idol

111

1 11

111

1111

101

101

111

1 11

1

0*.

iects"

schools

6 "A er 1"-% sans on 1-c-Z6 ana r4.nronmeihave ixn

and

EI OI th se

* 1*W-.S.**0-A1*(N^..g.-*1§t11._ff RAO

er-neral nature.

in High School Sub-Education. since 1890.

1948-49.with large numbers oftheir treatment is of a

by ,ithe Office ofbulletins la for

are concern.A E

DiA01

Specific (pitj1ftjye and quait.subimts ve L_,,=7_,n provided"The TcIi of General

and "TheTki 111 I-fX1 Statal"QT4-sg-t

4 11Lata_

Inc

ormationInt- on p-1,--1ye .*

E. A=,-%IT

111 cfflfl ULin tr koi . 0

Ahetxmis the Jag= uilnuai E

%Ftit-lt

g when coin with kwal to *= REIff 1_*1 E=a_a-a._a

for neede41 improvements. it is hoix-ii

AM.firtE W-7:aa _-= OLIVIA

HhM

JJ

SCh(K)IFV't V E

Apreft

LneE

_E

A

01 I glr-nA EE 1=4 -&-=2 ,/ 2

'Ak NA'

that A E1.0 WAA:

a asisa

thetA,

extent and nature of mathematics ft-hication in the --kublic highschools may serve such a parpose.

Many secondary school principals ana _petI.

ofexpresK-qi an a'n the facts of this stude bYand comments on the questionnaire used in gath:_)To the teachers and principals who gave t=enerously of rtune in supplying the data on which tbe study is based.-of &location is grateful.

ea_.Licx _ u.p

WAYNE

Assista, Commissioner,GALEN JONES, Director,

Instruction, Organization,and Servwes BramhirtSthri of Slate and Local

Systems.

Foreword

B

.The mn:iA, ynr,Since.

.z

great WI

1-1Airo

' m '; t

ofc

in writing notesthe

elOffice

*. A i.J.D9

.1 ri

S.

Contents

ForewordIntroduction_ _ _

Nature of the StudyCharacteristics of the Sample_

Seventhmand Eighth-Grade Mathematics_Offerings and Enrollments _

Time AllottedField Trips

Ninth-Grade Mathematics_ _

Offerings and, ents 8Grade Level of Pupils 10Required for Graduation _ . 11Time Allotted 13Field Trips 13

Tenth-Grade Mathematics_ 14

psi,

3

3

5_

Offerings and EnrollmentsGrade Level of PupilsRequired for GraduationTime AllottedSize of ClassesField Trips-

16

17_ 18

18- 18_

Elevcnth-Grade Math ties _ ...... _ _ _ _ ...... 19Offerings and Enrollments__ _ 19Grade Level of Pupils _ 21RetpLire-A for Graduation 22Time Ailott8d 22Size of Classes 23Meld Trips 23

Twelfth-Grade MathematicsOfferings awl EnrollmentsGrade Level of Pupils...Required for GraduationTime AllottedSize of Classes... _

Fiekl Trips

iv

23232526

2828

.

:.._ _ _ _ _ _ _ .. . _ _ _ _ _ _ _ _ _ _ tu.

_ ... 1 ,. a _ _ _____________ .......... .1

_ _ _ _ . _ _ _ _ _ _ ...... 1 ,.. a

_, _ ...... _ _ _ _....... ! M.. OM MP"...-m. dm. ..... -... . MO 4111P m. MO

MIM ,M. 4MD MO ..........melb0.M... 0

mo am. m mm OW GM a M..M MI OP MO M. OW 40 ... Moir 1M .m. MO Wm am

11 1 I i I .m M.. .. MM .. .. ../ OM. MP ..

IM 4. N M. IMO MN =I 40 OID =, ;. Ma

40. 1.

..MO ME, .. IMm. mp. amMIM0...^01.M.ON.

41M. 1M. mM,

4M, am

AM. am MP- dm MO M0 %S.

vim Am. mo a m a MM. GM

. m a Ma ...FP 1 ,M 4M ... e ........

am am MEW AMP

M0

... 11m. .. e 40. sm. MB

am mg. mm am .0. .M.6Amm

r

... _

. m, M. MP ..

M. Mb 411.1. MM. SM, MP- MO MP

AIM ..........111MD

.. 1M V.; SIM OM OM am WM OW M

..

MD S. tr.MI

dlo gm. OD OD M. Mil.

.......... _ a _

mo

ze4

27

MIL

_ _ . .

___ _ IM es

6.

7

_ . w. . .s

.

.

.

.

_ _ _ _ _ _ _

_

.

.

:.

6is a a1

1% r..j.ff-ffff ffs.a-m. E ea

* =w W *L-,a----'pnT

erTTIO STUDYAnn

-_I

ga.-22 a...)

needed

a 'aJL4L49

Ar,__,-,,,"Q.,.....SA -..- " aPat e e a8 a...4 5--a-'s V _W-1 a a a. . a -a

li U

ff-'1W--^ and

ran Y1 ATIa-5

I al.a_aa

M

fr

Schools

concerning 1) enrollmentsPnts in mathematicsforprovisions instruc63n

school year 951 ath th. brigm maLhem t---4u

semester of 1052-53investigationnature a tion wars influenced by (1) itigm,

m mathematkn %%cation as to information mostmathematics

concerninga

-7_ s-vw-akJ la

a%I -1

a I W

=L.

0Nag

=-=en ilia tg;y 99 W.A. a a a ay.-4g t--La

mst officers 2daMathematics,

author also

Z-1- A

ff.PaW.

wishes

edmathematics

furl rr-A-YinaLfaa

gfromAI

F nature of requests in corms-Unitedn to e ota

agm gge-tvo

=a-

a ae= a a ,=' =- a aa.affg ralUA V

a -affA A W

the author Iiiasa- == - g 9 s board of

ICouncil

a -aw a a-a.

education.I - g a

to et =a _E-# rat

pals 0 e a

which made the study pa ,___gctsrl!-_-,-a- -..,-g- -- -= = "a- = = .-A?-...# aE-

A p f_ ffL aa

high

oampie.

he gam* used in thisof ii75

- 4. public a schools of the Umit_c.kfi States.

study is

'-"4 110w

a(as

a Ag=11.47,4",u

I a' if g randomly a =9

a_ = tu,a,E

each-5 .5.E

a Iva

ti*eman princi-- a E

a_ -tilE..4 ;41

a a_ E

high schooLs, 965 provided ali or part of the informationIli = gl Pi 0-4 pubk. -a A A A 0 2Imre were oo i !ilea schools zzat prwrined COrnpieL.d_information upon which this study is ====L__---arile based.. w

g

a ==n e E.*w

a a a.0

f0 4

.,Si 111-= i I

E

a==.

ft- .= == =affE aa ta 2

'eM9 "t"-a-aa_gAga.3g a

....a

! compares the sixes the 85-Tiitm States.

higha*

data

Cl-Ia ra--13

F 71

and ,E '4=E-1 I

h whools with all highindicates that the schools in the study incl

large high schools and a smatter percentageud,, a

r=7er percentagea a

ff am schools.a aff -.et" g YlzrIJL

I ° Iv-HNg .g,

=

/IT

region,= the high schoo ;n the study witheachCPI the United SU* The types of high ethook in

As the Unitedff.-- ff _road with the typesW:a.%07

-===-- - = =a

a.

vAl

- 0

number of imAla molted ff schoolthe _ 9 E Onited States in

_

ww_

thatnoted

Or #1....4 -*

Sriaa_oug_--1 1

^rtt 0-taalletU&= - -,_........a - g_ high-__az

_n a itAI, w

4,

;.t*.kr 1I

tftv than the

i

raS

the

'

data0 (2) The

data are for thethis

of leaders

E Officeof

tilde

representatives of the ofo other leaders in

T:ke contributions r

148--n schoWs.

Characteristics

theserequested .

,t7

slightly -

th, schoolsthe eitti`

in table Z..study

Public High

gestimsand

directors,

ers

schoolsIt

of high ofThe esdki tip

inthat type of school. These data **AL

will be the echoobschools 'in the fa.t ;- . . . , .

===

- -

.

2 MAIIEMATICS IN .1:)t1BLIC HIGH fiCHOOLS

=e -fr:fitage of theso schools isa the United Statses (table 3), 0442 ismtof pupils enrolled in oie:ft Vim of schi.11 in the slu;y (table 6), ;;---.!c-,:_---

sentative of enrollments in these tying fstr the -_Tairsi: -41

differences between tit ,::,7hoo1s of th otay et:4 tativesampip of the high schools of the Ifni Stafaa &mid be Iviwt in --51117-11],cT_if the reatle the finiIf-ir.:-s of the study in .of all pubo7,i..

di-1-31nentat ,;--S.JOTtilf, ! ealav re-ii-4,17,

its in the study wItare *nee is for die erafi7 S'742.442).liovever, It thi Ations sa1411, the schools th study can is sato

fairly ,representativ4 of tie puliic -7*,-cols of the TiwiL.

Testae .4r

5e,0 tgeo nw_ -!- 'In the cUnited &atm;peaiyira -/Pe, oar-

-

tyk*,34

Tei)b _ e!W% VOSS-EM Ext-o_ h

1161114111414--.--------0,---

zt,%8

ZeLad

ENC

LIU

Lt3

_ , hrmiksz el eAuld

- -

i

Nsw 411-r

gl7B 'a0 Uniabo- Isaew

- - - r 4 41 IV!19 ,=== na -== a a aa awe. 1 I I I 11114811

*L)

0.91

e-.44 =a1ft,110

II--

i- -- --, ,......-....-ii--.1.1111-- - -..==. . - ,... - .... - _ -=6. ==-.2 - ..-.......---

intmAy

=-,-

I =

41r-, Phalb

= X41(

I' Mt

_

12. I t;çb

ei.ep EZIAtt<i QPI

fIglif ..491ARI Ertfr.a. OA. (g gi-000 i

_

. _

4.*.;

4.24

9.70

"90

17.

rII

1 i..--...., - _ E-h--.-. .-,, -,.-.-....

7.*-- M.---- ., -,- , 144414. '---r-,---, . .r- :' . t'

_______, of.--.)_.-. --...--,-0-1._ . op wow a.co ilp IP fED OP 1111110 4111411. / -----:.tr' -7, ''--- T. u-, .,- .

. , : . . .,. tt . .. -- : .' " .1 I- ite I.. _.,...., i . . A

5- 4 4 0:---4-`"$ cc..., ___. , t .

1 V r- . . - A #-...-ir 1011111dil 111. I I Il Iii 0

? . 4,_... ,. ; , -

a .01, 1,10 ID IP WI'S, 0111 fffff wes -: . MI

r II I I Irr-

a

,

1 In wsb Cte "-ei:!=T te3 eis study.

1111

1111

1111

1ibm

illiim

Mitl

ibila

mum

mai

mom

miii

miim

inift

V

ToWs

Sif A .._-_7-a-7ff

*. rnitsrin _

ea IN PUBLi-11J

bythe numbvir ==r e

_.=

qf the numberhigh schools in 4 United States

I 9SChOOIS ha the _,,_ Am. g -,.,,o&E___-= 1---_ -9., -: - =--- --4.,

3

"4--h

&boob.

In tbaUnited States

(195142)In

Nuabor Pereent I Numbw

ID 111. AID MI

..... fft Is 3,227ymr) and w_Joi 11.92 8arid undivkled. 8,5=

Total .

. ee c-er in tk.6

23,7.1.6 L V.] . Co.)

129 I 15.05368 va360 I cw3

857 100.00

v6by t , e E repart___1,n-

l'ace==-,-- 4.A. _ _

Lvla-a jrt,-;-a

fu.1*

ff: rmjis- of the=

StatesI

EuratIn tha Unit-M State*

(1951-52scbools in tt., study

(1952-53)

_ei /200a-t tWetuit

/HS

RZ-.......

1 ---- .. IN,

Fee asludag 4' soda inftsatimg tytm

Set aEKE-,

eA

A I 0=fr

19

school, see table 11.

W.-7_, ..-__--.- -.... - I_. A aGLi uri,/ and g '-41-UTI( 71-0M-1-3-. .

104505,,

100.0O3

Numbor Parcalt

69 A--A140 )115,111

396,640

adi t-'=i;11 In/YU& to pmvideUlA it WI ft' V enthral:Id efralthr I0_ 0

eXPeeKie InWleene- Trza''-t 111Z---to trie Pr=___,_!.3 of th-,- "" Thla 111(re1. omeder-__Ev traditicsal with" kfrefs* hymn w=f-tal mos of

mathanatks are Orrelated into a c, subYtict which is given tin tith"g=t;--,--necal mathanatka," The subject althGithi a remit widitkn to theci,u,-;_culunl irks Start :4 wfth arithnntk, kt banning acCepted as asubjmet fcas tin seventh and e4htit grades.

1Ibe m)orta fron tin w(6.44} in thk wtidy imikate dust gamal math.-maths k wee ptvulaw in tin jingly *11 school tim in dm omnbind

. kankr-ser WI school. Also, the percent d stutkets ennaml inmural =Unimak* kl ewegreakir bi tin haw schoc* (see takka

In fiwk WA 6 slows tktt the pima cd stahmts in tin seveitherack maul gftwaid mate taxi 4 to 23 (Wendingal tssof t silo& 9. .92 kt Wei6 r

7.;

3.

r:

tr

Typto kitsii

.. a WNW,

41.110

u--em4azie1

der .14

-Amionommonloli.t.

Th3 mkt koM u.=/ r4kities Om*.

-

...---_

aa-

Etezaamt

13.5950.22

1 . 19(-

aw-r-- 4 =kits a-Ado &got a&s pabi

1Vps cifl:W1

Total........ d a AM a

-

1 . .; T*S,

-ND -=11181=11111sam

.100.00

1 of

s

rpGrade athe t,

k_ tat. *s_1,:,

1: IriI ri=1 I

,

$

. '),/';

?. tit1 4 ,

1111.4.i.J41$. *v. 3 'lel. 'AtV , ..P4A /.4 ;1,40..14 ;- " , . r A ..*,-4's4se 4' 44. .4_

t 4-

_ r . out

1- I

,

.; t _

^lat

;

E-

C

e?.. A

..4

1111

1111

1111

1111

111.

1111

1111

11M

IIIIII

IIMI

1111

IIIM

mim

mtm

outo

mm

im

whoa thfiof the sniia SCIICkAB.

A Loo

.= 1- I k A

=a-a a _a is twice tt%.1,--

th.grack, ._,ff-te#6-411th------

Table 5.Enrolingrit seventh-zmdC_=

_

1b-t 1959-53

Juniorimnikarhigh whoa ot rE -NMP --M-.11UnM k

Numberl _ Numbe

un enic

N u m

......

1en Perowat

.rithmedel 7mks 7_ _

Arithmetic 8_ _

Gawal matimuliat-k 8_

13612316 V=-1

14.498.*70

.01

3614811 7

of the percznt o., A ltis in the sev-m-oTable 6.Distribution,_ by six. ientn arm eighth enrolled atis erteral m_Gttl------Trmticst- first semester052 53..-

toak

al3

schooI, offethsest

Pow-m-lt c

grft

I (LAO- 1260-09 141M1-1 99 4

40 e54,'J c. ImikTe 23

Table 7.Distribeigh I

ution, bite re _a_m_)"

N enrolled n _

trellsasot in gewal

h

10

10

Asse

I-= t3 72.A.ref F 1 - _ _ = Pj a al- e.

a

Region I

Asormemeoggall=111111111=111MMI A I I 1 0 I I I EMI / NM A r

PE---=-4wit wrazr-----t in wilwa asstbssnatim4missmimiong==.

th ends

NewMiddleEnt North CentralWest North Coutral....4&.thA1MMM.Etat South Contra._...... .........West Sc aUs CentralMountainpad& .

44

9Q

3717182

11

47190

Fcr moaning, see table 2.

cdRh the size and typestaieno eareit= m generalA

the whcaalis is mme of a (IP?

that in one

Acf ta ehooIthe

tore For

-s===mi-A7M

icK,,Ime,.1111. (or

tabk--w-FAAAy __---=154' of the stut of the e ar*kre

grae are (welled mamust we im eimiled. The varkthilt

tba peatant d wish

while k ianothir NL A A

, *rLgnre E-sW brtithil-subjtet

A

Ay,

,

;4! slY1,7.1

.` .74;_ ..._

4

p.

a.

7 nki

i= I tage

1

1=77

EN PUBLIC HIGH SCHOOLS

gen=r7_

by ar

el

SfiEV

.?

_r;

or v. en.. e ........! s e eib em

99____. tip

a ...............

a

7th

t.8425--....1100101111111150.

'40 thet t ctf sevonth cu-1952-&

4 1- . .......tlaatio.

...... .........AV 4100

01.

48..110 IN0 ....... 010 0.0 .1 401, 00 S ... a.......

.1 u_

\.

-

27

;

V

-

1-"r.V?

. :,' . ;es.; . r - 0.; ' 6 1,* ""tol-i" 4tav s-. ""

- - r.

1- . : -

1: 4.

=

,q" *._,A MI =. ,"-t-V :700 Ir ''.114'.`i;_,'": 46-1jr. :41", i e t

, L;;;t_ . .4-04141f,

r

rliII

IIII I

IIIII

I IIII

III 1

111,

111

III M

t It

IIT

T ,

TIT

1,1

11,W

1111

1'I

1111

Illf

Itfim

It,

I'Il

l !ne

n m

mi

/

eoncluc!equal tiE

11:7,A fait_ ATI I T MGR SCROC7-

that not all students in the seventhe instruction t.n math

Table 9.Distrib I 7_ flSet --V-7n

k-0-7E1

E1-1 t=- .4 ToN

es receive

scrttwassma

byknew=.0

. period

r

1 Lew than I -&=-1----oobi that affe4---A sibiwt hd_

Table 10. abaeon, ritgth

410.444=4.4.........7

MAEN CWNCSA Li e

EL:v-C _ .Wtibe

470- qyct 10 e-tvn

Nirr ..... _ _

9

0

1004650

Field

a Mid. 2 t

perimi3 of the 1.rth idktL

irE a &Li re- 0-= EN 0 _ Of= 04 4g g

161 0

06A

4 ft

41 7A r 0 g

7A

i'jI 5760 I

14-, 301 nn..-.,..-.1 18 IL a

01 =mg%) ..s -,--- I

Among- the many suggestions by leaders in mathematics c-_---:=:23,tionfor enriching the instruction in mathematics is the use of field trimThe purposes tnually given are to make the mathanatical erneriencesof the claiwoom mcwe mftningful and motivate the study of `the subject

owever, a weil-plam t oontribute to the building ofd Alls agnmunity relations. 4

For exampk, a clan that is studyingfvtory Agin, precifion floe,thp the management of a faci

-th

0 usai. inAry V

Demme aware the

develop.Talk 11 5" &=- & approxhnazrA

the use rag a. E E0

tighth-grade mat,thematia?"

Theschool.

a

fluedikla

0 IN

ptirp(MSpublic reir=7 -us

& 9 1,--------;--;rm. -04, ,- --_-_-=---- 0 7-.L..:_i

._y w

,7=f the fft4.41 v Ji

,a,-____-_# neki tiumi weirk,_...... fact f..., ... ..L

uni this_

be =mate pernilar in the==-_-12t of aim& that umi

nesm

6 IN

im

by length of-

ArithimatioCa-4.41su 7Aritbmate 0'

wantkr4v001:

PG.

-

and a

-

..... al (minutes)

S9 tis .60-44 a-494. 'a-

pinteet a um4

_

dew_ _ 111- - mg.

cf citEss 114%37-1111-1ti --

144-6113 8

_ .II- -- .... ........

- E. ....._ ....... ... ..

...... m. AM 41. m, e

Percent od A:Itccm-w., by parirtd (Ipiatatw)

F

1453

2947

1716

1

IL;

22

E41

13

0

I Fig ceseirkag .

7SS42

.1l --

1

13

39

9 -

:-.041

t. I

I ;

n.

01 Cf..-1_ _

:- -,--__

11 i 4 i-"_1_.1-..

'. -$:', :;- :1=10-g sMt. :al led

9vary r

2

F-' I 7*1- 1J1I az)

2-TA- _ _ 9,

- ,3,

erc2 atta:'t

e, 1 ',.

,,---

r:1

I II

-...-

.. -, i..a . a .1 . 4

. . 4. MX

1.., At :i ' ..":-. -el , I:. ig...J .1;I ft 4. k .".: ..j? 't *... '

'-_, =

r.Ort1,r

411.

7-;

".=

77-

.

"'"11

1111

1111

1111

,!111

1N11

1111

1111

1111

1101

1111

1011

1111

1111

1011

1111

1111

1111

1111

1111

)111

1111

1[11

11 1

111,

:r4

1111

1111

, 1

'

a

titff ga M

in i*vmth-and chthgjade mathematics inthree timft the percent of schools inwhools that use this learning procetfure .

school iiit prevent the flS of fieldwarrant this conclusion.

the

rff"

The

_zners of all types and sizes of szhoolsa rrall &'=4

T

_

= g FaN mitzi r

7

I

g__41

=

er-iion orHowever,

4-

Z--=-MgffE Ing o,%on m seve .-and

9

V.emfa

=4.=

-IF Ss,

9

limited useeighth-

of meaningfui tnstruc-_

t_.

A. tsIA Va-# TY P E OF SCH-pi

field trips

B BY SIZE OF SCHOOL

C. g

1aa

&---

1 _ M.-----_-f =g----_. -f _`-,. E 2-,_ = N ff _e---__TZ-__ z-r-:a --_,=. = = a- a- a =-- a:.a _

Mr = .=== = =

*kna 4

fti]J TICS IN PUBLIC &mom's

jusittrwo.Citsxclimatic of

Vt.alst

7

oiF fiate Ina 1: ewe Lrica. If

tion in solathqall.ttlisc theisameststi.

410.1 r

,

r

t _1 it

rIiin1:9_,L. solititc: iTr. don *Tilt ral

.2164)Za pewceng- of repaws gaol RIAoink--sLo1/44 e .th-grado ,.-xe-th49

Ro*Stict

Aellamathl 7:- - ...........rir -A Intatitte_ tim

Or.

ArliaK. _Jae 8_ .natatUitedliS I. 1

N160166,,+.

jUnit.V.*---=2-T141:q

A 4 e, Mk.arrA-

Noramkozw Pmmt

- ---,,

5-

Tamil

& WC.

=k,

e

T-

/fi.-7416 6116

411 41 11 11",NI-X44a1 -

I

BY

4: MOtry OS-r-k4Vr .",..51.,9

DIAd 37.11C WIAIC eAt1

Teat

a &= Qinnrat m*Aki- GI esofi)

I

,u, mifm el&Istr4,

If

4 -./ I II _

.

I.

41

I.

1_i 4ipT .1 .

(41-4

4 ) .4

45=7 _ t 1 4.: t kr 1 . -=1.. -.s t t

'14 ; "1.4.-,"4_

4-

.1

S.

Mr7-117 ill11.P.; #

-

:4,e17$

hasN a

the

-"a

MATHEMATICS IN PUBLIC

in education C--41

_

fèi _TUflJk-a_11

tbefr t " VE n

Witt vg ced by OIL v-

-a. LH I ,xap_fqti n

United 3LitA Lt tie LAA

junior hexrusnsionjunior-tvnior hih wiawl. e inabease ofand the attempt t_A-) provMe erwiences in =OxenLim a,....a, ..A. th.___xi,,,---

.. f ag-enerai education prwrain, Feneral mathematics for the ninth-gadepupil has been d veto During the last 30 years, it has .6L-Ayame a mAjor'1_, ing for pirils in tl-Ie ninth -grade.

&lag= sEa-i that

tho nn_

the junior hh whoei

Offerings and EnrodmvilsTab!t 12 presents, by type of school,

mathematics for the fu-st serne-Aeroerved that there is little chang--=-in either ra or generalhi ooth WMeSters, ofapproximately 1-1a

the percent oiLI-I. rilu

= -LAl kr I.

1

A I_ sti

-

the enmarnei T-1LA luti -grade

-52 and 1_ rWill be

the pervent ort elidAnts Anw-

1eut enrolledWtw-n

I= A a 11 in -E.1

UI ga-MeAteWS.mat

-rolirnent m nint maw= by type offirst and second mintesters, 195

-

Sukiect

A. FIRST SEMESTER. 1951-52

- 1 1

iirdar hieb athiOni

I

Number peromt iNumberl P&-mit

= "-tr411_

aublect

B. SECOND SEMESTER, )951-S2

Sisrert I- :2-

pearrai tera4Li-

Jmiior.seniarhigh salmi

7L.

Number1 Pereira

3 , 216 65

iJunkw high 0:thoo1

Numb.

type Li whoa, w tAkas 3.

, Percent I Numbert

I

0rA,

E

;t

high sOb...

If tie enrollments in general mathematics awl algebra are dettruL..=by the ability of the studenta, we would expect the percentage of thestukilts enrolled in the subject to beomatant irrw----Acfive of axe of school.me perceitages are approximately eiNal except in the ease of thesthods (see talAe 13). In this case, the permit eninikd inmatke immune. Of amine, a kakis in mathenatias edixatim d=a

Ii

7-r

a

anil

os

;

; .er

4.

v

HIGH IF.

V

-*woes..

c strp bm w :pt,

it -_;4 -1.-0.14 ge-ti 'it it : IA, 7

imAi3#'

6

4.

.1 4*'

*T001 ObiWit

Itis

rola- L..-;. tw.t

i -*IC Math*I I atud tv Aled '-_. gel:1;4

.. 41 --,_:,-r lie._-:- I, f&Ma ig ..11_,.., I "

aliVa tifiGbib :_oclAined

fitq.-.

t4

jtii k.7rie

Table E

aegukvi,,

u- c

u

57 I=

411, . :_ ....,,. 1 . --__.' ., . . - ,-.;:- 7., - - kii 4:-..., 1 i4.:

I ^ ' : '?' 1 4 : ,te..... %. .- .",.. .7. .. x-N.....

t.-.,, ht..; f .. .1. . ,,t-...!.4 '-rt,; rt; t .` 7,, ..0.,,:?'" V ,S44,:-,"4,', 4 6,. ' a-lf,(4 J.C-': .6-46-4...."

.;' a."' , .41,1 , : ..:1 r-"

1_,..

, t7 t* , : . 4 1,.. `... ,Alhot "4 7, .4, .,='..°4-. I 1.4 til.i...47 It?" '4"NAttitt.-:-

r .. Li' ....7: r.' ' ..fik4r-,' 4 .'4.-,t .-;.k., , i. .(.4 "..'-f.-r'.`'.;-V ;",:r 1 --14x. :, n ,.. ,. ., ttw____A,Lc.iiric4 -istio.,----VI-1z, - .a. -.7",/,... -- ..5.).1..

...., ., +_,

. .. . ..,,.

".'1:-.=.10-- -:-. -; ...... ,- .4...Z.,L L ...- v-z_i -. , _ , .-__,_ -_

17M

1111

1111

1111

11

Ir

10 MATHEMATICS IN PUBLIC RIGH SCHOOLS

Several questions might be rabed regarding the decrease in enrollmentbetween spn3esters. Do these studentik 12 to 13 percent of the pupilsin ninth-grade matbeniatica, drop out Of school? Do they fail the courseand never repeat it? Wily is the percent of decrease in algebra greateramong the boys? Are they len apt in algebra? I. it taught so it is Imreinteresting to girls? Dos the girls need algebra more than the boys?Similar questions might be raised concerning the loss of enrollment 'tillgeneral mathematics between the two earnest:era. More detailed dataon enrothpents have been, ipcluded in the appendix.

Tabla 1 .Enrollment in nits gnaw math,-ma tics for first e noes tors,1951-52 and 1952-S3

Ekabiort

Earament for first ammester. by year

Fat lithoCAS in study

1951-42 41 952-43

113ementar7 algebra.. _

General mathematic* 39.91224,614

46.74510.190

Estimated for UnitedStates 19118-53

1.115749,600

Table lb.Enrollment in ran th -grad. mustAema tics for first and secondotp moo Como 1951-52

s, Subject

Momentary algebra_ -General mathematics_

En:alimeat. by semester

First semester Se000d semestar

4 Pervent af dimmers

Gists Total Boys

18.161 17.07611.195 10,363

39.93224.614

15.6909,845

G1Toiris tal Boys

16,131 14.9458,786 21.352

1412

1213

Grade Level of PupilsMthough elementary algebra and general mathematks are timedninth- :4 r; subjects, not all the stixWIts enrolled in the courses areon the nintb-grade level. Table 17 shows that of the ducks:its in thisstudy 20 percent of the students enraed in algebra were in the Withgrade. In fact, a few studentskes than I percent--were postgraduate.

Table 17.Distribution, by grade, 4 the pwAsnt qf pupil. enrolled In algebraand immoral mathematics

816104 Percent d surainesst, bY Weds

11

sostberstias$1

rz;

7_

41IP

Am.

. &

c...--

!....ne,:_eAr-erilmeweememftrers....

IGO

G3r44

I

nom

1111

1111

1111

1111

1111

1111

1111

1111

1111

1111

1C1$

"'' I

ttlI

IIof

fi;I

N11

1111

1111

1111

1111

111'

"11'

'111

'"',

maNaa0

I

L. by type.

Juniar4ssior MA schoollivular (41-pm) and swim Kgik whoa.

B. B-1 sins 1........ II

5

EE 10-49 . -w

I 60-99Ure--IM.Ia 200-4-M__

N SOO gm snowsI C. BgiArV- : II . ow _______ .I Middle thoustic_____. .E

1 Mrd Nck-tb Central

I South CentraiMinutia_

. ..._ .

I Wmt South Central..Me----.----nthha1; PE--a_

5aaE1

I1N

i1

11

1E

11

6

w---- Pa $NE1

I1

I1

1

11

1 cm the reeion. ,

1,1

I Many what* stated that geonmitry wu not a *xi rixfuirenesit;i

however, jf the staked expected to mita a _Akwe inn where itIrma be needed, thi4 wed wtsiki be plated (*4 by tin student's (mfr."saki. Perhaps this viniktion in graduation reciuiremsde elmfri rainSW* INIIIMMi imit: If the ohm,/ pope* of liewnitg bi. to tem* kf---Aaw

MATHEMATICS

.tor Graduation

rewr FuE-41" vilIGH scrtooLsft 1 71

EdIt percent of the schools in this study reported that 'Lane geometrywas r-Nuire_-_ri of an Auden' fcas graduation. Two out of five schwisrinuire the subject of all colt, _ory pupils.

Table 25--A presents the graduation requirementain geometry by typeof sclux4. Approximately the same percent of schools in esich type re-

tcd that geometry was a graduation requirement of coil?;;-=;,---pre-para.-tory tuts;t j howeva, twice as many junior-senior high schaalsreluirvi the course of all students as did the regular 4-year senior higngawk

Table r=zrePat of iththe L-V1 tory Studeill.016

EV1 of

1 "

alai-g w±to E = Lartelln

= = = = =_ g ' "C. &,;-=

1a r

= e onw A _

schools rc_Aatli

g

01 all dents fOr A

re ofGjv-

tie

rt440)ot., =-=

is

4Vr

Thercent of schtLycm a u students

Pe.mztIMINImmENENI==1.

tym a grt)mct

...

4941'M A

9 1

37

364147

14

*L

6

98

a

10

a For unenthig of type, adze. and

Evan6

mfig0- NA -4 ti-1

9dee

V8TIRtb3fl 1-0nE7 111 geN3n et for--oat requirml"011)=-L5 ahowri in table

v.- .

m of thA revam,_

"la tni0. 6_ In geo.- -ora- -

,Nmetrytheykw graduaidm GI 4,11 stu.de_-_, In for o rezion 18 percent of these_hcele had suth a rt-auir====--ent. Even the nmi requirani=gt for cam,-prvaratary pupibs varke ban 21 to 49 percent of the whook depending

Required

25- JO-ik

RI 1 ova that ..:, Ir---!...

i C --,a ofthe 14 ea1.1r itra ill, - 4e -.:- .--;,-_-: I

,,J

_a. graduaseldom .6 I 67 oi 1114

25.---VoMategrva, by anta, ukse,'1ha1 ,try '7' &wry

2at al c*Iwei

ars.* .

-7 I

WO no ow on. ,00 an no

of/

-

-10d ....t.

..

.... ... . an loo -

rwwsk-s,

OSP

"` 11.

di. a .............. ..... 1I a OD fon

39

219

F.,

latr.p,

ft takto 1, &rot &

`titil iz.41

6

1

13

22

-:2,:,- -1111t

_

wkra

i

i

I g.,-, 4 ! ,t__,_,. _ _.

..

7_ a

t

\. ..... .

I5

;14_

1111

1111

1111

1111

P11

1111

3111

1MB

RIII

IIIIR

1111

1111

4111

1111

1IIII

IITm

onno

mm

omm

emon

wom

mit

1111

1111

1Nom

mus

gmilm

min

gedi

min

il

MATHEMATICS IN PUBLIC HIGH SCHOOLSa..

we should deduce generalizations with mution. For example, :f afterthe u-er,;

ohserving that no Khool in the New rd...al la= rmon rewi L-w-i" of

fi "IreLE ca. v..1

t6-ps we Coficluded that the odda.

iPaPOSSiLlk,.A

.1--=Y1L1FILP the assumvthe MountainAon in a(dt.

ftaCIIIC

on inames thewovia" no

in the Mountain region.as many sencrots rerxmic---1 the use ofPerl acts one conc.usion is valid. Field111 bLI1

'Fa bla

S.

I0

11_

P e tette ing of zwmetry

2Fv_s_ ExtDEt E ton. by V

-

IA°

timesaLne PacRle, retion.

-s are c-P.uom used by g

r

parta r glomCI 0.,. azg

A" Eure of j--W1-0 fripa Ert eometry11..!...E.ENEEIMIEMMIEK

Classification of mhool

.04

&.,-bectLs

A. By type: 1Ant ,,,--year) and w,ni.w. h

Junicaniew hith w±-4,x4B.

sebod

Schools

Numbez

3

16st=-3

C. By rftio-n:New F;gnd 0Middle tlantic 8EJA Ntx-th Central .9Wt North CentralSoith Atlantk,

7

El, MO IE M.F t smith CeLUzIWmt SCoath CemL-Mountg..nPad&

61261

q

Peroemt

69

4

12

3

Eaa

132

I Ircd- meaning d type, size, or region. s tablas

Offerings and

Eleventh-G

2 and 3

InatiCSr

Of the mathematim dames of the last 4 yem of high school, inter-mediate algebra 'is exceeded in enrollment 'only by eiementaz7 algebra,general mathematics, and plane gecinetry. The schools in this studyreported an enrollment of mate than 13,000 stthients in intermediatealgebra which was approcimately 23 percest of the number of studintsenrolled in the eleventh grade (eft table 27). The perceit of llth-gradestudents enrolled in the course was approximately the same for both theregular and sailor high school and the ccenbined junktr-senior high schooLThere was an increase in the actual number of stOdents enrolled in first

r, 1952-53, frau the Fevkius year; however, the increase in thetotal highmschool enrollment causes the percen of high-sthool staientain intaniediate algebra to retain 0pm:1E11110,4y constant

''

""Ii

II:11

111

I 111

11.1

.11f

1P. I

IIRIIP

IIIm

phom

mic

opop

opP

ipirm

po,-

a

in this

22=7. A

0-

frilleStVi al===

s

rta_A

haIivear 2 a-

4 -=3

riInd e _

ffnukietim,__ __ _

be a decrease ci 3 mow between tJ' enrollmentsHowever, the half-emir courm do not amount for all thenrollments. In fact, such quton migt 1-4 raiftd &q.

into intermediate TE- e mine

4__=r=z-

t*.# 1=-= rEL;

datatft the

7 -77-.41

studenbi who dreroa million pupils were enroIkxi in-Wes the first winestert-==-7-,.:revm one-Ulm' d the second mnestim

Mthoughmathematics

A

-termediate algthrs11.1

lcz

A

---A Ar-=

al study, TT=A _ _

waa the

considered the11th ers

LLI theT-

t7.1'_Z...7-Zri

ent

- -%-=

FIT=

51 perceit of those efitoiled in the subjct. (see table 28-C This is dueprimarily to two fiKilts. any small schools enroll lOth-and 11th.or:1th-and 12th-grede studeada LL the cour-L--z tYJ obtain an enrollment thatwill justify (Awing the subject evem in alternate y=====-,ars. (2) Some wthoolsare recommending that the pupil take intmnediate algebra before hetakes plane gixenetry.

Tabu tri bU t ek g adze) molt --- V schools ; I.rA- _

_-- = =:4--r #

_ = 2, = -_

p

aa p -Ego l3=- ..-a A- -. ,gipA F--..7=___., , --i r 4 af= region ci ..____,

. _.aa'I 1,. a f-_ = ___-=_=-_- - -44

ZU-- -?..------ a-a M---- .---===*1OW

theais,==*---AE- IAft=w te

a *

f--="1_ 1-17-2 r%3W.a

other region teas them ID1Praneat of intermediate

te-r-÷; or of.-

A

algebraas

student.1 1

A-A

2 2e="ra_ I EAa-a

O.% A A

not 02P=1-12 *---___. ,--_ - -. ---. ---,---- = ,--

=,.r,-'.. L- -= '___-.. = = _W .=# a kxation.A a

while

tti

M.41

t of these awl

elf OZ. I E. El

00t

*WA

o_

r _

these half year : ergt

40 TiI.

of tiiJs group Jt14,

to &ea" -

Level Pu

..7 atila-- ha,. 9

out?

a

two rir.,711tc-

Fwgio

Apii.'ia'aty gium.

enrollni

only

(1)

-

1W5

i .

'3 sift:......;"ter witrOb .

100-199......

by v.0,, of pupils,

_ '-a14.-. Wan'- - - - - 5.55

Watt-.-1--s

. 115

7.-..f, ow. 0!

otth _

. . ..... , 511 115,

_5541,.7.-}

l'fiV4Wt Spa*115

_ war 11,

te-il _11 -Ail

5 -65 NO 51..5.5 Mr 5.55 a

55. 41515 5. 55 45.

rs.Pails....... =; MP 5. 555 5..

co GT

_

.5 dm NI; 5M; 515

..

12 I

astga

ThefL;orl

0

" .. _ .7., ,

.... _the 1 t. .5

school no.1

s

6641 ,

so

37657363

472S657451

12

5.11115.511.5111

as.14

329

13

SS2417

0

200

0

t ff thef2tOje.. pupils., 9

enrolled.mr. ,raitit that

I 'V r 7--f I .- 4 6, 1 . _

..,4; 5,6;: .

%-4!, . ,t+t- -

z

.

. .

11:t A .- . . tAt .1 . .. q 4-7"N.

_

... -

PUBLIC HIGH 21

study, two-thirds the firstwould

decrease inAre

algebra? filling

intermediate algebrashoOd we to

Grade

subject comprised

in

of schoolAbram gi pup.. by

10 Postgraduat

A.

1100-499or

et

.. S. 1I

41111111v

ST

ss21

45SS

S5

18IS1713174

20ci

1

at sae

In ache* inalgebra (see

'--htt grade.does depend

u

1111111VAIFFIIIIIMili11111111-61

NEI

IllIhNINI

H1101111

I11111011M

II

.1Immo

rtti

meintiome

oorwir

ki.

grade,

MA

tj

- #

Cit

WO

7.4 =

A t tk

antwool

North

_ _

C t

-.a

At -

_Et

Lb tr-1W L

-4./itTh

Lb

Com

ma

For

12111-21,

nI Thai

mm

=1:--grade

N PUB

LIC

RI

G H SCII

_

= _

_ _ _ -

rt -= ,

rie

-As

in

unanY

IxJys

weT

-s st

dy rr

whc

expert

on

pursue

fu.

==

A

-

I fie

enrolknen

I

in triRon

ratio ;

W.-

Er;

# =

- -

t3

S4

-

44

th 1 7th

Us7

girls

ietth

usuftb-v

-

= =

v

_f m

_t_ A

&vegan

flj

-

due

Sukoecri

-

ered -n

1.

and

for

I

in A

F,g

-1

jallninit

-

saki

geometry

are

these

courses

Table

;Tow

n

k 41,,,-.0nonsetre;

" ato-*sc.

slaws-4344w

,

.1952-43

=-1

fflay

school

A

15 49. .

14703--W

mane ..R B

fl:-41

crt

.

.

. ,

sot .. . -M metals - . - . - -

f,

the

frit

-Aitm

ent,

by

22

66

22

66

44

5t)

11

.a-

SI-

,-*-

--7

else

sta.

fteluxd.

1 'mad

2-

the

borAjtx-i

w taai)

1 d the

.e.__-vrylAitm

omt

in

.....

a ,w

atel

y (OW

LIU

_

and S-0110

T-toart-gry

1D-

cic

by those

pupils

.

Ailaipm

e

or

elmw

t

tb

fl;

LTô

"4 . trigonometry

and a vo

geometry.

No

doubt

thin

that

talg

Ir[tiert

weather

_s,

first

.f sys

to gir

zaied

to

in

this

study

altow

the-;_rt

of the feu

twittery

Table

34Ffrati

qf &sw

ye

1-44

in t

second

gvi-o-44.----s

1951-52,

of

more

frequently

dining

the

latter

mathem

aticstJ schools

this

-I_

plane

4=

- t

Malijk

thet -j* _

25

in the i IA.

enroll-

geonsetry

to

aaarliaatiaa

at

Nivel%

cd stsb)ect

Trism

asmatry

IS

oli

.1 irmainstry

.

Ity dae:

MbadleZ

eal

Casts-al .

.

........

91

23

123

I at the neeat temthat as

(ses

table

Since

are

to related

fields,

might

ratio

be even

higher. for

secomd

semesters

an

in to the

fact

is

spring

the

permit

&Id

work

girls in study

bY amonar

la amm

ter

Id or

deareses

Bays

GM

.

Boys

Girls

Total

S.

+16 3

+1110

Grade

Level

of Pupils

Although

this

and

reteaTed

to as

enrollments

in

MATREMATICEI IN PUBLIC HIGH BC1100113 27

Wats S41.---Dietribatt4ow, by typo, ads., sold maims, th40 pormv; t qj echooladust roguing pian trigonometsy and otAid geometry qf coliege-prepora toryPOPaa

Ordiamaas a/ saboolPervmest ochoola, by .,

Mae triscammastri Sabel rangustry

A. D4-yesr) wog swim IAA

acilioai& by aim

1W-09110-1001011-1119110-0641111 ar mare

bAva1 4

Middie ilsotaa 10Po North Carina . 3Wialt Nerib Comma 3&NM Aihmtie 2Dast Saudi Casing 0wait South Casind 0MO11011118 2regale 2D. 'Mug S. 6

Far evessthas r amk ristase. mad type at =boot me tabies. 1. I., armiI Len thee 1 perosaL

43

0

(n

1

0

3

une A11o11e4

Normally Sawa in trigonotnetry and geometry meet 5 dayseach week kw 18 week& Less than 10 f the schools reporttd thatthe courses were given a full year. Five Otroent of the schools reportodthat the courses met 4 days a week and with one exception the remainderof tilm schools rvorted that both trigonometry and solki geometry metS days each week (see table V).

Table l7.Nstinbar of periods per week allotted to tioe(fth-grods meth:-~ties by the schools iss this study

Pitrabor al periods

46

permit at whoa& bi mak**

P%sas tsisiaballmotrY aced isovastry

;.

0

93

I LAis than 1 pawed.

The pipil's total high-school experiences are usually measured in termsof credits. These credits tr Carnegie units reprisent a certain numberof clock Imam spent in a class devoted to the subject. One might assumethat two pupils who have half a unit am* in trigonometry would have atleast pursued the subject for the same length of time. However, table 38indicates such an assumption does not agree with tims data in this sttmly.Tweoty want, of tilw classes in trigonometry were 40-44 minutes inlength and 16 percent were more than 60 minutes. Many pupils in both

Illfin

omum

illim

mim

Inim

min

mom

min

lioni

nini

nom

min

nini

um.u

siN

INIM

EIn

gin1

1911

1111

1111

1111

1111

1111

1111

M11

3111

1111

NO

MM

ININ

ININ

L-.

o="

.;

gk2. ry....mber pupils7-4blz_

ariammtk..

AdvancedMathessatkeCononnerar,,~aarrimm

first

3R a_11

nsathensaticm_2641

I Etat* 1a 01 aergy-A"-Win grades 9-12.

Table 43 N.ows that mathematics reviewtrig than in the whool

gum.7-= s-

41114.111744.17111.447.1=41010111.9.

&Wasted mrolliumt in theUnitd SWtna

is

12$ ,90016 , 80034,60041 , 80036,500

%wmlnrT.P

op isposite' true theconsumer atelm: tics. in the New Englard regionpercent

also=

no enr-TWMAiti

A--*.* 0inm dents In e 4 years of _

7-=-__=_-4 n7 7 ==,1

9 =- -c 3 B

iematks review; however, in the rtioun":er4 WA-7-1A7 = # ==.4

I- 2

Lite- et.g,

s t ft,%Pa student a.% fir

%FLtha=_--=-#=

1

a

VA CrlrtriN."

years %Fag-tt

-j41tO alltazi_a=d-1

119

t2 2. 99 g0-0,ar

ncluti I:SS

E 9 9 9 =9 _ A M.

2

A

are

tbe

ff"I able A43.Distra,.__tion, moreswi in percentage, the ra tlo el the essrowmente in the indicated misce.lianeous methentatka course. elp tha Won.ment in the i2th-gra4e, first semester, 1952-43..M.=

clFcatzi a orlocd

A. By dm:

100-199:=V-499

474.49.4==mamm.

.01 9! da.

500 w rff-eD. oy

NCw' Englands24,fivpg A tkntk

Eat k cgr.Lwrvunt_v. Northset. _ a .......r

=1,WEtftiMemnUin

119 %Mr ,W

44.1.4.=1110117

a:Imx4alma°

Ratio a ouraftmota, by object

Collew I Mvawed Methanol& CAmw3amslgebra I general t review I asetbeavt*/

4/00=10/10

1 Fly mw,ning gas and reionofsthog, see tables 2 am' 3.2 i t1wn 1 ceit.

74'.f I A eTable 44 shows dm gads kvel of the

odiaimmai nwthanatks muses. In mat

'"

sttkknta 'enrolled in do5hj

was compostxi 7-; nintilsand tesith*grukt stabil* kit init Wes ,a)1/1p01W. Of madly twcfthçe:11 LI-LPU aw(--ijawm ll

tt.

114._

4."'',. =4 ..."1 1- V

, f

17 4 7,1" It .,"°

Th

a few rim&aye: in

Bone tgiew111:

k

74

. 7 17

,*s f

r`_`;t4 ?'

V-0

"74

-771

I.

El

10'

r.

,

I

a.

-

V

Hi .`; etketh

r1;_- steabanceemravtlaw .....

CM'

citrc---

4_., AM

Jr I

k's1-"'- . 4 -la

p . Ar .1

,

A 4 7

P 40

-1610"1114=

the kil3zr...tc4 =Aiwa 1W-A

moreiffi

ofalso z

of

Lrk_

kit UM

rrez:tr- ?,f7. P.10

=

4.1kti One _

the_t

Mf-;

I.

4IFt`f

01.01

60-99AD

,r-treg=Th-_,:

....... G. SA, I. OD

N

'ISouth .

I.

L a , .

y ,. j -

14.!#' f-{"4-t_1,e !lad) 6;'...

_

.61.91.6S.62

31

12623

0.6.1

.3

I.

So.

.-1;(0:4;a1)):::1; .t .4. . t ' -

.,

.. t .1 -r SS US t7 ( -a ; 4 - ., . Pi.400 awl- . 7;42vYr,*A., ' -7 1:11117.4."2,,,z, ,24:4,e:c.".6_ k!lit

"A" $

'is J'.4-. . .

f .

I r _

'

A $

. .1e

gia741

jI41--

V

Per " " .. r

;

L.,

;t

. .r. . 4

.

. . ... t_. .

ik)4

. . .. ..; , 6 . ... .....: ...:i A. 7 % t ''4 o.4 % V. ,i; '..; .....se° /1)1i :irr, i I r , ....... .- -- i.. . 'I.. 'T"' 4 ii.i.ri a II* 11

: ."..-ix'-1,i;,.f:./1.,?:,....:;:i.!.,-4:744i.t,',..),Z4 : ...- ^%.1...',..-1A=.

- st ,,, '-4e- 1.,_

L-: :I., , ..',.....,..,_,.;:,;.- :-:::.-.. :1;../......

;(!._:_-1.,'"; id.: -'e14'.f'... 1:1:1:1.1;.4+11;1:1:fils7.41-

s . k r r ..)

: i.' :1.4,..,kji. ;.t...4,";:lit; xi: 1):.s. jr...'T -1-`;* 1*

-J.' J v-. '- ' %"- 1 .4`.. -AVP' k ire;tr, P.,..4 . ' a

, aifidt-4%)6 * lk 4/4-)yri art., ,.114 3,4S.?i i:,,-.: 4 11111.__....70,,,:g ,t .1,119.1.0.

-.___-?)...14,:101 ?e,-',., '-,r-- = ,. - ,----,

..-,--------

32 MATHEm -0 yy rUBL'iC HIGH pa---TILT .11

It of peritmis allotted to the wawa:am-int-a tigematiecourses by the schoob in this si

Leriedi period (minutes) Paving of scbools. bY OIXareb

anthimtto3

39 cc hos..45 to

6-0=-6970 ea. mom

Advanml generalmaihmstlas

023184118

MetbentatksrevUw

pnuthunatko

I Lass than 1 percent.

Size of Glasses

Table 47 shows the. percentac:e of the cla&ws re.4fA L.d the indicated enrdiments. It willof the classes in highaxhool

M.......

20204020(I)

A _a stud,d that 4 mrmnt

n:Pthe!nati=fconsumer. . . ,_,were in excm of 41 puras". In hign caA arithmetc, 18

* el----_,

f.

in cr,-%---re algebra may ;.1-5.ootitainfta mat a Et ,_.0.

. ... ....,dam&kr.-" .#

2

wrixnt were 57Y= r. =WI rn one" mg a__,review are rev1fw wrvnA

aff V =_YA_f 01". (ANS, one0 I- might mine such

1 51

1 a a *iner more magnostk v

others

L A* -s -a .fiszlitatiPS pa eLl Itiwy A

LYE 01 C;=sTv

shVr..4-2

.ff

aa a the %

e*

-ttua iLLr

= 3a one

I

a f 6I

smaller? Ofill,tiL dr

COU_L-FM

-21%2 a-

ifTnaill

w_a_a whVe '5r,= ef, it wmid seem unilely that all itadents in a2

class v,uuld Vbr mme sme skill leadiers niathe-_I=

Li (za - " t m= tend that nu- DAa- have had drill without underatami-ior 8 or more years without desirable results and -the

* a Is

4 -4L-_ Aution is individual or small grmip instiuction with emphasis.on the metuiing of the concepts and operadons. In any case, largeciaes seldom end theanselves effectively to remedial instruction.

,...,=.__---.,r.., .me, of die F---------i.. mnt.iabr-- A7 r" il) A- by 12i--r-r--i .* 0._wis ex- u- tek._um9,

_ . 0 . .VEWEWS c1/7= in this A---___gi. a 6 W*a v., ..-,J

&!= (.4 O.a se

1-10 OP AI*

11-20214031-4041-5,0 .. a _51 m4xe et, et

miscUanetnis math*

Percent of flalit by conies

High eVftnthm

616

1640

Gamealgebra

vo~wA

matb__=atike,--........0111MINE=.111.10..1110...MEMENNOI

14

272220

Metitanaluttkereview

4$9ss4

commusarmathirstfra

epifia rt

a413615

- 00

,........

Few-schools in this study use &Id trips na a pit of the indructbnthe inlianeoua mathematics muses. In factow ach9Q1

(Itil

ligIS

INO

1011

1110

1110

11ith

lICIIt

ttlIm

mum

mul

imill

mil

4

inA

-

tha

MATHEMA:TIES IN PULLLIC HIG:2 SCA-00Ma 6

411M.,

1

4

a

A Kan .1T A

gg

ov ww. The 86006 lilt .1 ,

g co- oi mi or_____ _...._,--

percent ofOf InM;_r-- t . ...

U.Number and of.=

trips in the rUscei

A 6A _A A sM Z.

"-A~-e reuorteoit

VP

-0/

a "widt,tav

td WV)A

co.wo)

schools which reported 1-w, u&r of ja..._,ito.371-0,144 miathenuscs COLfite4

tx-s-s I sLi

32

V

eubJect

school arithretk-ari *Ars

reVieW. IM

WilltillbeIBIWI4125 A .b

..Number

4

A

012

Permit

Mathernaticfr--Grades 7,42A

offeringt and EnrollmentsIn this stuAly,, 857 echo* rewted an enrolinmen of 326,640 pupils.

The total ienroliment in all comes in mathematics was 201,902. Anestimate, based on the data from dill =prey, of the total enrollment inil'all mathematics mums in the pubik high salwols in the United Seais 4,915,000.

Thereet PT ri11

W A=A

maT-cs is a

arithmec

pup In e'-"VM-thle& Qfls

ow. sqt.E I wiftrf_ heN

ff----Asr- I A_

-. .. 1

* ---

gaieralIAA

_ A 2lime-. 2

here mathe .last vmrs of "

1=

-1-A 1,1 n'inArat -r-41

A

eir-r--&-- &Ltd gietty, witranmdV gea"A matheena4.=tics review, and consumer mathenia*e. The enr011nialtmime fir the first eteneeter 195243 wes 51 rweest of the total enroll-malt of tin lest 4 yeare of high school in the schools. During a comparableWad in U3S44 the mailmen in the mathematks courz-offaedin &shot4 or rtika A W 7,

_Z_39 peroeni n vac=iwia

c

b"=4..-.= S.A.- AI

waled:,.,. grades 9.42...,A A

-...--., (Inge m thelbTh ...._, 2I ._ere has g A A . .-- .-_..'A --.1- E .m.-

mathemaLTu,sth decrease n.. a is s

.0# tet

t

vvars ne igh -.eh For

1-7- z arade piTD,_ enA

Ihas Dean m Lne uimerp'e, the enrollment the first seni

t_ N. i

-' ,-- V -'7- .--.-.-U. __-m- 0, 7 7=6 IMI. .7---- --7 T-211MA9 ma-__

-4'

tiU S.

-- . w i A are monika... ,==7

aligem==- plane9

maks swdms =

# A 0IV, A-

A ifl 1,io

f-LnAleras the _4enU enrakd in

1

eab*ts shavsd an atorimmt apni to 43

-rujb

I*

--z-rs ofcourses in math.*The vardessettin Wield =Ow

aye &maw awl trogio

YT'4

A A -_y 1 tA--%fi: rUDLgj 3LLi t=LttJ1

atgthraç tigonometry, and solid gometv. Itiiii1s of thee r&1e !fve1sw&o found n all mthj excen a:va;: q;:p; n!natc jflwhich no I2thgracI ixmi1 were -enroIi, The- mn:=ils enroli&i in intbe.

g UI the 9tI

i Gft!1i LI! L[ft I I Lu grade, ant-i ',- Mrt;e1i ill bile i LII gruue I L1t-

nELtiEa1 zid fcr tt±nicaj pon Sjj(1jf1 cç- n jicrp- innuinb' of 1Lhand 12Th.grade pupils st'jh n__

-' . I aiI(-T1)tf 7i t-I L-LI W'

Jfz1! Ot the sthcds hi this s:i=:lii:y rezinnxfat t I:Far (ii ofat aeiLs UUnJ1 1e ius eurs ci nizn

. -t ; 11 I i . h i t t ? ; { i-i :t

1Ld V Li V ; II! i-L jL; 3M=-U w c:i iij I'

or general nmthajthe st:iit1ents we earin to enttr x1Ie*e. tbree4ourth;

of JI riuir at least 2 yrs c;f than tflJfof thea state that aIR is xie oF tJ:'e re*I fl1B:flfl

:Lz=x!ci 4- ( aId induie gtnetrv.Gu1tNioted that many schools indicatec3= j ;:diiaonin1Lea kir graduation aUnpt were mk to gukie ixmils into

I=3UenatIcs co-ur athng Lo their nci.

7cbi S.Perce. q w1 iIdch rquire trióuasentrj LaI

The d. b

All :tudent3___._ - -

cd!z;::; rajv

Pw c by m iee In

C 2 6 S

8 M= '4 1

(')41

2& ,

; I iI

I sk M .th in the 1 j4: 4Z fquireweiit,f_i

.,

Tunic it 111c;lLed

L!:t of hoo1s in thu study eixrt&1 tht. th,dae in me the= each week. The 5hfn.I thatreixwted cia flfPtJTUp cw fifl fitp j- a weekfait1 eYeTil) distrIbt: amc tI and tyij of7he Icw;a2s we; mfinj fr=. !1a and Middle Miti

raphic regkJ1iE; =2Y? tIk: 5}= h4ct tiut few than 4c=:n cE tk&e schcds 1ëvinte1 from the fE: per week pattthLThe length 61 =kd of the 1ác in nheniti vat from

thut 30 mimst to moi than 7t)__ms 9=c=rti, nf fjjp.

rertj tMt the cliii ràii:s ia or niore m iitá [)thef f::JIi,!Of in the -tudiy, :crtI 4a roerksis of k than 4mrnmnut-; 2 pct, Sv:; ug nd 40 &cent 3,5çJ rnimitp

rt tbat aowe of t& time in the nt d

.--: .

- - .- -' :-.; ' _ c .:q-i :- 'r ''

w_ ' $

-1

I . =1111_

_ _ _ ixa

===

tA-v.1 rj =7-1

eiirollrn tA

-

_Z

t ,-_:Tv=tsMAj EAt

4 _A

nrs

eximisAvi iiiinThen

A

R

Lata - _ _

-

=

142"== --= 7===

1

cm is to

miPerksee- r

Y e

2-7m =---_ A=- =_--re z =

ti

BM= g.a I att= i_-__._;. _ ,__.

. ... .,.,_______ ____ it _,..zrnii,i ._,___._ ._

_..

MI " _,_

to =

aA

----=-,

-=-a _

i ==a-=

a

_

= - ---I AV =_===-- V-

-7,1:

_

g__ A= = ==-= _

-.=

-At-A

-

a 2- ==-- = _=

II. 111,111111M1 Ili)

1 'lam 111111 ITT 71 n 11

m ern, m rrn!

mr

S

_:

' -=

4: IN PUBIAC HIGH SCHOOLS

Table 6O.&&riL', by ubie f .chotZ wIso were ueed in thLsidy, b7 rgio;; Cóntin

lit 195142 1 1934

Bois1GithI,tIIBa1G1thTotaI

SOUTH ATLANTIC 8TAT'

Id . I%353- --,-,- -

Bc Gith Total- --- -- -

rith!nctk 7th rI 1,460 jI416 ti,1?3 1238 2,411 1,58 i1.5O9 O91540 48

,8761,199! ioo 3I a

Grata" 1852 I74O 3,592 It3i 1,575 3,2% 2,i4 2OI9 4,ItiI27 1J72 24B6 I36

.

1,012 2234- 1,44. 1,2922,157 2,Stç 4819 2.14ó c:7 2z 8 013

__j 4t!tk! 1, L45323k'

4786TrA

2,241 4,8 315$A7

345214

i nter.dia 1,G 936 2- 79 IcS4 1.OI 21-

------ " .Vi LL 19,7i80 DS 79

------ 1 2- 3o 12$ 12 1:L%ILI : n &O I fldyam-i g,iI &ht-itic 146 187 353

£&68 104

W172

£UI1 157 321

38 2) 4 53 4f 97!!: : jj:._i4- . - - - _ - J8 , z 0 9

IDwe ry1i Dtrt ot "+m"I&. yfrj Vfr N=th Cdh 8tb C-.4 . lina, Georgia, Fiii.

. EAST SOTjr1! CE=NTRAL BTATES

-""-"- !ic#s 4 2,106- 745 Tn ia i,O89 iOSej 2A3GI thali 7th o iso sAr1th1T*c8th1Tw ---- iO?O 993 2,521 i 820 Ii We 1:-Ge:a! atIak th g!e.. 146 199 345 1& 227 407 251 E1FAy i9 i,M 3,353 i,is 1418 3-C$5 563 1364

640 6!2 I482 502 492 9i4 $4 __326 32 7: -2 242 588 339 157iO 98444 2z b

j- 7 4=4LI 7 6 14 1 1351 ii c2 61, 12 81 53 6-::I - A ii , te ,

,i 4 25 3 5 8 42 23 655 19 164

J

49 53 132 56 8! IS!LIIZ , U j IS Ktzcky Tezussee, AIbama, Mki-i.

.

WIT &MjT:i CE'ThAL STAT1'- - __-.- - - -.--

:-_j ----- --

.L629 1,579 3!8 1,542 !S2= 3,C,8 177 1,754 8,530Gc!iruI ma;batk 7th gde... 374 j9 r3 3 3L0 687 $90 369 759Alithmetklthgr.d6dW I,& I 636 L64; i,7L3 I;739 3,583 iI.919 3972GrnI rntti 8th grade.. 325 :: 17 139 310 309 1 5931 rA 1A : g.ft g --

O 8t 932 9 2C9 1,328 I=1 262.

184 5 459 159 204 63 224 280 50

t.

904 775 1705 alO 751 1,589 972 U5- 1,904---u.---- 768 735 1, 72 676 I,Olo i' 1,67

;1 !: 8p*_ - tJ J a .;-u U U -

42 23 79 3 0 43517

vansd genirsi Lht1a.. 78 73 15-9 74 75 156 107 20410 5 15 0 0 0 20 11 31cUn&!!tk -"- 33 31 64 28 33 61 29 30 59

= 9:7 ArgQr . (flftbom, Tei.

MOUNTAIN STATk- - * .- . - - - -

;

44L h grad.Zi&iti; a:-------

Bib--=4 I - - -

Genft*I *atk . . . . -

1-! Lb- 'Ithznet&_ _

IW-=i 4 -.L_ _

I- - = . - - - -, - =_____ s_a__a

tino;; J _s s - a -AL àLF1nfJ:i=i1!jr: fVjW.,5 . S 50_ff-;

S S m - -

781

9512$

IM

715.

1O2t

ii

a

a

1,52

2,vi1.303252

I 1&1.

10500

i yU

831640

-

U

'I

97339

895546109

46AU

170

07

IB L

----(

g

It

827164779

g -

%

17

61 1,117LM9

*4

i,

1,16 I

68'J i;sss3i1

580 -

1j: 620 13$I 13

$1 44

S - n a s a - a -a4 iS**I fr3=-t= Idaho, Wyo, Meskx, Ufl,

.

;

--- ___ --i

: ;::Ift#

4

,

:

; 1 4

--,

.,i,,=_11.1,--1---.

_ _

.-7-AR-

..

watile. am

IT! - Wall°e

11-L-117- og

4

'

aliwt&r,

amo

-0E-- a,7-""-

--

5 's -,-c; 4, _ =

tra 110.....teklarW11--

(12 .......

r 0 S .....

aleth3aMMS3=

.4

1 rth-

jzi

r ...Ifig& InkaiL talfrP- -4 !--

i

.. I.

.. a 1

g t Tçi?L__t '1 I .5---149 I

_e arlier

, treVAIW 111.

-_Stal a_o-

-

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n ,

41

keatem.,--itto

... - - We 111

.0 =:;t, et._

r-

.

.. ....... =1 MO .

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*. 6278Re

I