O conceito de média em futuros professores do 1.º e 2.º ciclos do ensino básico

O Conceito de Média em Futuros Professores do 1.º e 2.º Ciclos do Ensino Básico

Paula Maria Barros pbarros@ipb.pt

Escola Superior de Educação, Instituto Politécnico de Bragança Campus de Santa Apolónia · Apartado 1101 · 5301-856 Bragança José António Fernandes

jfernandes@iep.uminho.pt

Universidade do Minho, Instituto de Educação e Psicologia Campus de Gualtar · 4710-057 Braga

Resumo

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Palavras-chave

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VREUHDVPHGLGDVGHWHQGrQFLDFHQWUDOHTXDWURVREUHDFRQWHFLPHQWRVH FRPSDUDomRGHSUREDELOLGDGHV(VWHVDOXQRVjH[FHSomRGHWUrVWLQKDP IUHTXHQWDGR FRP VXFHVVR D GLVFLSOLQD VHPHVWUDO GH 3UREDELOLGDGHV H (VWDWtVWLFDQRHQVLQRVXSHULRU 1DVHJXQGDIDVHHPTXHVHVHJXLXXPDPHWRGRORJLDGHHVWXGRGH FDVRVHOHFFLRQDUDPVHWUrVGRVSDUWLFLSDQWHVGDSULPHLUDIDVH0DULD -RDQDH7HUHVDXVDQGRVHFRPRFULWpULRIXQGDPHQWDOSDUDDVXDHVFROKD RIDFWRGHOHFFLRQDUHPDXQLGDGHGLGiFWLFDGH(VWDWtVWLFDGHžDQRQR kPELWRGDGLVFLSOLQDGH3UiWLFD3HGDJyJLFD,,(VWiJLR$WUDYpVGHHQ-trevistas semi-estruturadas, conversas informais, observação de aulas e recolha de documentos escritos acompanhou-se o seu percurso durante DOHFFLRQDomRGDXQLGDGHGH(VWDWtVWLFD(VWDVWUrVSDUWLFLSDQWHVDSyV terem leccionado a unidade, analisaram, ainda, as respostas dadas ao TXHVWLRQiULRDGPLQLVWUDGRQDSULPHLUDIDVHHLQGLFDUDPDVDOWHUDo}HV TXHIDULDPHPWHUPRVGHUHVSRVWDVHGHUDFLRFtQLRV

3DUDDDQiOLVHGRVGDGRVGRTXHVWLRQiULRSULPHLUDIDVHFODVVLÀFDUDP VHDVUHVSRVWDVHPFRUUHFWDVHHUUDGDVHGHÀQLUDPVHFDWHJRULDVFRPEDVH QRVUDFLRFtQLRVXWLOL]DGRV(PDPERVRVFDVRVIRUDPIXQGDPHQWDOPHQWH GHWHUPLQDGDV IUHTXrQFLDV UHODWLYDV HP SHUFHQWDJHP VHSDUDGDPHQWH SDUDDVUHVSRVWDVHSDUDRVUDFLRFtQLRVHPFDGDTXHVWmR

1RTXHFRQFHUQHDRVGDGRVGDVHJXQGDIDVHDVXDDQiOLVHIRLIHLWDFDVR a caso tendo em conta os resultados obtidos e seguindo as orientações TXHJXLDUDPRHVWXGR

4. Apresentação de resultados

Nesta secção apresentam-se os resultados provenientes dos dois FRQWH[WRV GH HVWXGR R TXHVWLRQiULR H D SUiWLFD OHFWLYD. De relembrar, TXHHVWHDUWLJRYHUVDDSHQDVVREUHDVTXHVW}HVHVLWXDo}HVTXHHQYROYHP H[FOXVLYDPHQWHRFRQFHLWRGHPpGLDDULWPpWLFD

4.1. Respostas e raciocínios no questionário

Neste ponto apresentam-se as respostas e os raciocínios elaborados SHORVDOXQRVQDUHVROXomRGDVWDUHIDVGRTXHVWLRQiULRYHU$QH[RHQ-YROYHQGRRFRQFHLWRGHPpGLDDULWPpWLFD Questão 1 5HODWLYDPHQWHjVSUHIHUrQFLDVGHFOXEHGHVSRUWLYRGRVDOXQRVGH XPDHVFRODFXMDGLVWULEXLomRHUDDSUHVHQWDGDVREDIRUPDGHXPJUiÀFR FLUFXODUSUHWHQGLDVHDYHULJXDUGDSRVVLELOLGDGHGHFDOFXODUDPpGLD $SHQDVGRVDOXQRVDÀUPDUDPFRUUHFWDPHQWHTXHQmRHUDSRVVtYHO FDOFXODUDPpGLDWHQGRXPDSHUFHQWDJHPFRQVLGHUiYHOGHWHUPL-QDGRDPpGLDGDVIUHTXrQFLDVDEVROXWDVRXUHODWLYDV $DQiOLVHGRVUDFLRFtQLRVSHUPLWHFRQFOXLUTXHDVGLÀFXOGDGHVVmR

PDLVDFHQWXDGDVGRTXHSRGHULDSDUHFHUDSHQDVSHODVUHVSRVWDVMiTXH VRPHQWHGRVDOXQRVMXVWLÀFDUDPDVXDUHVSRVWDGHIRUPDFRUUHFWD UHIHULQGRH[SOLFLWDPHQWHTXHVHWUDWDYDGHXPDYDULiYHOTXDOLWDWLYDou DÀUPDUDPHVVHIDFWRGHIRUPDPHQRVGLUHFWDDRDOHJDUHPTXH´HVWDPRV HPSUHVHQoDGHQRPHVHQmRGHQ~PHURVµRXTXH´QmRpSRVVtYHODWLQJLU XPYDORUQXPpULFRTXHH[SUHVVHDPpGLDµ7HQGRKDYLGRUHVSRVWDVFRU-UHFWDVTXHWLYHUDPFRPREDVHDUJXPHQWRVQmRPDWHPiWLFRVRVDOXQRV DSUHVHQWDUDPUD]}HVTXHWLQKDPDYHUFRPRFOXEHRXFRPDIDOWDGH GDGRV´HVWmRYiULRVFOXEHVHQYROYLGRVµ´IRUDPRVDOXQRVDHVFROKHUR FOXEHµH´QmRHVWmRHVSHFLÀFDGRVRVFOXEHVUHSUHVHQWDGRVSRURXWURVµ UHIHULQGRVHQHVWH~OWLPRFDVRjFDWHJRULD´2XWURVµGRJUiÀFRGDGR 'HQRWDUTXHGRVDOXQRVQmRDSUHVHQWDUDPTXDOTXHUMXVWLÀFDomR WHQGRGHOHVGDGRXPDUHVSRVWDFRUUHFWD)LFDVHDVVLPQDG~YLGDVH RUDFLRFtQLRTXHXWLOL]DUDPSDUDUHVSRQGHUjTXHVWmRVHEDVHRXRXQmR em argumentos válidos. Questão 2 5HODWLYDPHQWHjVFODVVLÀFDo}HVÀQDLVD0DWHPiWLFDGHGXDVWXUPDV A e BFRORFDUDPVHDVVHJXLQWHVDÀUPDo}HV´DVFODVVLÀFDo}HVPDLVDOWDV foram obtidas na turma Aµ´QDWXUPDAQmRH[LVWHTXDOTXHUDOXQRFRP DFODVVLÀFDomRGHYDORUHVµ´R-RmRGDWXUPDBREWHYHDFODVVLÀFDomR GHYDORUHVµ´GRVDOXQRVGDWXUPDBREWLYHUDPFODVVLÀFDomRLQIH-ULRURXLJXDODYDORUHVµ6HJXLGDPHQWHTXHVWLRQDVHVHDVPpGLDVGDV FODVVLÀFDo}HVGDVWXUPDVA e BSRGHPVHUDPEDVGHYDORUHV $PDLRUSDUWHGRVDOXQRVUHVSRQGHXFRUUHFWDPHQWHDÀUPDQGR TXHDPEDVDVPpGLDVSRGHPDVVXPLURVYDORUHVFDOFXODGRVWHQGRED-VHDGRDVXDUHVSRVWDHPDUJXPHQWRVYiOLGRV3DUDWDOFRQVLGHUDUDP a KHWHURJHQHLGDGHGRVGDGRV, usando alguns deles argumentos relacionados com a possível FRPSHQVDomRGDVFODVVLÀFDo}HV, como por exemplo: “podem H[LVWLUYDORUHVDOWRVTXHYmRFRPSHQVDURVPDLVEDL[RVµH´SHORIDFWRGH XPDWXUPDVHUKHWHURJpQHDKiYDULDomRGHYDORUHVµÀ]HUDPDSHOR ao DOJRULWPRGDPpGLDLQYRFDQGRTXHDPpGLDUHVXOWDGD´VRPDIHLWDD WRGDVDVFODVVLÀFDo}HVDGLYLGLUSHORQ~PHURWRWDOGHDOXQRVµRXDSOLFDQ-GRRDOJRULWPRDYDORUHVTXHHVFROKHUDPWHQGRDLQGDGRVDOXQRV FRPELQDGR HVWHV GRLV UDFLRFtQLRV +RXYH WDPEpP DOXQRV  TXH UHPHWHUDPDVXDMXVWLÀFDomRSDUDRHQXQFLDGRGL]HQGRTXH´QHQKXPD GDVLQIRUPDo}HVGDGDVLPSHGHTXHDVPpGLDVHVWHMDPFRUUHFWDVµ

4XDQWRjVUHVSRVWDVLQFRUUHFWDVHODVUHVXOWDUDPHVVHQFLDOPHQ-te, de uma LQWHUSUHWDomRLQFRUUHFWD dos dados fornecidos no enunciado, YHULÀFDQGRVHTXHDSHUFHQWDJHPGHUHVSRVWDVHUUDGDVIRLPDLRUSDUDD turma BGRTXHSDUDDWXUPDA$VVLPKRXYHDOXQRV TXH LQGX]LGRV SHOD DÀUPDomR GR HQXQFLDGR ´DV FODVVLÀFDo}HV PDLV altas foram obtidas na turma AµDFKDUDPQDUHOHYDQWHSDUDRFDVRH

FRQFOXtUDPTXHGHYLGRDHVVHIDFWRDPpGLDQmRSRGLDVHULJXDOSDUDDV GXDVWXUPDVHRXWURVDÀUPDUDPTXHFRQVLGHUDQGRDDÀUPDomRGR HQXQFLDGR´GRVDOXQRVGDWXUPDBREWLYHUDPFODVVLÀFDomRLQIHULRU RXLJXDODYDORUHVµDPpGLDGDWXUPDBQmRSRGLDVHUYDORUHV Questão 3 1HVWDTXHVWmRVDEHQGRTXHDPpGLDGRVSHVRVGHQRYHSHVVRDVp TXLORJUDPDVHTXHXPDGHODVSHVDTXLORJUDPDVTXHVWLRQDVHVREUH um peso possível para cada uma das restantes oito pessoas.

$PDLRULDGRVDOXQRVUHVSRQGHXFRUUHFWDPHQWHDHVWDTXHVWmRH não responderam 16% dos alunos. As respostas correctas foram variadas, VHQGRDVPDLVIUHTXHQWHVDDSUHVHQWDomRGHYiULRVSHVRVHQWUHH TXLORJUDPDVH´FDGDXPDSHVDTXLORJUDPDVµ1HVWHV casos, os alunos ou basearam-se na aplicação do DOJRULWPRGDPpGLD ou OLPLWDUDPVHDDSUHVHQWDUXPDVpULHGHYDORUHVSRVVtYHLVSDUDRSHVRGDV UHVWDQWHVRLWRSHVVRDVVHPGDURXWURWLSRGHMXVWLÀFDomRRTXHSRGHWHU implícito o recurso a HVWUDWpJLDVGHFRPSHQVDomR ou de WHQWDWLYDHHUUR.

O DOJRULWPRGDPpGLDFRPRQHPVHPSUHIRLXVDGRGHIRUPDDGHTXDGDj VLWXDomRQHPVHPSUHFRQGX]LXjUHVSRVWDFRUUHFWD2XVHMDKRXYHDOXQRV TXHÀ]HUDPXPDLQWHUSUHWDomRLQFRUUHFWDGRHQXQFLDGR²DSOLFDUDPR algoritmo a uma situação diferente da enunciada, outros manifestaram XPDFRPSUHHQVmRLQFRUUHFWDGRVLJQLÀFDGRGRVWHUPRVGRDOJRULWPRH SRUYH]HVLQGLFDUDPEHPDHTXDomRPDVQmRDUHVROYHUDP(VWHDEDQ-GRQRDQWHFLSDGRGRUDFLRFtQLRGHVHQYROYLGRWDPEpPRFRUUHXTXDQGR foram usados raciocínios de tentativa e erro ou de compensação, levando os alunos a respostas incorrectas ou inconclusivas.

Questão 4 1HVWDTXHVWmRGHWHUPLQDVHDPpGLDGRQ~PHURGHLUPmRVGRVDOXQRV GHXPDHVFRODFXMDGLVWULEXLomRpDSUHVHQWDGDVREDIRUPDGHJUiÀFR de barras. (PERUDDPDLRULDGRVDOXQRVWLYHVVHUHVSRQGLGRFRUUHFWDPHQWH DHVWDTXHVWmRDPpGLDpDSHUFHQWDJHPGHUHVSRVWDVLQFRUUHFWDV  p WDPEpP FRQVLGHUiYHO$V UHVSRVWDV FRUUHFWDV EDVHDUDPVH QD aplicação do DOJRULWPRGDPpGLDSRQGHUDGD. 4XDQWRjVGLÀFXOGDGHVVHQWLGDVSHORVDOXQRVDOJXPDVFHQWUDUDPVH naLQWHUSUHWDomRGRJUiÀFRRXVHMDRTXHVLJQLÀFDPHFRPRHVWmRUHOD-FLRQDGRVRVHL[RVQRFRQWH[WRGRSUREOHPD9HULÀFRXVHHQWmRTXHRV DOXQRVFRPHWHUDPRVHUURVGHQmRUHODFLRQDURVLVWHPDGHHL[RV RXVHMDGHWHUPLQDUDPRTXRFLHQWHGDVRPDGDVIUHTXrQFLDVDEVROXWDV HL[R GDV RUGHQDGDV FRP H[FHSomR GR YDORU FRUUHVSRQGHQWH D ]HUR LUPmRVSHODVRPDGRVYDORUHVGDYDULiYHOHL[RGDVDEFLVVDVFDOFXOD-UDPDPpGLDGDVIUHTXrQFLDVLVWRpGHWHUPLQDUDPRTXRFLHQWH

GDVRPDGDVIUHTXrQFLDVDEVROXWDVSHORQ~PHURGHYDORUHVTXHWRPD a variável; consideraram um denominador incorrecto na aplicação do DOJRULWPR²RVDOXQRVSRQGHUDUDPDGHTXDGDPHQWHRVYDORUHVSDUD FDOFXODUDPpGLDPDVFRQVLGHUDUDPFRPRGHQRPLQDGRURYDORUPi[LPR TXHDSDUHFHQRHL[RGDVRUGHQDGDVRXRQ~PHURGHYDORUHVTXHWRPD DYDULiYHOFRQVWUXtUDPXPDWDEHODGHIUHTXrQFLDVPDVQmRVRXEHUDP FDOFXODUDPpGLDFDOFXODUDPDPpGLDGRVYDORUHVGDYDULiYHO LVWRpGHWHUPLQDUDPRTXRFLHQWHGDVRPDGRVYDORUHVTXHWRPDDYDULiYHO SHORQ~PHURGHVVHVYDORUHVHFRQIXQGLUDPDPRGDFRPDPpGLD GDQGRFRPRUHVSRVWDRYDORUPDLVIUHTXHQWH )LFDVHDVVLPFRPDLGHLDTXHDOJXQVDOXQRVPDQLSXODPRVGDGRVGR JUiÀFRVHPRVLQWHUSUHWDUHPQRUHVSHFWLYRFRQWH[WRFRPRSURSyVLWRGH REWHUHPXPYDORUQXPpULFRTXHOKHVSDUHoDGDUUHVSRVWDDRSUREOHPD$ FRPSRQHQWHGHFiOFXORQDPDLRULDGRVUDFLRFtQLRVFRQVLVWHQDXWLOL]DomR GRDOJRULWPRGDPpGLDGHIRUPDQmRVLJQLÀFDWLYDHSRUYH]HVUHFRUUHQGR D´IDOVDVIyUPXODVµ)UHTXHQWHPHQWHRVDOXQRVGHPRQVWUDPFRQKHFHU DIyUPXODVHPOKHDWULEXLUQRHQWDQWRRVLJQLÀFDGRDGHTXDGR$VVLP HPERUDPXLWRVDOXQRVFRQKHFHVVHPRDOJRULWPRGDPpGLDUHYHODUDP todavia, uma compreensão muito limitada da sua aplicação.

Questão 5

1HVWD TXHVWmR FDOFXODVH D PpGLD GR Q~PHUR GH UDPRV GH URVDV YHQGLGRVGXUDQWHFLQFRGLDVGHXPDVHPDQDVDEHQGRTXHQRVTXDWUR SULPHLURVGLDVDPpGLDGRQ~PHURGHUDPRVYHQGLGRVIRLGHHTXH QRTXLQWRGLDQmRVHYHQGHXQHQKXPUDPR

(VWDTXHVWmRJHURXEDVWDQWHVGLÀFXOGDGHVMiTXHDSHQDVGRV alunos respondeu correctamente. As respostas correctas tiveram sempre como raciocínio de base a aplicação do DOJRULWPRGDPpGLD.

$VUHVSRVWDVHUUDGDVUHVXOWDUDPHVVHQFLDOPHQWHGHQmRFRQ-VLGHUDU QR FiOFXOR GD QRYD PpGLD D SRQGHUDomR GD PpGLD GDGD SHOD UHVSHFWLYDIUHTXrQFLDDEVROXWDDSOLFDUDlei do fechoLVWRp FDOFXODUDPpGLDVLPSOHVGDPpGLDGDGDFRPRQRYRGDGRLQWURGX]LGRH considerar ]HURFRPRHOHPHQWRQHXWURRXVHMDEDVHDUVHQDFRQFHSomR GHTXHDLQWURGXomRGR]HURFRPRQRYRGDGRQmRDOWHUDDPpGLD Questão 6 1HVWDTXHVWmRGHWHUPLQDVHDLGDGHGHXPDPLJRTXHVHMXQWRXDXP JUXSRGHWUrVDPLJRVFRPPpGLDGHLGDGHVGHDQRVVDEHQGRVHTXH DPpGLDSDVVRXDVHUGHDQRVSDUDRJUXSRGRVTXDWURDPLJRV $PDLRULDGRVDOXQRVUHVSRQGHXFRUUHFWDPHQWHRDPLJRWLQKD GHWHUDQRVHDSHQDVXPDOXQRQmRUHVSRQGHX

As respostas correctas tiveram essencialmente por base o recurso ao DOJRULWPRGDPpGLD2UDFLRFtQLRWHQWDWLYDHHUURHPTXHRV

DOXQRVHVFROKHUDPXPYDORUSDUDDLGDGHGHVFRQKHFLGDHYHULÀFDUDPD SDUWLUGRDOJRULWPRVHDPpGLDFRUUHVSRQGLDDRYDORUSUHWHQGLGRHPERUD WHQGRVLGREDVWDQWHXWLOL]DGRQHPVHPSUHFRQGX]LXjUHVSRVWDFRUUHFWD SRLVKRXYHDOXQRVTXHWHUPLQDUDPDVWHQWDWLYDVDQWHVGHVHREWHURYDORU H[DFWRGDPpGLDRXTXHLQWHUSUHWDUDPHUUDGDPHQWHRVFiOFXORVHGHUDP FRPRUHVSRVWDDPpGLDREWLGDQDYHULÀFDomR$OpPGLVVRHVWHUDFLRFtQLR WDPEpPSRGHVHUYLVWRFRPRPDLVHOHPHQWDUHPHQRVHÀFLHQWHIDFHDRV FRQKHFLPHQWRVTXHRVDOXQRVGHVWHQtYHOGHHQVLQRGHYHPSRVVXLU 'DPHVPDIRUPDTXHQDTXHVWmRDQWHULRUKRXYHUHVSRVWDVHUUDGDV TXHUHVXOWDUDPGDDSOLFDomRGDlei do fechoHPTXHRVDOXQRVGHWHU-PLQDUDPRYDORUGDLGDGHGHVFRQKHFLGDUHFRUUHQGRjPpGLDVLPSOHVGD PpGLDGDGDFRPRYDORUGHVFRQKHFLGRHGHQmRDIHFWDUDPpGLDUHIHUHQWH DRVWUrVDPLJRVGRUHVSHFWLYRIDFWRU1HVWH~OWLPRFDVRRVDOXQRV GHUDPDUHVSRVWD´DLGDGHGRDPLJRHUDDQRVµRTXHPRVWUDWDPEpP DOJXPDIDOWDGHUHÁH[mRVREUHDUD]RDELOLGDGHGDVUHVSRVWDVREWLGDV Questão 7 1HVWDTXHVWmRFDOFXODVHDPpGLDGRVSHVRVGHSHVVRDVPXOKH-UHVHKRPHQVVDEHQGRVHTXHDPpGLDGRVSHVRVGDVPXOKHUHVp TXLORJUDPDVHDPpGLDGRVSHVRVGRVKRPHQVpTXLORJUDPDV 0DLVGHPHWDGHGRVDOXQRVUHVSRQGHXFRUUHFWDPHQWHTXHD PpGLDHUDTXLORJUDPDVREVHUYDQGRVHDLQGDXPDSHUFHQWDJHPFRQ-VLGHUiYHOGHDOXQRVTXHDSUHVHQWDUDPXPDUHVSRVWDHUUDGD

De entre os raciocínios, o DOJRULWPRGDPpGLDIRLRPDLVXWLOL]DGR HFRQGX]LXVHPSUHjUHVSRVWDFRUUHFWD $VUHVSRVWDVHUUDGDVGHFRUUHUDPGDXWLOL]DomRGDlei do fechoRX VHMDFDOFXODUDPDPpGLDGDVGXDVPpGLDVGDGDVWHQGRFRQFOXtGRTXHD PpGLDHUDTXLORJUDPDVHGDDGLomRGDVPpGLDVHPTXHDPpGLD ÀQDOSUHWHQGLGDIRLREWLGDDGLFLRQDQGRDVPpGLDVGDGDVFRQFOXLQGR TXHDPpGLDHUDTXLORJUDPDV2UDHVWDUHVSRVWDUHYHODXPDFRP-SUHHQVmRUHODFLRQDOGRFRQFHLWRGHPpGLDPXLWROLPLWDGDSRLVRVDOXQRV DWULEXtUDPOKHXPYDORUVXSHULRUjPDLRUGDVPpGLDVGDGDV Questão 8 1HVWD TXHVWmR VDEHQGRVH TXH D PpGLD D PRGD H D PHGLDQD GRV YHQFLPHQWRVGRVHPSUHJDGRVGHXPDHPSUHVDVmRUHVSHFWLYDPHQWH 120 mil escudos, 80 mil escudos e 90 mil escudos, pretendia-se interpretar RVLJQLÀFDGRGDPpGLDQHVWHFRQWH[WR $VUHVSRVWDVIRUDPYDULDGDVVHQGRDUHVSRVWDPDLVIUHTXHQWH ´6DOiULRGHWRGRVRVWUDEDOKDGRUHVGLYLGLGRSHORQ~PHURGHWUDEDOKD-GRUHVµTXHpVLPSOHVPHQWHDGHVFULomRGRDOJRULWPRGDPpGLD. Na segunda UHVSRVWDPDLVUHIHULGD²´5HSUHVHQWDRYDORUPpGLRGRVVDOiULRVµ ²QmRVHDFUHVFHQWDQDGDGHVLJQLÀFDWLYRUHODWLYDPHQWHDRHQXQFLDGR

9HULÀFRXVHDLQGDTXHGRVDOXQRVDOXGLUDPjSRVVtYHOKHWHURJH-neidade dos dadosRXVHMDGHUDPUHVSRVWDVGRWLSR´9DORUPpGLRSRGH PDVFDUDURVH[WUHPRVTXHVHIRUHPPXLWRDOWRVRXPXLWREDL[RVQmR DSDUHFHUmRµ´«QmRUHÁHFWHRVDOiULRGHFDGDHPSUHJDGRSRGHKDYHU YDORUHVPXLWRGLIHUHQWHVµH´2VYHQFLPHQWRVYDULDPQRHQWDQWRVHMDP eles mais altos ou mais baixos, o valor entre todos os funcionários ronda RVPLOHVFXGRVµHFDOFXODUDPDTXDQWLDTXHRSDWUmRGHVSHQGH SRUPrVQRSDJDPHQWRGRVRUGHQDGRV

2VUHVWDQWHVDOXQRVRXGHUDPUHVSRVWDVVHPVHQWLGRQRFRQWH[WR HPFDXVDRXQmRUHVSRQGHUDPjTXHVWmR

4.2. A prática lectiva de três alunas

2VGDGRVGRTXHVWLRQiULRSHUPLWLUDPYHULÀFDUDH[LVWrQFLDGHGLÀ-FXOGDGHV UHODWLYDPHQWH DR FRQFHLWR GH PpGLD DULWPpWLFD 3HUDQWH WDLV GLÀFXOGDGHVQDVHJXQGDIDVHGRHVWXGRSUHWHQGHXVHYHULÀFDUVHHODV HPHUJHPWDPEpPQDSUySULDSUiWLFDOHFWLYDUHFRQKHFHUDVVXDVLQÁX-rQFLDVSDUDDSUiWLFDHDSURIXQGDUDVXDRULJHP &RQIRUPHMiIRLUHIHULGRQHVWDVHJXQGDIDVHGRHVWXGRVHJXLXVHR SHUFXUVRGHWUrVDOXQDV7HUHVD0DULDH-RDQDVHOHFFLRQDGDVGHHQWUHRV HVWXGDQWHVTXHWLQKDPUHVSRQGLGRDRTXHVWLRQiULRGXUDQWHDOHFFLRQDomR GDXQLGDGHGH(VWDWtVWLFDGRžDQRQRFRQWH[WRGDGLVFLSOLQDGH3UiWLFD 3HGDJyJLFD,,(VWiJLR )D]VHVHJXLGDPHQWHUHIHUrQFLDjVVLWXDo}HVUHODWLYDVDRFRQFHLWR GHPpGLDDULWPpWLFDTXHIRUDPH[SORUDGDVQDVDXODVOHFFLRQDGDVSHODV UHIHULGDVDOXQDVVDOLHQWDQGRVHDVGLÀFXOGDGHVSRUHODVVHQWLGDVHDV implicações para a respectiva prática lectiva.

Média envolvendo variáveis qualitativas

7HUHVDSURS{VXPWUDEDOKRGHJUXSRjWXUPDTXHFRQVLVWLDQDUHFROKD GHGDGRVDWUDYpVGHXPLQTXpULWRHGRVHXSRVWHULRUWUDWDPHQWRHDQiOLVH 1HVVHWUDEDOKRHUDSHGLGRRFiOFXORGDPpGLD3RUpPDVTXHVW}HVTXH IRUDPSURSRVWDVHQYROYLDPDSHQDVYDULiYHLVTXDOLWDWLYDVSHORTXHQmR ID]LD VHQWLGR GHWHUPLQDU D PpGLD &RQWXGR 7HUHVD QmR VH DSHUFHEHX GHVVHIDFWRQHPTXDQGRRVDOXQRVWLUDUDPG~YLGDVUHODWLYDPHQWHjV GLÀFXOGDGHVQDHODERUDomRGRWUDEDOKRQHPTXDQGRFDGDJUXSRDSUH-VHQWRXRWUDEDOKRjWXUPD

Na apresentação dos trabalhos pelos alunos passaram-se várias si-WXDo}HV8PGRVJUXSRVQmRGHWHUPLQRXDPpGLDSRUTXHVHHVTXHFHX RXWURVJUXSRVDUUDQMDUDPGDGRVDOXVLYRVDXPDQRYDYDULiYHOWDPEpP TXDOLWDWLYD PDV TXH QmR FRUUHVSRQGLD j TXH OKHV IRL DWULEXtGD SDUD FDOFXODUHPDPpGLD2XWURJUXSRDSUHVHQWRXGDGRVDOXVLYRVjVLWXDomR ´Q~PHURGHYH]HVTXHFDGDDOXQRODQoDRGDGRµHFDOFXORXDPpGLDGR Q~PHURGHODQoDPHQWRVSRUDOXQRFRQWH[WRHPTXHMiIDULDVHQWLGRR

VHXFiOFXOR2FRPHQWiULRGH7HUHVDDHVWDV~OWLPDVVLWXDo}HVIRLLGrQWLFR ´QmRFDOFXORXDPpGLDTXHHUDSUHFLVDSDUDRWUDEDOKRDSUHVHQWRXXP H[HPSORµ +RXYHWDPEpPJUXSRVTXHFDOFXODUDPDPpGLDDOXVLYDDRVGDGRV TXHWLQKDPUHFROKLGRHIHFWLYDPHQWH$VVLPSRUH[HPSORDTXHOHTXH HVWXGRXDTXHVWmR´8PGLDPDLVWDUGHJRVWDULDPXLWRGHVHU«µHVFUH-YHXQRFDUWD]HPTXHDSUHVHQWRXRWUDEDOKRjWXUPD´pDPpGLDGD WDEHODGHIUHTXrQFLDVµVHPTXDOTXHURXWUDMXVWLÀFDomR(QWmR7HUHVD SHGLXDRVDOXQRVSDUDH[SOLFDUHPRTXHWLQKDPIHLWRHJHURXVHRVH-guinte diálogo: (A₁6RPiPRVDVIUHTXrQFLDVHGLYLGLPRVSHORQ~PHURGHSURÀVV}HV TXHKDYLD)L]  DPpGLDGDWDEHOD de frequências. 7)RVWHYHUDPpGLDPDVQmRIRLGDWDEHOD (A₁) Foi do número…

(A_) Acho que ele contou o número de pessoas que escolheram… 72XVHMDHUDDPpGLDGRQ~PHURGHSHVVRDVTXHHVFROKHUDPHVVDV SURÀVV}HVeDPpGLDGDSUHIHUrQFLDGRVDOXQRV

2 JUXSR TXH HVWXGRX R TXH JRVWDYDP GH ID]HU QRV WHPSRV OLYUHV FDOFXORX WDPEpP D PpGLD GDV IUHTXrQFLDV DEVROXWDV FRQFOXLQGR TXH DPpGLDHUD'DPHVPDIRUPDRJUXSRTXHUHFROKHXGDGRVVREUH DFRUSUHIHULGDGRVDOXQRVFDOFXORXDPpGLDGDVIUHTXrQFLDVDEVROXWDV FRQFOXLQGRTXH´$PpGLDGDVFRUHVTXHRVDOXQRVGRž%HVFROKHUDP IRLGHµ

1HVWD DOWXUD XP DOXQR GD WXUPD FRPHQWRX ´'i D PHVPD PpGLD TXHQRJUXSR>DQWHULRU@«µ(VWDREVHUYDomRSRGHULDWHUDOHUWDGR7HUH-VDSDUDYHULÀFDUTXHDOJRQmRHVWDULDFRUUHFWR3RUpPHVWDUHVSRQGHX ´/HPEUDWHTXHIRUDPDYDOLDGRVRVPHVPRVDOXQRVHSRGHGDUDPHVPD PpGLDµ 0DLVWDUGH7HUHVDHPFRQYHUVDFRPDLQYHVWLJDGRUDDÀUPRXTXHRV DOXQRVQmRWLYHUDPG~YLGDVQHVVDSDUWHHTXHHODWDPEpPQmRUHÁHFWLX PXLWRVREUHRDVVXQWR&RQWXGRFRQIHVVRXTXHQmRHVWDYDPXLWRVHJXUD GDVLWXDomRSRLVQmRKRXYHQDGDTXHDDOHUWDVVHSDUDHVVHIDFWR )LTXHLQDG~YLGDPDVFRPRHVWDYDPWRGRVDWHURPHVPRVHJXLPHQWR QmRGLVVHQDGD« &RPRQmROKHVWLQKDIDODGRTXHKDYLDGDGRVTXHSRGLDPVHTXHVH SRGLDWUDEDOKDUFRPDPpGLDHRXWURVTXHQmRVHSRGLDID]HUDPpGLD GHYLGDPHQWHWDOYH]IRLPDLVQHVVHDVSHFWRTXHHXGHL[HLLUeTXHQHP RSURJUDPDGL]QDGDDHVVHUHVSHLWRHRPDQXDOQmRIDODYDVHTXHU

0DULD QmR DERUGRX D LPSRVVLELOLGDGH GH FiOFXOR GD PpGLD QHVWHV FDVRV7DPEpPQmRFRQVLGHUDYLiYHORVDOXQRVDYHULJXDUHPHVVHIDFWR DÀUPDQGRTXH´SDUDLVVRWtQKDPRVTXHGDUDQWHVFRQFHLWRVFRPRYD-ULiYHLVTXDOLWDWLYDVHTXDQWLWDWLYDVHLVVRQmRID]SDUWHGRSURJUDPDµ Todavia, perante a hipótese, levantada pela investigadora, de poder aludir a esses conceitos na sala de aula, embora de uma forma informal HDSURSyVLWRGHSUREOHPDVDERUGDGDVQDDXODDLQGDÀFDQDG~YLGDVH GHYHUiVHUXPDTXHVWmRDH[SORUDUFRPRVDOXQRV'HUHDOoDUTXH0DULD GDSULPHLUDYH]TXHUHVSRQGHXDRTXHVWLRQiULRQmRUHVSRQGHXjTXHVWmR TXHVHUHSRUWDYDDHVWDVLWXDomRTXHVWmRHDSyVXPDVHJXQGDDQiOLVH GRTXHVWLRQiULRHPERUDWLYHVVHFKHJDGRDXPDUHVSRVWDFRUUHFWDWHYH GLÀFXOGDGHV HP H[SOLFDU R VHX UDFLRFtQLR XVDQGR WHUPRV HVWDWtVWLFRV DGHTXDGRV (OD SUySULD DFDERX SRU DÀUPDU ´MXVWLÀFDomR FRUUHFWD H FLHQWtÀFDQmRVHLµ -RDQDWDPEpPQmRH[SORURXFRPRVDOXQRVHVVHWLSRGHWDUHIDVFRQ-IHVVDQGRTXHTXDQGRSUHSDURXDVDXODVQmRUHÁHFWLXVREUHHVVHDVVXQWR HPERUDWHQKDHQFRQWUDGRQXPPDQXDOGHžDQRXPDUHIHUrQFLDTXH DOHUWDYDSDUDHVVHIDFWR'HQRWDUTXHTXDQGRUHVSRQGHXDRTXHVWLRQi-ULRSHODSULPHLUDYH]QDTXHVWmRTXHVHUHIHULDDHVWDVLWXDomRTXHVWmR FDOFXORXDPpGLDGDVIUHTXrQFLDVDEVROXWDVHTXDQGRDQDOLVRXSHOD VHJXQGDYH]DUHVSRVWDGDGDDSyVWHUOHFFLRQDGRDXQLGDGH(VWDWtVWLFD FRQWLQXRX D FRQFRUGDU FRP R VHX UDFLRFtQLR 6y TXDQGR TXHVWLRQDGD SHOD LQYHVWLJDGRUD VREUH D YDULiYHO HP FDXVD p TXH VH DSHUFHEHX GD VLWXDomRGL]HQGRTXHQmRLQWHULRUL]RXFRQFUHWDPHQWHRVLJQLÀFDGRGD PpGLDSDUDHVWHVFDVRV

3RGHVHDVVLPFRQVWDWDUTXHQRFDVRGH0DULDHGH-RDQDDVGLÀFXO-dades em termos conceptuais podem ter levado a evitar explorar tarefas desse tipo com os seus alunos.

Cálculo da média para dados agrupados

-RDQDSURS{VQDDXODXPDWDUHIDVREUHRFiOFXORGDPpGLDVHQGR SHGLGR DRV DOXQRV SDUD ODQoDUHP XP GDGR  YH]HV H FRQVWUXtUHP D WDEHODGHIUHTXrQFLDVGRVUHVXOWDGRVREWLGRVTXHQmRWHQGRVLGRWHUPL-QDGDQDDXODÀFRXSDUDRVDOXQRVDFDEDUHPHPFDVD(VWHDGLDPHQWR SDUDDDXODVHJXLQWHDSUHVHQWRXVHEHQpÀFRSDUD-RDQDUHÁHFWLUVREUHD UHVROXomRGDWDUHIDMiTXHHVWDFRQIHVVRXHVSRQWDQHDPHQWHTXHWHYH DOJXPDVGLÀFXOGDGHVQRFiOFXORGDPpGLDQRFDVRGDVLWXDomRFLWDGD SRLV TXDQGR R WHQWRX ID]HU FDOFXORX D PpGLD GDV IUHTXrQFLDV ² ´1R LQtFLRWLYHGLÀFXOGDGHVDRFDOFXODUDPpGLDSRLVVRPHLDVIUHTXrQFLDV HGLYLGLSRUVHLVµ

$SHUFHEHQGRVHGHTXHDOJRQmRHVWDULDFRUUHFWRUHFRUUHXDWDEHODV GHIUHTXrQFLDVGLIHUHQWHVDOXVLYDVDRXWUDVSRQWXDo}HVHYHULÀFRXTXHR YDORUGDPpGLDFDOFXODGRSHORVHXSURFHVVRHUDVHPSUHRPHVPRRTXH

DFKRXHVWUDQKR6HJXLGDPHQWHUHÁHFWLQGRVREUHHVWHIDFWRHSHGLQGR DDMXGDGHFROHJDVFRPTXHPGLVFXWLXRDVVXQWRFKHJRXjFRQFOXVmR FRUUHFWD3DUDWDOFRPHoDUDPSRUGHWHUPLQDUDPpGLDVLPSOHVSDUWLQGR de dados não agrupados.

(VWLYHPRVDSHQVDU>-RDQDHPDLVWUrVFROHJDVHVWDJLiULRV@HGHSRLV OiFKHJiPRVjFRQFOXVmR«6RPiPRVQDSDUWHGRVODQoDPHQWRVH GLYLGLPRVSRU(QWmRSRURXWURSURFHVVRWLQKDTXHGDUDPHVPD PpGLDHOiGHVFREULPRVTXHWtQKDPRVTXHPXOWLSOLFDU+iDOWXUDVHP TXHSDUHFHTXHQmRUDFLRFLQDPRVPXLWREHPTXHVmRFRLVDVVLPSOHVH parece que quanto mais simples…

)LQDOPHQWHFRPHQWRXTXHQHVWHFDVRVHWLYHVVHGHUHVROYHULPHGLD-tamente o exercício na aula, teria sido um pouco complicado.

6HFDOKDUHUDFDSD]GHVHUFRPSOLFDGRHHXLDÀFDUXPSRXFREDUD-OKDGD)RLHQJUDoDGRHXWLQKDQDPLQKDPHQWHDLGHLDEHPpDVVLP TXHVHUHVROYHHGHSRLVYRXSHJDUQDTXLORSDUDUHVROYHU0DVHQWmR LVWRQmRpDVVLP"(ÀTXHLXPSRXFREDUDOKDGD 7HUHVDH0DULDHPERUDWLYHVVHPFRQVWUXtGRWDEHODVGHIUHTXrQFLDV FRPRVDOXQRVQXQFDDVXWLOL]DUDPGLUHFWDPHQWHSDUDGHWHUPLQDUDPpGLD recorrendo sempre aos dados originais não agrupados. As suas opções QHVWHVHQWLGRIRUDPMXVWLÀFDGDVQRFDVRGH7HUHVDSHODLQÁXrQFLDGD SURIHVVRUDGDWXUPDTXHOKHWUDQVPLWLXDLGHLDGHTXHVHULDPDLVFRP-plicado para os alunos e a Maria não lhe pareceu relevante os alunos explorarem situações deste tipo.

Determinação de um dado sabendo a média inicial (sem esse dado) e a média final

Maria propôs para trabalho de casa um exercício do manual dos alu-QRV²4XDWURDPLJRVWLQKDPHPPpGLDDQRV-XQWRXVHDRJUXSRGRV TXDWURXPRXWURDPLJR4XDOpDLGDGHGHVVHDPLJRVHDPpGLDSDVVRX DVHUDQRV"VHPHOKDQWHjTXHVWmRGRTXHVWLRQiULR 'XUDQWHDFRUUHFomRXPDOXQRUHJLVWRXQRTXDGUR  RTXHWUDGX]XPUDFLRFtQLRFRUUHFWRPDVSRUWHQWDWLYDV 3URVVHJXLQGRQDVXDH[SOLFDomRRDOXQRDÀUPRX´6RPHLPDLV«µ RQGHSRGHUiHVWDULPSOtFLWRDYHULÀFDomRGRFiOFXOR(VWDUHVSRVWDIRLGH LPHGLDWRFRQWHVWDGDSRU0DULDGL]HQGR´PDVDPpGLDGRVTXDWURQ~-PHURVpµ'RQGHQmRIH]TXDOTXHUPHQomRGHDSURYHLWDURUDFLRFtQLR SRUWHQWDWLYDHUURSDUDFKHJDUDRXWURPpWRGRPDLVIRUPDO 2XWURDOXQRQmRSRQGHURXDVIUHTXrQFLDVDEVROXWDVQRFiOFXORGD PpGLD  «QmRFKHJDQGRDDFDEDUDVXDUHVROXomR

SRUTXH0DULDDÀUPRXHVWDUHUUDGD)LQDOPHQWHXPDDOXQDGDWXUPD DSUHVHQWRXXPDUHVSRVWDFRUUHFWDð DQRVð DQRV ² DQRVTXHIRLSHUIHLWDPHQWHDFHLWHSHOD0DULD

Muito embora o exercício tenha sido corrigido correctamente na aula, QmRIRUDPDSURYHLWDGRVRVHUURVGRVDOXQRVSDUDRVTXHVWLRQDUVREUH DVLWXDomRQHPIRLDFHLWHXPUDFLRFtQLRTXHWLQKDSRUEDVHXPDHVWUD-WpJLDGHWHQWDWLYDHHUUR(VWDVIDOKDVQDH[SORUDomRGDWDUHIDDOpPGH SRGHUHPUHVXOWDUGDH[LVWrQFLDGHDOJXPDVGLÀFXOGDGHVHP´WUDGX]LUµ os conhecimentos numa linguagem matemática acessível aos alunos, SDUHFHPWDPEpPWHURULJHPQXPDFRPSUHHQVmROLPLWDGDGRFRQFHLWRGH PpGLDWUDGX]LQGRVHQDVREUHYDORUL]DomRGHXPSURFHVVRGHUHVROXomR ²SURYDYHOPHQWHDTXHOHTXHIRLSHQVDGRDQWHV²HVHPFRQVLGHUDURXWURV processos igualmente válidos.

&RQYHUVDQGRFRPDLQYHVWLJDGRUDVREUHHVWHDVVXQWR0DULDDÀUPRX TXHQmRWHYHGLÀFXOGDGHVHTXHWHQWRXSHQVDUQXPDIRUPDGHDERUGDU RH[HUFtFLRQDVDODGHDXOD´)L]FRPXPDLQFyJQLWD; e estive a pensar QXPD PDQHLUD GH HOHV UHVROYHUHP SRLV YL TXH QmR SRGLDP SHUFHEHU GHVWDIRUPDµ

'HUHDOoDUTXHGDSULPHLUDYH]TXHUHVSRQGHXDRTXHVWLRQiULR0DULD UHVSRQGHXLQFRUUHFWDPHQWHDXPDTXHVWmRGHVWHWLSRTXHVWmRQmR WHQGR HP FRQWD D IUHTXrQFLD UHVSHLWDQWH j PpGLD GDGD &RQWXGR GD VHJXQGD YH] TXH DQDOLVRX D TXHVWmR DSyV WHU OHFFLRQDGR D XQLGDGH FRQVLGHURXTXHVHWLQKDHQJDQDGRHFKHJRXDXPDFRQFOXVmRFRUUHFWD DSOLFDQGRRDOJRULWPRGDPpGLD -RDQDHPERUDXWLOL]DVVHRPHVPRPDQXDOTXH0DULDQmRSURS{V DRVDOXQRVHVWHH[HUFtFLRSRUIDOWDGHWHPSR²´)RLGDTXHODVDXODVTXH HXQmRVDELDVHLDVREUDUWHPSRRXQmRµ1RHQWDQWRDÀUPDTXHpXP WLSRGHTXHVWmRjTXDOHVWDYDPHQRVKDELWXDGDHTXHHQYROYHXPUDFLR-FtQLRPDLVHODERUDGR$HVWHSURSyVLWRpGHUHIHULUTXHHODUHVSRQGHX GH IRUPD LQFRUUHFWD j TXHVWmR  GR TXHVWLRQiULR UHYHODQGR DOJXPDV GLÀFXOGDGHVDRQmRWHUHPFRQWDDIUHTXrQFLDDEVROXWDQDDSOLFDomRGR DOJRULWPR6HJXQGRDDOXQDHVWHSUREOHPD´(UDEHPGLIHUHQWH6HLTXH WLYHDOJXPDGLÀFXOGDGHHPUHVROYrOR$LQGDHVWLYHXPERFDGLQKRDOL jVYROWDVSDUDRUHVROYHUµ

3RGHVHSRULVVRSHQVDUTXHSRUYH]HVRFRQWDFWRFRPTXHVW}HVTXH aparecem, por exemplo, nos manuais ou noutros documentos podem SURYRFDUXPDUHÁH[mRVREUHDVXDUHVROXomRHOHYDUDXOWUDSDVVDUGH-WHUPLQDGDVGLÀFXOGDGHV -i7HUHVDHPERUDTXDQGRUHVSRQGHXDRTXHVWLRQiULRWLYHVVHGDGR XPDUHVSRVWDFRUUHFWDjTXHVWmRFRQVLGHUDTXHQmRpXPWLSRGHH[HU-FtFLRTXHVHGHYDH[SORUDUFRPRVDOXQRVGRžFLFORSRLVVHHODWDPEpP WHPGLÀFXOGDGHVRVDOXQRVWHULDPPXLWDVPDLV

GDGDDPpGLDHXPGRVGDGRVHVHSHGHSDUDLQGLFDURVRXWURVGDGRVGD GLVWULEXLomR-RDQDFRQVLGHUDQmRVHUYLiYHODVXDH[SORUDomRSRUDOX-QRVGRžDQRSRUTXHHVWHVQmRWrPFRQKHFLPHQWRVSDUDDVUHVROYHUGD IRUPDTXHDFKDSRVVtYHORXVHMDDWUDYpVGDUHVROXomRGHXPDHTXDomR 7HUHVDSDUWLOKDDPHVPDRSLQLmRDÀUPDQGRTXH´HUDFRPSOLFDGRSDUD RVDOXQRVGRžFLFORµMiTXHWHULDGLÀFXOGDGHVHPDERUGDUDUHVROXomR de tais situações ao nível dos alunos.

3RGHVHDVVLPFRQVWDWDUSRUHVWHVHRXWURVH[HPSORVMiFLWDGRVTXH SRUYH]HVDVGLÀFXOGDGHVHPDGDSWDURVFRQKHFLPHQWRVDRQtYHOGRV DOXQRVFRQGLFLRQDPDVHOHFomRGHWDUHIDVDH[SORUDUQDVDODGHDXOD(VWH FRQGLFLRQDPHQWRIRLH[SOLFLWDPHQWHDVVXPLGRSRU-RDQDHSRU7HUHVDH WDPEpPVHYHULÀFRXQRFDVRGD0DULD3RUH[HPSOR-RDQDDÀUPRXTXH RIDFWRGHSHQVDUTXHQmRFRQVHJXLDH[SOLFDUEHPXPH[HUFtFLRHUDUD]mR para não o escolher e seleccionar outro para explicar a mesma coisa. 1RPHVPRVHQWLGR7HUHVDGHFODURXTXHXPGRVFULWpULRVGHVHOHFomR GDVWDUHIDVIRLDIDFLOLGDGHTXHWLQKDHPDVH[SOLFDU´VHUPDLVIiFLOGH HXOKHVH[SOLFDUµDGPLWLQGRTXHVHHQFRQWUDVVHDOJRXPSRXFRPDLV FRPSOLFDGRFRORFDYDSUDWLFDPHQWHGHODGR(0DULDWDPEpPPDQLIHVWRX DOJXPDUHOXWkQFLDHPDFHLWDUFRPRDGHTXDGDVSDUDSURSRUDRVDOXQRV DOJXPDV WDUHIDV GR TXHVWLRQiULR QDV TXDLV WHYH DOJXPDV G~YLGDV RX GLÀFXOGDGHVDRUHVROYrODV

O facto de as estagiárias estarem a ser avaliadas pode ter contribuído SDUDTXHDOJXPDVGLÀFXOGDGHVQmRWHQKDPVLGRHYLGHQFLDGDVMiTXH HODVWHQWDUDPHYLWDUSURSRUWDUHIDVHPTXHWLYHVVHPDSHUFHSomRGHQmR as conseguir explorar do ponto de vista dos alunos.

5. Conclusões

1RTXHGL]UHVSHLWRDRFRQFHLWRGHPpGLDDULWPpWLFDGDSULPHLUDIDVH GRHVWXGRSRGHFRQFOXLUVHTXHRVDOXQRVFRQKHFHPRVHXDOJRULWPR PDVQHPVHPSUHXWLOL]DPHVVHFRQKHFLPHQWRGHIRUPDVLJQLÀFDWLYD

3RUH[HPSORDDSOLFDELOLGDGHGRFRQFHLWRGHPpGLDTXDQGRHVWmR HP FDXVD YDULiYHLV TXDOLWDWLYDV DLQGD RULJLQD PXLWDV GLÀFXOGDGHV SRLVDSHQDVGRVDOXQRVFRQVLGHUDUDPTXHQHVVHFDVRQmRpSRV-VtYHOFDOFXODUDPpGLDHPXLWRPHQRVDOXQRVXVDUDPUDFLRFtQLRV FRQVLGHUDGRVYiOLGRV(PJHUDORVDOXQRVWHQWDUDPHQFRQWUDUXPYDORU QXPpULFRTXHUHSUHVHQWDVVHDPpGLDPDQLSXODQGRRVGDGRVVHPWHU HPFRQWDRFRQWH[WR1HVWHFDVRRFiOFXORGDPpGLDGDVIUHTXrQFLDVIRL RHUURPDLVIUHTXHQWH 2FiOFXORGDPpGLDDSDUWLUGHXPJUiÀFRGHEDUUDVWDPEpPJHURX EDVWDQWHVGLÀFXOGDGHVWHQGRVHREWLGRDSHQDVGHUHVSRVWDVFRU- UHFWDVIXQGDPHQWDOPHQWHREWLGDVSRUDSOLFDomRGRDOJRULWPRGDPp-dia. Muitos dos erros cometidos deveram-se ao facto de os alunos não interpretarem correctamente cada um dos eixos e a relação entre eles.

&DUYDOKRWDPEpPHPUHODomRjPpGLDYHULÀFRXTXHDOXQRVGH žDQRVHFHQWUDYDPQRDVSHFWRYLVXDOGRJUiÀFRGHEDUUDVHLJQRUDYDP as relações nele existentes.

3DUDYHQFHUHPDVVXDVGLÀFXOGDGHVRVDOXQRVGHYHPWUDEDOKDUGHVGH FHGRFRPJUiÀFRV&XUFLRTXHVXUMDPHPFRQWH[WRUHDOQRkPELWR GHWUDEDOKRVGHSURMHFWR$LQOH\2FRQWH[WRUHDOFRQVWLWXLXPERP PHLRSDUDGHVHQYROYHULQWXLo}HVDVTXDLVWHUmRXPJUDQGHSRWHQFLDOQD compreensão futura de aspectos mais complexos.

$GLÀFXOGDGHGRVDOXQRVHPUHVROYHUSUREOHPDVHQYROYHQGRRFiOFXOR GHXPDPpGLDSRQGHUDGDMiREVHUYDGDQRVHVWXGRVGH*DWWXVRH0DU\  /L H 6KHQ  0HYDUHFK  H 3ROODWVHN et al  IRL LJXDOPHQWHSURHPLQHQWHHPYiULDVGDVTXHVW}HVHVWXGDGDVQDSUHVHQWH investigação.

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