . . ... 1. ... .. . 2 .. .. · .. 3 ... . ... 5 .. .
22 12 .7 .42
4.1%
Average all Errors 14.7 6 . 9 1 2 ,5% 5.9~
2 .5~
.. .. Q ... '" .0 .. . . ... 0 .. . . ... 2 .. . . ... 0 .. . '" .0 ... .... 2 ... . .. . 0 , .. . ... 1 .. .
1 · .. ... . . .. . . Q . . .
.... 1 .. .
. ... 9 .. .
.. .. 4 .. .
. ... 1 .. .
... . f? .. · .. ,2 ... . ... 4 . ..
.. .. fL ..
. .. . ~ . ..
. ... J, . .. . .... ~ 00.
· ... J, 00. · ... 1, ...
.. ·300' · .. Q .. .
. . . g . . . · .. .0 .. . ...2 . . .
3
. .. P. 00 ,
· .. 6. ... 69 24
2.5 .9
7.8~
2 . 8~
Published by EDUCATIONAL TEST BUREA\f, INC. Minneapolis - Nashville - Philadelphia
DivisiOl
' .. . ~ .. . . .. 2 ... . .. .1 .. . . .. 0 .. . .. .1'00 · .. 0 .. , .. .2 ... . .. 2 . . . . . . 2 . . .
2 · ... . . .
· . ~? . . .. 3 .. . 14 .. .27 ..
.. .9 ..
...2 .. · .. 3 ..
· .. 0 .. . ... 4 . . ...Q ..
· .. q . . · i2.? .
2
.. .q . . ,002 ..
...5 ..
.. .? ..
. .. ~ .. · . . 5. ..
4
151 5.:
17.5 10'%
8-B Wisconsin Avenue School. 60 INDIVIDUAL RECORD Black - Test 1 Red - Test 2.
lis record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
Ande r son, Russell 014,098 .. 2 .. 6 . 0 .3 .... 1 .. 0 . .. 1 .. 3 .... 3. -.1214
:Chapela, Jennie 012,102
, Curti s , Gene 014,098
Curtis, Jane 013,077
,Daugherty, Handa 0 1 3,090
,Fisch, Dorothy 012,106
. . 0 ... 4 ... 0 .. 2 .. .. 0 ... 4 . . 1 .. L .. 3, ~7
.. O. ..0. ..2 . .4.. ..1 .. 0. ..0 . . :3. . .. 9. ---.ll17
.. 1 .. 5. ..2..4.. .. 2. ..2. . 1 . 11 . .12. .3Q.10
.. 2 .. 0 . . 3 .. 2 . .. 4 ... 2 ... 0 . . 3 ... 1~ ~6
.. 1. . O. . 0 . .3.. O. ..0. . .0 . .4.. .. 3. --.lJ.1.1
Fitch, Lawrence 013,101 .. 0. . .0 . .5 .. . 2 .... 2 ... 0. . 0 .2.. . . 15. 16 14
:F1int, John 013,087 .. 0. 2 . ~ .. 3 ... ;1.. 3 .0 . . ~. ),0. ~4
'Frenn , Edd; e 01 3 ,084 .. O. . .1 . . 5. . .4.. . .1. . .3 . . 0 . .6. . .13. -.3.,3 31
,Fuch s. Howa rd 014, 099 .. 1. ° . (). .3 .. .. 3 .. 0 . . 0 .? . 9 ' 1818
Gen s ler, J1lne 013.060
:Grinne11, Lily 014,102
:Hanson. Kenneth 015.075
2 .. 2. . ~ . ~ .. .. 2. ..4 .' . 'J.. ],4, . ),.8. 57 48
.. 1. ..0 . O . .4 .. .. 1. ..1. .0 . . 1 .. .. 7. --.1.5..25
.. 3...5. . 0 . .4 .. .. 2. ..1. .9.. .3.. .15. ~7
Hardel, Do10J:'..e.£. 012,082 .. 0 ... 0 .. 5 .. . 2 .. .. 2 ... 2 . . 1 . 12 .. . 11. ~O
iRea t.h, Robe rt 0]3,108 .. 1. .. 0 .. 0 .. 3 ... .. 0 ... 0.0 ... 2 .... 3. ~3
:Hering, Jane 014,040 .. 6 . .. 2 .. 5 ... 4 .... 4 .. 4 . . 5 .. . 8 ... 20. 77 63
'Hopper, Adrienne ' 015,046 1 .. t? .?.. 4 1 .. ~ . .7 .. 23.. .24 . ---.11...68
015.081 )" .. ~ . .0.. .4 .. ..4: . 0 ° 12 12 36 25
'Krueger, Henry 013,059 .. 5 ... 6 .. 5 .. . 4 .. .. 4 . .. q . . ~ .. 8 ],7. 58 47
,LaBelle, Paul 014, 0 3'7 .. 7. 6 5 4 4 3 8 15 28 '80 69
T,andrnm, Perr y ' 014,095 .. 3 ... 5 .. 0 .. 3 .... 1 ... 2 . . 0. . . 1.. '7 22 14
~Nicbols, John 014,098 .. 0 ... 0 .. 0 ... 4 .. 4 .. 0 .. ;1.. ... 2 .. 9 19 18
:011a, Tina 014,0'70 0 6. 5 4 4
3
1
o 4 18 15 47 32
Olsen, Claire 012,104 o 2 2 3 o 2 1 13 8
iPauno y icb, Nick 013,035 .. 6 ... 6 .. 3 ... 4.. 4 .. ~ .. ~ .. 20 ... 2~. 82 71
iPowers, Ma rianne 012,084 .. 1 ... 4 . . 0 ... 3 .... 4 . .. 1 . . 'J .. . 6 .. :i 7. ~2
'Radcli~fe, Carlyle 014~~L .. 0 ... p . .. Q . . P" .. . ~ .. ;3 ... +. ,,:1, , ... 7. 22 22
lReid, Kenneth 011,096 . J . .. 0, .. 2. .?.. .. .1. 2 2 2 9 21 17 ,
.S cheibe r, Dorothy' 013 ,08 4 .. 2. ..? .. 4 , . ~.. .. .~ .. ? .. +. ..~. )" ~ 33 29
,SChenk, Huhter 014,05'7 4 4 5 4 4 3 7 10 19 60 55
Wi tten', Marilyn 012.098 0 0 0 3 2 1 3 5 5 ' 19 11 {;
t
BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL Wisconsin Avenue GRADE 8~B ROOM ______ __
CITY Milwaukee, STATE Wisconsin DATE, ____ ~
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. The~ data will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
Fractions as Decimals
Addit ion Subtraction Multiplication DivisiOi.
I
:1 . .. 2 .... b ... 6 .. . . c ... 7 .. .. d .. . Q .. .. e .. . q ... . f .1.3 .. ..
g .12 .. . ". Total 51 55
II
. .. 16 .. ..... 6 .. .. .. 12 .. .. .. J, ? .. . .. .l..3 .. ." 18 ..
~1
IV
a ... .31 ..
b ... 22 ... c ... 2.Q .. d ... 31 .. .
Total 1 04 J 00 Average .3 • .3 3,2
82% 80%
Average 1.6 1.8_~2_lQ. 2 .3 23% 43% 269h 38%
III
Value of
Decimals
a .. 1.~ .. . b .... ~ .. .
c .. 10 .. . d .. l~ .. . e .. 1.8 .. .
Total 67 65 Average_~~ 2.1
44% 42%
REMARKS:
Decimals as
Fractions
V
a .. . 22 . . . b ... 23 . . . c ... 11 .. . d .. 14 .. .
Total 70 75 AveI'age_~, 4
56% 60%
Averages based on 31 cases. Average percentage based on 117
test situations . Black figures indicate t abulations
for first test,
1 ... 9 .. .. 2 . 12 ... . 3 ... 5 .. .. 4 ... 0 .. .. 5 ... 0 .. .. 6 .. . 2 ... .
7 ... 1 ... . 8 ... 6 .. ..
9 .. . 4 . . .. 10 ... 3 . .. . 11 ... 7 .. . . 12 . )'.Q ... .
13
14
15
Hi 17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Total
19% 15% 5671
Red fi gures indic ate t abulations, totals, and peTcentages for second test, Average 1.8 2 .3
.. . ). ... .
.. . Q .. .
...0. .. .
.. . . P ... .
. .. 1 .. .
...1. .. .
. .. 9 ... .
. .. 9 ... .
..10 ... . · .11 ... . . .. 0 ... .
· .. 0 .. .. .. . 0 ... . · :;:7 . ... ... 8 .. .. .. :1) ... ..
7 · ... .. . .
8180
2..!_6.J~.J 6
Total all Errors 1074 1098 15% Average all Errors 34 16 3.5.4 15%
29.6% 30,2%
· ... J. .. . . ... 2 .. . . ... 1 .. . .. .. 3 .. . . ... 3 .. . .. . .3 .. .
.. . .3 ...
· . . .3 .. . . .. A .. . . .. .:3 ... .. . .4, .. .
. .. .:3 . ..
. .. Q .. .
. .. A .. .
. .. 1 . ..
.... 7 .. .. 4 · .. . . . . .
· .17 ... . . . . 9 ... .
· .12 .. . ... 6 .. ..
. .. 9 ... .
... '1 ... .
... 7 ... . 1:3 · ... ... .
.. 11 ... . · .. 9 . . . . · .. 8 ... . ... 8 ... .
· .11 ... . · .12 ... .
2:3 · " ... , . 217 22 5
7.0 7.3
22% 22 ,8%
Published by EDUCATIONAL TEST BUREAU, INC. Minneapolis -'Nashville - Philadelphia
.. .2 .. .
. .. 5 .. .
. . . 5 .. .
. .. 1 .. .
. .. 5 . . .
...5 ...
. .. 6.·.
.. .4 ..
. ll .. .
.10 .. .
. 1.6 ..
. 1.3 ..
. 2..3 ..
. .31 ..
. 1B ..
.. B ..
.. :'l.. .
..5 ..
.14. ..
.13·· .
.16. ..
.25 ...
·10·· . .10 . .. 12
.1l ..
.16 ...
.2? ..
.15 .. .
.17 .. .
346 3~
11.2 :
37,3; 38%
~ ),
GRAPH III.
Test Comparison Graph
N. 27th Street School
8-B Class
Brueckner Diagnostic Test In Decimals
1st. test Diagnostic
2nd. t est Remedial Check
Experimental Group
N. 27 th street
Control Group Wisconsin Ave.
193 7
61
I ..
I f-fit ,j-J.
I-rI
++
I P;- Pt;0 1++ '-h-I-ffi
LEGEND
- ..u 1 I+;-,-
1++-',
Graph III.
8-B Class 2'7thSt. - Wis. Ave.
Compa.rison - Using Brueckner DiagnostIc Teet in Decimals
Experimental Group Red Line N. 21th street School
Control. Group Green L£ne Wisconsin Ave. School
Solid Line
Broken Line
Base Line
1st, .. Test Diagnostic
2nd. Test Following Remedial Work
( Brueckner)
I. Rea.ding and Writing Decimals II" Wrl 'ling and. Reading Decimale III. Value of De-eimals IV. Changing Fractions to Decimals V. Changing Decimals to Fractions ADD. Addition of Decimals SUB. Subtraction of Decimals lIDLT. Mul tlplica tion of Decimals DIV. Division ot Decimals
ft-'-',
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PRINTED IN U .S .A
1+..+
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8-A Twenty-seventh Street School Black - Test 1 62 1-400 series INDIVIDUAL RECORD Red - Test 2
his record is to be used to select pupils whose work should be studied. Indicate for each part of the test the number of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
Bassler,Dorothy 013,JJ7,098 .. 0 . ..0. .2. . 1 .. . .2 . ·3 · .0.. ·0.. 8 .. -l-9- 7
: Buh1. Harold 013.11'7.10'7 o 0 1 1 0 0 0 4 4 10 0
; Burmeister,Otto 013.126,105 .. J, . . 0 .. . 0 ... J., . ..1 .. ;3 .. 0 4 2 12 1
10 4 . Burns. Gladys 013,130,107 1 0 0 1 2 0 0 0 6
:---Dhel1, MiriRm 013,109,110 . .1 .. 0 .. . 0 .. l ... 2 .. 0 .. . 0 .'. l .. 2. .. ~ 0
Giese,E1sbeth 013,121,102 0 .0 .. 2 .. 2 .. .. ~ .. :J. ... 0 ... ~ .. ~ ... -..lLl
.. Q . .0.. ,0.. 3 ... 4 .. 3 ... 1 .. 2. .. 4 ... ~_ 5
. Held. Elaine 014.111. 098 .~ . 0 .~ .. g . ..1 . )'" .~ .. 9 .. ~... ~ 4
, Johnson, A1vera 014,095,105 o .0.. 2 l. .. ..1 . .1. . .0.. .3 .. 4 Jg 5
1ohnson, Betty 013,109,~14 1 0 .. .Q . ;t ... . 9 .. 0 ... Q. 9 :J. ... _ 3 _ 3
KudLia, Agnes Ol3,113,106 . ;1. . . 0 ... Q. 3. . ;1. . 0 ... 3. . 4 ... i ---1L.. 6
Locher, Susan 013,116,103 . 0. .0.. .1 .. l ... . 0 . 2 .. .Q .. 0... 0 ... ~ 3
Maddalena, Geo. 013,122,092 . 0 .. 0 ... 0 .. 3 .... 4. .. 2 .. .0 4 . . . 12 .. ~ 9
Meisel, Doris 013,113,098 .1 .. 0 .. 2 .. 2 .... 2. . . 2 .. l .. 1 .. 8 ... ~ 5
MensiDft;, John 013,109,105 :0 ... 0 .. 2 .. 1 .... 4 ... 1 .. .0 .. 2 2 ... ~ 3
Mie1ds. Hugo 013,108.102 . ;t ... 0 .. 1 . 1 .... l ... 1 .. .0 .. 4 ... 6 ... ~ 5
Po1zin,Luci11e 013,103,102 . 1.. 0 0 :3 .4.. 1 1 3.. 2 .. ~ 4
Prasser, Thora 012,124,097 1 1 2 4 4 1 0 3 4 20 1
Raebel,DongJes 014,111,069 . '1.. .0.. 0 4 4
Rasmussen, Marian 012,126,109 .0. 0 1 1 2
7
o
4 16
o
48 24
Runge, Lillian 015,101,105 .3 . . 0 .. .Q .. 3. 2
1
· 1 0
1
2
6
3
;L
9
8
12
o 4
Salamone, Vi6tor 013,108,090 3 :3
Schmidt, ~Ith 013,104,109 . 9. . . . 0 ..
Shevey, Reanette 013.104,099 1 0
Struebing,Bernice013.121.1l2 . J., . 0
5 3
o 2
2
o
3
1
2
3
1
2
1
2
o
1 0
o .1 ..
1
o
o
o
2
6
2
2'7 4
8 5
18
5
3
o
TomJey, Wi11ia.m '014,097,102 . 0 . . 0 ... :? .. 2 2 2 1 2 4 15 2
1'eit,Kstherine 014,JO~11'A- .6 .. . .0. .0. , .2 .. .. 4 ... J., . .;3 ... ~ .. 14 33 6 ~
_Yi.e.rgutz, Alice 013,121,10~ .0 ... 9 . .9.. .~ .. 2 2 1
Wall. Eileen 013,113,100
Zerza, Anna 013,120,111
.ZQesch. William 014.092.089
o 0
.0.. 0
1 0 'y
o o o
4
1
2
4 2
o _0
4 . 3
1
o 2
2 3 12 3
2 4 17 4
o 5 6 2
4 12 . 28 11
BRUECKNER DIAGNOSTIC'TEST IN DECIMALS
Class Summary Sheet
SCHOOL 27th Street GRADE a-A ROOM ______ __
CITY Milwaukee, STATE W!I;aeons:lll DATE, ___ _ _
Directions for tabulat ing : Indicat e for each item t he number of pupils who omitted or made an error. TheE data will reveal the t ypes of examples in which t he class is weak.
Reading and Writ ing of Decimals
Fractions as Decimals
Addition Subtraction Multiplication DivisiOl
I II
" ".3 .. . . . , .. 2 .
b ... 3 . .. . .. . .3 .. .
c ... '7 .. .. .. , .1 .. . d .. . 3 .. .. ... ~ .. . e ... 5 . .. . . . .. 1 .. . f ... 6 ... . .... 0 .. . CY 10 b •• •• ••••
Total ~'7 :2i a2. .l.. verage 1.2 .09 ------2--.-06
17% 3% 1.1% 1%
III
Value of
Decimals
a . . ~ . .. . .
b . . 3 .... . c .. ~. d .. 7 .. .. . e .. fj .. .. .
Total 26 0
Average~ O·
16% 0%
RE MARKS :
IV
a .. . 1.9 .. b .... 9 .. .
c . . .. . 7. .. d .. . 3~ ..
Total 66 15 Average 2 • J • 5
52% 12%
Decimals as
Fract ions
V
a . .. 20 . . . b .. 18 .. .
12 c . ..... ..
d .. 16 .. . Total 66 2
Average 2.L06 52% 1.5%
Averages based on 31 case s . % Averages based on 117 situa tions. Black figures indicate t abula tions
i'or fi r st t est.
1 ... 9 .. .. 2 . . 10 .. . . 3 ... 3 ... .
4 .. . 3 .. ..
5 . .. 3 . . . .
6 ... 1 . .. . 7 . .. 1 .. .. 8 . .. 4 . .. .
9 . .. 2 .. .. 10 ... 1., .. 11 .. . 0 . . . . 12 .11 . . . . 13
14
15
16 17 18
19
20
21
22
23
24
25
26
27
28
29
30
31 1.3% 32 11% Red figures indicate tabulations,
totals, and pet centage s f or second test.
Tot al 44 5
Average 1.4 1. 6
· .. ,1, .. .
.. .. 0 .. .
.. .0 .. .
...n .. .
. .'. 0 . . .
. .. 3. .. .
.. . L ..
...Q: .. .
.. . 1. : ..
.. . ~ .. . · .. 0 .. .. · .. 0 ... . .. , 1 .. . . .. 0 . . . . .. . 3 .. .. .. . ~ .. .. .. . S . . . . .
19 ~ .3 .1
Total all Errors 495 134 2% Average all Errors 15.9 4.3 .6%
13.6% 3 .7%
. ... ~: ...
.. .. 2 .. ·
.. .. 3 .. ·
.. .. 2 ...
. . . ·1···
.. . .2 .. .
.. . .2 . ..
.. ·2 .. ·
.. . .;3 .. .
.. .. 0 .. .
... Q . ..
... 2 .. .
.. .. 5. .. .
...2 .. .
... 1 .. .
...~ .. .
... 1 .. .
. .. 4 .. ..
. .. 1. .. .
... ? .. .
.. . 3 .. ..
. . . 1 ... .
. .. 3 .. . ;
... 2 ... ;
. .. 1 ... . · .. 4 .. .. . . . 0 . . . .
.. .0 .. .
· ··1· .. ... Q ...
: . . 1 . . . ... Q .. .
· .. 3 . . . .. .2 ...
· .. 0 .. ,
..·2 ..
.. ~ .. ,
.. .5 ..
.. 2 ..
. .. 9. ..
.3.Q ..
.. .'7. ..
.. ~ ..
.. 2' ..
..1 ..
.. 4. ..
.. ;3 .. .'
.. 'J .. .
.le .. . · . '1 .. . .11 . . .
· .6 .. . ..3 .. . ..7 . . ,
· .. 3.. .. .12 ...
. . ·9·· · · . ·5··· 4 5
... 9 ... ~ · .. 6 . .. .
75 22 154 2.4 .7 5.C
7. 5% 171< 2 . 2% 8. f:
Published by EDUCATIONAL T EST BUREA4, I.NC. Minneapolis. Nashville - P hiladelphia
B-! _Wi sconsin Avenue School INDIVIDUAL RECORD
63 Black - Test 1
. Red - Test 2 1is record is to be used to select pupils whose work should be studied. Indicate for eacli part of the test the number
. of examples wrong or omitted.
Name of Pupil I II III IV V Add Sub Multi Div Total
-Achtenhe gen, Betty 013,101 .. ;3 ... 0 ... 0 .. ;3 ... O ... l .. l . . ;3 ... 0 .. ~B
; Anthony, Marie 013.104 .. 0. .. 0. ..0. .~.. . ~ .. .J, .. ..J,. . 0... .4:.. ~4
. Barnes, }f.a rjarie 0l3,0~ .. D ... 3 .. .3 . . 4. .. 2 .. 1 ... 1 . . L .6 .. ---..2D5
Brown, RalDh 013,094 .. 1. .. 0 ... 0 .. 2 ... 3 .. 4; .... 1 .. l ... Q .. ~7
; Call i 11 a rd, Ma ry) yn 014,100 .. D ... 0 .. 2 .. 4 .. . 2 .. 0 .. . 0 .. 2 .. . 7 .. ~7
Flobd, T~is 013, OB3 o .. 5 .. 4; .. 4 ... 2 .. 4; ... .1 . . 2 .. 12 .. ~2
Fuller , Donald Q13,OBI 1 .. Q . . 0. .. ~ . )' " .~ .. .. ~ .. ~ .. le .. ~6
.Gross, Junel1en 013,106 .. 1 ... 0 ... Q .. 2 ... l . 0. ... l .. 1 ... 5 .. ----.l1J.l
,Hall, Rosemary 015,091 .. 1. 6 .2 . . 3 ... 3 . 1. . . . 1. .. 1 ... $ .. _:?§~5
,Heffling, Florence 013,101 . . .J... 5 . 0 . 2 .2. 1. . . 0. .2. . .3 .. ~3
Hillman, Eugene 014,0.77 .. 1 ... 0 . l.. . 2 .. ,:1, .. 1. '2 ... 12 .. 20 .. 40 29
:Hoffman, Roger 013,099 .. O. . .1. . 2. .4 .. .4 . . 1. .1. . .1.. .4 .. J.aJ,B
Jesmak, Vilma 013,107 .. 0. ..2. . 0.. .3.. .0 .. 1... . 0.. .2.. .2 .. J.QJ.4
Long, Filip
Mahas, Frank
013.114 .. 0 .. 0 .. 0 ... 1 .. .0 .. 1 .... 0 ... 0 .. .1 .. ~7
015,OB6 .. 2 ... 0 .. 0 ... 3 ... 2 .. 2 .. 2 .5 .. 1.0 .. ~4
McDonald, Ruth 013.106 .. 0 ... Q .. 9 .. 2 ... ~ .. 2. . 9.. .0 .. .5 .. ---.lL 4
Muriel, Edwards 014,OB4 1 2 . !5 ... 4: .. 4 .. 2.. .g ... 0 .. 1.~.. 33 42
Murphy, Herbe..rt U3,OB3 .. 3. ..0. .0.. .4 .. 4 .. 4... . L .5 .. 13.. ~2
,Norgman, Winifred 013,102 .. 1. ..0..0...3 .. 4.. l... .0.. .1 .. .5.. -.1!S~3
Oneby, William 013,102
Pubanz , Herman ' 013,102
RaMlins, John 0)4,080
Rich, Ma rion 013,097
Rodge rs, Ottis 014,099
Sande1ich, John 013,071
Shanahan, John 013,OB7
.. l. .. 0 . . 0.. .3 .. 4 .. 1... . O. . .0 .. 6 .. -1.5- 9
.. 0 .. 0 . . 0 .. ~ .. 1 .. 1. .0 ... 3 ... 7 .. ' ~O
.. 2. ..5 . . 0.. .4 .. 4 .. 2... . I .. .8 .. 11 .. -3.'L3 B
.. 2. .l . .0.. .2 .. 2 .. 0... .3... .4 .. 6. .. 20 ] 6
.. 0. . 0 . .0.. .3 .. 1 . 0 ... .2 .. .4 .. 8.. , R I B
.. 7 . . 4. . .4.. .4 .. 4. . 0... .2 .. .4 .. I?... ----4.6.-23
.. 0 . . 0.. .0 .. 2 .. 2. .. 1 ... .6.. .6 .. ']... ~9
Sinjakovic, George 014,09 L .0 .. .. Q .. 0 ... 4 .. :3 .. 0 .... 1. .. 6 .. 11 .. ~2
Smith, Curtis 013;095 .0 .... l. .0 .. .2 .. Q .. 1 ... 0 .. . 5 .. 1.5 .. ~l
~t . b arz, Dorothy 914,]02 .1.. .. 0 . .2.. .4 .. 1 .. 0 .. . 0... .0.. ?.. '.5 18
Welcb, Bob 015,097 . 2. . . .2 . . 0. . 2.. :3 .. l .. . P.. .0 .. 10. . . -..2JL].5
Northington, Flo. 014,087 4 3 0 3 4 . 2 0 5 9 ' :30 15
'1'
·BRUECKNER DIAGNOSTIC TEST IN DECIMALS
Class Summary Sheet
SCHOOL Wisconsin Avenue GRADE 8-A ROOM ______ __
CITY Milwaukee STATE Wisconsin DATE _ _ __ _
Directions for tabulating: Indicate for each item the number of pupils who omitted or made an error. The:;; data will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
Fractions as Decimals
Addit ion Subtraction Multiplication DivisiOl
I II
[\ . .. 7. . .. .. .l4 .. b .. .4.... .. . . tL .. c ... 3 ... .. . l3. : . d ... 3.... . . 1.G . . . e .. . 7.. .. .. .l,? .. . f .. . ~.... .. ;t.~ .. . g .1.G . ... ...... ..
Total 47 43 74 62 AveraO'e 1.5 1. 4 2 1 4 2
b ---- -
21% 40% 20% 33%
III
Value of
Decimals
a .. ;3 ..... b 4 · . . . . . c 6 · . , "
d 10 · . ... . . . e .. ~ .. . . .
Total 32 4 4
Average_l • O 1·.4
20% 28%
REMARKS:
IV
a ... 3.2 .. b ... :]..~ . . .
c ... 20 .. d ... 35 ...
Total 106 115 Average 3.4 3 .7
85% 92%
Decimals as
Fractions
V
a . .. 26 .. . b ... J, 7 .. . c ... 17 .. . d . . . 1.e .. .
1
2
3
4
5
6
7
8
9
10 11
12
13
14
15 16
17
18
19 20
21
Total 78 7 9 22
A verage--2...5-2 • 5 23
62.5% 24 62 . 5% 25
Averages based on 31 cases. Average percentage based on 117
test situations.
26
27
28
29
30
0 . . .. . .10 .... ~ . ...
.3 ... .
. 3 .... l . .. .
.1 ....
.4 ....
.2 ... .
.1 .. . :
.!? .... 11 ....
Black figures indicate tabulations for first· test.
31 1 5 . 8% 32 14%
Tot~l 53 60
a 0 · . .. . ... .. .1 ... . ... 1. · .. .Q ... . ... Q
...Q ... . .. . 4
... 1 ... .. .. 2 . · .. 2 . .. . ... 3 ... 4. .. . . . . ·5 · .. 5 . ... · . . .3 · .. 5. ... .. . .5
.. . 6 . ... ...~
. .. ~ .... .. .. 1,
. .. 1 .. . . ... 2 2 ... . ...1 5 ... 4
.9 .... .... Q
. 3 ... . ... 9 . 6 g
... 4 .. ..
.. . 3 .. ..
· .. 2. .. .
. .. 7 . . . .
· .. 4 . . . .
· .. 8 .. ·· · .. 3 . . . .
· . . ? .. .. 4
... 3 ... .
... 3 ... . · . . 2 . .. . · .. !? .. . · ~O .. . . · .1,0 .. . .. 118 125
1 · ... . . .
.. .4 .. .
.. .2 .. .
...0 .. .
... 4 . . .
. .. 3 . . .
. . ·1·· ·
. .. 3 . ·
· ~l · .. · . . 5 .. . ... 6 .. . . .. s . . . 1.5 .. . . 3.3 . . . 1.4 . .
.. 9 .. .
... 6 .. .
· .. 7 . . . ..B ..
.10 .. .
.14 .. .
.31 .. .
· .$ .. . .13 . . . .lO .. . .l:~ ... .16 . . .
.21 .. .
.21 .. .
.?~ .. .
321 2 Red f igures indicate tabulations,
totals, and pei'centages for second test. Average 1.7 1.9
52 5_9
1.7 1.9 3.8 4 . l.Q.c\
Published by
Total all Errors 881 881 Average all Errors 27.5 47 .5
23.5% 23 .5%
10% 11%
EDUCATIONAL TEST BUREAl.!1, INC. Minneapolis ··Nashville · Philadelphia r
11.9% 1 2 . 5%
32.7 31. 6
"f:J.-
GRAPH IV.
Test Comparison Graph
N. 27th Street School
8-A Class
Brueckner Diagnostic Test In Decimals
1st. test Diagnostic
2nd. test Remedial Check
Experimental Group
N. 27th Str eet
Control Group Wi s cons in Ave .
1 93 7
64
LEGENJ)
Oraph IV.
8-A Class 27th s t. - Wis. Ave •.
Comparison .. Using Brueckner Diagnostic Teet in Decimals
Experimental Group Red Line li. 27th $tree.t School
Control Group Green Line Wisconsin Ave. School
Solid Line
Broken Line
Base Line
1st. Teat ~iagno8tic
2nd. Test Following Remo·dial Work
(BruecknaT)
I. Rea.ding a.nd Writing Decimals II . riting and Reading Decimals III. Value of Decimals IV. Changing Fractions to Dacimals V. Changing Decim Is to Fractions ADD. Add! tien of Decimals SUB. Subtraction of Decimals MULT. Multiplies.tion ot Decimals DI V.o Di vision of Decimals
PRINTED IN U.S.A
-+ r ~ -or
.~ -reo- .o-J. ..
. ~ 3.0~
EUGENE DIETZGEN CO" CHICAGO·NEW·YORK NQ.3'16 C
BRUECKNER DIAGNOSTIC TEST IN DECIMALS 65
Composite Score Class Summary Sheet Black - Te s t 1
Red - Test 2 CHOOL
ITY
Twenty-seventh street GRADE 8A,8B, 7 A,& 7B. ROOM. ____ _
Milwaukee STATE Wisconsin DATE ____ _
irect ions for tabulat ing : Indicate for each item the number of pupils who omitted or made an error. These data will reveal the types of examples in which the class is weak. .
Reading and Writing of Decimals
Fractions as Decimals
Addition Subtraction Multiplication Division
I
a . . .. ll .. b ... .. 8 . . c . ... .23 . . d ... ;I..~ . .
e .... 17 .. f ... 3.1 . . g .. . 5.1 ..
II
. . 11 . . .., .8 . .. .. . .. 6 ..
. . .. !' .. . . . . .. 4 . . . .. . '1 . . .
Total 153 65 44 23 overage 1.1 .4~?_.17
15.7% 5.3% 6.9% 2.8%
III
Value of
Decimals
a ... 3.0 .. b .. . ;2.~ .. c .. . gf? . d ... P.~ .. e .. . 5.5 . .
Total 185 36
,verage~~ .26 27.4%
5.2%
EMARKS:
IV
a ... 115 .. b ' .. .. 59 .. c .... 38. . d .. . l,q9 ..
Total 342 l61 Average 2.5 1.19
62.5% 29.7%
Decimals as
Fractions
V
a . . 94 . . .
b . . ~.~ .. .
c .. P.q .. . d .. ~.f? ..
Total 305 106 Averacre 2.2 .78 '" -
56 . 2% 19.5%
1 .. . . 0 . .. 2 .. P.Q . .. 3 .. . . 8 .. . 4 . . ~8 ... 5 ... . q ...
, 6 .. .. 6 . . . 7 .. .. 4 . .. 8 . . ~Q .. .
9 .. ;L.~ . . . 10 .... ~ ... 11 .. J..'1 .. · 12 . . ~.? .. 13 14
15
16
17 18
19
20
21
22
23
24
25
26
27
. . . . 5 . . .
. ... 0 .. .
. ... 0 .. .
. ... 1 . . . · ... ;I. .. . . ... 7 . . . · .. 1;1. .. .
· .. 14 . . . · .. 1~ .. .
17
. . . . 0 . .. 4 .. 'i4'"
.. . 11. ..
.. . 14 . . .
. , .24 .. .
. .. 17 .. .
Averages based en 135 cases. 28 % Averages based on 117 situations 29
Black figures indicate t abulations 30 for first tes t.
Red figures indica t e t abul a tions totals, and p~rcentag es for
31 3.6% 32 ' 11.6%
second test. ~ Total 185 60 153 64
Average 1.4 .44 1.1 .47
Total all Errors 2865 1300 6 .5%
Average all Errors 21.2 9 .6 2 .-7% 18.1% 8.2%
.. .. 0 . . .
. ... ~ . .
.. .. 5 .. .
. .. 15 .. . · ... !3. .. .. .. 5 ...
.. .l-!3. ..
. . .. 6 ...
.. .:J.P ... 3
.. .. 6. .. 9 · ...... .
· .. 20 . . . ... 15 .. . · . .. 'J . . . . .. 22 .. . .. 15 .. . · .. 2800 ' ...l~oo.
· oo l!5 .. . · .. ?P .. . · .. l;l. .. .
· .. ~;5 . . . ... . 8 .. . ... l!5 .. . · oo~~oo. · . . l:? .. . .. 18 . ..
22
. .. . . 5 ..
. .. 17 ..
. .... 1 ..
. .... 1 ..
. .. .. Q ..
. ... . 8 ..
.. . 14 ..
. .. 10 . .
. .. ~1 .. 27
·· · 35 .. ... g~ .. · . . 6.8 ..
· .133 . . . .. 3.6 . . .. .23 ..
· .. 30 . . ... ~9 .. ... ;3.~ . .
· 00 ;3.~ . .
...~.? .. · .lP.l . . · . . ?~. , ..,5.3 ..
. . . ;3.~ ..
· . . ;3.~ ..
· . . ~.~ .. · .. 0.5 ..
35
.. . ~.4: . . . .. '2:7 ... · .. 43 ...
37 554 363 231 1035_
3.4 1.7 7.6 4.1
10.6% 25 .3%
5.3% 13.6%
Published by EDUCATIONAL TEST BUREAU, INC.¥inneapolis - Nashvill e' - Philadelphia
INDIVIDUAL RECORD
This record is to be used to select pupils whose work should be studied. Indicate for each part of the test the numbe of examples wrong or omitted.
Name of Pupil I II III IV V Add ·Sub Multi Div Totf
1
2
3
4
5
6
7
8
9
10
11
12.
13
14
15.
16
17.
18
19_
20
21
22
23
24
25.
26
27 ~
28
29
30
r
BRUECKNER DIAGNOSTIC TEST IN DECIMALS Composite Score Class Summary Sheet
66
~HOOL Wisconsin Avenue School GRADE 8 A,8B.7A, &7B.ROOM ________ _
[TY Milwaukee STATE Wisconsin DATE ________ _
irections for tabulating: Indicate for each item the number of pupils who omitted or made an error. These data will reveal the types of examples in which the class is weak.
Reading and Writing of Decimals
Fractions as Decimals
Addition Subtraction Multiplication Division
I II
[1 . .. 14. . . . .. .68 . .
b .. 25. · · .. ·33· . c .. 28 .. .
d .. 28 . . .
e ... 35 .. . f 48 . ... . ... g .. p5L ..
Total 237 220
. .. 66 ..
. .. 81 .. . ... 65 .. ... ~.Q ..
393 361
verage-....L8.5'1. 7 -.-3-<iO~ . 8
26% 50% 24.3% 46.6%
III
Value of Decimals
a .. ~~ .. .
b .. 4.2 .. . c .. 5.3 . . .
d .. '15... ." e .. 7.Q ...
Total 293 297
verage~' ~~ • 3
44% 46%
EMARKS:
IV a .. 136 . . . b ... 97 .. .
c ... 92 .. d . ~40 ...
Total 465 455 Average~~ 3.5
90% 87.5%
Decimals as Fractions
V
a ... l:I.~ . . b ... lOl ..
1 ... ~ ... .
2 . ~.4 .. 3 ... 9 ... . 4 .37 . .. . 5 . . . 1 ... . 6 .. . 8 . .. . 7 ... ~ . . . . 8 12 · .. ... . 9 14 · ..... . .
10 17 · ... . .. . 11 31 · . . .... .
12 . 5.5 . . . . 13
14
15 16
17
18 19
c ... . 7;3. . 20
d .. , .80.. 21
Total 368351 22
Average~ •. ~_2 . 7. 23
70% 24 67.5% 25
26
27
28 Averages based on 12~ cases 29
% Averages based on 1 17 situations 30 Black fi gures indicate tabulations
for first test. ' M 32
18.3% 16.6%
· .. J. ... . . .. ~ .. .
· .. J. ... . · . J..3 .. . · .. 1 ... . · .1l .. . . .. 0 ... . · .3.9 .. . . .. 3 ... . · . 23 .. . . . . 7 ... . · .30. . . .
· .~~ . . . . · .9~ .. . · .~? .. . · .?~ . . . · .~? .. . · .~g .. . · .~P ... . · .:J.~ . . . · .. ~ ... . · .~~ ... . · .12 ... . · .14 ... . · .:I. 7 .. . . .. ?P .. .. . '.26 ... . ..18 .. . · .4;~ ... . ...~ .. .. · .44 ... . .. 39 .. .. · .33 ... . .. ?P .. ..
.. 9~ .. .. · .43 ... . .. 4:;1. .. .. · .29 ... . .. ?P .. .. .. 37 .. .. .. ?~ .. .. .. 38 ... . · .43 ... .
32 · ...... . .. 34: .. .. .. 34: .. .. .. 52 .. .. .. 72 .. .. .. 90 .. .. Red figures indicate tabulations,
totals, and percentages for second test.
Total 254 .285 324 3~6 . 1JL35 998
Average~.O 2.2 __ ~ .52.5 ·8.Q 7.7
Total all Errors 5113 4977
Average all Errors~._9- 98.7 33.8% 33% .
15% ~510
P"blished by EDUCATIONAL TEST BUREAU, INC. ¥i~neapolis - Nashvill~' - Philadelphia
25% ~4%
.. .. 7 .. .
.. .25 .. .
.. ~1 .. . · • .. !;) . ••
. . ·18· ..
..21 . . .
.. .34 .. . · .. 26 .. . .. ~.4 .. . .. :4.S . .. .. ~E? .. . .. 6.1 .. . ..~.\:) .. . .138 ... ..~.\:) .. . .. 39 .. . · .4.Q .. . .. ;;.Q .. . · . 5.7. .. . .. p.'L .. · .1.4 .. . .1lB .. . · .51 .. . .. 6.4- .. . ..5.5 . . :
..'.2 ... 80
.:I.P.Q .. .
.. ~.4; .. .
..9.6 .. .
1684 1744 l~_.~ 13
45% 43%
INDIVIDUAL RECORD
This record is to be used to select pupils whose work should be studied. Indicate for each part of the test the numb{ of examples wrong or omitted.
1
2
3
4
5.
6
7.
8
9
10
11
12
13
14
15
16
17.
18
19_
20
21 --
22
23
24
25
26
27
28
29
30
Name of Pupil I
~
~
r
II III IV V Add Sub Multi Div Tot:
I' .
.....
~ /v
GRAPH v.
Test COOlparison Graph
N. 27th Str ee t Wisconsin Ave.
Composi te Score-
Brueckner Diagno s tic Test In Decimals
l .st. test Diagnostic
2nd. test Remedial Check
Experimental Group
N. 27th Street
Control Group Wisc onsin Ave .
193 7
67
I i++
tI-.--j- -titt
d ii:t W '''-:21-4+
+~if4;: .tic:nf~~ I ~f,'
-I++- ft4-"1"'
l ti"
+ -++- t-'. !-It- +- -t 1++.
e.r;... -e -lt:.'f -e
if ~j;1: iP , +
LEGEND
Graph V-.
Composite Seore 21th st.-Wi •• ATe.
Comparison .. Using Brueckner Diagnostic T'ast in Decimals
Experimental Group Red Line w. 21th St~eet School
Control Group Green Line W1aconsin ATe. School
S01.id. Line
Broken Line
Base Line
1st. Test Dlagnos.tlc
2nd. Test J'oll.owi.ng Remedia.l Wo rk
(Brueckner)
1. Reading and Writing Decimals II. Writlng and Rea.d~ng Decimals It I • Value of Dec'i maLe IV. Changing J're.ctions to Decimals V. ChangIng Decimals to Fractions ADD. AdditI'on of Decimals SUB. Subtraction ot DecimaLs JroLT. )luI tipllca tion ot DecilllAls DIV. Division of Decimals
+ r
p.., Q
:ff:;:: ~++ +t :t L
'-'
ti±- --
- Hili i±Ql.. ,
, ""1"
-+t.
j: ±t
f+.
. ·Tt .. +rli- 1-1-1
'.- ~ t!1:
I f+ .
.trt, .
PR I NTED I N U. S .A
I
:rt
I tcc
.'-'-'
.-h-
'../...
1++-
t I tt
.~ t 1+ :"- -+_: i' tt:-'-+
F~-r:i
+r ± 1m +"1++
-+t
1+
H-t- i++ 1
1-1 ri+
:i:
H=
I tT
I~ + I-'-h-
1-' :F~ t " i+. P-t T'"
-++- t j: --p. - 't-
,-.
,+
. ttM-t ,
+'4-=1=1= +-1-, L
I i+ i+T 1++
1"r
E'h-' . :.r+! ....-'-
+ 1+*-"'; ~
it...±t:t- --t-H- +
-.::t:::-lt EUGENE DIETZGEN CO., CH ICAGO·NEW-YORK NO.3't6 C
' I rh , 'l.- 68
GRAPH VI.
Test Comparison Graph
N. 27th Street School
Composite Graph
7-B Class 7-A Class 8-B Class 8-A Class
1st. test Diagnostic
2nd. test Remedial Check
Experimental Group
N. 27th Street
Control Group Wisconsin Ave.
1 9 3 7
Graph VI.
C""'JIoat", a...llh ~".11 Sl. 8e11oo1
Coau. .. lao" _ 11e11tg ~ D1atteoeUo 1' ... , .ta llect.aal
a Blaelc Li11S a.d LllJ. G.reeIl Lt.a. Blue Lift.
21th Street. "-11 Clae
• 27th S~r •• t ?-A Cl
ae•
27th Street 8-:e CIa •• 21th St.r •• t 8..A else •.
Solll1.t1.a. lat, 1'.01 D1"Po8tl •
.\!role.., 1.iD. ~'1' ... t J'ol
lewlltg . R8JJ1ecl.ta.l Worle
Ba •• ttll. (Bl'Ueo1atSl")
I. ll"",\tltg...... IOJot Ultg Dee_Ie n . lVPltfltg ...... lie .... fItg llee1Jaa.te Ill. lralu • . or 1>e
C1male .
IV. ~ baou"". to lleeJ.aIe V, ~ D."_Ie to FraoU_ ADD. Add1&to".t Deo1.;;l. SOB, Slll>baO&lOl1 ot lleet..u. 1Il1:t1'. lIiUUJ>llea t.jo" oct :o.C1Jaa.te Drv. Dhtal." ot 1leot"'le
Graph lnt.erp;(·(;tatiol'l I?nd Swmna:ry
The mass of.' tabul at10mJ l'eaul tine; fl1'om the testing pro
gram. to the casual reader e>f t hJ. s thesis :may prove less
fruitful with~ut the accom~anytng graphs. Eaoh ~rada 7.B,
.,.A. 13 ... 13 , and a-A was tested with ~he Bru~ckl1$r D1agnQstLo
Test in Dec 1lnc.le; t hE) results wer~ tabula ted and analyzed,
lI'rom thee .• tabulatl0n$, eon ala.lytlgal graph bt the percenta.ge
of error was dre.wn to }lll'esent the rela.tive. plaoonl?nt of the
e::cpe:r1mental. ol.a.$S tJ'ade i n comparieon w1~h t'he o(m'h'o1 group
I)re' the same gro.d.et and the compa.rison ot the initia.l diag
nQllItlotest with t he x'8sulta ·of t he remedial oheQk test tl'lree
weeks later~
A caJ'eful indi:vidual scrutiny of the Gra.pha I. , I I.,
IU,., and IV. tor grad$8 '.B, '.A, 8 ... !. a,ncl a.A reapedt1Tely
or a study of the general Composite Graph V., the Twenty.
s e'"J'enth s treet sehool Comp~s1te Graph vt., the l'rogrcss
Com.pari8on Ch.' l;t,pb ot the infV'enty pall'S Graph VI I,. or the
Sp~Q'al study fl'aph V:Ul:. wtll l'ovEtal a number of things.
1.. 1'he,re to wide d1ff$r.enC)e 1n the relatlve ievela of
the tWQ grQUl>U of' pu:;piil.s. Cn Graph V. the 801~d U.ne at green
indicates the oontrol group's level of percentage of errQJ',
whl~h is l' t/. ther high l;a:nglns for-om 16 per <)ent on E!ubtra.ct10n
to 90 per o-~nt i n group lV~. changing traQt10ns to dacima18t
Or ail avel'&ge peroen1tage for all groups o'! problems Qf 33.8
per centH atld the solid red ltne indica tea likewise the level "
. of 'I;he ·sxpeJ'i.men t,al group for the tnt t1alQr dU.gnO$t!c t$st J ~ .
ranging ':rom 5 per cent to 7 per cent {or Gr~upn. and Sub.
~
•
69
traQ*1on respectively to 65 per OrJnt for Graup IV., O,r an
avera.ge percentage for all grQUPS of' problems 0,1 18 .. 1 per
cent.
2. The two sOhoola havo relat1vO'ly the same defioien
oiGs. Th~ low~l' and highs1\' peake. are col1i.tOOn to bot)!.,
3. 'rna remedial l"epul to were most effeot! ve in problem
groUps having th~ grea.test peroentage O,f e~ro*, in the initial
teat SQora .On ·Gra.:ph. V. th~ do ttec1 l'$d H.ne . t he rem.$.dial
check acore, shows t he progress as n (u.r~ct result of remedtal
work .
4. 11'1. t hree week period without remedia.l work for the
control group netted 1Tery little gain in decilOO.l knowledge.
On Graph V. following, the green dotted 11118, the aecond tee'
score, wh1Qh 8.1most colnoldee with the broken black dotted.
l1ne charta this gain of leas than one point.
6. The grades, l~ast, removed f:rom the Gra.d.e level tor
dec irr..al instruQt1on , commit,ted the greates't; numbe:rot errore.
Composite Gra.ph VI. for all grades of the experimental group
pio.tu re$ qu.#.te graphioal1Y the :1nit1a.~ a:nd ;remed.ia l oheck
test SQQl'EH3 for each grade showing the range of error.
6. The gra.de farthest removed fl'Q.m th~ gr a.de level for
deeimal lhstruc"Uon responded more readil.y to remedial in.
etructlone in decimalih Graph VI . rev€8.ls the a-A grade .
with the eXQe}Jtion of proplem gl'GUp lV, to have less than
3 per cent e)'ror i.n all nj.ne l'lE'o'blem grQUps. ( See also Gra.ph
IV~ ) ~
~
r
70
,., .. The weekly gro1.'th r :1. tio of remedia.l study to regular
class growth j.n c'.eci:male is 22 to 1. Pictorial G-rarJh VIII
of the epeele.latudy discloses the 1m!)ortance of th!$ ftl.c t.
A speoie.1 sma.11 e.vere,ge growth graph is atte.ched..
~
'(
71
SECT'ION V.
Caee Studies
1. Study of Sevent~ Pair Compe.1t'!son
Ttlbul.atlon (')t Ma.tcl:ling rosreiSf.-Compn.r1son Eiraph VUe
Sh Special s tudy Seyen1;y .. ·tjve Oflses
Ta.pulationot' '{'hree Tei;lts '1nal Summary table s ta'tist108 Su.mmaryandConolu8·1~n8 Value Compari80n Grapb VIII.
~
,
study of Seventy Pair Cempariaon "'.
It was the purpOse in the out~,t to organ1~e tAe pupils .\ . \
studied into one hundred pairs; one of each pair from the
8xPe:r1mental and control groups respectivel)/', e,J'ld paired by
grade, age, I.q, •• 9-nd test score . ., Because of the inaTalia"
bUtt)" of I .Q. ra.tings for many of the con'firol group, this
factor was eliminated from the matching. F\l;riher because
of the apps,rent. dissimilarity at the, two groups, it Was
found. 1mpoasibl.e to secure a. sufficlent number of pair., un
le,s the seore pairing was permitted to vary more than 81~
points, to ma.ke an even one hundred pa1rs_ Keeping within
this range seventy pairs we:r;-e secured tor this stu,dy.
The following tables of matched pall'S are organized by
gradel, and the matching is contrOlled. by the .grade-age
score grouping ideal! 'the first of each :pair 1s trom the ex
peri:tJlental group. The first column number t., the base lin.
indelE on the accolILpanying graph, and the three suooeedine;
oolwnn. al'esel:f'''''expla~tory~ The SOhool Improvement Columns
toiio.ing, ahow the gains made by each pupil as given in the
ro-medial check or 8000nd testacore. Gain$ are l1eted 1n
the first half of the school'soolumn, "htle thsaeoond halt
rsoords Dept!Te soores or 10$8e8 registered and reTealed
by ~heae,coild test acors.
:By an analys1s of the totals and aotual improvement.
one oan dete~lne the relat1ve value of the three"week ex
perimental period to ea,oh group . Turning to the summary ~
total tor all gradee, the t'ollowing ' po1nts are noted:
~
r
73
1. Oomparatively no tmpr evement wa~ made during the
three week period. by t he control group_ Gains ot 30me pupils
totalling one hundred and f1ftY'l!'seven points were lost by
others who did not do 90 well and who ;Produced, a negative
score or on~ hundred and sevente~n. The a.ctual imprOVement
was forty o!' su tenths pOints POl' per80n,
2. )!uch improvement was rea1.1~~d through remedial study,
the experimental group maJdng So total gain o·f nine bundred
and n1noty points, or an average gain 'Ot fourteen and one
'tenth pOints.
$. Prom the above oomputations this a't,udy shows an
.average weekly growth per pupil ot two ~enth8 pollnte tor the
control group and tour andeeven tenths potn1is for the ej[ ...
per1mental group, or a weekly gain ratiO 'twenty-three and
five tenths to one for remedial actlvlty.Comparison Graph
vn. Yh~'d1Y pictures the actual advancement of each pupil
as well as the a. verage 1ndi vldu~,l growth t o r each school.
the e1'1dence presented here is sufficiently conolusive
in !itsel.f.. ;a-emedial work, as shown by this project :in d.oi ..
mala wl~h SQ high a weekly gr~wth ratio, haa a decided ad.
vantage over regular class activity .•
~
r
74
75
~ABLE III.
Tabul a tion of Matching of "to Pairs
Note: Number in the oolumn heading of t he followi ng t abu-l at ions refers to the pair number as t hey r ange in placement from the highest t o the lowes t aocording to their first teet score . The fi r s t of each pair is a 1'wenty-seve!1th Street pupil, t he seoond is Wisconsin Avenue School pupil. The pair number re-fer to the base line nuraber on t he a ccompanying gr aph .
Tabulation of Matching of ?O Fe.irs -- 8- A Section
Number Age Test-l Te6t- 2 Impr ovement Improvement Score Score Wis . Ave . 27th s t .
70 13 114 114 .... --- 0 13 114 110 fIII-- - 4 -. -
6? 13 10? II? -..-- --- 10 13 107 100 -, ---
66 l~ 107 113 _ . ... .-- 6 ---13 106 113 ? --- -. -
62 13 105 114 --Mi' --- 9 ... _-13 106 106 0 --- .. --
61 13 105 116 --- --- II ---13 104 103 --- ... 1 --- .......
60 13 106 114 --..... --- 9 --~ 13 102 97 -_. 16 .. -~- ~ ....
59 14 105 112 -ep"- --- ? ...... -14 99 99 0 _ ..• ...... ---
58 15 105 11:3 --- . -.. 8 15 99 102 :3 W!t _. --.
55 14 102, 1115 ---- ... - 1:3 14 102 99 --- - 3 .... -
54 13 102 112 -... - 10 ---13 102 104 2 _ .. -
53 13 102 113 --- .. - 11 1:3 102 ~ 108 6 ---
---------------Sub-tota l " 18 - 20 94
r
76
TABLE III. CONTI NUED
Tabula tion of Matching of 70 Pairs ~- a-A Section
Number Age Test-1 Tes t-2 Improvement Improvement Score Score Wis. Ave. 27th st.
52 13 102 116 .. -.. 14 13 101 99 ---- -2
51 1 :3 102 113 --- 11 .. -... 13 101 104 3
48 13 100 112 ... -- .. -- 12 ---1:3 99 99 0 ~-- ---
45 13 99 114 15 13 95 96 1
43 14 98 113 ~ ...... --- 15 --.. 14 100 100 0 .-_ ..
40 13 98 110 --- -_. 12 1:3 97 101 4 --- -- .. ---
:.59 13 98 112 _ .. - ---- 14 ---13 96 102 6 --~
30 13 92 108 _ ..• 16 13 94 100 6 -.-.
28 13 90 113 --- 23 13 87 93 11 -_ ... ---
27 14 89 106 --- 17 14 87 102 15 --.- _.- ---
16 14 84 III --- 27 .. --14 77- 88 11 --- ----
-------_ ..... _ -----Pag~ total 57 _2 . 176
1st. Page total 18 -20 9.4
Cl a ss 8- A To tal 75 - 22 270 Cl ass 8-A (22 cases)
Actual Improvement 53 270
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TABLE IV.
Tabulation of J,,fa tching of 70 Pairs ... 8 .. B s ection
Pair Tes t-1 Teat-2 Number Age Score Score
69 13 . \ DO 114 13 108 104
63 13 108 115 13 104 109
57 12 104 111 12 106 106
56 12 104 112 12 101 106
50 12 101 116 12 102 100
49 13 101 108 13 101 103
41 14 98 103 14 98 100
35 13 98 107 13 90 91
34 12 95 111 12 96 100
4 13 74 98 13 77 77
-- ,-------------Class 8-B To t a l
Ol ase B- B ( 10 ca ses) .Ac tual Improvement
~
, r
Improvement Wi s . Ave .
_ .... --. - 4
_.- ---5
..... 0 --"-
--- ---5 ----
... -- --.-- 2
---. 2
~ , --2 ~--
.--1 .,.-...
--- ---4 ----
... - ---. 0
19 - G
13
Improvement 27th s t.
5 · .-_. 9 .... -
--. ---12
8 ------15 -.. -
7 .. -----
5 •••
11 ---_.-16 -----.. ---24 -_ .. ._ ... -_ ....
112
112
77
'l!ABLE V.
Ta.bula tion of Matching of 70 Pairs - .. 7- ./1. Section
Number Age Test-1 Tes t .. 2 Score Seore
68 12 108 108 12 105 101
65 12 106 110 12 108 99
64 13 106 115 13 106 97
46 12 99 115 . 12 97 93
42 12 98 105 12 98 90
38 12 96 112 12 97 96
37 13 96 109 13 96 91
36 12 96 113 12 96 97
33 12 94 107 1 2 91 91
32 13 93 93 13 87 87
31 12 92 104 12 95 96
29 12 90 105 1 2 89 89
26 13 88 107 1:3 88 87
21 12 84 93 12 85 81
- -- -----------~
Sub-tota l
k r
Improvement Improvement Wis . Ave . 27th s t .
--- 0 ------ ... 4 -.. -,._- 4 -- .. - 9 --.
-~. _ ... - 9 .-. - 9 ----.... 16 .. ... . --- -4 . ...
... -. --~-., ---
.. 8 ---16
..... .. 1 .. -- .. _ .. --. , .. "" 13 ........ '-~~ - 5 _ .. ---- ---- 17 1 --... --- -_.
.. -- ... - 13 ._-0 --- ._. ._.,.
• •• --- 0 .. ,.-0 --- .. , ... , --.,..
.. ~- .... 12 .--1 '!III!--- .. -- ---,-.
15 0 --- -.-- ._-
.-.. - .-- 19 "*'~---... -1 ...... _ ..
.... --- 9 ------ ... 4 -.'.
2 ... 45 150 •••
78
79
TABLE V -. CO!>.l"TI NUED
Te.buia tion of lEa tching of 70 Pairs 7- A Dection
Number Age Tes t-l Test· 2 Improvement Improvement Sco re Score Wis . Ave . 27th s t.
20 12 84 100 --- 16 12 85 8 5 0
15 11 83 97 --- 14 11 83 83 0 -.. - --- .~~
14 13 83 103 --,. .'-.- 20 ---13 80 80 0 --- --~
13 12 82 107 -..... --~ 25 ---12 84 85 1 _.a.. -.- ---
12 14 81 97 --. ~~~ 16 .. _-14 88 89 1
__ 1III!t ---7 12 75 98 23
12 74 72 --- ... 2 --- -- ...
6 12 75 102 --- -.. 27 --.-. 12 72 68 .. -- .. 4 --,.
5 13 75 93 ..... .. -- 18 .-.... 13 69 67 '.-. .. 2 .--. -....
-- '------------Page Tota l 2 . s 159 ....
1st . Page Tota l 2 -45 150
Class 7-A Tota l 4 - 53 309 -----01a ss 7-A (22 cases)
Actun,l Improvement -49 309
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80
TABLE VI.
Tabu1a tlon of Matching of 70 Pairs .. . 7- B Sec ·l:.io11
Number Age Test-l Test ... 2 Improvement ImproV'ement Score Score Wis . Ave. 27th St.
47 12 99 112 .".- 13 12 100 102 --- - 3 .--
44 13 98 103 --- -.,... 5 ---13 100 99 --_. -1 --. ~--
25 11 88 99 ._- -_ .. 11 -.... 11 84 89 5 --- ---
24 12 87 103 --- .' ... 16 12 85 99 14 -.,.- --.-
2:3 12 87 107 -.-- 20 .. --12 82 73 ••• - 9 '--- ... -
22 13 86 100 --- --- 14 13 79 77 --.. -2
19 12 84 103 -.-- .-- 19 12 83 90 7 --- . -.' --.
18 11 84 93 . _. _ ..... 9 11 81 87 6 --.... . .. -
17 11 84 99 .... --- 15 11 "I" 80 :3 e -• • ... ... ---
11 12 81 101 --- -... 20 ---1 2 81 71 --... ... 10 -.. - -.-10 12 79 101 _ ... .. -~ 22
. 12 79 86 7 --- ---9 12 76 93 --- .-. 17 -... -
12 76 73 - 3
8 13 76 96 . --., --... 20 _.'. 13 69 '77 8 ---
:3 12 69 96 .. - .it.....-_ 27 12 69 70 1 -_ .. --- ---
2 13 64 102 --.. 38 13 63 ~ 55 ,- 8 .. _-. ...--
- - - ~ - ----- .------
Sub-tota l 51 -36 266
TABLE VI. CONTUWED
1'e.bul a tion of Matohing of '10 Pabos .. .. ? - B Section
ITumbe.r Age Test- l Tes t - 2 Score Score
1 13 64 8'1 13 5'1 71
--:------.-----------Page Total
l et . Pa.ge Total
Class ?-B Total
Class ' - B (16 cases) Actual Improvement
~
f. r
Improvement Wis . Ave.
--- ----14 ._""
14 - .... ... 51 - 36
65 . 36 ·
129
Improvement 27th st .
23 ---
23 266
289
289
.... -
.. ...
--.
81
TABLE VII .
Tabulat i on of Matohing of 70 Pairs
Summary To t a l ... - All SectiOl'lS
Section Cases
7. B 16
7- A 22
8. B 10
8. A 22 - ?O All
Actual lmprovement Average Improvement
~
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r
Improvement Wis. Ave ..
65 -36
4 - 53
13 ... e
75 - 22 - :IT.., 157
40
.6
82
Improvement 27th St .
289 -_ ... :309
112 ~~-
270 ----990
990
14.1
Graph VII.
Progress-Comparison Graph 70 Pairs
Exper i mental Group 27th street School
Control Group Wisconsin ~venue School
1.9 3 7
83
PRINTED IN U.S.A
LEGEND
So~ld black line with dots: Twenty""seven ti. street School pair placement first test soore.
So11.d red line with dots (upper 'margin o~ red): Twenty-seventh Street School placement s cond test score ..
Broken black line with dots: W!sconsln. Avenue SchOOl pair placement first test score.
So11'd green line w;1 th dots: Wisconsin Avenue School placement second test score.
Area. in red indicates the progress of Twentv-seventh street School due to three weeks of rem84ial study in decimals.,
Comparison of broken black dotted line wi~h soli4 green line indica.tes progress of Wlscons Avenue School during the same three weeks per (Uo remedial work given.)
Lower bar graph shows avera.ge progress II!Ol1DR.rison ot . the two schools during three week peri
EUGENE DIETZGEN CO., CHICAGO'NEW,YORK NO.3'T6 C
A Specia.l Study
To augment this thesis on the value of remedia l study
in decimals. the following t abula tions, analyses , and summary
of results from a. testing progr am. a re i nc luded. A series of
three testa, survey, di agnos tic, and remedi a l check were used
to show as f a r as possible t he va.luG 'of remedi e l work .
Incidentally in 1936, 89 people, i ncluded i n t he major
study and known as the experimental group in this t hesis,
were given a survey test i n decimals. This i nformat i on
ava ilable for use in connection with the t hes is makes an in-
terGsting added study .
In 1936 the Brueckner Di agnostic Tes t was given to ab out
150 people of t he North Twenty"seventh s treet School gr ades
6. A, ? ... B, 7-A, and a .. B. One year later there are of these
150 people, 89 remaining at the school . To these 89 was
given repeat t est for d i agnostic purposes which wa& followed
84
by remedial ins truction. In turn the remedial work wa s follow-
ed by a third tes t . Seventy-five cases a re here lis t ed com
plete with :3. preliminary survey test of 1936, a di agnostic
tes t, and remedia l check test. These furnish the bases for
t his report.
The survey test g iven in 1936 had a s its purpose a study
of the reasons for f a ilure in decimals a,s associated with
fa ilures in aritlunetic. One hundred fifty pupils were t es ted,
nd the r esults analYzed . Si nce this summary is a l mos t i dent ..
1eal to t he one included in thi s thesis, the few minor di f .. ~
ferences ~o not warrant t he i nclus ion
~
r
second time .
The score i n 1936 was 93 or an a verage error of ap-
proximately 20 per cent. In 1937, a year following, the
score showed an average i norease of approximately 5 per
cent or 6 poin t s . he average per cent of error being t hen
reduced to 15 per cent. This, shown on t he a ccompanying
gr aph, is t he result of one year of normal olassroom activ
ity with no spec i al emphasis being placed on decimals .
In t he general ana lysis of the second tes t, the dif
ficulties, t hough somewhat less ened; for most part s till re-
mained . The score now 99, six point increase over t he sur-
vey test, becomes t he base level for remedi a l work. ( Since
t his is part of the general remedial study and nota tions
being the same the informat ion will be included under this
heading in the main analysis.)
remedi al program having as its purpose an a t tack
upon the deficiencies in the decimal background was put
under way. Three weeks of intensive study followed . De-
t a ils a re given under the heading Remedia l St udy in the mai n
body of the t hesis . Following t he remedia l study a third
test wa,s g iven to check the reaul tsof the intensive s tudy
8,nd drill . Thi s three week period of remedial program re ...
sulted in decrease of error from the survey and d i agnos-
tic average error of 24 and 18 r e spectively to an average
error of 8. Thi s is a leveling off of the percentage of
error through the three tests from 20 per cent i n t h e sur
vey te s t, to l5~per cent in t he diagnostic test, to 6 8/10
per cent ,in the remedi a l cheek test . "
, y
85
It is quite obvious then that three weeks of oarefully
pl anned and skillfully executed remedial study in deoimals
which is preceded by a complete diagnosis of difficulties is
equal to or better than a year of general activity _
The following compilation and sta tistics are the bases
for the summary presented above.
~
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B6
TABLE VIII .
Special Study Tabulation, Seventy- five Cases
Twenty-seventh Stree t Sohool Tota.l Teats '75.
(Listing a ocording to 1st. soore, lowest to highest.)
Ns,me Gr ade Age I . Q. 1936 193'7 1937 193'7 1937 193'7 Test 1 Test 2 Test 3
1. Glavin, Theodore '7A 13 96 54 56 83 2. s trauss, Jean '7A 12 124 '70 '75 98 3 . Rosenthal, Marvin 8D 13 102 '72 99 115 4 . Weisaenfluh, Glen BB 13 121 '75 '75 98 5. Kent, James 7A 14 93 '79 81 97 6. Williams, Jamee '7B 13 103 80 87 107 7 . Kremmerer, Robert 7B 13 114 81 86 100 8 . Uuel1er, Geo r ge 7A 13 96 82 93 93 9 . Schroeder, Eileen 7A 12 104 82 97 107
10. Sal amone, Victor 8A 13 108 82 90 113 11. Tooley, William 8A 14 97 82 102 112 lla. Sohneider , Richa rd '7A 12 123 83 90 105 13. Borges, Russell '7A 12 112 85 84 93 14 . Wallner, Elizabeth 8E 14 99 85 98 103 15. Zoe6ch, William 8A 14 92 85 89 106 16 . Landisch, Jeanette 8B 13 105 86 99 105 1'7. Powell, Ada 7A 13 111 86 88 10'7 18. Kurt z , Rarry 8B 13 100 87 101 114 19 . Ahainger, Joseph '7A 13 98 88 96 109 20. Bachman, J!ary1n 7A 12 91 88 92 101 21 . Rein, Sherbourne 7A 13 100 89 94 101 22. Pape, Howard 7A 12 109 89 96 104 23 . Anderson, Ernst 8B 12 109 89 95 111 24 . Drake , Marion 8B 13 92 . 90 96 107 25. Kirkland, Walter 7A 26. Korthaus, Hertha 7A 27 .• Masek, Fred 7A 28. Petri, Arlene 7A 29. Raley, Vivian 8B 30. Va1cq, Norman 7B 31~ Meisel, Doris 8A 32 . Pr esser, Thora 8A 33 . Ball, Ruth 7A 34 . Cl ancy , Betty 7A 35 . Cranmer, Cons t~Jlce 7A 36. Beyer, Be o.trlce 8B 37 . Cole, Shirley 8E 38. Bassler, Dorothy 8A 39. 3m! t h ,. Do ro t hy 8B 40. l~enslng , John 8A 41. Eggert t Iia:n1d 7A 42 . Snead, Sue 8E 43~ Zerza, Margie 7A
"
13 14 12 12 13 13 13 12 13 12 13 13 12 13 12 13 11 13 12
, "
111 91 97 100 89 91 99 109
123 91 96 113 129 91 96 112
93 91 99 102 95 92 98 103
113 92 98 112 124 92 9'7 116
97 93 93 109 127 93 99 115 118 93 101 101 117 93 101 108 112 93 101 116 117 93 98 110 122 94 102 114 109 94 105 114 1],9 95 95 113 118 95 106 113 136 96 101 108
87
TABLE VIII ••
Na.:tne Gr ade Age I. Q. .1936 1937 1937 1937
44. LahIna.yer. Lorra ine 813 45. I.ewia, William 8:8 46. Johnson, Alvara 8A 47. :Polzin; Lucil le 8A 48. Byrd, Jack 813 49. Smith, Helen 8:8 50. Gelee, Elsbe t h 8A 51. Mei1ds , Hugo 8A 52. Byrd , Dilly 7A 53. Kr ause , Shirley 7A 54~ Moll, Dorothy 8:B 55. Kudija., Agnes 8A 56 '. Viergut z, Alice SA 57 . Gross, Gloria 7A 58. Jahnke, Shirley 7A 59 . DUdovic, Elizabeth 8D 60 . .TOMson, Be tty 8A 61. Duehring , Cl a renoe 8B 62 ·. Watson, Jess ie BE 63. Homa.r, llaria lyce 7A 64. Peterson, Cornelia 7A 65 . Shade, LaVaughn 813 66. :Bu111 , Har old SA 67. Struebing, Bernice SA 68 . Burmeister , otto 8f. 69. Chell , Miriam 8A 70. Locher, Susan 8A 71. Zerza , Ann SA 72. :t~atoushek, Martin 8:8 73. Scru:nidt, Ruth 8A 74. Wegner, Robert 8:8 75 . Eisenach, Robert 8B
Score tota l 75 tes t s.
~
1937 1937 Test 1 Test 2 Test 3
13 13 14 13 13 13 UI 13 12 12 13 13 13 12 12 12 13 13 12 12 12 /1.3 13 13 15 13 13 13 12 13 12 13
~
r
117 96 107 96
95 96 103 . 96 120 97 110 97 121 97 108 97 130 98 123 98 109 98 113 98 131 98 115 99 110 99
97 99 109 99 108 100 117 100 III 101 136 102 130 102 117 102 121 102 126 103 109 103 116 103 120 · 103 121 105 104 105 135 107 119 108
6936
105 105 102 109 105 112 102 113 106 115 101 114 102 116 102 112 100 112 106 110
97 110 106 111 105 114 110 110 101 107 104 III 114 114 105 109 106 103 106 116 106 112 105 117 107 117 112 117 105 116 110 1:)..7 103 114 III 115 110 112 109 112 113 116 109 114
7426 8179
88
TABLE ! X •.
Speci al Study SUmmary . Seventy-five Cases
Twenty-s eventh s treet School
Final Summary 1936 1937 1937 Test 1 Test 2 Tes t 3
Tot~ l Scores 75 Teats 6966 7426 8179
verage Score 9 3 99 109
Averag.e percentage of error 20% 15% 6 .• 8
Average percentage correot 80% 85% 9:h2~
Based on t he i nitia l score of 1936:
One year general arithmetic tra ining without spec i a l
reference to decimals show decrease of erro rs amount-
lng to 5 per cent; 15 per cent error i n the second test
and 6 . 8 per cent in the third following remedial teach-
ing .
tota l of reduction of error from 20 per cent to
6 . 8 per cent or 13 . 2 per cent is accredi t ed to one year
of regular cl ass Instruction and a three week remedi al
perio·d.
~
89
TABLE X.
Special Study, Seventy-five Ca.s es
St a tistics
Summa.ry Sheet Special study
Grade '7 B (3 Cases) Percentage of error (Total) ' Amount of decrease
Percentage of decrease over 1st. test (Year aotivity)
Percentage of decrease over
Test 1
28%
-.-
Test 2
237<> 5%
17.8%
Teat 3
12% 11%
2nd teet (RemediB.l wor k) ... --Value of Remedial work va. year ac tivity :
47.8% 2.68 to 1 _M _____________________ • _____ ____ _______________ ~--__ ~ __ _
Grade 7 A (27 Cases) Percentage of error (Total) Amount of decrease
Percentage of decrease over let. tes t (Year activity)
2470 .... -•••
19% 5't
20 .8%
10% nt1f '(I / V
---Percentage of decrease over 2nd. test (Remed i al work) -.- 47 •. 3
Value of Remedial work va _ year activity: 2 . 20 to 1 -----------.~-----~--------------.----~-.--------~---- ---
Gra.de 8 B ( 24 Ca6es) Percentage of error (Total) Amount at decrease
Percentage of decrease Over lst~ test (Year act ivity)
19.6% ---
. '--
13.6% 6%
30 . 67~
5 . 97~ 7 . 71,
--. Percentage of decree.se over 2nd •. tes t (Remedia l work) --- .. -- 56 •. 670
Value of Remedial work va. year activity: 1.85 to 1 -------------------------------.-----------------~-------
Grade 8 A (21 Cases) Percentage of error (Tota l) Amount of decree,se
Percentage . otdecroa,se over 1st. tes t (Year activity)
~
Percentage of decrease over 2nd test (Remedial Work)
l87q ---
.. --.
12¢' 0 '7.,
33.3~"
2 .5;:, 9 . 5~
..--
Va,lue of Remedial \'10 rk vs. year aet:1 vi ty : 797r)
2 ,.:3.6 to 1 - - - --_ - _. '. - -- -- -. -- - --- .. --,.. - --_ - - -- --___ ---- -.-_ "'.->M!t ___ ~_..,
~
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90
TABLE X'. COliTI NUED
s t a tistics
Summary Sheet Spec i a l Study
Test 1 Tes t 2 Tes t 3
Composite (75 Cases) Percentage of error (Total) Amount of decrease
Percentage of decrease over 1st. ttst (Year activity )
20~
... --15
57"
25
6 . 8i'D 8 .2~
.....
Percentage of decrease over 2nd. tea t (Remedial work) •• ~ -~. 54.6~
Value of Remedial work va_ year activity: 21116 to 1 -------------------------------.--------------------------
~
y
91
SUl!Ima'1fY
Several conclus10ns may be drawn from the foregoing
compilation and statistical s\1JmD8.ry and the accompanying
graph. The comparative value ot the three weeks remedial
period and the years norrn.al ac\iv!ty in arithmetio is ex.,.
pressed by Graph Vi II. This show8 an inoreased average score
of 10 points tor the three week remedial period ae compared
with e Poln~s tor the one year activity.
In light of comparison, the gJ;'owth 18 10 to 6 while the
time element 1s ~ ~o 40 . 01' a weekly achi .... ement rete of 3.33
poin\a grow"h tor deoimals per .eek tel' remedial work and .15
points of growth for deoimals per week for nOl'inal arithmetiO
Qlass prooedure, Based on th1' aotual weekly grel'lth oompar1.
son, ~emedlal aotivity produoed a weekly growth value ratio
of 22 to 1.
The value ot remedial "ark was greater 4.n the uppel'
gradel, being 79 per cent, !56,S per cent, 4~h3 per cent. and
4'7.8 Pfilr oent for grades a-A. a.a. 7.A. $ond 7 .. B respectiv.ly.
This percentage shows the progress as expressed 1)y the dlt ...
terenae in 800re8 of the cUagnostio and remedlal cheok testa.
It 1s the author's opinion that the remedial score which
&8 the .re8ult ot progres8 in the more diffioult Pl'ocessel of
deoimals, whlch remained to be corrected atter the year'e
aC'Uvlt7, d.oes not show the full aocompli.ehment which may
haYe been .8.chleTe'" had the remedial program been made et:f'ec • .
tiTe a year ear~ler.
ObTloU817 from the above discussion two major eonol~.
92
atofts can be ma.de;one, that the diagnostic e,nd reme41al
work reveals a dec:l,ded lacking in l'esearch into the methods
and prooed~res 1n teaching as appliijd to doc1w~ls; two, that
the more rapi.d gl"Qwtb restllttng from l'ftmedial atudy 1n the
uppel' .rades and the relatively h4ghor soores show, a PQss:1 ...
'b1$ mal· .. pl aQoment of the study of deoimals in the ourriculum .
A reierenoe to Graph VI 'tVill reveal more graphlcallt the
remedial gro.wth comparison tor all four gradefh and will shQw
that e 6ree.ter percentage o·;f' e,J"ror exiBt$ in the lower grades
which are ne$.rer to the grade and time of .o..r1ginal instruo
tion_
~
,
93
Graph VI I I.
Value Compar ison Graph.
Special Study .
75 Pupils.
N. 27th Stree t School
Individual Achievement
Normal Activi ty vs . Remedi a l Work
Br ueckner Di agnostic Tes t I n Decimals .
1st • . Tes t (Lower Black Line Marg i n Survey 1936 .)
94
2nd . Test (Upper Gre en Margin Di agnos t i c Test 1937 .)
3rd. Tes t (Upper Red Margin Remedi al Check 1937 .)
1 9 3 7 .
LEGEND
Black line, lower margin of green, indicates level of 1936 test score.
Green line, upper margin of green, indicates second test score . Green a rea indicates growth due possibly to a full year of normal acti vi ty'.
Red line, upper margin of red, indicates third test score. Red area indicates growth attributed directly to three weeks of remedial study.
Base line numbers indicate listing of pupils, see accompanying table.
PRINTED IN U.S.A. EUGENE DIETZGEN CO,, CHICAGO-NEW·YORK NO,3~6 C
~
SECT1". 'Vl,
SUlllnlatlon ot Th$sll
1. Thesis Limitation.
2. Summary and Conolusions
SlllTllDIll'i'Y eoncl~61one
~h 13ibliograp:by
Text.s MagaJilin • .,
k r
Il'he,sis I,1m! ta tionfj
itt ''lill b 'o 0'b,,10ll8 "hQ the' reade, a s it is to theauthol" . .. , -
t~t thls thesis ha ll! l\l. number ot 11m1tatlons V'/htoh a.re quite
beyond control S
1. Ntl ana.,l),,(3lspt enV1r<:lmnallt,sotJial, 01'so11001 back ...
groU!'lQ. with any degreeQi' aocurtil'(J'Y 1$ eva11a.'ble. Th,is fac
tor m£y Dr ItfJa71 r10t effect in some way the test analY$!S e,uQ.
in ltke manner th~ I's.medlal r.esul ts.
2!\, Intetl,)ret.at1013e e.s to the, qauae of error may a.U·f.er .
,A.ne,),yses TlJlJ.71 dU'f'et a.ccordltng to the view of the examine1l'ii
. ;5. No &.lterne,te teet was e.~llable as ·a check on the
resUlte ae!hleTed. th~ u13'~f the same teet was neceseary.
;rt is l>OlHJible, howevet', 9flly s;'l$htly ;proba."l~ tha.t am.m
pleQ and ans,1fers may bave beObme tamJ,11a.:r to thfilsubjeet.
4.. Va~bus teaQ"h.1ng m.thQds. 1)y Vlh!1.chde9t~la hav~
been t~l2.ght to the QaGe$ analyzl:i<1 1.n this t.bea1a, 118\'"e ~,d.e
remedial. lnstrU('iUon dU'f'iCult. and pose1b.ly l$.,a aeou!I\'ate.
5. 1he rl'Wnf}'e:ro,.t ,c::ae'$S s'tiudiad .. tW<;I hliUld;red. sixty.
fou, ttl al1,'f!$Y' be to,_srnal1 a nwn'b$r upon which tG base
cO.nciu,~ton8" A larger grQUp 1ras not avaH.ablet
e. 'OQ!i-c;1\l8ione 1"egardtng tlHt val Ue of dhl,gnbstl0 and
i'emecUal teaChlng W.as restricted to but & single a.r!thmeU~
tunothm, 8, lltl,;rro'W one, namely, c:lecb:1l1th C!3nsalluentl,
Q(mcl.ual~n. must bao.:rawn :rega.rding dl$,g~c;;st10 e.nd remedial
teQ.(jh1ngas tl1e.y e.re l'Gstricted by the l1m!f;.ta"iollS of this
~has;l.(foi ~
, r
96
Summar.y and Conclusions (' 1. SwmualT
tn the tOl"ego'pg e8Ciit1onsJ e. prog;ram for the study and.
interpretation p't dl1fticulties in the use of deotlDB"l numbe1'8.
and tor the improvement of instns·otlon and results has been
desoribed 1n d.,tall. The tollcw1ng is a sWIlJl'l&.r;y of the ete1>a
ihlTOlytcU
I.. Xntr~d.l1(Jtt'Jl and Objective,
1. b exper1m~nte,1 study in at"snoetic $ond remedial
1iee.ehit.J.S ;ttl the use of decimal., and theh' func;tione
was \Uldei'1)uen with an fi,verage group of seventh a nd
eighth g~e.ders, 136 pup1.J,s . 0' the Twenty .. seventh
Stteet Sc11091 d.uring t.he f irst aemester of th~ 1936-
1937 B~hG~1 year as the elLtperim(lntal group. A 001'.
reaponcu.ng group Qtaeventhand etgh,h graders of
WhQone1n Avenue SchoQl compJ"18ed the {,Iontrol group
of 129 pup!la.
2, It fias the aim of this study to pl;'odu.ce reliable
1nfQrD:Ja t:toJ,1 and da;~$. to I!In"ble \ihe Quthol' to determine
. ,6 e.ecurately as possible wi thin the 11m! te of 'th1a
lnvestigat1.on the 1'818. til. VQ value of diagnostic and
re~edlal teaching in deQ1~1 ••
II. Stat~a ot the Inyest1ea.t1on.
1. '',the OllrPerlmental gr~up consiat. of an average clae.
;ot p"pl1. ,.
2. The testing progrrurJ:' 8 wiele varla.b11i',. of Boore. ~
indioated a lacking of unU'Qrm4 ty in handling deo:lmal.,
r
97
3. The B:rueckner Diagnoetto Test in Deoilna.l~shewed
particular de1'1cienoles.
lIt. Diagnostic M~thOdG.
After an ana.lysis of errO'r8 determ1nlngBpec,itio and
individual weakne'$ses, t he remecUal 1>rog~e.ln WIIU~ 8&11 up.
The following method, was Eunpl01ed J
1. .A diagno,stic test WS,3 81vtn eAch pupil.
a, lila! vidual recorda were ~,;pt a l}d pupil t s errore
record_d.
3. Failures of lD&Jor consequltnce Vlel'e I3tudi$d in ..
divldual1y by 0 .. a1 ellCaJIdn$.t1i,onlh
4. TabUlations QterrOl'S were ·used. to regis ter points
.,alen,se $no. n •• 4 for :remediAl study,.
IV. Remedial Instruction.
1. A workbook '8.p.01a111' 4'91&ned to~ the pupili. n.ede
was oon,'bruoted..
2. Regular elas. time b,cam~ tbe romecUal period,
3. Individual analysi.$ wae given a.s needs aroee .
4. Pupils wer e t aught. tQ determtne ca.useS (;I,f error.,
In l'emed1al wOl'kbQok and to lllf),keQorreotionao.
5. Ha'bi ts a nd vaille of good \i'ork ware emphasized .
V. Final Testing.
;1.. A s$co·nd tee'iing program was ~na.ug\lra. ted, 'tasting
b9tb. g,roups to d~t~nnine rela~1v8 prog:oes$it
2, Ana lYei:ia of t.he oompai'iS011 r~"(ijals the value ot
remedial instructions .. ~
r
98
2. Conoluai()n.
~..,1tmf: -UNIVfRSITV
T2 1 f %
Atte!' a d.lagno.t.~ of the two hw;dred aixt, tour OaaeB,
a pe1'101'101' remedial instruction baaed on the tindin&8, and
a ffUDltlUU'Y" 01 results achieved the following conQlu$ions were
reaohe_,
1. Standa~(U.~ed tests are etfeott va in determ.1nlng _he
.tatuB of the group studied, in analy,lng 8p801f1,0 weBlme.,selil
and in measuring lmp:rovemen\. atandardl~ed tests at-e an a1d
to 'tfhe teacher in 4etermlni:tlg the ~ ting of he.r Qtaas in a.
part1Qu1ar work.'l'he superiority 'otso1-entlf1qally con.
etl'Ucted testa <)'ve~ lnforma.l tests used by teacher1!) in the
pe.$t has lc;ng been conceded by moat progressive educ~tor',
2. t'lle ~lue 0' diagnos1a Is olearly evident to the
author. The methode of 4taPOBi, us.d in tbis study wert
.It.oU ... e .in cu"sooTering weaknesses In 4eolma.ls wh1o:tl could
not haTe been diue:losed by ord1nal'1 methodf3. Ana1yela ot
er;y:ooi'S in teat paperiB,: .obqer1'ation and oral ex&m.1natlon of
pUpils must be combined in order to determine difficultie ••
The PJ;'tt.ctiO$.biU.tY' of the methods tnTolTed has been 4emon",
atrated by the resul te.
ne need tor diagnosti0 tea.ching 18 e.,ident, WhfJll
teachers are aeked t() outline their difficulties tn \eaohing
deCllna1s t they rind themselves faced with genel'alittes.
They may know that the 01$.88 ts having dU'.1'1.cultleB with de
clmala, but tew catl tell just ho,w muoh I!>t 1. t 1s due to zero
dittiou1t"es) fundamental weaknesses, decimal"fract;ion oon .. ~
capt • . , eto. It 1s necessary to know .pec4.f1c <Hlr1cu1 ties
99
to be able to "each 8pec111cal17_
When the teacher haB 2.ea~ned ot ~he many and various
obstacles encountered In the fUnction of decimals or 1n any
other phase ot arithmetic a. mo;"e ,ympathetlQ view will be
ostablished. This ¥'lUi lead to a. 'better pupil understa.ndb1fh
and. an 1mptovement ,of her teaching b1 the. developm~nt ot a
8ci.nt1f~c a.ttitude.
:s. Remedial. tee-ching 91 d;ect%nal." through a 'Qy.t,omat1c.
dla.gnoali baa alJnQst startling ir~ '8ults_ The provision ot
an espe01al1y organized notebook to moe. the specific needs
of the pupil 1s most pra.ot!oa.l,
Oonsiderable remedial W'orl< oan be a.coomplished wi 'bhout
the aid of specia.l rooms or Gpaoial ola,SstHHTilne is r.·
qUirad, hO't/ever, to accomplish the beet l"esults. l'ea.chel'.
of uppe~ gradee w111 find the praotioability ot a d1agno.tic
and remedial proa;rrun in deo1r.ml. adv1~abl. when t .hey exp,ct
to teat',lh percentage, profit and lo~s, commission, eto.
D!8.gnosie w111 leaoon the period and the eleI!1ent, of ohanoe
in inst.ruction, Remedial instruot ion in most oases wtll be
well worth the time and ano~gy expended.
4 ,. The l ack or unit~rm1ty 1n teaching methods cause4
l'IW.ny dU't!oulties. Se-rel'a l o$.eee in this study hA.,. re
vealed that, a ntt.rnber of fa.ilur~B wert) ca.uDed bY' a oontusion
a.ttr ibuted to So variety of teaching methods to which the
pupil wae eltpoeed. Ur.d.tQtm proeedureshould be stressed
t hroughout t he 8chool or systexl'l e~ercising oare, howe.,er •. ~
to avotd habituating pupi l s to a stei"eotype4 torm. Pro-
r
100
cadu:r,-e that takas on the analytio nature rather than the
tixed tQrJnula method 10 advised,
5. The absence of home.wQrk asalgnm$Dtst since all reme ..
dial wcrk was taught in class, proTed to be a great stimulus
to cl.asil activity, and a cheek on oonfusion a.nd the formation
ot false concepts resulting from h0»16 instruction. It 18 a
mistaken assUlnjJt10n that homework is ~arg$ly bene~i,cial.
F'nm the. ,Gb,jectl, va ot thh thesis it might be ooncluded.
that remed!e,l teaching.hould become a permanent phase ot
our sohool curriculum, It 1s the authu,ts op'n1Qn .. hc>weTer,
that While ,diagnosis and remedial or 'orrebtlvB teaohing is
.at present a neeessity,. and an 1mportant int;?trument in
teaching act! vi ty. grea tel' emphaeie bhould be placed upon
this pballe of instruction at 11;. aB8um~B the mor-e lmportan"
lro11 of prev.ntive teaQhlng.
Analysis of difri~ult1.es ie the. 'best ;meeuiS Qf bringing
before the teEl>cher the importance of CO'i"l"E)ct and adequate
teaohin~ in the beginning instruotiQn,
~
~
r
101
Bibl.t;Bgra~ht
BrueQlmer. teo 1., Diadl,)l,. anjRtmelUaJ. ~~e,Ohtli, In
Af,~.,t."t lohn C.Wln8~ol'1 Co •• 19$0; Chi.oago, pp. 31.2.
A d180uss1on of tee~8) teChnique •• analyeee and applications to the .,..rloue 'branche.Qt elem~ntary .ohool eubJect.. It oont. ... ! •• h'. test and. analysis Or difficulties in decimale_
B~.okDer.. Lc!u) J., lte"" .. t£ lU. §O'$'I»'~'· QQa& tit •
.R.U ~41.f\J,oM~D',q!lUU'h Tbt,\y.tollr1ih Yearbook of the
'National 80.01e\1 tor the stuq of lllclucat.loll, Public Sohool
Publ1.hinsOo. f ~935J B1.oo1ll11'1gton. 11111'1011,. p», 533.
Seo\1on It, OM-pte,. I, t, V. 1nolus!'" and Sec .. \10)'1 XX., Chapters. VI, t.O Xl. tnoluslve deal. with taotor.8 . ae80ci"'d ,,1 \h leai1llJtg dltflcul .. Uee. and prlnoiples a~d tecbn:lque ot edu'oatlonal dtagliod.s and tre,a~nt. Chap'.' XIV. deals 8pecitlQal17wltb diainO$1e In Arj.'bmet'.,~
Brueolate", Leo l~, 'A }1eOI.8a17 Step in the Diagnosis
of Pupil D1ftloul tiea 1n Art thm.tlc, • Thitd YeArbook st. T • ~, • • _
the D'Plr1m1te$ .!.t!.em,p$au Slbso, Prln$l&.a. •• 1924, Pp.
290-300.
A <U.ouI.lon 01 the majetprlnQ>ip18a lnvolTe4 in • . GOUl'ate d.lagn~B1s with sUggested pr.ce4ure and a U.st of typioal cU.ttleul tl,s.
Brueokner; Leo iT.. -Analysis of D1ffioult.ies tn D4;)01.
mala, II EiS!S.ilMJ% .SCUslloVitnt!:., September. U~28 •. 11P.
3241.
An "alyt;ioaiL dl~euBslon ~t the failure Clauses in arlttunetic with 8W11JfJaJ'Y ot findings in t.he MtnneapQl18 Publio Sohoolate-nd 8ugge,tiTe remedi... The aUlhol" 4ilcu.8e, three types of dtagno.tic prooedure to determlne $bl11tlea of pUpil •• and presente .ample diagnoetio teeta and l1s,1; diffloultles tn deoimals as c1etemin.d trom the.e teetai
r
102
BIileckner, Leo J'. t a.nd l.ielby, Ernest 0., Diagnostio , , ,
B,ng Remedtai Tea.ching, H01ighton l.i1tfl!n co." 1931, Boston, , t . •
pp. 593.
Genera l d,isoussion of diagnosti0 and remedial tea Qh1ng .
Burt()!), '¥m . Hil. and Others. Th, S~Rarv19i9n R1, :m~emen"
~ 83:1'O.1e2t.. D. Appleton and Co~. 1929 t , New York.. pp. 697. - ~,.,
,J>. oompi;Lation of 'fIo'k" of8eTeral authors with ~l'Ueolmert., cont ,ri"bu~.on in ChaiPte~ :t,ll. A genere.l dteeu •• 10n of the superv1.e1oD ,of ad thlit.t10 wi th JOeteTenoe to d1agn081ilc and remedial work ,.
Buswell, GUy T., and Judd, Ol1arles Hubbard. SBJPl!'l!u.2t
Eduoat19nal lny.stlAAtton, Rela~,pg 12.. At&ijp,ttg, Supple.
ment&J!Y Educational )!on()graph. no "II 2'. Univerdty of Chioago;;
1925, Chicago. nU.noia,. pp.212,.
, Oha:pter VII. on "Ind1vi4ual Ditference. and Remed1al Xethods." and Ohapter VIll. on "Methods or Teach-1.Qg." st.e an exoellent pres.nta.tlon ot the various 8cienttt1c studies rele.'Unc t9' these two important topios, '
Buswell., Gil Tit, and Lenore, J'oM, Dtagnott_lgS$udi,. l!!
Art tJun.titR. Supplem,nta.!'y' Ed.oat1onel.lJ.. lKonPct"aph. #30, UniTel''''
81t7 'ot ehlcago Pre.8, 1926. Chioago, ,Pp. 212,
A brief analysts and aummaryof diagnostio aot1 '9'1t1 in al'ithmet1QIt An analYsie ot mental Pf'ooessee and a 41agnosil Of pupil'" work ha.b1~1.
Garrison, S, O. and G$.l"r180n. K. 0 •• ,Pltoholp&y £1,
E)ementap; Schgol Sp,bJ!cts • .Johnson PUblishing eo~. ; 1929. 'New , . - . . ~ ... - .. .. , ',' ~
York, pp. 56.,. ~
103
A disous.ion of individual ditterenoea, ~easul'ement. learnin,. an,d their applioation to the Tar10~. elemen\ar,y sohool l!Iubjeots.
!
r
Greene, Charles E. , and :Buswell, G. , T,. ~ RepOl't .2!. the ,
§OQte1l 's Oo~ttee , ,n A!ithmet!9. twenty.n~nth Yearbook Of
the National Soctety for the Study of Eduoation. Public
SohOQl Publishing Co ,. ; Vol. let 1930, Bloom1neton. Illinois,
pp. '722.
thl!1 book contributes muoh to th~ study of ar1tb'!!" metle to 'Which the entire book 1.8 devoted, In Part I , dealirtg with modern thought on this subject. treatment of testing ~ diagnosis, and remedial \'101'1£ is r EI. ther eare. tully oOTered in Chapter V¥<
K18.pper, Paul. The~eachinl1t AF1,~etlcf D. Applet..m
and Co., 1916_ New York, pp. 3".
'fhi., )001£ inolude. 4t80\1881Ona Qt the ped;agogloa.l and pe.ychol~glcal principles go'tCltrning the teaching of Arithmetio and the teaching methode.
La.zal.',li&~, DtagnOlt1c ani Rem.dial ~, ill Atlt.hmlt1g
J\lpd!!mental'. Bu~ee.u ot :Reterepce, Re.,arch and Statistlcs.
:Soard of EducaU .• n, Wew York, 1928, 1'1't' a04.
A very compleiediseuseton of the actiTtty and pro. ceduJ'e 1n dlagno.'Uc and iremedt.al work is given fO J; , art tl:i:ine.clc fundament al tor' 1nteJ'Dlodia te .grades.
Len-nes. N .. Jil, !lll, T!8;,¢hAns R.1 Arlt"e~19 . ¥aom111an eo •• 1923,5 •• York.
Thla book 18 conCerned with general proble$8 bearing on the ~eechlng ot ArithmetiC; and with epecial problems tn methode cf teaching. l!eaeureme,nta in Arithmetio 1. inoludl!td.
104
J(anoheeter , Raymond E,. Outline, 121. .etmull! in Arlthmet,o.
Department, of :vainemattca, Kent State '1'ea,chars College, 1924,'
Kent, Ohi, , pp. ~268 •
. Thi. boo., i. 8. backg.fQundcourse fo r t ea che:ra 1n arithmetlc, and 1. supplied with many plans and drill ••
! r
MOnrae, W. s., )!,6sul'lnstheRt8ul\e. at 1'!6.Chlns.
Houghton M1ttU.n Co.; 19.18, Boston.
Chapter IV. is devoted, to the mea.urement et ab11-1 ty #On the opt;lratlons ot A·ti ~lunetlc.. eM.pter V. 4eal, with diagnosis and Q·orrecUT' instruotion. in Aritlnnetic. The section on analyttcal dlap,els ,., partloularly important.
JIo.nroe, Walter SIf, liThe Aliilt, to Place the Decimal
Point In Dd:tla1on, It lile,l!!r:ttflnScllt!t J'9uF'laJ, Vol. 18,
December. 1917,. pp. 28' ... ,9.3.
Shew. that the methodl5 of plaQ~ng the decimal point in divi'e#.on ftri •• aG_ording t, a large lu.unbeJ' of funda· .. mental type. of eptnpiel5 and suggests the t .ra1ning in each type ot example 8epa.,8;\.11,
Monr;., Wal te,.. S_, and Engelhatt, v.x l:)" h. Orit&sm1.
105
S\Ultlrlal:X; CIt. Re,ea'eh 't1at.1!s:to .!b.t. 'teachina !t Ar!'hm.t1 c:;
UnlTera1tyot Illino1., Bulletin 6S8, Sap'. 15, 1931, pp. 10',
A o:d. t10al auney of research 1~ t.eaohingar! tbmetic.
O.'burn, Wox-t'h J. jj ColI,ctt!., Arlt;tJm'Ut. Volue :t.
Houghton Mifflln CCI., 1924.. Boeton, pp. le2.
Olburn. Worth :r If 02E[.o~1!,Ar&U!m.t19' J Volume II.
HO\lShtOil. lIltflbt Co •• 1929, Bosion; Pl'. ~"4 ..
O.,burn .hae done ~ltt.n,i.... reaeareh work 1n Ari ih. metic Qnd the •• book, ,are largelye. d.escription 01 hi' work. Suggestions tor dU.gaesle ot .rrol'land r.medial work are ,ivan,. Va,l11al)l. exerciee, are. suggested.
Paulu, Emanuel :fl .• , Dlae2Jrt.l,c ;r'.'&eCI!!! ,Bemtt4&.1 '!eaph&". D. C'liN.ath and Co., U~24. Ne .. York,. Plh 3$3 •
. Chapter, I. to V. 1nolU81"'e g1 ve a pl'elim1ui7at'lilci7 of d'agne.~s and 1 i8 tunoticma together with general ' 4.1Ia12 •••
r
Chap'er X. ie devoted to dtagnoe1s 1n Arithmetio. standal:cU.sed 'ests are described, their use ,xplainect. and "nterpretatiol1 of results are pointed QU~. Paulu giTes a dtscussion ot the methods ot diagnosis and of tel'S suggeetions 1'01' remedial teaohing,
~
l'
106
Btblt.ogro.pl:\y
l$ag~zine Artioles
:Sl'U~ckne:r, LeQ J .. , oA.nalYfJil5of' Difficu.lties in :Deci
mala,· :E:Jr.ementa:rz Sehool. Jouma •• Vol. 29,. Septel11bel', 1.928,
pp 32-41_
A orlt1cnl analysis of the causes of error in the use ot decimal numbers,
l)J:.£J'ted, B. W.,. "An Analysb Qt the Drill l'rov1eions in
Dtvision of Docl~l. in Ten At'l1thmttlc Ser1ee." Journal.u:
Eduoatione,a,Sel!'1'2h, Vol. 2'." Ma.rch 19:54, pp. 509 ... 52~.
Anal,.sis of s1~ty ... one dttll })roblema and the fre-· quenoy ot 151'1'01'. \fork paralltle Brueokner analysis of drill tn tracU.one,
HUrd. A,. '8,. * "DC)es llemedia1 In,truct.on Pa1. "SQh901
e! S09&.ty. October ~t 1931 .~ . - -~-
. e.ncl~etQn on the value Of remedial \eachlng follo.wing dispoetic su:rvey ba.sed on a.n experiment with pbystce.
lletealt. Arthur Ansel.. 'llIls.eno.tic Te~t1ng and Remedial
'reachina." §Qbg·121IHowUx't Vo:l~ 49. April 1\)30. pp. 358·
360.
the authoX'explaint the 1,1Be of diagnostic. t$st1ng 1n connee'Uon wi ~h the miiS!l t in eohoo1 with a purpose et readju8tm~mt. A gerleral dlsQusaion 'Of aiagn08i. lI,nd l'Eunedlal acUT! ty,.
_ere, Ge.t!'J'1 CleiTelancl, "Who).e Number. and Dec1ln.e.l .... , GmSi 'f.&gbl.r. VG.li · 49. ~roh 1912, pp_ 540 f ..
A ~ll;touss:l.on of faulty ute of blaokb9ardiS and de. Tioos In tdacblng decimale. suggested mttho4. tor teRchj.ng the whole numbel'.traotion-4ec1mal rele.tionship,
~
r
107
~
SECTION VII.
Appendix
1. Sample 'fest
2. Test Scare Sheeta
3. !besis Supplement
(A) Compass Testa (B) Curr 10ulpm Study
r
Sample Test ' BRUECKNER DIAGNOSTIC TEST IN DECIMALS
NAME '., .. '' ...... '''.' """' .. "' ..... , ... " " , .. .... ,"""', ..... " ............. ,', ....................... GRADE .................... AGE ................... .
SCHOOL ......... ' ............................................................................... .. DATE ................... , .. , .. ....... , ............ .
I. Below are numbers written as words. Write each in decimal form.
a. Five tenths .... _________ _ d. Three thousandths"'-~ ________ _
b. Four hundredths e. Forty six thousandths. _______ _
c. Sixteen hundredths _ ____ _ f. One hundred seven thousandths. ___ _
g. Forty nine and eighty four hundredthsi ___ _
II. Write the numbers below as words .
a. • 65
b. 1.4
c. 3.75
d. .146
e. 1.09
f. 20.056
III. Arrange the following numbers in order of their size. Write the number of greatest value first.
a. 23.3 b. 2.33 c. 233.0 d. 2.303 e. 200.33
IV. Express as decimals:
Write here
1. ____ _
2. ___ _
3.
4. ___ _
5. ___ _
~
(a) 7 8 ----- -
9 (c) 100
V. Express as common fractions : (a)
(c)
.5
.09
(b)
(d)
1 .!. 4
7 ~ 9
(b)
(d)
.75
.149
- '- - -----_. ---------
Published by
EDUCATIONAL t TEST BUREAU, Inc:, Minneapolis - Nashvill e ~. ~iJade-lphia ~.
109
ADDITION
Can you find the following sums correctly?
1. .4 .1 .3
6. .05 . 09 .08
2 • . • 3 .5 .8
7. 1.06 2 . 08 3.04
3. .16 ' .25 .37,
10. Find the sum of9.65 + 8 .375 + 6.4
11. Find the sum of .8 + 3 + .125
12. 1 i' + .25 =
8. 1. 75 2.125 3.8
4. .28 A3 .95
Work No. 10 ' here , i
SUBTRACTION
Can you do these subtraction examples correctly?
1. .8 .3
6. . 375 . 269
11. 9 .6 3.4
2. .5 .5
7. . 7 .35
12. 18 . 5 4.6
16. Subtract 3.82 5 from~20
17. Subtract . 5 from . 75
3. .16 .04
8. .9 . 275
13. 27.08 15.17
~
r
4. .38 .15
9. .4 .375
14. 9 .3 6.25
Work No. 16 here
5. .02 .03 .04
9. 2.75 4 .
16 .375
Work No. l1 ·here i I
5. .43 .41
10. .6 . 004
15. 18.2 1.625
Work No. 17 here i i
MULTIPLICATION
Can you do these multiplication examples correctly?
1. 4 X .2 =
4. 5 X .3 =
7. 8 X .5 =
10. 2.6 4
14. 85 .4
18. .4 X .2 =
21. 7.8 6.4
25. 10 X 8.5 =
28. 100 X 8.5 =
31. ~ of6.4 = 8
2. '4 X .02 =
5. 6 X .04 =
8. 6 X .05 =
11. 3.5 8
15. 20 .6
19. .5 X .03 =
12. 3.28 4
16. 32 1.4
3. 4 X .002 =
6. 7 X .008 =
9. 4 X .005 =
13. 4.647 5
17. 2.5 48
20. .8 X .25 =
22. 6.5 4.8
23. 18.4 . 26
24. 8.04 .03
~
26. 10 X .96 = 27. 100 X . 14 = _-,--
29. 100 X 8.65 = 30. 200 X 9.4 = __
1 32. . 08 X 25 X '2 =
~
-r 'io':
110
'l
DIVISION
Can you work all these division examples?
1. 4) 8.4
4. 2):8
7. 4) .12
10. 8) 4
13. 25) 64
16. .3) 3.6
19. .3) 6
22. .7) 4
25 .. 11) 3.3
28. 1.25) 6.75 .
~
2. 3) 7.47
5. 4) .76
8. 6) .042
11. 8) 6
14. 33) 87
17. .3) 18 .63
20. .2) 10
23 . . 11) 1.21
26 .. 12) 6
29. 6.48) 7.128
~
3. 8) 16.896
6. 6).972
9. 24) 1. 2
12. 25) 2
15. 25) 8.725
18. .4) 1. 2
21. .4~
24 .. 11) 1.342
27 .• 12) 9
30. .834)' 91. 74
BRUECKNER DIAGNOSTIC TEST IN DECIMALS ANSWERS
~
.5
.04
.16
Sixty-five hundredths
One and four tenths
49.84
Three and seventy-five hundredths
One hundred forty-six thousandths
One and nine hundredths
Twenty and fifty-six thousandths
233.0
200.33
23.3
2.33
2.303
.875
.09
f.
112
9/100
1.25
.003
.046
.107
7.889
3/4
149/1000
111
.8
.22
.5
.106
6.2
BRUECKNER DIAGNOSTIC TEST IN DECIMALS ADDITION ANSWERS
1.6 .78 1.66
6.18 7.675
.09
23.125
.5 or Yz 24.425 3.925
SUBTRACTION ANSWERS
o .12 .23 .02
.35 .625 .025 .596
13.9 11.91 3.05 16.575
~
16.175 .25
.. ~ X~ _______ _
112
10.4
34.0
49.92
BRUECKNER DIAGNOSTIC TEST IN DECIMALS MULTIPLICATION ANSWERS
.8 .08
1.5 .24
4.0 .30
28.0 13.12
12.0 44.8
. 08 .015
31.20 4.784
85.0 9.60
850.0 865.00 ,
2.4
r
113
.008
.056
.02
23.235
.120 .
.200
.2412
14.00
1880.
BRUECKNER DIAGNOSTIC TEST IN DECIMALS · DIVISION ANSWERS
2.1 2.49
.4 .19
.03 .007
.5 .75
2.56 2.6364/11
12 62.1
20 so
114
2.112
.162
.05
008
0349
3
705
5.713/ 7 11 12.2
30 so 75
5.4 1.1 110
~
,. f
U5
(A) Oompass Test In Arithmetio IX. and X.
Parallel with the testing program ot this thesis in which
the Brueokner ' Diagnostio '1'est in Decimals was used. the OQmpass
Dtagno,tic Tests in Arithmetic. teet, IX. and X •• dealtng with
deoimal. were given. Data was not eufticiently complete tor
all oases to permit its use in the main portion of this thesis
and, therefore. shall be included 1n the appendix.
'rho ihllowing table l1'~s t;he information on 8otJ~es for
tifty ot the .eTe~'1 pairs 8electe~ tor the Seventl Pair Oom
parison, aoot10n V.; page. '73 t •• and Graph VII. P. 8S. Other
than the number ot c&..e. .tudied, the only major ditterenoe 1n
the .et-up 1s that onlY one test was given to the control group.
Becau.e of the cl08e parallelism of the two telt. in the teatina
Pl'op&Jl1 with Brueolmer'. teat .hl~h ;reg~8tered a mera.e point . . ...
improvement, approx!m&tel1 .~% increase in the average loore.
the au\her felt that a seoond t,.ting with the Compass test
might be unneOe88ary. 'The experimental group was given the
test betore and atter the r~edlal period,
The following tabulation of th1eeupplement reveals, when
oompare' with the Ind1vldual Gtotrth Graph VIt .. p. 8~, a startling
s1m11ar1ty in the avex-age growth :results for the exPerimental
group resulting from remedial work.
BrueOkner Diagnostlc Teat in Decimals exPres. an average
galn ot 14~1 polnts using seventy oases, a 12% gain for reme·
dial work. ''4'he Qompe..1B Test eQores show an averag, gain, in
tl,tty of the .e..,ent,. oases, of' 13.8%. The al1thol' teels the
olose 81m11ar1t1 of the two gatns to be a tail' indeX at the
reliabllity of teat aocuracies, and rem.dial aohievements,
r
. ' 1.16
Compass Diagnostio Test In Arithmeti0 - Decimals . . Flft~ Pair Compar1.son
PfLtr WifoloonB1n Ave. 27~h .. . lst. Test 27th.. 2r..d. Test Numbe~ l~. X. IX. X. U. X.
1. 112 1~ 94 S 116 30 ·3. 45 2\? 99 22 129 28 8 ,. 124 41 131 24; 158 81 "I. 1'72 10~ 15Z .51 1'13 83 8. 1.26 32 120 2'1 141 51 9, l.~ 27 153 5~ 190 98
10. "l5 26 lA5 32 1'15 92 12, 135 -ttl l$e 35 1,49 49 14,. 135 2 141 4'7 142 68 1.5. 1'04 eti 1.3.21 51 13e :i l6,. 1$0 ,27 1$6 '7D 1;57 19. 120 38 148 S3 16~ 62 ~O. 152 6~ ),07 2~ ~36 85 21- 145 eo :7.$6 42 HiS 58 22. iL24 41 161 19 169 100 24 . 152 3'1 1513 2~ ~e3 4'1 25, 15~ 6~ 110 15 135 52 26. ;L51 36 157 ~i 1'72 99 27. :UH; 6\6 14~ 55 :1.';0 70 31- 16' 90 161 83 1'78 81 32. 1;43 72 1,.2 36 leO 72 33. 149 ,69 130 61 lee 69 M. 174 ae 1152 39 161 100 3~. ' '.58 89 169 44 1'73 11'7 37' . U$,l 94 12" ''7 150 89 38. 13:5 1o, 158 " 170 101 39. 142 5' 174 '5 173 111 43 . 199 2'1'- 153 80 156 98 44. 162 3e 111 '14 1ft. 89 45. ;tM 2t) 1.~ ~'1 lee 111 46. 160 el1 141 62 1'16 '15 4'7~ 158 )0,{5 17'" 2i 16'7 75 48. 1~1 '1. 14" " 1'2 94 52. l~O 96 17' 72 185 89 53. 17$ ~4 178, 80, 17t5 lOO 54. 16' 68 16e e~ l'Q 70 55 .. ].f;,O S6 128 86, 169 121 56. 14'1 /57 130 82 186 117 5'1. l'1S 109 lS4 8$ 188 113 58. 152 92 176 loa 181 112 5~_ 125 47' 154 ~2 ~!$9 120 elf Ul5 89 182 1.14 190 123 62, 153 72 174 ,60 ~"$ 102 63. '1~4 12'1 1'4 64 J.~~ sa 64,. 1'8 9O. 168 8' l'tO 105 · e~. lts'8 110 ' 170: .89 187 120 6'. 14? ~ 92 186 104 188 112 ee ~ 1'11 19 173 87 186 83 e9', 160 , 89 158 104 184 119 70. -W! ...ll2 ~ ..JJ..a
1
1'.
~ .. '
TOT.At · 7·$83 3291 "99 ~091 . 83.4 4442
... ~
r
Brueckner .. Compe.ss Teat Result Table and Compar~sons
50 Cases
Compass Test 10 Tote.l improvement po-llnte ... it .. ...... . " • 1351
Compass Test 10 Average improvement points ••• ~ ....... 27
Compass Test 9 Tota l imprcveinElnt point s ~ p........ .... 845
Compass Teta i <3 Avera.Se i mprlDveme:nt poj,llts ". ~ " . ~ ••• • , 16.9
Compa •• Teets 9 tmd 10 Total improvement po.ll.ntfl; .' i • • • • • 2196
COJllPas. Tests 9 and 1,0 A:V'erage UnP1'Qvement po,lnts .-... 43.92
ompass Tests 9 e,nd 10 TQ tal pOints "'.q.n .. ." ., . . .... 320
Test 9 and 10 (1st . test ) Average points correct " ~H . 211.8
Test 9 and 10 (2nd ., tea t) Aver a.ge P()111t.~ correct h" ,. " 256.72
Test 9 anel 10 (1st. t es t) Average per cent CO ;l~rect ... . 66.1%
'res t 9 p.m1. 10 (2nd . t ast ) Avera ge per cent oorrect ".. 79.9%
Individual Growth Compari8o~ (See -Graph Vl!I ~ p,GS)
Increase in average peroentage, Exp.er1mental Group -
Brueckner ~nd.. teat ever lst. teet
Oompe.eu 2nd. test ovor 1st. test
~
~
r
12.11t.'
13,8%
117
(l3) CurriQul,\ijIi study L~see.
In oomple.ting the remedial work in. lJ;eoimals, the exper1 ....
menta.l gro\lp lye,s gi Yel! 1ntens1vedr111 and study 1ndeQ1~ls.
The t1l!le used tor this work was at theexpenBe of tegu~Ql'
class work in arithmetic. ASSUU11ng either that the resula.l'
cur;rlculllm in the expe:rlment.al gll'oUp may have suffered bees,us.
o.! e. 10B$ ot t1lnet~ regUla.r cUrrioulum !II tu~v tn a.rt thm.'t1c.. or
that the lose of t~.me to curricular Qaures of s tudy may be
amply co.mpel'lsated tor 1.1'1 the $.dded kno?Jl.(fa.ge of decimale a.nd
its t.;r-..nst'er in grea.'e'r efficiency of a.pplication, teste cover ...
ing the semester's WQl:'k wert designed l':Ind a.d!nlnhtered t.o the
SA. an.d 7A pairs in the seventy Pall' eQ.mpa,riaon te deteil"JDine a,
tar as Possible under exietlng c1r~Wfletanoes w'ltl'l,t U' any lose
was auatein$d..
!he original pa.l1"1n~ waa on an ag8, ... g~de ... e0ot'e 1'~81 ••
(Seo Table lIt. p. '75 a.nd 'rable V. p. 78). !hose being equal
for aU pairehe.l;"8 atudied j the author assumes a l!1m!lnr eq'(.\8,l
lty ex1fJting in arltlrune't1c aohtevom.nt and skill t6r that pal''''
t1cular gra.de prioJ' to th" 'tleet~ng and r.~ediail program 11'1
deoiJ!lf)..l..,.
]3a,sed 'on theee' assumptions, the f ,ollowlng taole of 800:re,
t()r thepa1l1'. lJ.e~edtn gtadee 7A an. SA wil1eetve a.s a
crltter1s. for the 'coneluatQna r 'egardlng the losees U'S,flY to
the regu1.ar cur:r!oulum.
~
r
11&
Table tor nurr1culum study
Note l This table 18 a copy ot table lII. p. 75 8,nd table V. p, 78 showing the original pairing according to .the Brueckner Diagnostic T'asting Program as expl.ained in the JIlEi.in body of the thesb above. The last column, an addition, ' beara data pertinent to the conoludon. of this added survey. The last column headed "Cur~ rioulwn Test" shows the sc~r1ng of the pairs on the test on our1l"1culum material tor their respective grades.
Tabulation of 8·A S.etion
Number Age Tes,-l Teat .. 2 Improvement 6coreSeore Wh. 27th.
70
6'1
66
62
61
60
59
!55
54
63
52
51
13 114 114 13 11' 110
13 10'1 117 13 107 100
1;5 10'1 113 l~ 10~ 1.13
13 105 114 1S .106 106
1S 105 116 18 104 103
1$ 1015 114 13 102 97
14 105 112 14 9' 99
i4 3,.02 1115 14 102 99
13 102 112 13 lOa 104
11 102 lIS 13 102 108
13 ' 102 116 13 101 99
13 102 ~ 113 13 101 104
Sub .. to't&l
o .. , 10
-'1
6 'I
9 o
1,1 -1
9 -15
7 o
a3 .. :3
10 2
11 (3
14 -2
11 3
r
Currioulum Test W.1so. 27th.
80 G7
73 "10
'79 62
70 70
81 61
67 48
74 70
72 74
63 57
59 52
60 49
71 60
84o--t149
us
Table tor burriculum Study
Note' This table i8 a copy ot ta.ble III. Ii. 75 s,nd table V. Pi 78 showing the original pairing according to .the Brueckner Diagnostic Testing Program as explained in the xna.in body of the theeis above. The l a.st column. an addit1on,bears data pertinent to the conclusions ot t his added survey. The last column h~aded "Cur~ J"ioulum Test" shows the scoring et the pairs on the test on curriculum materia.l tor their respective grades.
Tabulation of 8 .. A Section
Number Age Test-I Teat .. 2 Improvement Score SeOre W1s . 27th.
CUrriculum Test Vase. 27th.
70
6'7
66
e2
61
60
59·
!S5
54
53
52
'51
l~ 114 114 13 11' 110
13 10? 117 13 107 100
1;5 10'7 113 1:5 10~ 113
13 105 114 11 106 10e
13 105 116 13 10, 103
is 10!S 11' is 102 9~
14 105 112 14 99 99
i4 102 1115 14 102 99
13 102 112 13 loa 104
11 102 113 13 102 108
13 102 1113 13 101 99
13 102 ~ 113 13 101 104
Sub .. ~ol;al.
-4
.. '1
'1
o
-1
-15
o
.. 3
2
6
.. 2
3
o 80 6'7
10 73 70
6 '19 62
9 '70 70
11 81 '1
9' 67 48
'7 74 '0 13 '12
'14
10 e3 57
11 59 52
14 eo 40
11 '11 60
841)~- ---~9
r
U9
120
Tabula tion 0,1' a-A Section Oontinued
Numbe,.. Age Test ... l Test .. 2 lmpl"ovemen" Curr10ulwn Test Score Score Wi". 27th. Wi.,. 27th.
48 13 100 112 12 80 1:5 99 99 0 63
45 13 99 114 15 62 13 95 96 1 59
43 14 98 113 15 6'7 14 100 100 0 41.
40 13 9a 110 12 63 13 9'7 101 4 63
39 13 88 112 14 '71 13 96 102' 6 62
30 13 92 108 16 !5€1 13 9'4 100 6 31
2S 13 90 113 23 51 13 8'7 93 11 5'1
27 14 89 106 1'7 53 14 8'7' 102 15 5'7
.. Page t.otal. 4$3 50'5
1.t. Page total 840 849
elaas a../t 'rota1 1273 1354 Class a-A (20 ca"8a)
~
'I.'e.bu].a,tion of 7-A $eotion
'!Tumber Age 'fGst .. l Tcs t .. a ;un1)l'oVemol1~ ScoJ'e
68 12 106 12 105
615. 12 106 12 108
64 13 10e 13 106
46 12 99 12 97
42 12 98 11 90
38 12 96 12 9'
3' 1" 9~ 13 96
36 12 9~ US 96
S3 12 94 .2 91
31 12 92 12 90
29 12 90 12 69
a~ 13 a6 '13 88
21 12 M 12 ees
2e 12 84 12 815'
15 11 83 11 83
SUb ... total , ~
Score
108 lOl
110 99
115 97
115 93
105 90
112 96
100 91
113 97
10'7 91
104 96
10& 89
107 87
93 83.
100 85
9" 83
Wis.
-4
-9
.. 9
... 4
.8
... 1
·5
1,
0
1
0
... ~
-4
0
0
~
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27th,
0
4.
9
16
, '3.6
is
1'1
13
12
1&
19
9-
16
14
121
Curriculwn Test Wis. 27th.
80 ?3
'19 54
62 51
40 42
54 ~e
67 42
67 53
.,~
61
19 48
49 42
48 47
48 39
52 45
62 39
61 56
-728 899
Tabulation ot 7 .. 1t. Seetlon Continued
Number ABe 'l'est-'l Teet .. 2 Improvement Ourriculum 'rest Score Score Wis •• 29th. Wis' 27th.
14 13 83 103 20 50 ,13 80 80 0 :'55
13 12 82 10'7 25 157 12 84 815 1 41 , 12 75 98 2S 5~ 12 74 72 ·2 2~
6 12 '715 ,.02 2'7 38 12 '12 68 *4 42
& 13 '15 9S 18 49 13 69 6'7 ;/02 21
, .
!'nBe total 166 247 let ~ Pv,ge to.ta·l 728 299
Clasa7 .. A '1'otel ,Class ,.A ( .20 ,cas88"
894 114e
'the toregolng ta.bulation 01 ,curl'toulwn Test Fine,is tor
the respective ,gl'ades reveel the following median and a\terage
grade Bcores :f'or the teatsi
Gr ade 7As (20 cases)
l4'edifl;D
Average
Wi s. Ave.
42.0
44 .5
27th St.
fHh3
56.8
Grad, SA r (20 c~3es)
Median
Aver s.ge
~
Wle. Ave.
60.5
58 .5
k r
27th st .
68.5
t57.7
122
123
Based. on the assumption that the two groups of pairs tor
7A and SA grades, seleoted tor the1rnumbers for th1s test
check, were relatively equal as to gi'adestandings at the be
ginning of the semester; and knowing the experimental group
sutfered cUJ,'rioulum time losseSt the faots reveal in 'both oasea
that the median and average scores are higher for the experi
mental group than for the control group, ( ?A, 12.3 points
higher - SA,. 9.2 ;po~ntB higher). It is therefore .opnoluded
in 80 tar as theae facts Show, tha't the loss of time in taTor
of remedb.l work in deo1m&ls was beneficial in as much as the
starldings of the t VfO groupe remain relatiVely the eame. and
that the losa ot time was oompensated tor in eithe:r: a trans
t er of training, or a. better und~rstandiIlg of decimals re
sulting in II: l!'.ore accurate appli·oat1c:a1, The 2'lth Bt. School
Experimenta1 Group no t only maintained the relv,ti ve equal! t7
in s t anding with Wie. Ave. School au flSSUlilod iff'om the grouping
but showed an 1mp~ovoment.
~
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Name ,School
I ~ Find the ar-ea of 8_ rectangle 9.25 feet by 6.75 f oet i
III, Vlhat ,is the: diBr;leter, c i r- ; cumf orence, and ar ea of a circle , whose radius is 12 f ee t ?
~
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8- A Score
II. Find ti:l P., nUl!1herof -;quare yards of concrete in the road ,-ay of a bri dge that is 20 feet wide and * mile long.
IV. Find ' th8 , squar-e i'cetof surface in each of th~ _ following areas p:i. ctured below: r ' ql
11~Vr--~~-'-:-\ \~~ , \ ,/' 4, ,3' \
L ____ ~ __ --.l __ ~ 13.3 "
;1): (!0 I. 5' \_ ':Y 0 '
L I ,
--7),5 7 '::.
124
V, A cylindGl' i s 63 fCl.;t ' high a'nd has ~diamet6r of 12" G fe Qt~ "rha tis its vol:um0?
VII. Ona sale arnbunting ' to $908~50 a ' salc suanrl-'c0iv0d a COr!lIliis8ion of 6-}%. Hb'w muc h did ' h e r oc(;ivc? '
" ,~
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:VI. vilhat is the length of a 1Nire a t tached to thb t6~ of a 60 foot flc:;,g pole and to the ground 40 foet from th~ base of th0 pole?
'HI .. !
Name School
Using the 60 clay 6% :method find following two example~: I. $18900 @ 6% for 100 days.
125
7-A Score .
the: interest and amount, on the . '
II. $2400' @ 7%f6r126 ~ays.
Using 365 days as a year find the exact interest and amount on the following examples : i III. $73 . 50 @ 5% for 135 days ; I IV. $3600 @ 4% for 73 days •
. ...... ~ .•. ~ . - .• I: .- .• .
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V. Discount the following note and find the proceeds.
Note for ~1250 for 25 days discounted at 4~ %.
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VI. State, the equivalent, fraction or per cent for the following:
(1) 31 _____ _ (2) 40%, _____ _
(3) 1. 25 ____ _
(4) 37}%
(5) .85
~~l16 2/3 ~{ h II (8) 31
VII. COi'J)ute t he in~cr c !:> t ,.-COili_:)oUnG." 1. "~III :~.' Fjji'd ' th~ :area of ' the fo llowed annually on tht; f oll o', 'lng :lng fIgure: $3000 Gl 5% for 3 years. ' . . ; , , : . , " I '. " , ; " 12.2
I
I g' I
-.!
• " , _ Co ... . ... . . ' " ,_ " - ." ••• · . ,· • ••• • • ~., 14 .• ~ , ••.. • ~ _ M • ___ .. . . _ .......... ~_.~. " _._ • • __ ••• _ ' ~ _M _. " __ .~ • • , _ _ . _ , _ • _ ,
! ', '
, . : -
Find the volume of the followl ng IX. A rectangular solid 32 feet . long, 2 . 5 feet Wide , and 2.09 fe et high.
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solids: X. A cube 15.5 feet on a side.
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I L'~ ·· .,! :,. , .... \. ; :' .: ; . i.:. .. ~ .
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