JOAQuN GA1RIN SALLAN

APRENDIZAJE y CAMBIO DE ACTITUD EN LA DIDACTICA

ESPECIAL DE LAS MATEMATICAS

VOLUMEN I I I

TESIS DOCTORAL DIRIGIDA

POR DR. ADALBERTO FERRNDEZ ARENAZ

DEPARTAMENT DE DIDACTICA I ORGANIT-ZACI ESCOLAR.

FACULTAT DE LLETRES

UNIVERSITAT AUTNOMA DE BARCELONA

ANY 1.986

ANEXO

-1-

CENTROS DE OOCUmENTACION UTILIzaoos

.Centre de Oocumentation Sciencies Humaines.Pars

.Servicio de Informnci6n OIALOG (Base de datos ERIC). USA

.Puntos ~e informaci6n Cultural. Ministerio de Cultura.EspaAa

.Centro Nacional de Informaci6n y Oocumentaci6n.C.S.I.C.Madrid

.The British Library lending Division.londes

.Servicios de Documentaci6n e Informaci6n Educativa Iberoameri-

cana, recogidos en el Repertorio de la O.E.I.Madrid

-2-

REPERTORIOS 8I8lGG~ArICOS CC~SULTADOS

1 ~ r ~ 001

.Boletn Internacion~l de Bibl;'ografa sobre educ2ci6n

.Boletn Bibliogrffico m.E.C

Documentacin e Informncin Pecaggicas

.Bulletin Signaletique.Sciences Hum2nes de l'Educati8n

.Current Index to Journals in Education

.Indices ce revistas espaolas y extranjeras.

'"" o .. ~ c. E Q U

-3- 10G2 ESTRUCTURA DEL SISTEmA ESCOLAR DE U.S.A.

Doctor's degree

MaSler's degree

I ~----------------------------------~~I

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-- - - --- - -~~_ ..... o ::::l z ;:

Collegel

and ~ t------i- - -- U

19

18

17

11

10

9

8

7

3

Edad

Communlty (or junior) ColI.gu

Technlcal Instltulu

Hlgh .chool (4. years)

Mlddle school

Kindergarten

Senior Hlyh .chool

Junior Hlgh .chao!

Elementary $Chool (or Primary ,chool)

= c:i z :J U ....

Hlgh .choo' VI (6. yo.rs.

Junior. SenIor)

c:i z :J U .... VI

a: :: a: a.

a:: :s O U -

ANEXO 11

o.

-l-O p 1 ~n C~: (" s ::; E ,: lI..!:V e s s o ~F E U' S ;;, i E:. r~: ,c" TIC ;", 5 O G 3

What the Pupils Think

STEPHANIE KIRVLUK Oxford Univ8rsity Deparlment 01 Educational StUCll8S

MIUas la lalernllna when:--w r~I 011 wit" our work alld ar~ nol dislur~ by 1M I~a~"~r unlen wt' do som~Ihinl wron,. -w havt' ti IUI. Th~II you htlw 10 Ihink for youruU and it is ti C"hall~nle 10 lel high~r Ihan your Jritntls. -w learrr tlbouI how Ihings wtr~ dis~overed and who disaJwrwJ Ihem: for ~xtlmp/~, PylhtlgorllS tlM 1M 1typoI~nuse. -IwO subjecu link up tlnd you realise why you did ,h~m. -w do tlSSor/~d quulions, nOI jusI tllSy sms Ihtll wasl~ int -Ihe leachen do ;1 jusI 10 kttp us quiel.

Malhs Is borlna when:--you're sluck on Ihe same old Ihing. -you don '1 know how 10 do som~lhing and have lO wail houn before Ihe leaC"her comu and helps you. -you jusI do exereises from Ihe book. -Ih~ Itacher goes loo fasl and lells you Ihe answen befare you 'vt' had lime lO work Ihem oul. -Ihe leaeher lalb half Ihe lesson and / slill don '1 undenland. It is boring lowards Ihe end of Ihe lesson. Praeli~ is imporlanl, bUI lOO many similar problems tire ledious.

Many pupils reh lhey could do belter ir Iheir tcacher explained more clearly, but (his was not the only suuestion, ahhouh it was one of lhe most common ones.

I could do beUer In mlahs If:--1 WllS allowed lo work al my own speed inslead oJ Ihtll of 1M dtlSS in general. -1M leacher wenl ti bit slower. -pJplt would SIOp muekinl aboul. -1 htld more c:onfidenC"e in my own abililies and did nol m;nd lISkng if / did nOI undemand, ralher Ihall SII1I"/e 011 alone. -1 C:OIICflllrtlltd ti b;1 more. BUI, Ihis is hard when 1M subjec, i.r bor;ng and holtls no nleresl and use al all. -w didll'l htlve sud a dull dtlSSroom. -we didn', have lo spend so mueh lime on easy Ihlnp. -Ihen were lus peoplt';n Ihe cltISS so I could gel mon tlllenlion. -1 hlld " Mller leach" bec:ause my leacher does 1101 malle OUT books"tlnd'never sen if you htlve done your hom~work. -1 chktd my tlnsVHrs. -1M Ietlche, c:ou/d ap/a;n rttllly w~" and makt;1 Cf'Y$11I1 elNI flnllime ;nslead of go;n, 011 IInd on.

11Ic pupils were asked to describe a load maths leacher. Their ideal teacher seemed to be one who explains well, does not shoul and does not spend too Ion oa one subject. Here are some of their sugestiona.

A 1000 mllhs leacher Is one who:--gives en~ouraging marks and commenls and quil, a 101 of homework Ihal is inl"esling. -explains Ih, work you are doingJu/ly tlnd osb if you undenland, or nOl, ond if you don '1 undersland loes over il again. -is slrict and makes you wor/t hard. -carn and c:an underslond Ihe problems in hand. -doun'I slay 100 long on one subjecl. -aploins Ihlnls slowly, using diagrams 10 siras th, point and also says why Ihe m"hod worb, lIS w,1I lIS how. -wanls 10 help everyone ;n difficullY and nol only Ih, on,s Ihal are more ;nlelligenl. -Iaku lime explaining and ge/s it Ihroullh finl lime lO Ihe c:lass. -is putienl w;lh the slowtr workers in the formo Ilhink nOlhing is wone Ihan o leacher who won '1 help you when you 're sluck. The leacher, in /l/y mind, is no goad when Ihe resl uf Ihe c:lass are t'onlinually playing around as Ihey IIr, spoiling olher people's chan"s of goad grades. My tea('her explains Ihings well and helps you when you 're slu('k and we can work logelher, la/king quielly if we wish.

By far lhe least popular Icacher behaviour was " Ihat of shouUna. Whcre Ihis occurred. it was menlioned by about half Ihe dass and very strongly disapproved of.

I could do beller in malhs if Ihe teacher exp/a;ned il a bit clearer and did nol shoul every lime you do somelhing wrong. A goad maths leaeher shou/d never gel imptlli,nl. llike maths when Ihe leacher is in a good moad. when Ihere is a pleasanl atmosphere. She lells us lo ask if we don '1 undenland, bUI, when we do. she shouls al us for nOllislt'ninl. The IHC"her SlarlS yelling und when you say, "/ don '1 undenland, " she says il's because / haven '1 lislened and / have.

Don't be too serlouli IIi/te leaC"hers who can late a joke. Teachen who clamp down on pupils en"ourage bad work bec:ause of boredo"" , A goad malhs leucher is one who has a bit of a laug", bUI drives you hard so you can achieve your ulmosl. /like malhs because iI's inleresling and goodfun. / like Ihe malhs leacher becaus, while he's expla;nin, he milites jokes and laughs with US, nOI al ur.

Eay IDUncult M.lha Is InlernUna whea:-

-VH dofairly tllSy lopies, which / undersland and don '1 flnd 100 hard.

b. -you hove a fairly difflcult uerdse and so you ho~ to conctnlrate hard. -the topie is not 100 hard and questions art short, Ihen you can gel a /01 o/ work dOlle.

M.lh. l. borinl wbea:--on exereise is toSy and doun'l require mueh Ihoughl lo gel Ihe answen rghl. -Ihe work is either 100 toSy, or mueh 100 hard and you don'l undersland whal Ihe leacher is la/king aboul.

One of the most frequently menlioned limes when malhematic:s was said to be interesting, or enjoyable, was at lhe beginning of a ReW tople. Conversely, accordina 10 their pupls, tcachers must beware of spendina 100 long on any one subjec:t.

M.lhs l. Inltreslln, when:--we slarl on somelhing new, when we get a ehanct lo do somelh;,;, thal we hu ven 't do"e be/ore. -we move on to somelhing new and il's a ehallenge.

M.lhs 15 borina when: -we do Ihe same thing /or weeks on end. I hale doing revision. Sometimu, il drags on and Ihe leacher keeps on about Ihe same Ihing /or IwO or Ihree weeks.

Mathematics was viewed as an Importanl and u.eful subject by Ihe majorilY of Ihe sample (although there were some who had their doubtsl. In faet, its importanee sometimcs seemed to be overestimaled.

II is Ihe masl imporlanl subjtcl, a/ong with Eng/ish, beeause we use malhs every day of our lives. I know when I/eave sehoo/ it will be 01 greal he!p lO me in gtlling a Job. I don'l like malhs btcause masl o/ Ihe Ihings eovertd wil/ never be used oul of schoo/. I/ite malhs btcause wilhoul maths you wou/d nol be ab/e lO gel Very far in lile wor/d. I1 main/y has nOlhing 10 do with /ife, especially Ihings like /ogarilhms and matrices. I flnd ;/ he/ps me in Ihings I do oulSide o/ schoo/ mon Ihan any olher lesson. I don',like malhs because it SHnIS a bit poinl/f'SS lO ItGnf Ihings thal will nOI really help you in !ater life. I like malhs beeause I flnd iI helps me considerably with scienee subjtcls lite chemistry and physics.

One of lhe questions asked why mathemalics was dlfrere from olher lubJeds. One of the most strikin, thinas was lhe way in which sorne pupils saw m.ths as a very varied subject, while olhers took the opposile viewpoint.

10G4

It has many different aSptclS and no single tapie is really the same. Maths has such a varied range o/ innN sub~ts. You do the same Ihing day in anc. doy oul. I don " like maths, il's so boring and jt's tlle SGme thing all Ihe time. I flnd it interesting beca use you never knaw quite what subjeet you are going lO do nut.

In malhs JOU really have lo think. U lakes a 101 more thinking and brainpower. You have lo use your brain in a dif/erenl wayand il is a mueh harder subjecl than any other. U in va/ves a lot more eoneentrating and a /01 more work.

U lests how quick you are. When you gel Ihings righl you ge, greal satis/aelion because you know you've done il yourself. One ,"in/lle you can't see how, or why, and the nexI minute it becomes clear. The subjecls carry on geUing harder every year. /1 is.more a matler of having lO undersland whal you are doing Ihan learning facls off by hearl. Malhs involves only numbers and has a slight/y "inhuman" air aboul il. It is eif