ERIC EJ1018630: The Mathematical Content Knowledge and Attitudes of New Zealand Pre-Service Primary Teachers

2012·3.5 MB·English

by  ERIC

‘Lhe Mathematical Content Knowledge and
Attitudes of New Zealand Pro-serviee Primary
Teachers

-Loveridge Brenda Bickel juci7h Mills

1 anrersity of Waikato

“Thin pages pote he be eimai! rice
ie eases 2+ im foi
ive ard ere Wat sce, wets suystiee ahem “rcIhe

i
nei
salsa

ctten claimed Fuithvuchoes enna zach whl Hey do not knew tiene. es

flac of primary seachers Wving watficiemt kaw edge ut
rica carten: aes the Teng dasa easing wnhntas
Fe cildven is Tongye in een. hare haa pe. bsnl reveal
rmeatremsies? enulanl kivetedge of priessrview trachery gaat allele. Ie
aenglws this lowielegge fag, Ceuplars & Beswick, 20% Ways, 28:
Wate, 201,

Thy ruvent wea, Joraraments rel extention systems Ive hog fy shove
suegin az004 tne ae nf eck Oust fe, Rs nds Cound of Lean oh
Vocation [ACHR 2012 Amtrelign Thstitule for lacking and Sehvol
Lenderahip [ATIST], 20; Comosonreallv ot Anchatia, 2008 Depot tiant for
Beucptices 2e19, Neve Zealand Gatenmment, 20 Cngaaatinn lie Baan
Cucpecutiss Development [OFCT], AUS), Acceuding de ths Carmau:aventhy oF
Australia ONS, j 20), ere ot ese main ier miaveateel with una’:
iathematies ura mesceracy teaching vor! thie pany lacie al
‘being mlespurely pucpared fr teaching, ewienicy and matamalie", Corser
dies heen expeessed soul levee Io attsthigh-avhvawing alot no feasner
vaca, Wilh 2 pool orang the lop 39% ef le pepultion “here har
Aso een disivasiox, about wheshar asamment of mathemalirel cone
nce should be mandetenp ow onlay te ang eat fron aiid onc
fectucation (TE) progam. Acedia, ty ae ACT npn, "iho snes ot
othemat ns dopandsaot only ona [teacher's wehematical content MO ee
bout also on their attudes (a laching eaetaaties and tle caesar ng of
athesnatioe Fedegagy® OR 12,4. 34
ae Keel

Altituides towards Mattemat

Nocualy da progpertive teachers sel goudynuentandng afte wchacti
they will evenisly wary hat » punitive setts towards talhemalics Fe We
lmpostant (YS, 21, McGinnis otal, 2012; Suto, Wns, Wag, & Very,
5). Ay ome, Ladctenacey, td Allard (202) Paww wetted wat, Exes
relitvely tee scoent research an alludes toranls mathematics, Lidulgh
(CM) eporied Unal only puespairie of New Zanled HE tudan's curved
‘alieay tho. gh thei ist yt sulore stating mathematics esas er
postive, aad mune than heat vars distinaliy regain shut aathertes, OF
nie rearing the end ofa Bacto of Teeny pragrina fst over ele 578)
von postive abunt matherralis, with only 16 per at eaprensing nbgaive
Joolngg Titang--qves ig, 201, hen aakee aul ease earl te
looper. of tetc:ing mudhcmaiss, emihinds were sve ancl only 17 per ean
"weom negative, The zlatocship heteyeen rawral spends toweacda malhanval ty
an atiinaes sara tac mtamstios aan Io be pes sl rane.
Sume shuderis wee pantie sent mathenalis, ontibly boring experienced
Scaess with «chau ahem, bu erase avalon «cut the seapemAbiiy
teavking ners, anc haree negadve.abpal te prosavct of tasking malhenal ws
Ghee re Regrtive about sachets because at unpleanenl wsperionces
Tarning seoal mathemati, Wookie turer Io le" spy mthecnasiey ene
cfietively then Ubwir core fuckers, 40 were prion vbout the prowpert pf
teaching maths
Evidenr shows that tecchers’atitudes idence thai lassien practices,
sun Mis impacts onthe alitedns al kendo the alae, Scilla
(21s) entitiee “ten indepwowene faetone, inaeruely and. corsdence
tuitibnting 0 boli thitades towards mathemates ane te teaching
mothematis. Recugnitum af the connestion betwen stitades a2 Elis ahve
nisthe-ratic! comteat Lnowldge end eelennsee axathamalies pedrgssy
TTR proprams have led tp ritaliens ty weprove lhe fUiledes wel leet ot
prospective aches, with wnciunsierg rel (2g, MeCnniset ly 2403),

The Impact of Mathematics Fatwentict Kefor

‘Mathur afiessucacon zeform hastess ules way toe several derades, Foomp's
(1972) lew of fmetrmantal versus roan! undaraianting, oyitumises The
‘nina of traditince? approrc'ns to matcemalirs Iesriung, feumsing on the
rusmorisation a ule, fats, aed procedures a acs ust commet ee, 2
oso recent wineururiented appuogches. “he lather emphsize “acing seve
balding roveptual undesanding, mmeynising the coaneclednese emong
rcpt, togutes with ‘hiking vd “stan nathennalicall. A Though ts 49
sar vines Skemp’s aviginal work, change dn Ute seach erstnenatin Bae
bboen extremely sto Psidonce shoves trek esary of tay’ tears coin ae Ie
‘eae: mathemalincfhe wry shey were taught 8 scioul (Cevotenboet 2008 hay
perpetuating the ey LLL ottege the ngysrierity ty ixermapt the eyo
pening, up vet possibiliee ky alum: prospective sachs
Fe many davatee, the Iadinional appreseh involve teaches fas exons}
lBomanatratey, Br “rh soap tesa a problony, fllnged by extonsive atic:
by aiderss Lois meat that haces cuul swear Guiry toe lacking a
paricuay melind they wanted theiv etsdests ke ade Reform-aared
optics pi sian the esponeiity ts coming up with ways vt lr,
fovea a soike serve Uv sen, Mwanien, here ean expect Pat
“elects wil cunsnoonicate Me Miking, ant veesoning will: each esace anc
their teacher, Ihis press ssypins foaclers ie aighipate 8 ange 9 popeble
‘statues students might nae to syle puro peony ed 9 Suppor their
tlforis to expinis the meted processes they vss to acvdt a su aiun. Thy ene
Ia teaches need ar elabaraie ard connected cndertacding uf mathematical
uutent kupoocelgr eewepinniy the hey mabhemales ideas ad proceseer text
they ate tenching cue at soho). Le denen’ wo futur 60s mc
fgrester none an 2 oonequeae ol mathematics canta rear. Hopes,
Zevcayds in lero a sudan! understanding anc enjoyisent oF atacematics
prsansee ite reerespeadingly gale Dhan previously

Pedugotgicnt Content Knaroldge

‘Peaagogical Comtent Koowledge (PU; has bavane ie focus of mich research
in atlases wa? uicanee edo ot Shean, 19AS. Mave vacenly Hal's
work ans ban iiuotilin writing about uccthcanties CK ie, Pll, Trgem,
4 Phelpa, 2905), all's model of PCK provides a pingrin: bast theery far
pealeainnall. reel sujet mallee Rovers in enathemalice” CF, p.
S89). Maturvecwal cond bowslalye fsx Kis Pah a che Ben mai
igmnpuneis ofthe rude Subject Metter Kris lye GRAY seat Poinpeal
Content Knowledge ICA} bs mathematics, scoring te toe mel MK
subdivided ilo Utes pautr: Comune Coptent Knowledge, Kawoveledge at the
Matioalical Hoists, and Spevialsal Corlent Kapeladge, Sag KC
compris, Rinnskatge uf Coutil ae Shatvates Kinser
“Teaching, sivd Kate of Cynical

esoarchers invesdgsting the eomseciors setcut mathemati! comttt
knowledge ana PUK (eg, Askew: ING; Werd & Thomas, 2008) Save Souns no
clan naar rela‘ionahip baaveen Ives tera cflegocien, Llaving tery love
Iateenatcy sl eel. alata ov pinay albemates) aches,
although faving ante ar derstanding ef themes ey be ease pce
for them. Ward erd Thomas (200%) foune eat teaches with iow -evels uf
alheratical nae knmelege ales had Inn levele af PC, bs enna th gh
There future Tad enn scon gr Has wags PCR ba 15,
soon teachers With eiemig conlen? knowledge Lad tase levels of MOK hie
eviclence support the rlgim thal 2 cevlaéy thiesbael a mathematical eantent
Brosvladge te ware for gised havdeng, bul Tiny, w'e Ib nna thi
Fajisamient i set acid on its oe (exp, see 0G Sulven, Clark, oe
‘Clarke, 208,

Many ITE programs tecuite sudan. enary

provide evidence of win
achieved a specified level of mathematics novslacge, Despie thin seoent sadn
ontince in reveal sonverang gaps in prespeclice warherss metematce
lundersiandings Livy & Mule, 500%; Zork, Leki, de lolewe, 21). Cased,
Niey Zusiane Laiveniiy Entance Geclading 12 exits mathematics at
INLAY Covel: suamally completed in Year “iL, tio yaare betere leaving
socondany acho) if taken an gvnviding sulirien. evidence of numeracy
competency (Neve Zealand Teechers Cane NZTCY, EIN, Tom 203, saloons
‘ils speral Anise? ty university ane epic by the ICL provi “rock
eunmarale omeracy equi nts as stove enluring with Livwensty Letranc
(MZIC, 2010; Peary teaches in NZ.are qualiie le ach up Ur Year {2-13
satel, seheceas in many sles skater Miya a bgt y pest
‘macheenalics teary in hs sonny pate

eucher Qumlity at Initial Fatry

Lesisonsd augers that eacher quay and aradeini pe itucluamay lave dan
-gabatanially acer the Tal Tew deal af Tot the US and sala Les
fe Tigh, 2001; Fgh & Kya, 2€0G Fhe US shud examloee. a “pull and push
Iiypethei tot pay pasty wt malas ia nontaaching pe: waists Te
dri sabie-women oul of leaching, whee lacs oF somunecation for high
ashigver has eflesiviy pushul Hm wa of weeckeng mya pone carer. Ligh
nd Rivan (2506; found that she average perso entering leacher sduraon
‘Austen in the ently IMUs Was ab the Plh persalile far aconedsry ache
aeloretiers (Sear 9), whaneas [0 wenacee al I gevnoge prc rank had
slippsst to 61. The Austialian analyse ig euné ei dats colleced ist
sngitdina claro lnlints seas Eseroey cmumtorany tage 14, and
Firveyed shut uuivessty comes and sarees choir. Wheile, suse
acheveutats a aqy Hf pentide a vellae i'vation of Invi ecrntud sues 3
the conelasiny.aF Lies evondary educition mgt well be cunstoned, Celie.
(2O1L} compated the leather ccicoton wscticey bf cratags td delan dos
Singapare, Fined, yd Sonth Korea, att camtasted. them 72 Lines of
Auslesi. AN! thy wrgtris danvy dex teasers L200n Une lep 39 pa so
secondary wou eradnatss, whereas Acssuala (and the C53 have relation fo
Slivivrty foum the tap eme-Uunt apalying in basins finclws, Thise thie
countries alse dilleee (oin’ Ausie'ia, ine high sats dat the aching
Plototion. is aroacdied, wt Hae geveenani?s ee im famsling programs wd
Zegulating say f match cera. though there is no cazspatable analysis
Dt Now Zena teacher qaality ed academic spank, Tne, “hely pt th
potters ace simi to the of Aumalia ind The US.
» Fete Yen ant

Assessing Mutiemtical Proficienry

Severs] wens hace emphasized che importangt of teachuzs towing nal only

iat undertone ane misconveptian’ he espe fom stems, bet fl iy
Ero miseonaepeans ocak” jeg. Tinh, 2G, Some teseasere hav
ina vidual diggreeti intent ty sacas te mauhaataliral sete! kore
cof smallmumiberfTRavilants pte eg, Troe, 2H all, 1s), Phe
‘have une ‘wll oczensmenty Wile Lager runny ef LIL stucents fe. 20
S300; Bel, 100%). the verion Wael uae eory curd ta whethar the usin
fen opsmende’ oF muliplestiite fey, Bel, IME} Whatever farm ey te
Thos mstsmnen’s aoe clbsgoyel Ip catemale eludenls’ Grawksige (Shuman,
ER)

‘Alliugh ues i 4 eumaicerable body uf mouth at che mathemati!
conten! krovlnlge uf preservne alewwevary teacnein, there THe gr re
nga! about neuzthemal ical stenchads qos far ase von nd oe LL
Pronsn, Mowaver, re av inca that ches ents accepts oe sbane ITF
programs in the US are.aeasicatly siving, otbemaealy fog. 9 6" Mae 10
prospertive priminy scliaol leerirs infrvdewed i Hall's 15 shely eral
Sugessfally Solve (=: Ta contrat, saseesnen cl New Zealand ore-aervi
lomentary students shine Eanes than oe thie of shscate anling TT
prugaan 27% of 189 ip 9002, and 18% of 151 in Rj rok ale 6 Frome
Lovesidge vs

Misconceptions in Mothemution

Titeraure oi Une rena errs 2eaple make on mnathernaes Lasks sapycute
that there may evel imporantinfertuation sou te ¢alure vl Mie Cains
and prchloy solving {Ureher, eal, 1999), Aoonliny ty Tons (20), ie
luapteart eo distiguish bets ragthemali aro sand s:scuneepsinns- The
fe ruomy weatons shy e-rors ges be oy as putt uf schution teary ta
mmathemaics pines. bey skample, ser ores axe simply the net of
ciceiownesy Phil there may bea srinorpsace et mitialeepn lrg sytzbul or
seat A person may lace experience Inawledge af thi parccalar ‘opie 9
concapl. Alteenatived. he arear may be ti rndull of a iscourapsion
‘Miscanceptinns diflerirow athor Sypes of ere i that dey afin re»
tts of unndergviwrabation ofa a's. Acconding tn Swan (2N, lrets make
slnilar errors the weqeid evar, igaess of lel they ase vught. Brew 209%,
rate an “mie: uf errs” potion i fehers elt the view De
Swdentitying a0 abdesone eos” can panvale yppartunil fos irony the
ncchematial ur cerstading of él nrrens. Uoweves sich a posiLon mists 2
fon thst laches ae sto recogae the vers ha role auc
iasteatione io mathematics Sephens GAN) Amur thf LLL slUeaas ton
hot sble Ip omnbeipste tae misaanewptns chitdian might Taye ach
vundanmanang the aan sign. Fo ime ngacts tts some TTF stents mae
satis at sila e haa of keen thay ae arin hove to teach he
efor basea abit towanls utcaumnging suse in thinking teaaaning, 4
jetting their peublemeoolving.elegies can help teaccers te hits ne
felon ieenaneziians in wathanstas fog. Sullvar etal, 2009). lowever itis
fila Thal Ine leachere-aecogmuse hen tizcenceplions:peves. Heres 2k
pprugrhins have an impociantenle te aay ia helping praspeticy Inachecs 10
become aware of flvir own understanding and seanonceptaie au thst they a
iva postion to do thi for Ente stints snce they howe practising wacker

This paper proseole the Landings of 3 stubs ft assssed the numer
ompsttcy and alludes of AID ITE students, the majoity uF selien sseue
tasted io 4 theayear pima’y Beckalor of leaching program wd th
semainde: in a one svar Graualn Diphua gf Teaching

Method

“The povticpints in Ihe siecy"ipeluded 3UY accent, 23 mndengadatss

boing three Hacalor of Teaching dag ang 71 graduates srrolsd

a Gradume Liplama of Lisching (je Tah Th The maivity of the under

srstluates bce beer. seared: Leuvensity Lazanae (UL), gneffch oF de hac

Twn given Som al Adoneson, jst over one-eighth had cont Hem ether ters

‘nuttin, anlar mainder had Dis etionary FoUre™ The goacuates eet
of the partite

Caiegaeg a Fp in Gnven =

Tiacle gradu enrolled in Bleng) 238 ws
Univuraity inteince 50 wo

Spec Ad wieion 6 pe

‘Dag Teter Tostietions a uF

Dissvetionary Bay 5 25

Caadlaakss nied in Gasp) a 29
Talal 2 we
he stadeata were given the Mathematics Ihinking a! Tog ny eos ene

(designed ty tse authors) dusing Urieotasoe: priar fo their UL prugeee staring,
fustenyradaes) be during Uaeie Tmt class (geacuzsen!. “Une astostmaent
fcunssted of rine tsky,ine’alhig, 2-8 yi sompulations. and proportional
essoning, "Theo of the tke were st Level 3 of Mie Ms Tosbiet Cumin
sy Baste i Be

(NZ) Ministry of kAveation, 2097) and secer unit Loved & ke expestation
Ws! stadents 9y he evd ov Yeare [10- fg 7 yose ell) sho have ated
Tvol 3 uf the custicalum (and im warned akdtive part-wbale “nine, oh
Uhosat tae and Year (i-ty 8 yr es] auld See achieved Teel fom
be advanced mullisedtice part wisas tink

‘evel 4 task vere deooen parily In aaies content knows atts level
boutateu to bai theattassment Wilh esse biks Leva aca ee honor fo

uscd previouaaseessinerste scr the inattton ila fm,

ilecimals, ua praposions horsuse thoes concepts averbans elem prcecushy
tube challenging for sor-ur pricy sehoel re aoal T7P tees fe
all. .000a, 99%: Mays, 2905 Broly 8}. The curdoe ot tasks wag ema ad
lors any or themanber demain irsuse ft Laat time availaore during,
svlmsy otiestation peried (undorgrudates} and noemal “alba ccusatin
Shes igvzelyalet Brose te tke wane in Ine treo, key ete eos
loaligrs ei the love im tee curren Cocunnaut (Minty of Pu ten, 30

STudente were asked inane theisks and shore Keele hiring ase ors

umikers, ancl/ox pintuwe/elingrams ‘calealators vere re permitted}
Pecqucaces af ened nayponses and le mas Fomunin incorrect Teepasees We
cleaved

On Pw ack page ute assesemerd shoot we a bc smmvey asking sluts

{avai thei flings about rethemnatics st pcr? ane erin whol as wel
i cumently.dlounpeia ert fyporaiing scale esl nein om "Reet
(e/a to "Really Disheyid” mathemati, “al primey acho "ae raconary
school”, snd "row", Stccara, were ale inv.aal to ene enemies ty exalain
thar remams.foe te raikage fl Himeebed Use prowided howe iesights >
‘heir eperionses ae! aliadssfovurls mathersaui

Results

The results an: eiganisad inie fos waar wections. The find fused ge the
splationship berean mathewatwst cuorene iiiee gran ontrystita a te
FT, progeam. ‘The secoed eanmines Le alludes, of students, tow? fs
inihematrs "The thie seccoa Jonke ol # y avotionstip betwen sc neyement
and atliuces towards mathernalice ‘Ile inal saciny exes sauder
>isvoruecptions on tas thal siestcanty aera Hh pres

The Relationship beraven Mathematiial Content Knowledge
and Frtry Stats

Sind pertormorce oo sly af a Faretion feukey soe fso she ATR
progern gente vs deren lS nesses Rvs OL)
The pacers uf arden hs succor comple’ eath tek coli
Ieirntey stator prenenelerTble2 Oval lus maps mote sacs
tls tevin, where rir bens ana acon af el neti, The mes
thallengiog as eine tse elle ra} juss ae propor onl
‘Saulents with University Flvance i aighy buco thar she show
Univesity lance on must rks On avenge sledents wit) Laver
Fulani alain at average fol cone ol « mark ipher INP Rowe thou
(h- €2) and MP2 7H Ine Laone wit and ithont TR, rmoeative
emesporuing Ss son P sal my The Pig dltarences wen oar
te tak voting sabtuseion vf eval eeyaupiag actors place val
(eae. ve. S98), addition of common fracas (75 vs 22%, are converts
Iratise: it penenlages ISU ta, 2b: Ror show ch act wee. UE
revvcetiidy. Ory nn Ques ian 7, adsion uf commen (ations Sid
funderadans with UT de igen ber aan uve itn LE Ty 1

Bis pe 8)

“fable: ehows cat sens in dhe ute yor gree program were
sige han nndengrasles on each 72h teks On averng gradi oa
Srotes week Tells nach phe han cae ok uncngraduares th UT od

thos onc mea highs tt hase wi TF Ql = 7 te RCT, SD = 14
L7I Lae diforarce ston: sane ctw gnome’ 2e3ak
ove eat a teal signet [13271 O'Hare anal
Stille prin on lidual ass evened = still wut
{Uiktense for Queso stra vy tinal will agp 0) 5,
pr U8) ive larger ciferenecswesfowed wo Qasim 8,72, ae peuentage

fies = MA,

be i= 971 p= 0), and Quevton 7, adding cesium fe
ys a0

68 suf in sch goa onl set

Tinsengead
Cucstion UF a9 UR Total Gazde
8 m7

Teel 5 Tasks

1 Tama tas stickers, He nes 27 Bw
vile ls ay ears
Fis my lace has

wie

Tisha ucede 13 to haya some. ne
lcs ive 29? Hy ma
smoney dor he slvest?

Level make

ho

3 Sue vio 63 mete of ned mae oe
arg 2.37 mates of blue material to
nat conbames fr ke play. Hise
fins atrial blah us anger?
2 ey Fog ip de Bea aia

edergraduates
Q2esien LE OTF Thuil Grads
ar16) APR desah on FL

2 Amaboep tanec obzape emake 6S Ca.
Skipping ups but aly eed 289
setts. Hour mach f0pe was lll ce?

SAIS parkas ech hold 26 tall pos, wo 2
Ine sug pee ie thal alnge tl

TS ome ane haved aug Uh en)
ep, ew macy plums el
neh pets gr

: m6

ca rn Rave Lay tiv plaza
‘emia e316 44 ufone pizza while
ares wats 7/8 of te eter one. Huy
cca pt do they 2a alpen?

2 11 Den yore out of a pore % 8
lela e€ 80 marks, eh percentage
sis ta

2 Fusrune SeC on cationery She got oS

(ne: thi aff he erginal pice
hhecause hs wie tenet bt
was the ovigial pice?

‘he eludont, were rankelsicondingt their eure sdoumnce an tie nie
tase. Tu undetgradu's studants answers aly ue question enrietly Boon
ft these students a mit he Usivansity Paton ogpicercane, elle the
Numeracy Cress Cnc was servmfal on the briedigl swhiraction asd ie
cher divided 56 by 14 Thyee undengrahuty enudente eid eave saedeies gt
fray tne eespurzescortec= Con the wndargcedush sudents had Conve sty
Ehlncusume 36 Bec versa toma nether ay thai

OF thes students wo tad only eo vorctsgenee, Zine ere stcceset2!
‘ry one 0: both bacco carr. Ne ofthe student udu the subrafi
of decunals with regrouping, multiply 18.24, add vernon actions, preter
725M persennage, Onlyrone saident mand hs gra eu Ue egal soe
Uli she eneth'nd dicount

wan stivocts gota scare a toe, inctaing 8 wohmgraduates 571
Wu and ts gredustes. Not tne uf Siege sludants send comvest 72,90 Io
peivenlnge, Only: one ai heey waa suciutsta: in uccing commen fection
Avior ene nal rulliply 1a x 22, auc iyo were sammenvul en ye Cecil
sulfaction lack. hace found the cri price dete ne one dsenan

(Ourall, 17 percent oF the stints gat lee That ha of the lsca ered,
and wave arson dtu of erg. ast seul UR is pag
Tate 3 cost over lil of he ste gut berveea halfze almost 0 per ce uf
fhe tasts oeecet OF tne 27 per emt who mada no more then one exer (U
orc, the biggest poupurtion wexe gradsater fad'S) and the acalleat
‘uuporson were undargrectniee withon, UE (8%)

Toren

cae yon oe
Al
vegas 1° 7 WOW mo

Grstos 04k

Altitudes tovwirds Mutherutics

“The pervert ef atudats wb kee! malhemaliss at primary ancl secondary
schoul and costenly 18 ahsten in Table 1. Slagerly etme most punitive about
thomasce primary sche! (78% of svcengradvates ant 7% ob graduates
had i AL tude taardy mathraties dipped at eeconeagy school, with 262
sents urtergraduates and 42 percent at he graduala indicating a! they
Vee nothucestics then, Undergeduras’ alliuden Lynas athens ha
haga él by Bas time they stated iste TTR pregran, th ust under half
$9) of them hiking mathersaick. Gralustes waco me positive a the ant of
te ILE program, wi more thor. ull Shs) sowing a msinve anne nears
amuthematicy. Sludvals withunt Ue were eighty moce.pesiive Ioseace
mamas eareutly hs Chase with LE GE ve ISS. Hed unatlnati
‘onuntis), his aight be a ek ectinn 0” age ara’ epson, as those with UL
weve mene ike lo reve ene ner school leayets with Etsb-memotion of
axcondayy malhomals, whuroie those without UL ofn hed a verily of
experince prior to engeling the EE pengram. nian The pei wer
Trove fac amin of che years sian Iiaving, ssinlary chock Fe was
iunoresting “9 note that i was thee vill Ue wh com mast posive asc

etheralics a seraedery sei 95s Feed i td tat betce ones and
neal a the naecTTF enlergagnatte aad te gmachates (als end 42%,
respeively Mod mathomnaties a sowanaaey eco