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 ~ - .

f. l'

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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I.

II.

Ill.

"'V_

v.

'II.

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

54

68

(;1

64

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68,

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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

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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 . ,

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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

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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 .

~

r

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

k -r

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=!+ ~- ' ~'.

:irtl i:h ~t 'ft f~ ±ffi l$$ i=ffi: 4t.l ~t± i= -~11 -t, -ti-l P,: !tIlli~JE ~t rr+-:t~tt~+~H#1

+

,t:l. . ' ;::;:r :p+:;. t- .. c':EF -'- .. 1--+++ - ~ t -,+t+ Ii$IfI +. r+-:, 'j .. ' , -;:;::.::!:t::: t-" ' '-i-'-. t- - ',,~...., '-'-t, ft!t ~. f-l-~l '--++ ::!:J;.:~~ ::.-t: -:.---r ~'--- ~ 4, . . , j:~" J-: j ~ FltRG ~w. ~(J~:j:f+ 01 :$ Rft~R $&~1tRIt'-iI$t

4"" Tn r..ut~::t~ljUg;:A-·tm 1il tmr:' wl1rH-ftlftf

MI$ $t ~ I.

H++t-hl"ttt+:' , p4c;.-t;--..-1 ·t i:I'~:r~±±:.t..:..t T¢i+tr+-t:;....- -,I:t:t l:=t ,+!+i "TTTrTTT1 I, C'- ' r-; 1+- ~ ~t t.;i+=i+~ .:p- -+' ,,~fTI+t '7'1 1=!ti+'. , 1m I rrtrr r

Hi+

tJ:+t:j:..~ tih~

--'-'­ll...._

H+f-I+l ,'+ H--+t---4.

~-Ht±::i:. 1 tr-r.t '~

-r-t-

~~: ~ t -r+ 1-4~

" .. ~ ,_J:.' ~i+I- T • . -'tilt..::j::l:::j 'fL I '-+ -'-f-,-j 'l-r: r4:j: H+ '+ IJ±-t=tt ::I::!:h-'1+:t' ·:a=.a:a:a-r· 1 • rtJ:· , :. -H-r7t f*! .x;- ~f-+o--t-H+! .

I -+ -r-i4-t+ 1-++ ~++ f--t ~, -I . r-.-t

". t t rt+ -r;-H. ~ .. + :;:::::-'--H--T' L- Ly, ~t~· ':;:. . '~~:;'Z~ t =i=" ~;'E::'+Mf+. 1+,

1:

~ I T

, ~ lOOt'" .. ~~. ~. .1'+ i-1tr-ti-'--c-h-r'- +r . ,- -W-,-+ --t+ I-rt-r' 'f ,t-.;.:- l:f-;. . , -1±::;::r::i=f-'-..:;:;:. itr' . .r:;::F,r +-,,_r±J4j:tB±

I 1 iTII Hf I- --!=i+tr- I I j , . B +, ::...+t+-I t-lH l-4tt ;:;:q: ';1"-- H t 0- ..., +::t .. -F-rPr' +-' -+-j-i 1++++ -t.+ IH

'i;!1 """ t7 ~

ti, .w - + .. '[:fEI- ~ j-'-H+tI t- C:tt t' 't·· t;.ttl-t. ,'. . . h-j- ~.. ' -;- ,-c++ '-ri-t --1-" F 'i++-Ft; t- r-;- Irj-+T:::;"~ . I- 8~

t l~ 1-'+ -I

--! ~ .. ~-:£::::.~ 1:" +- :--H+-I+ .. LFI=r~c t 85t ,. H. +t-tit-1·-1 B+!jt..J::):; f::t" 4~F j --. - f-ri- -++' ,- '-1-+ -"+..;.++, " " - ce \.fql";e ~...,

f-H-+t ~ _f ~I .-1 .. • t -+--"~ ;::i ~. -rl-f7-. IT '~ , - ~ :"-,-,-q::r- ' ::;::;:;::r: , ~'-h ~-H----;. ,

~ --+-> 1-'-+-- - .-ct-I- .- ~l :1 -++----l--.-'-- ' I~tt,-

Ht1HBf .. ~ .. , ' -t-=- -:- ~ f i~ .. ri..£ ~ ,-' i-::~ r;:m :W. -~. H+. , 1++ fll=l~ Jfj - ,j... ~ , ;. ffip:. ~'H-I -;-I~h-.r' ' J.., , , ,l-r;::;::;::J ,...y~·rr+-t-t-'- -;- - ~ -++ I ~'t, ..-'

i-' ~ I-I-tt t

Il±±

l-±±±tal;.

i· ,:1'1 r L e! . ~ , t-t-t-r +I=!t -F ::t1~ l. 1:':1 -;'l.{, l' I l-i-it-l f-l-tt+ +it ~t+tn .H+F f-tl+ *rt m r+ : ftr +I-+t . ill

P' f++ R-+ If I 1-'-'-"- -11 I 1=It I-H 11# j+ir j' t 'L -H-t rr-.~ + 'it FP =S' . -j- f-H 4· +-+1= It:;± 1 ttm

"

-1-+f

,~~: 'I" ,-+++c -r- - ..;. +- -+- I 'I i-t-i-L=-~ .. ~-t-+- f-.i-+- -t-!~_I I~ t+-j- .:; jftSf I~ ~., !=f+f' t- -tt+ ;ttl I • ,

i++ ' tti1i :-f

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

1:::- c~ h-+-,

,l-L t;±:

I#iij:$

j±j:j::lf:'-

. IlllJ 1-13(} H+

~(l) t-' ,

t-

m

r~~K~ .Im ht~1fIl ~ .:J:H F1 rtt-:- l i-tt Ii' r~ ::d±t +itt. . '.j.. +I- ±::j::tj::t.!:: 1-+.-

4t-1:

M , I , ~-H-

~

I-ri-t I t+

tf1lli±± .. (-f

1%

~-

-'"1. .....

;!::-I---. ..--,..-

g TmBTI4-- ,li- ,-j-t- n, I-,I t-';- ~l:t

.. . I :t H- +It R+!+ .~. . ' Ii "!' ''''''' *tt j , i-r ;~ , L ltJ±t . :j: ,L ' -++ ., :PC;-' +11= p:::-" J if ' , ! '-iP :-+ -- +i. +l+ +4 I+- +il-r -'- 1 d

~i -tt . +r It-, -+ . j i-' {14=. ,.d • -ltLt +tT:":I-t:, +.1 ,1+-+ +-H I-+- q -;" . i 1 -j, + J..~l+ H+ 'i--++++ I ', ,. . ,' - .... ,+ ,

Solid Line

Broken Line

1st. Test Diagnostic

2nd. Test Following Remedial Work

I.~. 1J~. I·-i .,- ..

, .~-i:t

! ~(i)

+4- H+' t~. ~ - , -:;:::;:;:td ' I-- .~ , . - ' .- .tt::: " ;t++ ~- d -\' ...,. , -t-+< ++- --l--+ -++ ,r ++ '~-++ tl1tE-iff7I+tt1=:S=t ~++t / t-ttr+t"n, ';" 1 -++. .p '.if.:.L.... t'. [-.,:;-

ti±i: :j:t!:i- 1-1-1-+-+ - -1- t +~ fH4tt. . " ;1 , , ,:..;. • -+ , ,+ -H-;--I- -'-i ' t "F' -

cr: !-f+ + ~11=;+ ~ t1-. tl1 id- ~. +~l-tf ~ '1 T:tt ~." ~+r-. ,-t *- ',. 'tri ttU-::n:;± L~ f· ·f q:+j- + r \-+ . -, ,"1 .-t-+-t-+- -+H-- _ l=t T:I i--'- r !+f';::::P:="r ,r 11; --t:tf::-r-

J~ t- I+-- ".~' W ' . .,J: . j-j-j- t-r it:ttt ' ~ -.t+ ft,..i h !:;lIt -'~;..jlr:±E h' I Base Line (Brueckner) T n -4+ ::p: .. ..,1 1:-1-1 :l:~-ll ";-:1 ~ --t'~ ~ ~ 't;+ t+ -+i-~ cl-f+ + '. q.f!; ~ +itr i-4- +i, -I-4-l-'-+ +:---4 ,: t It "i+:;:~,

'. . • 'ol;l:t:l:tl-J; , ~ -H

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.

1+-1+'

~+-i- I -___ ++

1++ I~ --;:::: r:;::; t I:±H~ f ,++lfu +. ' -t+:t ~ H- H+ ."" -+ f-!-I-t ' . t- r,-f'PTF+!' +;::i: r~H-r I tfttT1 g-,- r.t-ttIJ -! T+t H--t++l-+-c 1++ i-f-L I+ffi. r4+p·::r 1.h. -itrJ+t-!+ R-I+~H-- '-H- H++ Y' ~ +++ . ~t rmr::.+:q::...;.p: ~ ~ r 11+++'++++ t±±l± I· -'t"

!+t ~t -'-h ~H =±L ~' rtltl- R+th+++ +'"7 +f"t"'I..:mh1~ ..!i:t! ,+j-'~ 1+, , 'm L 1+1 ~ I-+-H--! ~.,.. p: = nc-::;:' 1. ,i-'~>-i++ 1'-1. +, f -+:.;.... . ..;. H-r' _ +- I ...:: "" I q.~,-= 0-- -:r 11++-t - ~ _ ++++1-4+ -rr l-t-+tf++i "1" -'-I_-H' I"+- ' C'+" -+ - , c 1-'+ ',-.-rr- I+-' ,.,. ,~ l-4 '" +

-'--'---CT~ h "'H' ,+; +r ' -;-+-+ .. '+-I->- ','+'-I"-'-i-t- + 1:d±1-<-o·,!-'-,; C J. -- ;:1.0---t-L ,- '-r-ro"....--; . .ttl' ,'be" __ " .+++ ,~ ,Ie , , :;,. . f'Ii~C-:='-" ' ...c! t'-'-rH...;:tc....... I:i~ I--F- ~- . i±t-f-I-i' I-H 1:-' t +j-; '.,-I-1-p: 1+ 1+>--1 r++'+ -j-+- .:.:r.. 1-::;-'-1-= r~ ' f t-W- . "+ -j-' -++ ~P+ I+t+t

, , 1++++ ,rh . ,...:ltltrc+h, t1t' c ----,+ ft-.,~ I---+'-"-, +1"; H-.", r,i ii±1l u-:.ft. . ;:i:t [+f' :; T 4, h : '':.l wt.r=-: 4 f [ L 1-,- I:': ~\ ++ V~~ :j:JT~"""'" -"T+-+ h1 lJ)D. ,-r4- t-<S~ iD-.+t4 J'+M.tj~ ~H' mr+hD Y~. H- 11'-+-L ~: ~l

H: t L 1±1:t! H~J trt+ L':tt-. I t. '+~'-I-IWR f. 'tt!- c",' r~ i+l++ 1+1+.- T~-1,-L l a· ,. -t.. :I -I-i-rm, 'T'f-ffi 1+ - ':1m , .J, . , . f-'-.J: . ; ~. ~n:ffi+ F ,.l. Ii 9<1, I , 0 " .. , +- e'0 r; ~ Ug: t -". ft-f-;..;- it+ ~ ' 1f+14 I-++-+:j: '. k I:J+ i +, ,\-t-++ -

tH-tt-~r

trl~: -of 1-4+ H-I.L m l+ ,-t -c l-t-~ "-E;:t l-t-:-" ....... r+- 0 hi +++ f-r+-r ittH ,+, I r+t-t l+l "Her:' 'f-'-+'-, " Iii- t b±:±1:-:.+:::t+ 1t3§"R.ltE~rt.N] lR::n:r= tGl h~-'1I'tc rrHf T i-'-'! 4J GH.lA S- . 1-H1~ p:::::;F:I-." ++-!:L -H t!J: .,.. I~ ;.;:i IlWrt

... '-0+ -++-'-

I-rr-t-I iTt-

::j::h:t-t7tt-Ht-

.l¥ ~i=lwil!-:-

+t +-+ ,.. ~tit~' . , , -h-t , eM- h-+'-i - tt h-i- ,1+ ti I '-;--h- rt ~±' ~ .' ~ f t .. ~ ~.:r . .' '~L'-'::t l::tt.. 1+++: b±1-'-t' ~' I ~-, ,+ -, T';'r-' ~ t--'---t+ :+' r", "". H.·· 1 1+ 1-+ ' t1=' ~ +t l---:r ' ;:u ~ I-,l;:~ .' , ',-,+ I-'-t-4 -'-4-'- ,., , " .. !.r- r++ i+J:, ' ,...-+

-;. ~, ' fa It-;- - tt+ , ,tTr" Il+:->--I-+- ~ --+t- t-,~ I-F .-L;-I-;+ .m:;= t~P=:=-t I-t-~l:=t;ci:t±±:t ~ ~ .--+- l-..-i--++-l' ~ rr I t+ I-+---t~_f+ l i++t -1-'-4- 4-'-H-t -.-t '+ I-t-h .rl- 'r+-;-

-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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~~~

i+t++ "Cj:.j: R+ ~I 'lli ,-it h-J+'.

rt-::-+ - I-i-l.

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PRINTED IN U .S .A

1+..+

h fi+t

r;:m

ffl=1$ _-2

H+ 1-1+ 4-1H++.J:!::i:

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1,4-1- .+ ':;: f+

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..

~

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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 .•

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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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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

~

r

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.

~

r

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 ?

~

~

r

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? '

" ,~

1 ', '

~

r

: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: .- .• .

" ,

• ; ' ... " . ., . ~ "" p

V. Discount the following note and find the proceeds.

Note for ~1250 for 25 days discounted at 4~ %.

~

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r

.. " ". -, .... -~ .... , .' " . ..... ... .

.. ' ("." ::

, , '~ • ..c , ' \". -~! j. • t ~ ~

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.

, .

~

.' ,

.. : '., '

, '

,

!' !.,f

"­-, .r

,

' , )

"j" {

.', , ,, ' 'c'

r

-. :.'!, ': r ' :'; : ,-... .. : ' .

"

.. " .; , ,

solids: X. A cube 15.5 feet on a side.

I,'.' . "! !

I L'~ ·· .,! :,. , .... \. ; :' .: ; . i.:. .. ~ .

' . " .... , • .L ... . t, : ,'.. .• ; . ,',

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