Learning Mathematics and Logo

492 Pages·1992·22.385 MB·English

by  Celia Hoyles, Richard Noss

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withoupte rmissiionnw r itngi fromt hep ublisher.
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Includbeisb liograprheifcearle nacnedsi ndex.
ISBN0 -262-08207-1
1.M athematics-Computer-ianssstirsutcet2di. o nL.O G(OC omputperro gram
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Copyrigdh Mtaeterial
Contents
Contributovrisi
SerieFso rewordi x
ForewobrydS eymouPra pert xi
Prefacexv ii
Acknowledgmenxxtisi i
LOGO INT HE CURRICULUM
IntroducttoiP oanrt I 3
TheN otioonf V ariabilnte h eC ontexotfT urtlGer aphsi c 11
JoeHlil ell
2 WhatI sA lgebraic aPbroougtr ammiinngL ogo? 37
RosamunSdu therland
3 ConceptuaDlleyf ineTdu rtles 55
HerbeLrote the
4 TheT urtlMee taphoarsa ToOflo rC hildreGne'osm etry 97
ChroniKsy nigos
5 A LogoM icroworflodrT ransformaGteioomne try 127
LaurDi.eE dwards
II STYLESA ND STRATEGIES
IntroducttoiP oanrt II 159
6 LEGO-LogoA: V ehicfloerL earning 165
SylvWieai r
7 On Intraan-dI ntrlendviiduaDli fferencienCs h ildreLne'asrn inSgty les 191
Tamaar Lemerise
Copyrigdh Mtaeterial
Contents vi
8 Mathematiicnas L ogoE nvironmeAn Rte:c ursiLvoeo ka ta Complex
Phenomenon 223
ThomaE.s Kieren
9 Between Logoa ndM athematiAc Rso:a do fT unnelasn dB ridges2 47
Jean-LGuucrt ner
", EXPRESSINMGA THEMATICASLT RUCTURES
IntroducttoiP oanrt ", 271
1 0P rocesseAs D:y namicIanlt egraotfiC oonm puteSrc iencien tMoa thematical
Education2 79
BrunVoi tale
11 Of GeometryT,u rtleasn,d G roups 319
UrLie roann dR inZaa zkis
12 PatternsP,e rmutatiaonndsG ,r oups 353
TrevFolre tcher
13 AvoidiRnegc ursion3 93
BriaHna rvey
IV AFTERWORD
IntroducttoiP oanrt I V 429
14 LookinBga cka ndL ookinFgo rward 431
RichaNrods sa ndC eliaH oyles
Index 471
Copyrigdh Mtaeterial
Contributors
LauriDe.E dwards DepartomfeE ndtu cation
CrowCno llege
UniverosfCi atlyi fornia
SanCtrau zC,A 9 5064
TrevoFrl etcher 44 Cleveland Avenue
Darlington
DL37HG
UK
Jean-LuGcu rtner InstidtePu styec hologie
UniverosfFi rtiyb ourg
CH-1701
Switzerland
BriaHna rvey FacuolfCt oym putSecri ence
UniverosfCi atlyi fornia
BerkeClAe9 y4,7 20
JoelH illel DepartomfeM natt hematics
ConcorUdniiav ersity
Montreal
QuebeHc4B, l R6
Canada
CeliHao yles DepartomfeM natt hemaSttiactsi,&s Ctoimcpsu ting
InstiotfEu dtuec atUinoinv,e rosfLi otnyd on
LondoWnCI,H OAL
UK
ThomasE .K leren DepartomfeS netc ondEadruyc ation
UniverosfAi ltbye rta
EdmontTo6nG2, G 5
Cop:yJii�ted Material
Contributorsv III
ChroniKsy nigos 19K leomenoSutsr eet
Athen1s0 676
Greece
TamarLae merise DepartmdeeP nsty chologie
UniversdietQ eu ebeac M ontreal
MontrePaQl ,H 3C3 P8
Canaad
UriL eron Deparmtento fS cienEcdeu cation
Technion-InsotfTi etcuhtneo logy
Haifa3 200
Israel
HerbertL oethe PaedagogiHsochceh schule
D-714L0u dwigsburg
Germany
RichradN oss DepartmeonfM ta thematiSctsa,t is&t Ciocmsp uting
InstitoufEt deu catiUonni,v ersoifLt oyn don
LondonW,C 1H OAL
UK
RosamunSdu therlaDnde partmeonftM athematiSctsa,t is&t Ciocms puting
InstitoufEt deu cation, UniovfLe ornsdiotny
LondonW,C 1H OAL
UK
BrunoV itale UniversoifGt eyn eva
LDES-FPSE
Meyrin
CH 1217
Switzerland
SylviWae ir TERC
206M7a ssachusAevtetnsu e
CambridgMeA, 0 2140
RinaZSzkis DepartmoefS ncti enEcdeu cation
Technion-InsotfTi etcuhtneo logy
�fJJ¥f ighdt Meaterial
Israel
SerieFso reword
The aimo ft hisse rieiss t oe nhancteh es tudoyf t opiicnst hea rtsh,u manities,
mathematiacnsds, c iencweist ihd eaasn dt echniqdureasw nf romt hew orlodf
artificiinatle lligence-sptehcein fioctailotlnhy ai,tn b uildian cgo mputmeord el
ofa construocnteg, a intsr emendous iinnost tihgahctto nstruct.
Each voluimnte h es eriperse senat pse netratyientpg l ayful excursion
throuag shi ngslueb ject areaa-sls iuncghu isvtiiscusma,ol d elinmgu,s icn,u m­
bert heoroyr,p hysics-wriftotrae gne neral audience.
E.P auGlo ldenberg
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Foreword
byS eymouPra pert
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anda c ertapiono h-btaohn bee campea infualslsye rtIit vheo.u gohftd eletitnhge
filea nds tartaifnrge sBhu.ta nothsetrr atfeogryp ursuianp gr ojeicntt r oubilse
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offi rsitm pressitohnesay;r eo fterni ghAt .r elatheedu risftoirdc e aliwnigt ah
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expresasnei sn choaitdee tah ahta sb eenw aitifnogra no pportuntioft oyr mo,r
perhaapnsi dea twhoartk eodn cein a nother context. iSfyo omupe ltaiwymi etsh
andn urtuyroeu prr ojeictwt i,l l ctooml ei fneo;ta lwaybsu tw itehx perienacned ,
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therGei.v incgh ildrtehneo pportuntiodt eyv eltohpi esm powerisnegn siesc en­
tratlot hep hilosoopfhl ye arniIan sgs ociwaitteLh o go.
Int heu nfoldoifnt gh isst orsyt,i cgk wiintmhy firsatp proadcohe sse emt ob e
leaditnogs omethitnhgaf te elbse tteIrfy. o up ressmeed, I w oulhda vet oa gree
that tehxiasmp lei sa t lesalsitg hsttlrya inAeldt.h ougIwh antt ob elietvhea t
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arep rotsetintgh astu cthr icks mwiogrkhi tne xpresswirviet i(n"gw heryeo uc an
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