/DERUDWRULRGL 'LGDWWLFDGHOOD0DWHPDWLFD

Transcript

1 6SHFLDOL]]DQGL *UXSSR $QWRQLHWWL6WHIDQR %HWWDOH$QQD 'DOOD9HFFKLD)DELR 'D9LOOD0DGGDOHQD /D]]DULV*LXOLDQD 7HVLQD GL /DERUDWRULRGL 'LGDWWLFDGHOOD0DWHPDWLFD 3URIVVD/RUHGDQDOHWWD 9LVRQRWUHWLSLGLPHQ]RJQH OHPHQ]RJQH OHPHQ]RJQHVSXGRUDWH HODVWDWLVWLFDµ 'LVUDHOL DD

2 (FFRODQRVWUDPDSSDFRQFHWWXDOH /$67$7,67,&$1(//$)250$=,21(&8/785$/('(,&,77$',1, 1HOOD )250$=,21(&8/785$/('(,&,77$',1, LQWHUYLHQH &203(7(1=( R OHFXL / ('8&$=,21( 3HQVLHUR 0$7(0$7,&$ 5D]LRQDOH WUDGRWWHLQ IRQGDPHQWDOHQHOOD &XUULFROR 6FRODVWLFR 2%,(77,9, 6FRODVWLFL QDVFHO HVLJHQ]DGL 6FLHQ]D 7HFQRORJLD SHUFDSLUH 62&,(7$ &RPXQLFD]LRQH DWWUDYHUVRODFRQRVFHQ]DGHL 02'(51$ (FRQRPLD««««««««««/LQJXDJJL FKHVLVHUYHGHOODVWXGLDWHWUDPLWH 6FLHQWLILFL HVVHQ]LDOLQHOOD SHUGHVFULYHUH STATISTICA VYLOXSSDQR )(120(1, XWLOLLQ &2//(77,9, &RQVDSHYROH]]D 6HQVR&ULWLFR EDVDWDVXOOD &DSDFLWjGL*LXGL]LR XWLOL]]DWHSHUVWXGLDUH 5$&&2/7$GL,1)250$=,21, WUDGRWWDLQ 5$335(6(17$=,21(,17(535(7$=,21( H

3 3DGURQDQ]HWUDVYHUVDOL &RPSHWHQ]HLQPDWHPDWLFD &RQO 80,DEELDPRLQGLYLGXDWRDOFXQHGHOOHPD[LSDGURQDQ]HGHOFLWWDGLQRDOFXLUDJJLXQJLPHQWRFRQFRUUH O HGXFD]LRQHPDWHPDWLFDHFKHFRVWLWXLVFRQRGHLFDSLVDOGLGHOSURILORIRUPDWLYRGLXQRVWXGHQWHLQXVFLWD GDOODVFXRODVHFRQGDULDELHQQLVRQR Ã(VSULPHUHDGHJXDWDPHQWHLQIRUPD]LRQL Ã,QWXLUHHLPPDJLQDUH Ã5LVROYHUHHSRUVLSUREOHPL Ã3URJHWWDUHHFRVWUXLUHPRGHOOLGLVLWXD]LRQLUHDOL Ã2SHUDUHVFHOWHLQFRQGL]LRQLGLLQFHUWH]]D Ã6FRSULUHSURSULHWjUHJRODULWjDQDORJLHHGLQYDULDQWL / 80,LQGLYLGXDVHWWHQXFOHLTXDWWURWHPDWLFLHWUHWUDVYHUVDOLHQWURLTXDOLXQGRFHQWHSXzRSHUDUHGHOOH VFHOWHSHUFRVWUXLUHXQFXUULFRORFKHFRQWULEXLVFDDGHOLQHDUHLOSURILORIRUPDWLYR 3HU RSHUDUH WDOL VFHOWH q QHFHVVDULR SURFHGHUH DOO DQDOLVL GHO YDORUH IRUPDWLYR GHOOD SURSULD GLVFLSOLQD VHFRQGRFULWHULGLULOHYDQ]DFRQFHWWXDOHSUHJQDQ]DFRJQLWLYDHVSHQGLELOLWjVRFLDOH 6LQWHWL]]DQGR SRVVLDPR GLUH FKH VLLQGLYLGXDQRDOO LQWHUQR GHOOD PD[L SDGURQDQ]H GHOOH SDGURQDQ]H SL PLUDWHµHVLFHUFDGLFDSLUHFRPHVLSXzFRQWULEXLUHDOORURUDJJLXQJLPHQWR,O QRVWUR JUXSSR VL q RFFXSDWR LQ SDUWLFRODUH GHOOD PD[L SDGURQDQ]D HVSULPHUH DGHJXDWDPHQWH LQIRUPD]LRQLµQHOODTXDOHDEELDPRULFRQRVFLXWRLQJOREDWDODSDGURQDQ]D 6$3(5'(6&5,9(5()(120(1,&2//(77,9,,/0(72'2',,1'$*,1(67$7,67,&$ 3HUGHVFULYHUHFRUUHWWDPHQWHLIHQRPHQLFROOHWWLYLHTXLQGLSURGXUUHLQIRUPD]LRQLFRUUHWWHqQHFHVVDULR FRQRVFHUHOHSUREOHPDWLFKHHOHSURFHGXUHGLXQ LQGDJLQHVWDWLVWLFD &DSLUHVWDWLVWLFKH &DSLUHLQIRUPD]LRQL 8WLOL]]DUHVWDWLVWLFKH 8WLOL]]DUHLQIRUPD]LRQL 3URGXUUHVWDWLVWLFKH 3URGXUUHLQIRUPD]LRQL &RPXQLFDUH /DVWDWLVWLFDqODSSOLFD]LRQHGHLPHWRGLVFLHQWLILFLDOODSURJUDPPD]LRQHGHOODUDFFROWDGHLGDWLDOODORUR FODVVLILFD]LRQHHODERUD]LRQHDQDOLVLHSUHVHQWD]LRQHHDOOLQIHUHQ]DGLFRQFOXVLRQLDWWHQGLELOLGDHVVL 9HGLDPRQHO GHWWDJOLROD QRVWUDDQDOLVLGHO YDORUHIRUPDWLYR GHOOD GLVFLSOLQD LQUHOD]LRQH DOODSDGURQDQ]D LQGLFDWD

4 /DULOHYDQ]DFRQFHWWXDOHq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

5 /DSUHJQDQ]DFRJQLWLYDqLOFULWHULRSHULQGLYLGXDUHOHPRGDOLWjGLUDJLRQDPHQWRSULYLOHJLDWHGDOPRGHOOR HVSHUWRYDOXWDUHOHGLIILFROWjHFHUFDUHOHVWUDWHJLHGLJXLGDFRJQLWLYDGDPHWWHUHLQDWWR2ULHQWDDOOD GHILQL]LRQHGHOOHPRWLYD]LRQLFKHVLYXROVXVFLWDUHHGHJOLDWWHJJLDPHQWLFKHVLSUHYHGHGLULVFRQWUDUHLQ XVFLWDGDOPRGXOR/ DQDOLVLGHOODSUHJQDQ]DFRJQLWLYDFRQVHQWHGLWUDFFLDUHLOTXDGURGHOOHFRPSHWHQ]H LPSOLFDWHHGLUHQGHUOHRSHUDWLYHQHOFRQWHVWRGLVWXGLRSUHYHGHQGRDQFKHOHSRVVLELOLGLIILFROWjDOOH TXDOLIDUIURQWHFRQRSSRUWXQHVWUDWHJLHHVWUXPHQWLGLGDWWLFLIDFLOLWDQWL 3URFHVVLFRJQLWLYLDWWLYDWL,QGLYLGXDUHFRQWHVWR 5LFRQRVFHUH PHWRGRORJLH GDWL SURFHGXUH GL HVHFX]LRQH«3LDQLILFDUHO DWWLYLWj 5DFFRJOLHUHHRUJDQL]]DUHGDWLHWDEHOOH 6HOH]LRQDUHGDWLVLJQLILFDWLYL 5DSSUHVHQWDUHGDWLVLJQLILFDWLYL 2SHUDUHFRQJHWWXUH &RQFHWWXDOL]]DUHHIRUPDOL]]DUHPRGHOOL $VWUDUUHHJHQHUDOL]]DUHO RSHUD]LRQH 5LFRVWUXLUHO HYHQWR &HUFDUHDQDORJLH *HVWLUHWHFQLFKHGLPRQLWRUDJJLR *HVWLUHWHFQLFKHGLDXWRYDOXWD]LRQH $WWHJJLDPHQWLGLEDVH 5LJRUHGLDQDOLVL 5LJRUHORJLFR 5LFHUFDGLQXRYHVROX]LRQL 0RQLWRUDJJLRGHLSURFHVVL 9HULILFDFRPSDWLELOLWjULVXOWDWL 5LFHUFDFRHUHQ]DQHLULVXOWDWL 5LFHUFDGLWUDVIHULELOLWjLQDOWUHGLVFLSOLQHGL PRGHOOL IRUPH UDJLRQDPHQWL VWUXWWXUH OHJJL SURFHGXUHULVROXWLYH,QWHUURJDUHODQDWXUD IDUVLOHGRPDQGHJLXVWH 5($/7$ 0LVXUDUH )RUPDOL]]DUH,QWHUSUHWDUH 2VVHUYDUH 02'(//2

6 /DVSHQGLELOLWjqGDLQWHQGHUVLFRPHVSHQGLELOLWjFXOWXUDOHQHOVHQVRFXUULFRODUHVLDWUDVYHUVDOHFKH YHUWLFDOHPD DQFKH FRPH VSHQGLELOLWjVRFLDOH HWLFD HFF«*XLGD QHOOD ULFHUFD GLVLQHUJLH QHL FROOHJDPHQWLFRQDOWULQRGLHGDOODGHILQL]LRQHGHLSLSUREDELOLSXQWLGLFRQWDWWRFRQDOWULPRGXOL /DVWDWLVWLFDFLIRUQLVFHJOLVWUXPHQWLSHUODFRQRVFHQ]DGHOODUHDOWjFKHFLVWDLQWRUQRSHU &DSLUHLQWHUSUHWDUHH FRQWUROODUHODUHDOWj 2VVHUYDUHFRQVSLULWR FULWLFRHVHOHWWLYR $FTXLVLUH LQIRUPD]LRQLFRUUHWWH 3UHYHGHUHO HYROX]LRQH GLXQHYHQWR /HJJHUHLOLQJXDJJL 'LVFULPLQDUHOHDQDOLVL VSHFLILFL IDOVDWHGDLPHGLD )DUHVFHOWH &RPXQLFDUHLQPRGR FRQVDSHYROL DSSURSULDWR 1HOOD VSHQGLELOLWjµqLPSRUWDQWHDQFKHLQVHULUHO XWLOL]]RGHOIRJOLRHOHWWURQLFRGDWRLOVXRGLIIXVRLPSLHJR QHOPRQGRD]LHQGDOH / DQDOLVL SUHFHGHQWH FL KD SHUPHVVR GL SDVVDUH GDOOD SDGURQDQ]D DOOH FRPSHWHQ]H VSHFLILFKH FKH UDSSUHVHQWDQRJOLRELHWWLYLGHLQRVWUL&RPSLWL(VSHUWLSURJHWWDWLSHULOAELHQQLR SHULQGLYLGXDUHLOFRQWHVWRLQFXLFLVLWURYDDGRSHUDUH 6DSHUHLGHQWLILFDUHLIHQRPHQLFROOHWWLYL 6DSHUHTXDOqO LQVLHPHGHJOLHOHPHQWLRJJHWWRGHOO LQGDJLQHFKHVLYXROHVYROJHUH 6DSHUHTXDOqLOFDUDWWHUHRODSURSULHWjFKHVLYXROHDQDOL]]DUH SHUODULOHYD]LRQHHO HODERUD]LRQHVXFFHVVLYD &RQRVFHUHOHSUREOHPDWLFKHHOHSURFHGXUHGLXQ LQGDJLQHVWDWLVWLFD 6DSHUHUDFFRJOLHUHLGDWL 6DSHUHHODERUDUHLGDWLHVVHQ]LDOL 6DSHUHRUJDQL]]DUHLQWDEHOOHLGDWL 6DSHUHLQWHUSUHWDUHOHVWDWLVWLFKHSURGRWWH 6DSHUHXWLOL]]DUHXQIRJOLRHOHWWURQLFR,QROWUHO DQDOLVLFLKDFRQVHQWLWRGLULFRQRVFHUHTXDOLVRQRLSUHUHTXLVLWLTXDOLSRVVRQRHVVHUHLFROOHJDPHQWLH LSRVVLELOLVYLOXSSL,QTXHVWRPRGRDEELDPRVWDELOLWHGHOOHFRQQHVVLRQLWUDVYHUVDOLHYHUWLFDOLFRQDOWULQXFOHL

7 /DQRVWUDLQGDJLQHSXzHVVHUHVLQWHWL]]DWDFRVu,QULIHULPHQWRDOGRFXPHQWRGHOO 80,OD VHGHµQDWXUDOHGHOQRVWURODYRURqFRQWHQXWDDOO LQWHUQRGHOQXFOHR 'DWLH3UHYLVLRQLDQFKHVHFRPHYLHQHVRWWROLQHDWRDQFKHQHOORVWHVVRGRFXPHQWRWDOHQXFOHRPRVWUDLVXRL OHJDPLFRQWXWWLJOLDOWULQXFOHLVLDGLFRQWHQXWRVLDWUDVYHUVDOL,QROWUHYLqODSRVVLELOLWjGLXQDLQWHUD]LRQH VWUHWWLVVLPDFRQLOODERUDWRULRGLPDWHPDWLFDQHOTXDOHVLSXzDGHVHPSLRHIIHWWXDUHO XWLOL]]D]LRQHGHO IRJOLRHOHWWURQLFRSHUODFRVWUX]LRQHGHOGDWDEDVHUHODWLYRDGXQDUDFFROWDGLGDWLODUDSSUHVHQWD]LRQHH O HODERUD]LRQHGHLGDWLVWDWLVWLFLQRQFKpODVLPXOD]LRQHGLGLVWULEX]LRQLGLSUREDELOLWjUHODWLYHDGRSSRUWXQH YDULDELOL DOHDWRULH A ELHQQLR 7XWWR FLz VHUYH D PHJOLR FRPSUHQGHUHHG D UDIIRU]DUHL FRQFHWWL GL VWDWLVWLFDHSUREDELOLWjHGDVYLOXSSDUHTXHOOHDELOLWjGLUDFFRJOLHUHWUDWWDUHLQWHUSUHWDUHXVDUHDQFKHD ILQLSUHYLVLRQDOLLQIRUPD]LRQLTXDQWLWDWLYHFKHVHPSUHSLGHYRQRHVVHUHDFTXLVLWHGDOFLWWDGLQRPRGHUQR 9DDQFKHHVSOLFLWDWRFKHOHFRPSHWHQ]HLQGLYLGXDWHHVXOOHTXDOLFHUFKHUHPRGLFDOLEUDUHLQRVWUL FRPSLWLHVSHUWLQRQVRQRIXQ]LRQDOLVRODPHQWHDOUDJJLXQJLPHQWRGHOODSDGURQDQ]D (VSULPHUH DGHJXDWDPHQWHLQIRUPD]LRQLµPDFRQWULEXLVFRQRDQFKHD 3URJHWWDUHHFRVWUXLUHPRGHOOLGLVLWXD]LRQL UHDOLµH 2SHUDUHVFHOWHLQFRQGL]LRQLGLLQFHUWH]]Dµ /DQRVWUDSURSRVWDqULYROWDDVWXGHQWLGHOSULPRRVHFRQGRDQQRGLXQDTXDOVLDVLVFXRODVHFRQGDULDGRWDWD GLODERUDWRULRGLLQIRUPDWLFD/HFRPSHWHQ]HFKHJOLVWXGHQWLGRYUHEEHURDYHUDFTXLVLWRDOODVFXROHPHGLH SHUPHWWRQRGLDIIURQWDUHLOWHPDWUDWWDWRDQFKHDOO LQL]LRGHOO DQQRVFRODVWLFRDQFKHVHDEELDPRLQGLFDWR FRPHSUHIHUHQ]LDOHODFROORFD]LRQHGHOPRGXORGRSRODWUDWWD]LRQHGLSDUWHGHOQXFOHR1XPHULH$OJRULWPL

8 3$'521$1=$GHVFULYHUHIHQRPHQLFROOHWWLYLLOPHWRGRG LQGDJLQHVWDWLVWLFD Riprendiamo ancora le parole dell UMI: Qualunque sia il problema conoscitivo che riguarda un fenomeno collettivo e qualunque sia il motivo da cui tale problema ha origine, per giungere alla sua soluzione è necessario definire ciò che si intende studiare, pianificare la raccolta dell informazione, raccogliere i dati, rappresentarli, analizzarli ed interpretarli. 3HUFRUVRGLGDWWLFR &(5,/(9$=,21(3,$1,),&$7$','$7, &(5$335(6(17$=,21('(,'$7,7$%8/$7,0(',$17(',9(56,7,3, ',*5$),&2 &(35,1&,3$/,,1',&,',326,=,21((',63(56,21( LQJUDVVHWWRVRQRHYLGHQ]LDWLL&RPSLWL(VSHUWLGDQRLSURJHWWDWL &203,72(63(57215,/(9$=,21(3,$1,),&$7$','$7, 'RSRXQDVWLPRODQWHHOXQJDGLVFXVVLRQHDEELDPRGHFLVRFKHDOODOXFHGHOODQRVWUD PD[LµSDGURQDQ]DGL ULIHULPHQWR HVSULPHUHDGHJXDWDPHQWHLQIRUPD]LRQLSHUFRPXQLFDUHµqLQGLVSHQVDELOHWUDWWDUHLQFODVVH ODTXHVWLRQHFKHVWD DPRQWHµGLXQDVWDWLVWLFDRYYHUR FKLIDOHGRPDQGHDFKLOHIDTXDOLGRPDQGHSRQHLQ FKHPRGRSHUVDSHUHFRVD«µ( HYLGHQWHFKHLOFRQWHVWRqH[WUDPDWHPDWLFRHSRWUHEEHFRLQYROJHUHDOWUH GLVFLSOLQH 1HOO LSRWHVL SHJJLRUH GL QRQ ULXVFLUH D FROODERUDUH FRQ DOWUL GRFHQWL GHO &RQVLJOLR GL &ODVVH DEELDPRFHUFDWRGLFDSLUHFRPHSRWUHPPRJHVWLUHODVLWXD]LRQH,OULVXOWDWRGHLQRVWULVIRU]LQRWHYROLqLO VHJXHQWHODYRURLQFXLVL JLRFDµPROWLVVLPRQHOOHDUHHGLLQWHUVH]LRQHGHO02'(//2,/9%XRQDOHWWXUD 1RGLGHOODWUDPDFRQFHWWXDOHIHQRPHQRVWDWLVWLFRFROOHWWLYRVWDWLVWLFRSRSROD]LRQHXQLWjVWDWLVWLFD FDUDWWHULTXDOLWDWLYLTXDQWLWDWLYLGLVFUHWLHFRQWLQXLVWUXWWXUDGLXQDWDEHOODGLGDWL 'DOOHFRPSHWHQ]HDOODSDGURQDQ]D ¾ 5LFRQRVFHUHSUREOHPLFKHVLDIIURQWDQRFRQULOHYD]LRQLVWDWLVWLFKH ¾ 6WDELOLUHTXDOLHFKHWLSRGLLQIRUPD]LRQLGDWLJUH]]LVLGHYRQRUDFFRJOLHUHSHUXQ LQGDJLQH VWDWLVWLFD ¾ &RVWUXLUHHGLVFXWHUHTXHVWLRQDULSHULQGDJLQLVWDWLVWLFKHLQSDUWLFRODUH SUHGLVSRUUHODVWUXWWXUD GHOODPDWULFHGHLGDWLJUH]]LULVSHWWRDGXQDULOHYD]LRQHSLDQLILFDWDGLGDWL80,µ ¾ 5LOHYDUHLGDWLVWUXPHQWLHPRGDOLWjRUJDQL]]DWLYH ¾ SDVVDUHGDLGDWLJUH]]LDOOHGLVWULEX]LRQLVWDWLVWLFKHGLIUHTXHQ]DSXQWRDSSURIRQGLWRQHO&(FRQ H[FHO

9 62*/,$',3$'521$1=$$77(6$ /RVWXGHQWHqFRQVDSHYROHGLDOFXQLDVSHWWLSUREOHPDWLFLOHJDWLDOODFRQRVFHQ]DGLIHQRPHQL FROOHWWLYLHVDDWWLYDUVLSHUXQDUDFFROWDSLDQLILFDWDGLGDWL,GHDJXLGD/ LQVHJQDQWHLQYLWDJOLVWXGHQWLD FRPLQFLDUHµXQDVWDWLVWLFDFKHSHUPHWWDGLGHVFULYHUHODORUR FODVVHHFRQWHPSRUDQHDPHQWHGLUDFFRJOLHUHLQIRUPD]LRQLVXXQ DOWUDFODVVHHGLHVWHQGHUHODULFHUFDD WXWWDODVFXRODLQPRGRGDDYHUHPROWLGDWLGDWUDWWDUHH«DUULYDUHDOODSDUWHGLODERUDWRULRGHO&(/ LGHD qtxhoodglidyruluhodsduwhflsd]lrqhdwwlydghludjd]]lfrqo RELHWWLYRGLLQWURGXUUHRULYLVLWDUHDOFXQLQRGL FRQFHWWXDOLHYLWDQGRODFODVVLFDOH]LRQHIURQWDOH,QSDUWLFRODUHO LQVHJQDQWHFHUFKHUjGLIDUULIOHWWHUHJOL VWXGHQWLVXDOFXQHSUREOHPDWLFKHIRQGDPHQWDOLULJXDUGDQWLLOPHWRGRGLLQGDJLQHVWDWLVWLFDTXDOLLOJUDGRGL LQIHUHQ]DGHOO LQWHUYLVWDWRUHODFRVWUX]LRQHGLXQTXHVWLRQDULRHODVXDYDOLGLWjORVSRJOLR«*HVWLRQHJUXSSRFODVVHDEELDPRULWHQXWRFKHTXHVWR&(VLSUHVWLDGHVVHUHVYROWRLQJUDQSDUWHFRQ /$925,',*58332,JUXSSLVDUDQQRGLDOXQQLDFRPSRVL]LRQHOLEHUD,1)250$=,21(&KHFRVDVDL" ADWWLYLWjEUDLQVWRUPLQJFRQLQSXW VWDWLVWLFDµFRQORVFRSRGLDWWLYDUHLVDSHULQDWXUDOLGHJOLVWXGHQWL HOHORURFRQRVFHQ]HSUHJUHVVHVXOO DUJRPHQWR /DVXFFHVVLYDGLVFXVVLRQHVXTXDQWRHPHUVRGRYUHEEHFRQGXUUHJOLVWXGHQWLDULFRQRVFHUHFKH ƒ SHU GHVFULYHUHIHQRPHQLVRFLDOL VRQRXWLOL LQIRUPD]LRQL VWDWLVWLFKHµVLSUHVXPHFKH JOL VWXGHQWL DEELDPR WLUDWR IXRULµ O,67$7L FHQVLPHQWL SHULRGLFL LQGDJLQL VWDWLVWLFKH DOOH TXDOL KDQQR SDUWHFLSDWR FRPH LQWHUYLVWDWL«,Q FDVR FRQWUDULR O LQVHJQDQWH ULFKLDPD O DWWHQ]LRQH VX TXHVWL DVSHWWLFRQGRPDQGH &KHFRV qo,67$7"6dshwhgluplfrv qxqfhqvlphqwr"4xdoqodsluhfhqwh VWDWLVWLFDFKHKDLLQFRQWUDWR"«ƒ SHUIDUHGHOOHVFHOWHSROLWLFKHHFRQRPLFKH«qLPSRUWDQWHGLVSRUUHGL VWDWLVWLFKHµFLVLDVSHWWD FKH JOLVWXGHQWL DEELDPRSDUODWRGHJOL H[LWSROO GHLVRQGDJJLG RSLQLRQH«,Q FDVRFRQWUDULR O LQVHJQDQWH PDQWHUUj OD GLVFXVVLRQH VX SUREOHPL SL VSHFLILFL *OL LVFULWWL LQ TXHVWD VFXROD GLPLQXLVFRQRGLDQQRLQDQQR&RPHVLSRWUHEEHFHUFDUHGLFDSLUHOHFDXVHGLTXHVWRFDOR"µ2SSXUH *OLLQVFULWWLLQTXHVWDVFXRODDXPHQWDQRGLDQQRLQDQQR&RPHVLSRWUHEEHIDUHSHUSUHYHGHUHLO QXPHURGLDXOHQHFHVVDULHIUDWUHDQQL"µDQFRUD,PPDJLQDWHGLHVVHUHGHLSURGXWWRULGLVFRJUDILFL FRVDULWHQHWHFKHVLDXWLOHFRQRVFHUHSHUGHFLGHUHTXDOHGLVFRLQFLGHUH"µ«SHUFRQIURQWDUHVLWXD]LRQLqQHFHVVDULRGLVSRUUHGLGDWLTXDQWLWDWLYLFRQIURQWDELOL ƒ OH VWDWLVWLFKHµSRVVRQRHVVHUHLQWHUSUHWDWHHRXVDWHLQPRGRVFRUUHWWRHWHQGHQ]LRVR6HTXHVWR SXQWR QRQ q XVFLWR FRQ LO EUDLQVWRUPLQJ O LQVHJQDQWH VROOHFLWD /H VWDWLVWLFKH GLFRQR FKH q SL IUHTXHQWDWDODVSLDJJLDURPDJQRODULVSHWWRDTXHOODFDODEUD'XQTXHODFRVWDDGULDWLFDqSLEHOODµ 2WWR GHQWLVWL VX FRQVLJOLDQRLO GHQWLIULFLR 3LSSR 'XQTXH3LSSR q LO PLJOLRU GHQWLIULFLR LQ FRPPHUFLRµ 'DXQ LQFKLHVWDULVXOWDFKHJOLLQFLGHQWLDHUHLVRQRLQDXPHQWR'XQTXHqSLVLFXUR YLDJJLDUHFRQO DXWRµ«ADWWLYLWjODYRURGLJUXSSR SCHEDA PER L ATTIVITA DI GRUPPO (Sk_1),PPDJLQDWHGLYROHUFRQRVFHUHQHOVXRLQVLHPHXQDFODVVHGLFRHWDQHLGLXQ DOWUDVFXROD HRFLWWjHGLYROHUIDUORURFRQRVFHUHODYRVWUDFODVVH

10 4XDOL DVSHWWL ULWHQHWH LPSRUWDQWL IDU FRQRVFHUH H FRQRVFHUH" 'LVFXWHWH L VHJXHQWL FDUDWWHULSRWHWHWRJOLHUQHPRGLILFDUQHVSHFLILFDUQHDJJLXQJHUQHTXDOFXQRDUJRPHQWDWH EUHYHPHQWHOHYRVWUHVFHOWH ¾ VHVVR ¾ HWj ¾ VWDWXUD ¾ SHVR ¾ FRORUHGHLFDSHOOL ¾ FRPSRVL]LRQHGHLQXFOHLIDPLOLDUL ¾ VXGGLYLVLRQHGHOWHPSRGLXQDJLRUQDWDWLSR ¾ DWWLYLWjVSRUWLYH ¾ DWWLYLWjULFUHDWLYH ¾ PDWHULHSUHIHULWH ¾ FLELHEHYDQGHSUHIHULWH ¾ DQLPDOLGRPHVWLFL ¾ JXVWLPXVLFDOL ¾ JXVWLWHOHYLVLYL ¾ JXVWLFLQHPDWRJUDILFL ¾ OHWWXUHSUHIHULWH ¾ DOWUR«&RPPHQWRO LQVHJQDQWHYROXWDPHQWHLQVHULVFHYRFLGHWWDJOLDWHHVFRORUHGHLFDSHOOLHYRFLJHQHULFKHHV VXGGLYLVLRQH GHO WHPSR JXVWL PXVLFDOL SHU LQGXUUH JOL VWXGHQWL DG DSSURIRQGLUH OD SUREOHPDWLFDVH OD TXHVWLRQHQRQHPHUJHLQTXHVWDIDVHFRPXQTXHJOLVWXGHQWLVDUDQQRFKLDPDWLDGDIIURQWDUODQHOODIDVHGL DSSOLFD]LRQHWUDQVIHU $OWHUPLQHGHOO DWWLYLWjO LQVHJQDQWH UDFFRUGDµOHVFHOWHGHLVLQJROLJUXSSLLQXQDVFKHGDWLSR CARATTERE *58332 *58332 *58332 *58332 * HVVR (Wj 6WDWXUD 3HVR &RORUHFDSHOOL

11 QXFOHLIDPLOLDUL 6XGGLYLVLRQHWHPSR $WWLYLWjVSRUWLYH $WWLYLWjULFUHDWLYH 0DWHULHSUHIHULWH &LELHEHYDQGHSUHIHULWH $QLPDOLGRPHVWLFL *XVWLWHOHYLVLYL *XVWLPXVLFDOL *XVWLFLQHPDWRJUDILFL /HWWXUHSUHIHULWH ««««««««««««««««««««««««««««««««««««««««««««««««««6L VHJQDQR FRQ FURFHWWH OH VFHOWH GHL JUXSSL DQQRWDQGR FRQWHVWXDOPHQWH OH PRGLILFKH SURSRVWH H OH HYHQWXDOLDJJLXQWH 3XQWLVXLTXDOLULFKLDPDUHO DWWHQ]LRQHGHJOLVWXGHQWL ¾ LQTXDOFKHPRGRKDQQRJLjIDWWRXQDVWDWLVWLFDFLVDUDQQRYRFLSLJHWWRQDWHGLDOWUHHVLSRWUjIDUH XQDFODVVLILFD ¾ q YHURVLPLOH DVSHWWDUVL FKH L JUXSSL DEELDQR HIIHWWXDWR OH ORUR VFHOWH LQ EDVH DOOH SUHIHUHQ]H SHUVRQDOLVHLQXQJUXSSRQRQFLVRQRFRPSRQHQWLFKHSUDWLFDQRVSRUWGLIILFLOPHQWHDYUjLQGLFDWR DWWLYLWj VSRUWLYHµ GRYH F q TXDOFKH VWXGHQWH REHVR QRQ FL VDUj OD YRFH SHVRµ 4XHVWH FRQVLGHUD]LRQLSRUWHUDQQRDGLVFXWHUHVXOJUDGRGLLQIHUHQ]DGHOO LQWHUYLVWDWRUH ¾ VLFHUFKHUjGLDUULYDUHDGXQDWDEHOODFRQGLYLVD/ LQVHJQDQWHDYUjFXUDGLIDUULHQWUDUHHVHPSLGL WXWWLLWLSLGLFDUDWWHUH 5DJD]]LWHQLDPRDQFKHODVWDWXUD6HULXVFLDPRDPHWWHUFLLQFRQWDWWRFRQ XQD VFXROD GHO 6XG VDUHEEH LQWHUHVVDQWH FRQIURQWDUH OH DOWH]]H 3RVVLDPR DQFKH FHUFDUH GDWL QD]LRQDOLLQPHULWRHYHGHUHGRYHYLFROORFDWH&KHQHGLWH",QIRUPD]LRQHTXHOORFKHGHYLVDSHUHAIDVHGLPDSSLQJ / LQVHJQDQWH ULFKLDPD FRQFHWWL FKH JOL VWXGHQWL GRYUHEEHUR DYHUH JLj DVVLPLODWR QHOOH VFXROD GL JUDGR LQIHULRUHULIHUHQGRVLDOODYRURSUHFHGHQWH D /DSRSROD]LRQHVWDWLVWLFDRFROOHWWLYRqO LQVLHPHGHJOLHOHPHQWLFKHYHQJRQRRVVHUYDWLSHUHIIHWWXDUH O LQGDJLQHODYRVWUDFODVVHODFODVVHGHOO DOWUDVFXROD E / XQLWjVWDWLVWLFDqO HOHPHQWRVLQJRORGHOODSRSROD]LRQHVWDWLVWLFDLOVLQJRORVWXGHQWH F,OFDUDWWHUHqXQDSURSULHWjFKHVLYXROHVWXGLDUHLQXQDSRSROD]LRQHVWDWLVWLFDDGHVHPSLRLO FRORUHGHL FDSHOOLµOD VWDWXUDµL JXVWLPXVLFDOLµ,FDUDWWHULSRVVRQRHVVHUH ¾ 4XDOLWDWLYLGLVROLWRHVSUHVVLLQIRUPDYHUEDOHDGHVHPSLRLO FRORUHGHLFDSHOOLµOH SUHIHUHQ]H PXVLFDOLµ«&LDVFXQFDUDWWHUHSXzSUHVHQWDUVLFRQGLYHUVHPRGDOLWjDGHVHPSLRLO FRORUHGHLFDSHOOL

12 SXzHVVHUH ELRQGLµ FDVWDQLµ QHULµ UDPDWLµ«LOFDUDWWHUH VHVVRµVLSUHVHQWDFRQPRGDOLWj PDVFKLRµ IHPPLQDµOH SUHIHUHQ]HPXVLFDOLµSRVVRQRSUHVHQWDUVLFRQOHPRGDOLWj FODVVLFDµ MD]]µ OHJJHUDµ URFNµTXLJOLDOXQQLGHWWDJOLHUDQQRPHJOLR ¾ 4XDQWLWDWLYLHVSUHVVLGDQXPHULOHPRGDOLWjVRQRLQTXHVWRFDVRLYDORULQXPHULFLGHOFDUDWWHUH6L VXGGLYLGRQRLQ ƒ GLVFUHWLHVSUHVVLGDQXPHULFKHDSSDUWHQJRQRDGXQLQVLHPHILQLWR HWjµ QXPHURGL FRPSRQHQWLLOQXFOHRIDPLOLDUHµ«PRGDOLWjDQQL«FRPSRQHQWLOD IDPLJOLD ƒ FRQWLQXLHVSUHVVLGDQXPHULFKHYDULDQRVXXQLQWHUYDOORFRQWLQXRGLYDORULDGHVHPSLROD VWDWXUDLOSHVR $SSOLFD]LRQHTXHOORFKHGHYLIDUH ODYRURGLJUXSSR SCHEDA PER L ATTIVITA DI GRUPPO (Sk_2) (VHUFL]LR$SDUWLUHGDOOD7$%(//$&21',9,6$FHUFDWHGLLQGLYLGXDUHSHURJQLFDUDWWHUHOHSRVVLELOL PRGDOLWj 3UREDELOPHQWH YLDFFRUJHUHWH FKH q SL FRPRGR HVSOLFLWDUH GLYHUVDPHQWH DOFXQL FDUDWWHUL $G HVHPSLRLQYHFHGL FLELHEHYDQGHSUHIHULWHµFRQYLHQHVFHJOLHUHGXHFDUDWWHULGLVWLQWL FLELSUHIHULWLµH EHYDQGHSUHIHULWHµLQIDWWLVHLQGLYLGXDWHQPRGDOLWjSHULFLELHPPRGDOLWjSHUOHEHYDQGHGRYHWHLQVHULUH Q[PPRGDOLWjSHUFLELHEHYDQGH6SLHJDWHSHUFKp (VHUFL]LR 6FHJOLHWHSHU RJQLFDUDWWHUH OH PRGDOLWj FKH ULWHQHWH SL VLJQLILFDWLYH DUJRPHQWDQGR EUHYHPHQWHODYRVWUDVFHOWDWHQHWHSUHVHQWHFKHVLHWHLQWHUHVVDWLDOODYRVWUDFODVVHHDGXQDFODVVHGL FRHWDQHLRGHOODYRVWUDVFXROD Discussione e sintesi dell attività precedente (ricostruzione) A questo punto l insegnante focalizza l attenzione degli studenti su alcuni caratteri: sesso, età, statura, materie preferite,letture preferite, gusti musicali, attività sportive [in realtà, qui sarebbe preferibile lasciar scegliere agli studenti, ma per chiarire la nostra idea (a chi legge), fissiamo noi le categorie]. Viene chiesto ai singoli gruppi di illustrare le loro scelte. Si discutono (anche qui alcuni gruppi avranno ignorato qualche modalità ritenuta significativa da altri; riguardo alle materie preferite sarà interessante vedere se gli studenti avranno tenuto in considerazione la possibilità che ci siano materie diverse nell altra scuola ). Scopo dell attività è arrivare ad una scelta condivisa (ma l obiettivo formativo rimane quello di essere consapevoli del grado d interferenza dell intervistatore). Informazione: quello che devi sapere (2^ fase di mapping) / LQVHJQDQWHULFRUGDDOODFODVVHFKHORVWUXPHQWRSLGLIIXVRSHUOHLQGDJLQLVWDWLVWLFKHqLOTXHVWLRQDULR$ WLWRORG HVHPSLRVLGHVFULYHUDSLGDPHQWHLQFRVDFRQVLVWHO,QGDJLQHVWDWLVWLFDPXOWLVFRSLRVXOOHIDPLJOLH FRQGRWWDGDOO,67$7VLFKLHGHFRPHVLVYROJHXQFHQVLPHQWRSUREDELOPHQWHJOLVWXGHQWLULFRUGHUDQQRO HQRUPHIDVFLFRORGLVWULEXLWRDFLDVFXQDIDPLJOLDUHFHQWHPHQWH«

13 / DWWHQ]LRQHYLHQHIRFDOL]]DWDLQSDUWLFRODUHVXOODQHFHVVLWjGLSRUUHGRPDQGHVHPSOLFLFKLDUHHSUHFLVHLQ PRGRGDHYLWDUHFKHXQDGRPDQGDSRVVDHVVHUHLQWHUSUHWDWDLQPRGLGLYHUVLRULVXOWLQRQFRPSOHWDQHOODVXD IRUPXOD]LRQHSHUHVHPSLRXQFDUDWWHUHVHPSOLFHFRPHO HWjSXzHVVHUHVRQGDWRLQPROWLPRGL TXDQWLDQQL KDL"µ q XQD GRPDQGD SRFR SUHFLVD SHUFKp QRQ VSHFLILFD VH JOL DQQL VRQR TXHOOL FRPSLXWL R TXHOOL FKH VL FRPSLUDQQRQHOO DQQRLQFRUVRqSUHIHULELOHTXLQGLFKLHGHUHJOLDQQLJLjFRPSLXWLRDQFRUDPHJOLRODGDWDGL QDVFLWDLQPRGRFKHLGDWLVLDQRXWLOL]]DELOLFRQUDSLGLWjDQFKHLQIXWXUR,QROWUHqSUHIHULELOHFKHOHGRPDQGHVLDQRDULVSRVWDFKLXVDLQPRGRFKHOHDOWHUQDWLYHGLULVSRVWDVLDQR SUHYLVWHLQDQWLFLSRLOODYRURSUHOLPLQDUHGRYUHEEHHVVHUHDQGDWRLQTXHVWDGLUH]LRQH,QTXHVWRPRGRJOL LQWHUYLVWDWLSRVVRQRULVSRQGHUHYHORFHPHQWHHJOLLQWHUYLVWDWRULSRVVRQRJHVWLUHSLDJHYROPHQWHOHULVSRVWH 6LGLVFXWHDQFKHGHOO LPSRUWDQ]DGHOO DQRQLPDWRGHOOHSHUVRQHLQWHUYLVWDWH 6L ID SUHVHQWH FKH DQFKH OH PRGDOLWj GHL FDUDWWHUL TXDOLWDWLYL SRVVRQR HVVHUH WUDGRWWHLQQXPHULµ DG HVHPSLR 3RSROD]LRQHVWDWLVWLFDODFODVVH XQLWjVWDWLVWLFKHLOVLQJRORDOXQQR,QGDJLQH *UDGLPHQWRGHOPRGXORGLVWDWLVWLFDLQFRUVRµ 9 TXHVLWR 5LWLHQLLQWHUHVVDQWHTXHVWRDUJRPHQWR"µ PROWR DEEDVWDQ]D SRFR SHUQLHQWH ODYRURGLJUXSSR $SSOLFD]LRQH48(//2&+('(9,)$5( SCHEDA PER L ATTIVITA DI GRUPPO (Sk_3) Sulla scorta del lavoro finora svolto e delle informazioni ricevute, provate a costruire un questionario da somministrare agli studenti di questa scuola, per raccogliere informazioni su: materie preferite, gusti musicali, attività sportive,letture preferite. Discussione e sintesi dell attività precedente (ricostruzione) 6LGLVFXWRQRLFRQWULEXWLGHLVLQJROLJUXSSLHVLDUULYDDGXQTXHVWLRQDULRFRQGLYLVRFRVuDUWLFRODWR VH]LRQHGRYHVLFKLHGHVHVVRGDWDGLQDVFLWDHVWDWXUDLQFPGHOO LQWHUYLVWDWR VH]LRQHTXHVLWLVXOOHPDWHULHSUHIHULWH VH]LRQHTXHVLWLVXLJXVWLPXVLFDOL VH]LRQHTXHVLWLVXOOHDWWLYLWjVSRUWLYH ¾ VH]LRQHOHWWXUHSUHIHULWH $TXHVWRSXQWRLOTXHVWLRQDULRYLHQHVRPPLQLVWUDWRDGXQ DOWUDFODVVHGHOODVFXRODFRQO RELHWWLYRGLYDOXWDUH O HIILFDFLD GHO TXHVWLRQDULR R PHWWHUQH LQ OXFH SXQWL GHEROL, TXHVWLRQDUL FRPSLODWL YHQJRQR QXPHUDWL SURJUHVVLYDPHQWHULSRUWDQGRORVWHVVRQXPHURVXFLDVFXQDVH]LRQH6LVXGGLYLGHLOPDWHULDOHULVSHWWRDOOH VH]LRQL 7UDQVIHUHVHLQYHFH«SURYDDQFKHWX &RPSLWRSHUFDVDLQGLYLGXDOH&LVRQRPROWLPHWRGLGLYHUVLGDOTXHVWLRQDULRSHUUDFFRJOLHUHGDWLFKH YHQJRQRSRLULHODERUDWLVWDWLVWLFDPHQWHLQWHUYLVWDGLUHWWDLQWHUYLVWDWHOHIRQLFDTXHVWLRQDULRQ OLQH«3HURJQXQDGHOOHWLSRORJLHFLWDWH SURYDDGLQGLYLGXDUHVLWXD]LRQLRWWLPDOLSHUO XVR 9 SURYDDGLQGLYLGXDUHLSXQWLGHEROL

14 ODYRURGLJUXSSR$RJQLJUXSSRYLHQHFRQVHJQDWDXQDVH]LRQHRSDUWHGLVH]LRQH SCHEDA PER L ATTIVITA DI GRUPPO (Sk_4) 5HODWLYDPHQWHDOODVH]LRQHRSDUWHGLVH]LRQHDVVHJQDWDDOYRVWURJUXSSRSURYDWHDYHGHUHVHLO TXHVWLRQDULRqYDOLGR6LJQLILFDVRSUDWWXWWRFDSLUH VHOHULVSRVWHFKLXVHFKHDYHWHDQWLFLSDWRVRQRHVDXULHQWL 9 RVHWURYDWHVSHVVRFRQWUDVVHJQDWDODYRFH DOWURµ 2) Nel secondo caso, si potrebbe pensare che nel questionario non siano state incluse voci importanti. Proponete le modifiche che ritenete più opportune L attività precedente non dovrebbe richiedere molto tempo visto l intenso lavoro preliminare che ha portato alla costruzione del questionario, anche se l emergere di qualche difficoltà è auspicabile ai fini formativi. Discussione e sintesi dell attività precedente (ricostruzione) I singoli gruppi espongono il proprio lavoro e si arriva alla versione definitiva del questionario. Il questionario viene somministrato a tutti gli studenti della scuola (e i dati raccolti, data la loro numerosità verranno rielaborati durante o dopo i successivi compiti esperti) In questo momento riteniamo opportuno proseguire con la prima elaborazione dei dati riguardanti la nostra classe. Abbiamo deciso di ridurre al minimo la fase di mapping (daremo informazioni solo se richieste dai gruppi) e lasciamo ampio campo di manovra agli studenti. Questa scelta è dettata dalla considerazione che nel successivo CE gli studenti lavoreranno intensamente sulle rappresentazioni grafiche e partiranno dalla rappresentazione tabellare delle distribuzioni statistiche di frequenza e quindi aumenteranno comunque il loro grado di consapevolezza a riguardo. Ancora transfer (e se invece adesso prova tu) (In realtà se hanno già lavorato alla medie sulla statistica, questa è un attività che riguarda il cosa sai ) Lavoro di gruppo: si distribuisce ad ogni gruppo una delle sezioni dei questionari compilati (dovrebbero essere tante quante i gruppi) che sono state preventivamente numerate e la seguente scheda: 6&+('$3(5/ $77,9,7$ ',*583326NB 2VVHUYDWHODVHJXHQWHWDEHOODSURGRWWDGDYRVWULFRHWDQHL Studenti delle classi prime dell ITIS Silvio De Pretto Per tempo abituale di percorrenza casa-scuola 7HPSRGLSHUFRUUHQ]DPLQ N studenti ILQRD GDD GDD GDD ROWUHL 7RWDOH NB in rosso è indicato il collettivo statistico in esame; in blu il carattere secondo il quale si sta effettuando lo studio del collettivo stesso. Cercate di arrivare ad un risultato simile con i materiali in vostro possesso. Suggerimento: Per ogni quesito della sezione del questionario in esame, costruite prima una tabella del tipo:

15 N questionario carattere dove inserite sulla seconda colonna le modalità contrassegnate nel questionario corrispondente. Oppure ispiratevi alla seguente tabella: Studenti delle classi prime dell ITIS Silvio De Pretto Prospetto di spoglio: carattere colore dei capelli Colore naturale capelli spoglio N studenti Castani 32 Neri 30 Biondi 24 rossi 4 Totale: 90 Alla fine dell attività esporrete metodologia seguita, difficoltà incontrate e risultati ai vostri compagni. Fine CE1 &203,72(63(572 5$335(6(17$=,21('(,'$7,7$%8/$7,0(',$17(',9(56,7,3,',*5$),&2,QWURGX]LRQH /RVYROJLPHQWRGLTXHVWRFRPSLWRHVSHUWRDOO LQWHUQRGLXQRRSLPRGXOLGLVWDWLVWLFDqLQGLVSHQVDELOHVHVL YXROHFKHXQRVWXGHQWHLQWHUSUHWLHSURGXFDUDSSUHVHQWD]LRQLJUDILFKHGLGDWLVWDWLVWLFL /D VRJOLD GL SDGURQDQ]D DWWHVD q SURSULR TXHVWD UHQGHUH OD SHUVRQD OR VWXGHQWH GHO ELHQQLR FRQVDSHYROHGHOO LPSRUWDQ]DGLXQDUDSSUHVHQWD]LRQHJUDILFDGHLGDWLDYHQGRFDSLWRFKHXQEXRQJUDILFR SHUPHWWHGLFRPXQLFDUHLQIRUPD]LRQLFRQLPPHGLDWH]]DHFKLDUH]]DPHJOLRGLTXDQWRSXzIDUHXQD TXDOVLDVLWDEHOODSXUFKpVLDVFHOWRLQPRGRRSSRUWXQRULVSHWWRDOODQDWXUDGHLGDWL 1RGLGHOODWUDPD FRQFHWWXDOH UDSSUHVHQWD]LRQHJUDILFDGL XQ LQIRUPD]LRQHFODVVLILFD]LRQHGHL GDWL UDFFROWLFRUULVSRQGHQ]DWUDGDWLHJUDILFLDJJUHJD]LRQHGHLGDWLXVRGLXQSURJUDPPDFRPSXWHUL]]DWRSHU ODFRVWUX]LRQHGLJUDILFL 'DOOHFRPSHWHQ]HDOODSDGURQDQ]D Riconoscere l importanza della rappresentazione grafica di dati statistici 6DSHUUDSSUHVHQWDUHGHLGDWLLQXQJUDILFRELGLPHQVLRQDOH

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µLQIDWWLOHIDVLGHO FRPSLWR HVSHUWR DVVXPRQR VLJQLILFDWR SURSULR SHUFKp VRQR FHQWUDWH VXO SDUWLFRODUH VRWWRFRPSLWR FKH WUDWWDQR,OPDSSLQJDGHVHPSLRVYLOXSSDSULQFLSDOPHQWHLSXQWLHORVWXGHQWHFRQVROLGDLYHFFKLFRQFHWWLHSDVVD JUDGXDOPHQWHDTXHOOLQXRYLF qo DFTXLVL]LRQHGLQXRYHFRQRVFHQ]H 'XUDQWH OD IDVH GL WUDQVIHU FL VL SXzLQYHFH FRQFHQWUDUH PDJJLRUPHQWH VXL SXQWL H FKH ULVXOWDQR SDUWLFRODUPHQWHDSSURSULDWLLQ XQ FRQWHVWR QHO TXDOH OR VWXGHQWH VL PHWWHDOODSURYD HG HODERUDOH LQIRUPD]LRQLFKHGRYUHEEHDYHUDFTXLVLWRILQRDTXHOPRPHQWRFUHDQGRQXRYHFRQRVFHQ]H,QILQH OH IDVL LQ FXL HPHUJRQR L VDSHUL QDWXUDOLH O XOWLPDIDVH GL JHQHUDOL]]D]LRQH VRQRSL JOREDOLµ SXQWDQRDGXQDSULPDHGXOWLPDYLVLRQHJHQHUDOHGHOSUREOHPDHFRLQYROJRQRWXWWLLFRPSLWLHVSHUWL $57,&2/$=,21('(//()$6,HGHL&203,7,(63(57, &( 5$335(6(17$=,21( '(, '$7, 7$%8/$7, 0(',$17( ',9(56, 7,3,',*5$),&2 6L SXz VXGGLYLGHUH LQ

17 35,0$)$6(6$3(5,1$785$/,&KHFRVDVDL",O FRQFHWWR GL UDSSUHVHQWD]LRQH JUDILFDµ YDLQWURGRWWR JUDGXDOPHQWH TXDVL GLYHQLVVHQDWXUDOH YROHU YLVXDOL]]DUHLGDWLWDEXODWLLQXQ DOWUDIRUPD3HUWDQWRQHOODIDVHLQFXLGHYRQRHPHUJHUHLVDSHULQDWXUDOL SDUWLDPRPRVWUDQGRGLYHUVLWLSLGLWDEHOOHFKHVLULIHULVFRQRDYDULFRQWHVWLDQFKHH[WUDPDWHPDWLFLFRPH O HGXFD]LRQHFLYLFDRODJHRJUDILDODILVLFD 'DOO DQDOLVL GL YDULH WDEHOOH DWWUDYHUVR GRPDQGH GHO WLSR PDVHFRQGR YRLQRQVDUHEEH EHOOR SRWHU UDSSUHVHQWDUHLGDWLGLYHUVDPHQWH"µHPRVWUDQGRTXDOFKHHVHPSLRVHPSOLFHGLJUDILFRVL LQWURGXFHµLQWDQWR LOFRQFHWWR 3HUWDQWRDGRJQLWDEHOODVLDIILDQFKHUjXQJUDILFRFKHUHQGHSLVHPSOLFHUDSSUHVHQWDUHLGDWL,O FRQFHWWR FKH ELVRJQDLQWURGXUUH q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jH VXOODFRVWUX]LRQHGHOODWDEHOODFRQOHVHJXHQWLGRPDQGH

18 /DWDEHOODqFRPSOHWD" &RVDVLJQLILFDQRLGDWL",GDWLVRQRGLUHWWDPHQWHRVVHUYDWLRGHULYDQRGDXQ HODERUD]LRQH" 3RWHYDQRHVVHUHHVSUHVVLLQDOWURPRGR" 4XDOqLOVLJQLILFDWRGHOYDORUHSHUFHQWXDOH" 6DSHQGRLOQXPHURWRWDOHGLSDUODPHQWDULFRPHIDUHVWHDULFDYDUHJOLDSSDUWHQHQWLDGRJQL SDUWLWR" 9RLFRPHIDUHVWHDUDSSUHVHQWDUHLGDWLFRQXQ GLVHJQRµ" 'RSRGLFKpVLPRVWUDQRORURLJUDILFLVHJXHQWLHOLVLFRPPHQWDQRDVVLHPH *UDILFL&DPHUD &RPSRVL]LRQHGHLJUXSSLSDUODPHQWDUL *UDILFR *UDILFR

19 &KHGLIIHUHQ]HQRWDWH" 6RQRO HVSUHVVLRQHGHJOLVWHVVLGDWL" 4XDOLLQIRUPD]LRQLVLSRVVRQRULFDYDUH" 6HFRQGRYRLTXDOqLOPRGRPLJOLRUHGLYLVXDOL]]DUHLGDWL" 6LSRWHYDQRUDSSUHVHQWDUHGLYHUVDPHQWHLGDWL" &RV qlqglfdwrvxoo DVVHGHOOH[" (VXTXHOORGHOOH\" &KHGLIIHUHQ]HQRWDWHFRQLJUDILFLSUHFHQGHQWL" (VHLGDWLIRVVHURVWDWLUDJJUXSSDWLGLYHUVDPHQWHFRVDVDUHEEHDFFDGXWR" /DWDEHOODqFRPSOHWD" 7DEHOOHFRQGDWLGLWLSRTXDOLWDWLYR $UHDJHRJUDILFD 0LVXUDGHOOD6XSHUILFLH LQPLOLRQLGL.PT $IULFD $PHULFDGHO1RUG $PHULFDGHO6XG $VLD (XURSD 2FHDQLD ([8QLRQH6RYLHWLFD 7DEHOOD 4XHVWRWLSRGLWDEHOOHVRQRIDPLOLDULDJOLVWXGHQWLSHUFKpOHLQFRQWUDQRVSHVVRQHLOLEULGLVWRULDHJHRJUDILD 4XLODGLVFXVVLRQHSXzFHQWUDUVLVXOIDWWRFKHXQDUDSSUHVHQWD]LRQHJUDILFDDGHJXDWDSHUPHWWHGLFRJOLHUH DFROSRG RFFKLRµOHGLIIHUHQ]HWUDOHGLPHQVLRQLGHLFRQWLQHQWL 6LSXzTXLQGLDQLPDUHXQDGLVFXVVLRQHFRQGRPDQGHGHOWLSR &RPHIDUHVWHDUDSSUHVHQWDUHFRQXQGLVHJQRTXHOORFKHqGHVFULWWRQHOODWDEHOOD" (LQXQGLDJUDPPDFDUWHVLDQR" 6DUHEEHURG DLXWROHUDSSUHVHQWD]LRQLJUDILFKHXVDWHQHJOLHVHPSLSUHFHGHQWL" &KHWLSLGLGDWLVRQRUDSSUHVHQWDWLQHOODWDEHOOD",QILQHVLSXzPRVWUDUHLOJUDILFRHFRPPHQWDUORFRQJOLVWXGHQWL

20 Grafico delle superfici di alcune aree geografiche superficie in milioni di kmq Africa America del America del Nord Sud Asia Europa Oceania Ex Unione Sovietica aree geografiche *UDILFR &RVDYLHQHLQGLFDWRVXJOLDVVL",OJUDILFRFLGDWXWWHOHLQIRUPD]LRQLGLFXLDEELDPRELVRJQRHFKHVRQRVFULWWHLQWDEHOOD",OJUDILFRqGLLPPHGLDWDFRPSUHQVLRQH" 4XDOqLOYDQWDJJLRLQTXHVWRFDVRGLXQDUDSSUHVHQWD]LRQHJUDILFD" &KHFRVDUDSSUHVHQWDQRJOLDVVLGLULIHULPHQWR",YDORULUDSSUHVHQWDWLVRQRDVVROXWLRSHUFHQWXDOL" 6DSUHVWHFRJOLHUHGHOOHDQDORJLHFRQLOWLSRGLGDWLFKHDEELDPRUDSSUHVHQWDWRHLOWLSRGLJUDILFR XWLOL]]DWR" (WUDTXHVWRJUDILFRHLOSUHFHGHQWH" 7DEHOODFRQGDWLUDFFROWLLQFODVVLGLIUHTXHQ]H Si può sfruttare a questo punto il lavoro di gruppo. Gli studenti vengono suddivisi in gruppi di 5 persone e viene consegnata loro una bilancia per pesarsi (sensibilità 0,2 Kg). A turno i componenti del gruppo si devono pesare e costruire una tabella che riassuma i dati raccolti, poi devono provare a costruire un grafico. Poi l insegnante controlla il lavoro che è stato fatto e riassume alla lavagna i dati raccolti, ad esempio come segue: 3HVR 1XPHURVWXGHQWL >> >> >> >> 7DEHOOD A questo punto come potrebbero essere rappresentati i dati? Che differenze ci sono tra la tabella fatta alla lavagna e quella che hanno fatto gli studenti?

21 Che tipo di dati abbiamo rappresentato? C è una relazione con i dati visti fino ad ora? Come descriveresti questo grafico, con tutte le sue caratteristiche? Istogramma della distribuzione di pesi di 30 studenti numero studenti [45-50[ [51-56[ [56-60[ [61-66[ peso studenti *UDILFR / LQVHJQDQWHSRWUHEEHDQDOL]]DUHXQRDOODYROWDLJUDILFLSURGRWWLGDLVLQJROLJUXSSLHFRPPHQWDUH IDFHQGRHPHUJHUHOHGLIIHUHQ]HOHDQDORJLHHLSUHJLGLRJQXQR 7DEHOODGDWLGLWLSRTXDQWLWDWLYRGLVFUHWR,QTXHVWRFDVRVLSXzDGHVHPSLRIDUIDUHXQDSLFFRODVWDWLVWLFDDJOLVWXGHQWLYHORFHPHQWHLQFODVVH FKHGRYUDQQRSHUFRQWRORURRUJDQL]]DUHLGDWLUDFFROWLLQXQDWDEHOOD'HYRQRHIIHWWXDUHXQ LQGDJLQHVXO QXPHURGLOLEULQRQVFRODVWLFLOHWWLGDDOXQQLLQXQDFODVVHLQXQDQQR,ULVXOWDWLFKHULFDYHUDQQR SRWUHEEHURHVVHUHDGHVHPSLRLVHJXHQWL QOLEULOHWWLLQXQDQQR QVWXGHQWL 7DEHOOD &RPHQHLFDVLSUHFHGHQWLVLJXLGDXQDGLVFXVVLRQHLQDXODFKHSXQWDDOO DQDOLVLFULWLFDGHOODWDEHOOD &RPHIDUHVWHDUDSSUHVHQWDUHFRQXQGLVHJQRTXHOORFKHqGHVFULWWRQHOODWDEHOOD"

22 (LQXQGLDJUDPPDFDUWHVLDQR" 6DUHEEHURG DLXWROHUDSSUHVHQWD]LRQLJUDILFKHXVDWHQHJOLHVHPSLSUHFHGHQWL" &KHWLSRGLGDWLVRQRUDSSUHVHQWDWLQHOODWDEHOOD" 6LPRVWUDLQILQHLOJUDILFRVHJXHQWH QVWXGHQWL /LEULOHWWLLQXQDQQRGDLUDJD]]LGLXQDFODVVH QOLEUL *UDILFR 6LFRPPHQWDDVVLHPHDJOLDOXQQL 4XDOLVRQRLGDWLUDSSUHVHQWDWL" 4XDOLVRQRLGDWLUDSSUHVHQWDWLVXOO DVVHGHOOH[HGHOOH\" &RQLOJUDILFRFKHLQIRUPD]LRQLVLSRVVRQRULFDYDUH" (JXDJOLDQROHLQIRUPD]LRQLHVSUHVVHGDOODWDEHOOD" 4XDOqVHFRQGRYRLLOYDQWDJJLRGLTXHVWRJUDILFR" $YUHPPRSRWXWRXVDUHXQRGHLJUDILFLJLjYLVWLSULPD" 1HOJUDILFRVRQRSUHVHQWLLQIRUPD]LRQLLQXWLOL" 6LSRVVRQRHOLPLQDUH",QILQHOHVWHVVHGRPDQGHVLSRVVRQRSRUUHPRVWUDQGRDJOLVWXGHQWLORVWHVVRJUDILFRFRQLGDWLSHUzXQLWLWUD ORURGDXQDOLQHDVSH]]DWD

23 QVWXGHQWL /LEULOHWWLLQXQDQQRGDLUDJD]]LGLXQDFODVVH QOLEUL *UDILFR &KHGLIIHUHQ]HQRWDWHWUDLJUDILFL" 4XDO qlovljqlilfdwrghoodvsh]]dwdfkhfroohjdlgdwl" 4XDOqVHFRQGRYRLLOPRGRPLJOLRUHSHUUDSSUHVHQWDUHTXHVWLGDWL" 7DEHOODFRQIURQWRWUDVHULH 3UHVHQWLDPRLQILQHDJOLDOOLHYLXQ XOWLPDWDEHOODFKHVSHVVRVLLQFRQWUDQHOOHVWDWLVWLFKHXIILFLDOL $QQR 7HOHYLVLRQH 5DGLR 7DEHOOD E necessario invitare gli studenti a rappresentare i dati, anche alla luce dei grafici visti fino ad ora, sottolineando il fatto che anche in questo caso il grafico consente di visualizzare meglio il significato della statistica. Le domande da porre agli studenti potrebbero essere allora: &RV qlqglfdwrlqwdehood"

24 &KHWLSLGLGDWLVRQR" &RPHIDUHVWHDUDSSUHVHQWDUHLGDWL" &KHLQIRUPD]LRQLVLYRJOLRQRWUDVPHWWHUH" 4XDOLWUDLJUDILFLYLVWLILQRDGRUDYLVHPEUDQRSLDSSURSULDWL" &RPHGHVFULYHUHVWHLGDWLUDSSUHVHQWDWLVXJOLDVVL"/DVFDODqDSSURSULDWD" 2VVHUYDWHLOJUDILFRTXLVRWWRULSRUWDWRHIDWHXQHOHQFRGHOOHVXHFDUDWWHULVWLFKH $QGDPHQWRGHOQXPHURGLDEERQDWLDOODUDGLRHDOODWHOHYLVLRQHLQ,WDOLDGDODO 7HOHYLVLRQH 5DGLR QGLDEERQDWL DQQR *UDILFR 6(&21'$)$6(0$33,1*'HYLVDSHUHFKH In questa fase l insegnante introduce in modo rigoroso i tipi di grafico associando ai tipi di dati la rappresentazione grafica più opportuna. Dividiamo la lezione in due fasi distinte: 1. Analisi ragionata della rappresentazione grafica. Si mostrano agli studenti 4 diversi tipi di grafico, facendo loro notare che ad ogni tipo di

25 dati si può associare una rappresentazione grafica ottimale, che consenta cioè una lettura efficiente ed oggettiva del fenomeno studiato. 2. Analisi di una tabella riassuntiva che colleghi dati-grafici. Caratteristiche fondamentali di un grafico 2.1 Prima fase del mapping Si considera assieme agli studenti un grafico alla volta Diagramma circolare. Si spiega che è stata svolta una statistica (fonte ISTAT) e si mostra il seguente grafico. %DPELQLGDLDLDQQLSHUWHPSRJLRUQDOLHURGLHVSRVL]LRQHDOOD WHOHYLVLRQH 20,60% 4,10% 15,30% 3,80% 4,70% 5,50% PHQRGLRUD GDRUDDRUH GDDRUH GDDRUH 28,90% QRQYHGHOD WHOHYLVLRQH QRQVR QRQLQGLFDWR Si tratta di un diagramma a torta, che risulta particolarmente indicato per rappresentare una distribuzione secondo un carattere qualitativo con poche modalità. In questo caso il carattere è tempo trascorso davanti alla televisione (e gli studenti dovrebbero saperlo). Il diagramma a torta è un cerchio suddiviso in settori circolari, con angoli al centro di ampiezza proporzionale alla frequenza di ciascuna modalità. Per agevolare la lettura di tale diagramma si usano solitamente colori diversi per i vari settori.

26 Il diagramma circolare è utile per rappresentare i caratteri che non possono essere ordinati e permette un agevole lettura e un confronto immediato dei dati. Per disegnare il diagramma circolare della figura bisogna trovare l ampiezza degli angoli dei settori circolari corrispondenti alle frequenze nel modo seguente: Riferendoci alla frequenza del 20,6%, consideriamo l angolo al centro di una circonferenza; impostiamo quindi la seguente proporzione: 100:360 = 20,6:α da cui α = 74,16 ο Si procede in modo analogo per ricavare le ampiezze degli altri settori circolari. Si riprende infine l esempio considerato nella prima fase (tabella 2.1, grafico 2.1), e si notano le analogie e le differenze con gli studenti. Si fa allora notare che sono in entrambi i casi, dati espressi in percentuale, che si distribuiscono secondo un carattere qualitativo discreto. Sul grafico bisogna inoltre sempre indicare, con una legenda i colori dei vari settori, e accanto ad ogni settore il valore percentuale Diagramma a barre. Si mostra agli studenti il grafico 2.3 utilizzato in fase iniziale. Dalla discussione dovrebbe essere emerso che il grafico consente di mettere in relazione un area geografica con la sua dimensione. Anche in questo caso il carattere è qualitativo. Il grafico in esame si chiama diagramma a barre, costituito da rettangoli verticali o orizzontali aventi tutte le basi di ugual

27 misura (arbitraria), che poggiano sull asse verticale o orizzontale e altezze proporzionali ai dati statistici. Questo tipo di rappresentazione grafica viene usata frequentemente quando le modalità del carattere sono gli anni (qui si può riprendere l esempio visto in fase iniziale, rappresentato nel grafico 2.7) oppure le aree geografiche Istogramma Si considera nuovamente il grafico 2.4. Dalla discussione dovrebbe essere emerso che, i dati vengono raccolti in classi. Il tipo di grafico particolarmente indicato per rappresentare questi dati è l istogramma. La particolarità del grafico è che la base del rettangolo rappresenta l ampiezza delle classi che si stanno rappresentando, mentre l area è proporzionale alla frequenza della classe. Nell esempio considerato nella prima fase (grafico 2.4), la base era sempre uguale, perché avevamo scelto intervalli di 5 Kg. Può accadere che si abbia a che fare con classi di dati di ampiezza diversa, nel qual caso è necessario uniformare i dati prima di procedere con la costruzione dell istogramma. Consideriamo a tal proposito il seguente esempio generico: si hanno delle classi e delle frequenze.

28 Si vede analizzando la prima tabella che i rettangoli che si ottengono con un eventuale istogramma non sono confrontabili perché hanno una base diversa. Quello che bisogna fare è, per ciascuna classe, tenere ferma l ampiezza come base del rettangolo e prendere come altezza, non la frequenza, ma il rapporto fra la frequenza e l ampiezza della classe: tale rapporto prende il nome di densità di frequenza. Questo significa uniformare i dati e in questo modo l area del rettangolo continua ad essere proporzionale alla frequenza della classe. E importante che questo fatto venga sottolineato, perché poi verrà ripreso in fase di transfer e generalizzazione Diagramma cartesiano

29 Si tratta del tipo più importante di rappresentazione grafica. Gli alunni conoscono bene, anche dalle scuole medie questo tripodi grafici, i più usati in matematica. L attenzione qui va posta, pertanto sulle unità di misura: gli assi cartesiani contengono diversi tipi di dati, e può anche variare l unità di misura. Si può riprendere quindi come esempio quello già considerato in fase iniziale (grafici 2.5, 2.6) facendo notare che il tipo di dati rappresentato è quantitativo e discreto. Molto spesso i punti rappresentati sul piano cartesiano vengono uniti tra loro da una spezzata, per offrire al colpo d occhio una visione grafica dell andamento del fenomeno (grafico 2.7). 3.2 Seconda fase del mapping Lo schema che abbiamo, pertanto, scelto di seguire è il seguente: 7LSRGLGDWL 'LVWULEX]LRQHVHFRQGRXQFDUDWWHUH TXDOLWDWLYRSRFKHPRGDOLWj 'LVWULEX]LRQHVHFRQGRXQFDUDWWHUH TXDOLWDWLYRPROWHPRGDOLWj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

30 7LWROR /HJHQGD,QGLFD]LRQHGHOOHXQLWjGLPLVXUDVXJOLDVVLSULQFLSDOLRGHOOHSHUFHQWXDOLVXOOHSRU]LRQLGLWRUWD 6LSRVVRQRSHUWDQWRULYHGHUHDVVLHPHDJOLVWXGHQWLWXWWLLJUDILFLLQFRQWUDWLVLQRDGRUDHFODVVLILFDUOLLQ EDVHDOODWDEHOOD 7(5=$)$6($33/,&$=,21((75$16)(54XHOFKHGHYLIDUH(VHLQYHFH«SURYDDQFKH WX A questo punto gli studenti vengono messi alla prova, per testare se hanno capito ciò che è stato fatto in aula. Le competenze che ci si aspetta che abbiano acquisito sono: Saper costruire un grafico a partire da una tabella Saper leggere ed interpretare un grafico Capire, da un grafico, il significato di una statistica In questa sezione presentiamo pertanto degli esercizi sia applicativi, sia di generalizzazione, che riguardano la conoscenza dei vari tipi di grafico e di collegamento con quanto acquisito durante il loro percorso in statistica (faccio riferimento al primo compito esperto). Rimandiamo al paragrafo 4 gli esercizi da svolgere in laboratorio di matematica. Verranno allora consegnate innanzi tutto delle schede di lavoro (per ogni tipo di dati/grafico, quindi 4 in totale) di questo tipo:

31 $QDOL]]DWHODVHJXHQWHWDEHOOD 7LSRGLEHVWLDPH %RYLQL 6XLQL 2YLQL &DSULQLHGHTXLQL 'LFKHWLSRGLGDWLVLWUDWWD" Sk_1 1 QGLFDSL 4XDOqLOJUDILFRSLRSSRUWXQRSHUUDSSUHVHQWDUHTXHVWLGDWL"VHJXLORVFKHPDFKHWLqVWDWR FRQVHJQDWR &RVWUXLVFLLOJUDILFRTXLVRWWR &RQFKHFULWHULRKDLVFHOWRODVFDOD" 'DLXQDWXDLQWHUSUHWD]LRQHGHLGDWLUDSSUHVHQWDWL 5LSRUWLDPRVRORXQDGHOOHVFKHGHGDFRQVHJQDUH/DQRVWUDLGHDqGLSUHVHQWDUHVFKHGHXJXDOLLQFXLYDULDQRLOWLSRGLGDWLHTXLQGLGL JUDILFR

32 6NB Analizzate il seguente grafico: 6HQDWR &RPSRVL]LRQHGHLJUXSSLSDUODPHQWDUL 4XDOHPHWRGRGLUDSSUHVHQWD]LRQHJUDILFDqVWDWRXWLOL]]DWR" &RVDYLHQHUDSSUHVHQWDWR" 3URYDDFRVWUXLUHXQDWDEHOODFKHUDSSUHVHQWLLGDWLWUDVIRUPDSRLLGDWLLQSHUFHQWXDOH 6LSRWHYDXWLOL]]DUHXQDOWURJUDILFR"4XDOH" &RVDYLHQHLQGLFDWRVXJOLDVVL" +DLXQ LGHDGLTXDOHSRWUHEEHHVVHUHODIRQWHGDOODTXDOHVRQRVWDWLWUDWWLLGDWL" 'DLXQDWXDLQWHUSUHWD]LRQHGLTXHOORFKHYLHQHUDSSUHVHQWDWR 2 $QFKHLQTXHVWRFDVRYHQJRQRFRQVHJQDWHVFKHGHFKHIDQQRULIHULPHQWRDWXWWLLGDWLJUDILFLVWXGLDWLXWLOL]]DQGRVWDWLVWLFKHGD LQWHUQHWRJLRUQDOL

33 &RPSLODQGROHVFKHGHVLFKLHGHDJOLVWXGHQWLVLDGLDSSOLFDUHFLzFKHKDQQRYLVWRLQFODVVHHVWXGLDWRDFDVD VLDGLHVSULPHUHXQDYDOXWD]LRQHSHUVRQDOHVXFLzFKHLOJUDILFRUDSSUHVHQWD $TXHVWRSXQWRVLSRWUHEEHFKLHGHUHORURGLFRVWUXLUHGD]HURWDEHOODHJUDILFRGDQGRGHOOHLQGLFD]LRQL HVHUFL]LGLWUDQVIHUHULFRVWUX]LRQH (VHUFL]LR/HWHUUHHPHUVHGHOQRVWURSLDQHWDKDQQRFRPSOHVVLYDPHQWHXQDVXSHUILFLHGL PLOLRQL GL.P H VRQR FRVu GLVWULEXLWH VXSHUILFLLPSURGXWWLYH PLOLRQLGL.P GHVHUWL FDORWWHJODFLDOLDUHHXUEDQH«ERVFKLHIRUHVWHPLOLRQLGL.P SDVFROLPLOLRQLGL.P VXROLFROWLYDWLPLOLRQLGL.P 5DSSUHVHQWDLGDWLFRQLOJUDILFRFKHWLVHPEUDSLRSSRUWXQRJLXVWLILFDQGRODWXDVFHOWD (VHUFL]LR'DWHOHVHJXHQWLGLVWULEX]LRQLGLWHPSHUDWXUHPHGLHPDVVLPHH(VHUFL]LR/HWHUUH HPHUVHGHOQRVWURSLDQHWDKDQQRFRPSOHVVLYDPHQWHXQDVXSHUILFLHGLPLOLRQLGL.P HVRQR FRVu GLVWULEXLWH VXSHUILFL LPSURGXWWLYH PLOLRQL GL.P GHVHUWL FDORWWH JODFLDOL DUHH XUEDQH«ERVFKLHIRUHVWHPLOLRQLGL.P SDVFROLPLOLRQLGL.P VXROLFROWLYDWL PLOLRQLGL.P 5DSSUHVHQWDLGDWLFRQLOJUDILFRFKHWLVHPEUDSLRSSRUWXQRJLXVWLILFDQGRODWXDVFHOWD (VHUFL]LR'DWHOHVHJXHQWLGLVWULEX]LRQLGLWHPSHUDWXUHPHGLHPDVVLPHHPLQLPHLQ*HQQDLRLQ DOFXQHORFDOLWjUDSSUHVHQWDFRQLOJUDILFRSLRSSRUWXQRODVLWXD]LRQHJLXVWLILFDQGROHWXHVFHOWH 6DSUHVWLGDUHXQ LQWHUSUHWD]LRQHGHOO DQGDPHQWRGHOIHQRPHQR" &LWWj 0DVVLPD 0LQLPD )LUHQ]H 5RPD 1DSROL %DUL 3HVFDUD 7RULQR 0LODQR (VHUFL]LR6XSSRQLGLGRYHUSUHVHQWDUHOHVHJXHQWLLQIRUPD]LRQL,OLPLWLGLYHORFLWjLQFLWWjHVXVWUDGDLQ$XVWULDVRQRH.PKLQ%HOJLRH.PKLQ %XOJDULD H.PK LQ'DQLPDUFD H.PKLQ)LQODQGLD H.PKLQ*UDQ %UHWDJQDH.PKLQ1RUYHJLDH.PKLQ6YH]LDH.PK 4XDOHPRGRVFHJOLSHUUDSSUHVHQWDUOH"3HUFKp" 'DLODWXDUDSSUHVHQWD]LRQH

34 (VHUFL]LR/HJJLLOJUDILFRHULFDYDWXWWHOHLQIRUPD]LRQLFKHSXRL6WDELOLVFLWUDOHDOWUHFRVH TXDQWHSHUVRQHVRQRDQGDWHDVSHWWDFROLWHDWUDOLJLXVWLILFDQGRODULVSRVWD 3DUWHFLSD]LRQHDVSHWWDFROLHDLQL]LDWLYHFXOWXUDOL $QQRSHUSHUVRQHGLDQQLHSL teatro cinema musei, mostre concerti classici altri concerti discoteche spettacoli sportivi (VHUFL]LR,OJUDILFRFKHVHJXHqVWDWRULFDYDWRGDIRQWH,67$7RVVHUYDORHULVSRQGL SHUTXDOLFRUVLGLODXUHDVLUHJLVWUDLOPDJJLRUQXPHURGLLPPDWULFROD]LRQL" 4XDOqODSRSROD]LRQHVWDWLVWLFD",OFDUDWWHUHSUHVRLQFRQVLGHUD]LRQHGDOJUDILFRqGLWLSRTXDOLWDWLYRRTXDQWLWDWLYR 6LSXzVWDELOLUHLOQXPHURGLLPPDWULFRODWLQHOO DQQRDFFDGHPLFR $WXRSDUHUHLOJUDILFRqFRPSOHWR"&RVDDJJLXQJHUHVWLRFDPELUHVWLSHUUHQGHUORSL FKLDUR" 6,2,PPDWULFRODWLSHUJUXSSRGLFRUVLGLODXUHD$$ FRPSRVL]LRQHSHUFHQWXDOH 3,4 4,4 5 3,1 6,6 3 2,7 10,2 2,3 1,7 10,6 15,5 11,3 14 Giuridico Economico-statistico Ingegneria Polico-sociale Letterario Insegnamento Linguistico geo-biologico psicologico Chimico-farmaceutico Architettura Medico Scientifico Agrario Ed. Fisica

35 /$%25$725,2',0$7(0$7,&$/$925$5(&21(;&(/ 0$33,1* 2UV GXQTXH GRSR OD WHRULD SDVVLDPR DOOD SUDWLFD YHGLDPR FLRq FRPH VLD SRVVLELOH WUDVIRUPDUH L GDWL UDFFROWLGXUDQWHOHQRVWUHLQGDJLQLLQTXDOFRVDGLUDSLGDPHQWHFRPSUHQVLELOHHXWLOL]]DELOH /RVWUXPHQWRFKHXWLOL]]HUHPRSHUTXHVWDIDVHGHOODYRURq([FHOPDSRWUHEEHIXQ]LRQDUHEHQHDQFKHXQ DOWURIRJOLRGLFDOFRORFRPHSHUHVHPSLR2SHQ2IILFHRUJ&DOF 6LLSRWL]]DFKHLUDJD]]LFRQRVFDQRJLjOHIXQ]LRQDOLWjGLEDVHGHOO DSSOLFD]LRQHVDOYDUHLILOHVFULYHUHQHOOH FDVHOOHIRUPXOHHOHPHQWDULULIHULPHQWLDVVROXWLHUHODWLYL«TXLQGLVLGDUDQQRSHUVFRQWDWHTXHVWHFRVH /DSULPDFRVDGDIDUHqIDULQVHULUHLGDWLUDFFROWLGXUDQWHO LQGDJLQHLQXQIRJOLRGLODYRURLQSDUWLFRODUHLQ XQDWDEHOODDFRORQQHLQFXLQHOODSULPDVRQRLQVHULWLLQRPLRPHJOLRGHLQXPHULLGHQWLILFDWLYLSHUJDUDQWLUH O DQRQLPDWRGLFKLKDULVSRVWRDLQRVWULTXHVLWLVFULWWLVHJXHQGRLOVHPSOLFHRUGLQHFURQRORJLFRGLLQWHUYLVWD HQHOODVHFRQGDODULVSRVWDDOTXHVLWRVWHVVR,OULVXOWDWRVDUjXQDWDEHOODPROWROXQJDGLGLIILFLOHVHQRQTXDVLLPSRVVLELOHFRQVXOWD]LRQHQHOFDVRLOQXPHUR GHJOLLQWHUYLVWDWLGLYHQWLSDUWLFRODUPHQWHJUDQGH &RPHIDUH SHU UHQGHUH L GDWL SL OHJJLELOL" 8Q SULPR PRGR SRWUHEEHHVVHUH WHQWDUH GL GDUQH XQD UDSSUHVHQWD]LRQHJUDILFDSHUHVHPSLRFRQXQJUDILFRDGLVSHUVLRQHVHQ]DQHVVXQWUDWWDPHQWRSUHOLPLQDUH GHLGDWLUDFFROWL,OULVXOWDWRqLOJUDILFRVHJXHQWH

36 &RPHVLSXzQRWDUHLOULVXOWDWRQRQqPROWRFRQYLQFHQWHLQTXDQWRVRQRVuUDSSUHVHQWDWLWXWWLLGDWLUDFFROWL PDQRQqSRVVLELOHLQGLYLGXDUHQXOODGLLQWHUHVVDQWHGDWRFKHSLFKHDOWURVLYHGHXQD QXYRODµGLSXQWLVSDUVL XQSR RYXQTXH 3URYDQGRDFDPELDUHLOWLSRGLJUDILFRSHUHVHPSLRXWLOL]]DQGRXQJUDILFRDEDUUHLOULVXOWDWRQRQqPROWRSL FKLDUR DQFKHLQTXHVWRFDVRLOULVXOWDWRqXQDPPDVVRGLJUDWWDFLHOLGLVRUGLQDWLFKHDOPDVVLPRFRQXQSLFFROR VIRU]RSHUPHWWHGLDYHUHXQDYDJDLGHDVHVRQRSUHSRQGHUDQWLTXHOOLDOWLRTXHOOLEDVVLPDVHQ]DDOFXQD VFLHQWLILFLWjµSHUTXHVWDLGHD ËQHFHVVDULRTXLQGLSUHQGHUHFRVFLHQ]DGHOIDWWRFKHUDSSUHVHQWDUHLULVXOWDWLGLXQDVWDWLVWLFDQRQqQp LPPHGLDWRQpEDQDOHPDFKHqQHFHVVDULRDQDOL]]DUHLYDULWLSLGLJUDILFRLQPRGRGDWURYDUHLOSLDGDWWRH VRSUDWWXWWRSUHSDUDUHLGDWLJUH]]LUDFFROWLLQXQIRUPDWRWDOHGDHVVHUHHIILFDFHPHQWHULSRUWDWLLQXQ JUDILFR ( PHJOLRSHQVDUHXQSR DFRVDYRJOLDPRYHGHUHHDFRPHVLVWHPDUHLGDWLSULPDGLGLVHJQDUHXQJUDILFR«

37 &5($5(81*5$),&2 $EELDPRFDSLWRFKHLJUDILFLQRQVRQRWXWWLHJXDOPHQWHHIILFDFLPDFLDVFXQRqSDUWLFRODUPHQWHDGDWWRD UDSSUHVHQWDUHDOFXQLWLSLGLGDWLPD««FRPHVLIDDFRVWUXLUHXQRGLTXHVWLJUDILFLFRQ([FHO""" 1RQqGLIILFLOHHDQ]LOR VL GRYUHEEHIRUVH JLj VDSHUH GDO FRUVRGLLQIRUPDWLFD PD ORULSUHQGLDPRSHU VLFXUH]]D,QQDQ]LWXWWR q QHFHVVDULR SRVL]LRQDUVLVXO GRFXPHQWR LQFXL VRQR SUHVHQWL L GDWL FRQ FXL VL YXROH FRVWUXLUH LO JUDILFR HYLGHQ]LDUH OH FDVHOOH FKH OL FRQWHQJRQR H SUHPHUH LO ERWWRQH FUHD]LRQH JXLGDWD JUDILFRµQHOODEDUUDLQDOWR&RPSDUHDTXHVWRSXQWRXQDILQHVWUDGLGLDORJRLQFXLSUHPHQGRULSHWXWDPHQWHLO ERWWRQH DYDQWLµqSRVVLELOHFRQILJXUDUHHSHUVRQDOL]]DUHLOJUDILFR ODSULPDFRVDGDIDUHqVFHJOLHUHLO WLSR GL YLVXDOL]]D]LRQH FKH FL LQWHUHVVD YHGUHPR QHOOD IDVH VXFFHVVLYDLYDULWLSLGLJUDILFRSHU RUDFLDFFRQWHQWLDPRGLDFFHWWDUHLO WLSR FKH SURSRQH LO SURJUDPPD DXWRPDWLFDPHQWH LVWRJUDPPD D EDUUH

38 ,OVHFRQGRSDVVDJJLRVLGLYLGHLQ IDVL QHOOD SULPD OLQJXHWWD LQWHUYDOOR GDWLµ VL SRVVRQR HYHQWXDOPHQWH FRUUHJJHUH OH FRRUGLQDWH GHOOH FDVHOOH GD FXL ULFDYDUHOHLQIRUPD]LRQLQHOQRVWUR FDVRGDOIRJOLRGHOILOHFRUUHQWHL GDWLWUDODFDVHOOD $µhodfdvhood $µ«

39 «PHQWUHQHOODVHFRQGDIDVHVHULH qsrvvlelohvshflilfduhshufldvfxqd VHULH GLGDWLQHO FDVR YROHVVLPR UHQGHUHFRQXQXQLFRJUDILFRPROWH LQIRUPD]LRQL UHODWLYH DOOR VWHVVR FDPSLRQHVWDWLVWLFRVLDOHFDVHOOLQH LQFXLULFDYDUHLGDWLFRPHSULPD VLD O HWLFKHWWD GHOO DVVH GHOOH FDWHJRULH ; 4XHVWH HWLFKHWWH QRQ VRQR FKH TXHOOR FKH YRJOLDPR YLVXDOL]]DUH OXQJR O DVVH GHOOH [ QHOO HVHPSLRTXLDILDQFRLQRPLGHL PHVL H VRQR FRQWHQXWH QHOOH FDVHOOLQHFRPSUHVHWUDOD %µhod %µ /D WHU]D IDVH SHUPHWWH GL LPSRVWDUH QHOOH YDULH OLQJXHWWH WXWWH OH DOWUH LPSRVWD]LRQL GHO JUDILFRFRPHSHUHVHPSLRLOWLWROR TXDQWH WDFFKH YRJOLDPR QHJOL DVVL VH YRJOLDPR OD OHJHQGD R QR VH YRJOLDPR FKH SHU RJQL GDWR VLD YLVLELOHXQDWDUJKHWWDFRQLOYDORUH HDPHQLWjGHOJHQHUH«

40 ,QILQHSRVVLDPRGHFLGHUHGRYH LQVHULUH LO JUDILFR FLRq VH SRVL]LRQDUORQHOORVWHVVRILOHLQ FXL VRQR SUHVHQWL L GDWL GL SDUWHQ]D FRPH RJJHWWR LQ )RJOLRµ RSSXUH VH FUHDUHXQ IRJOLR D SDUWH SHU XQD YLVXDOL]]D]LRQHSLRUGLQDWD 'RSRWXWWRTXHVWRODYRURLOULVXOWDWRqLOJUDILFRGHVLGHUDWRHYYLYD $QFKHGRSRDYHUFUHDWRLOJUDILFRqFRPXQTXHSRVVLELOHPRGLILFDUQHWXWWHOHFRQILJXUD]LRQLEDVWDIDUHFOLFN FRQLOWDVWRGHVWURGHOPRXVHQHOODSDUWHGHOJUDILFRFKHVLLQWHQGHPRGLILFDUHJOLDVVLXQGDWRORVIRQGROD OHJHQGD«HVHOH]LRQDUHGDOPHQODYRFH IRUPDWR«µ$WWHQ]LRQHFKHODVHOH]LRQHQRQqVHPSUHIDFLOHH EDVWDIDUHFOLFNDSL[HOGLGLVWDQ]DSHUYHGHUVLFRPSDULUHGDYDQWLODILQHVWUDGLLPSRVWD]LRQHGLXQDFRVD FRPSOHWDPHQWHGLYHUVDGDTXHOODFKHLQWHUHVVDDQRL ËDQFKHSRVVLELOHFDPELDUHFRPSOHWDPHQWHWLSRGLJUDILFREDVWDIDUHFOLFNVXO JUDILFR HSRLVFHJOLHUHLOWLSRFKHYRJOLDPRGDOERWWRQH WLSRGLJUDILFRµQHOODEDUUDLQ DOWR

41 7HU]DIDVHLYDULWLSLGLJUDILFR 9LVWR FRPH FUHDUHXQ JUDILFR YHGLDPR RUD TXDQGR q FRQYHQLHQWH XWLOL]]DUH XQ WLSR GL UDSSUHVHQWD]LRQH SLXWWRVWRFKHXQDOWUR«*UDILFRDWRUWD 4XHVWRWLSRGLJUDILFRFRPHHYLGHQWHQRQq DGDWWR D UDSSUHVHQWDUH GDWL PROWR VSH]]HWWDWLPD VROR VWDWLVWLFKH LQ FXL VLDQR SUHVHQWLSRFKHLQIRUPD]LRQL,QROWUHGDWRFKH VL WUDWWD GL FHUFKL HTXLQGLqXQ SR GLIILFLOH WURYDUH O LQL]LR H ODILQH GHOOD FLUFRQIHUHQ]D QRQ q DGDWWR QHSSXUH SHU UDSSUHVHQWDUH VWDWLVWLFKH LQ FXL q LPSRUWDQWH PDQWHQHUH H HYLGHQ]LDUH O RUGLQH GHL GDWL TXLQGL OR XWLOL]]HUHPR VROR SHU VWDWLVWLFKH FRQSRFKL GDWLHWHQGHQ]LDOPHQWHGDWLGLWLSRTXDOLWDWLYR HQRQULJLGDPHQWHRUGLQDWR *UDILFRDEDUUH 120 ( OR VWHVVR GL SULPD PD RUD 100 VRWWROLQHLDPR LO IDWWRFKH DQFKH TXHVWR JUDILFR QRQ q 80 SDUWLFRODUPHQWH DGDWWR TXDQGR OD 60 VWDWLVWLFD FRLQYROJH JUDQGL QXPHUL QRQ VL ULHVFRQR TXDVL SL D 40 GLVWLQJXHUHOHEDUUHXQDGDOO DOWUD 20 DPHQRFKHTXHVWLGDWLQRQVLDQRLQ TXDOFKH PRGR RUGLQDWL $YHQGR 0 LQIDWWLXQDVVHRUL]]RQWDOHTXHVWR JUDILFRVLSUHVWDDQFKHPDQRQVRORDUDSSUHVHQWDUHGDWLRUGLQDWLHLQTXHVWRFDVRDQFKHVHOHEDUUH GLYHQWDQRPROWRVRWWLOLSHULOORURJUDQGHQXPHURVLULHVFHFRPXQTXHDGDYHUHXQ LGHDGHOULVXOWDWR1HO

42 QRVWURFDVRLOJUDILFRQRQq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«PDVRQRXWLOLVRORQHO FDVRVLD LPSRUWDQWH XWLOL]]DUH XQ DOWUD GLPHQVLRQHµ TXDQGR FLRq VLD QHFHVVDULR UDSSUHVHQWDUH QHOOR VWHVVR JUDILFRQRQXQDPDSLVHULHGL GDWL UHODWLYL DOOR VWHVVR FDPSLRQHPHWWHQGRPDJDULPDQRQQHFHVVDULDPHQWHLQHYLGHQ]DOHUHOD]LRQLWUDOHYDULHVHULHGLGDWL1HO QRVWURFDVRHLQWXWWLLFDVLVLPLODULDYHQGRXQ XQLFDVHULHGLGDWLO XQLFRPRWLYRSHUFXLVLSRVVRQRXVDUHL JUDILFL WULGLPHQVLRQDOL q GL FDUDWWHUH SXUDPHQWH HVWHWLFR H GL PDUNHWLQJ XQ JUDILFR WULGLPHQVLRQDOH ID FUHGHUHFKHYRLVDSSLDWHXVDUHLOFRPSXWHUPROWRPHJOLRHFKHODVWDWLVWLFDFKHVWDWHDQDOL]]DQGRVLDPROWR LPSRUWDQWH«S1

43 (6((/$%25,$02,'$7,',3$57(1=$"IDVHGLWUDQVIHU (FFREUDYLEHOODSURSRVWDqSURSULRTXLFKHYROHYDPRDUULYDUH,QIDWWLWUDYDVDUHVHQ]DSLHWjLGDWLUDFFROWLVXXQJUDILFRQRQqXWLOHVHSULPDTXHVWLGDWLQRQYHQJRQR VJUH]]DWLµXQSR 0DFRPHIDUOR"%HKVHLUDJD]]LKDQQRFDSLWRTXDOFRVDODSULPDSURSRVWDFKHGRYUHEEH VDOWDUIXRULGRYUHEEHHVVHUHXQDFRVDGHOWLSR HVHSURYLDPRDPHWWHUOLLQRUGLQH"µHVHLUDJD]]LQRQOD SURSRQJRQRVSRQWDQHDPHQWHqLOFDVRGLJXLGDUHODGLVFXVVLRQHLQPRGRFKHTXHVWDSURSRVWDVDOWLIXRUL 2UGLQDUHLGDWLLQH[FHOqPROWRVHPSOLFHEDVWDVHOH]LRQDUOLHSRLVHOH]LRQDUHGDPHQODYRFHGDWL!RUGLQD,O VLVWHPD DYYHUWLUj D TXHVWRSXQWR GL XQ SRVVLELOH SUREOHPD VH ULRUGLQLDPR VROR L GDWL VHOH]LRQDWL WLSLFDPHQWHWXWWLVXOODVWHVVDFRORQQDVHQ]D VSRVWDUHDQFKH WXWWH OH FDVHOOLQH DGLDFHQWL L QRVWUL GDWLSRWUHEEHUR YHQLUH IDOVDWLSHUHVHPSLRVHLQRJQLULJDDYHVVLPRLOQRPHGLFKLKD GDWRODULVSRVWDQHOODSULPDFRORQQDHODULVSRVWDQHOODVHFRQGD H ULRUGLQDVVLPR L GDWLLQ EDVH DOOD VHFRQGD FRORQQD VHQ]D WRFFDUHODSULPDFLWURYHUHPPRFKHOHULVSRVWHQRQVDUHEEHUR SLDFFRSSLDWHFRQODSHUVRQDJLXVWDËTXLQGLLOFDVRDSDUWH VLWXD]LRQLSDUWLFRODULGLDFFRJOLHUHLOVXJJHULPHQWRGHOVLVWHPDHVHOH]LRQDUH HVSDQGHUHODVHOH]LRQHµLQ PRGRGDPDQWHQHUHODFRUULVSRQGHQ]DWUDLQWHUYLVWDWRHULVSRVWD1HOFDVRLQFXLLQYHFHQRQVLDLPSRUWDQWH PDQWHQHUHTXHVWDFRUULVSRQGHQ]DSHUHVHPSLRSHUFKpLTXHVWLRQDULVRQRDQRQLPLHLQWHUHVVDVRORODULVSRVWD VHQ]DVDSHUHFKLO KDGDWDqSRVVLELOHVHOH]LRQDUHODYRFH FRQWLQXDUHFRQODVHOH]LRQHFRUUHQWHµ,OJUDILFRULVXOWDQWHFRQJOLVWHVVLGDWLGLSULPDVROWDQWRRUGLQDWLqLOVHJXHQWH

44 *LjVLLQL]LDQRDFDSLUHDOFXQHFRVHPDODUDSSUHVHQWD]LRQHWULGLPHQVLRQDOHQRQDLXWDDFDSLUHHVDWWDPHQWHL YDORULGHOJUDILFRLQRJQLSXQWRF qo HIIHWWRSURVSHWWLYDFKHLQJDQQDSURYLDPRTXLQGLDWUDVIRUPDUORLQXQ JUDILFRDGXHGLPHQVLRQL 0ROWRPHJOLR$GHVVRSHUHVHPSLRSRVVLDPRILQGDVXELWRFDSLUHSHUHVHPSLRFKHSLGHOO GHLGDWLq QHOODSDUWHPHGLREDVVDGHOODFODVVLILFDKDYDORULLQIHULRULDPHQWUHLOPDVVLPRqSRFRPHQRGLFRVD FKHFRQLGDWLQRQRUGLQDWLHUDLPSRVVLELOHGDLQWXLUH &HUWRFKHQRQVHPSUHTXHVWDHODERUD]LRQHqXWLOHVHSHUHVHPSLRLGDWLRULJLQDOLIRVVHURVWDWLOLQGLFHGHOOD ERUVDGL0LODQRQHOOHXOWLPHVHWWLPDQHVLFXUDPHQWHORDYUHLYROXWRYHGHUHRUGLQDWRSHUGDWDHTXLQGL FRQ L GDWL JUH]]L FRPH QHL SULPL JUDILFL H QRQLQ RUGLQH FUHVFHQWH GL YDORUH,QTXHVW XOWLPR PRGR QRQ ULXVFLUHLDVVROXWDPHQWH D LQWXLUH ODQGDPHQWR H OD WHQGHQ]D GHOOD ERUVD 4XLQGL RFFKLR L GDWL YDQQR ULHODERUDWLTXDQGRVHUYHSHUXQDLQWHUSUHWD]LRQHPLJOLRUHPDTXDQGRQRQVHUYHVLODVFLDQRVWDUH

45 &217,18,$02$(/$%25$5($**5(*+,$02 4XHVWR WLSR GL JUDILFR GDOWUD SDUWH QRQ q DQFRUD FKLDULVVLPR SHU TXDQWR ULJXDUGD DOFXQL DVSHWWL SHU HVHPSLR VH FL LQWHUHVVDVVH VDSHUH TXDOH q OD ]RQDµ GL YDORUL PDJJLRUPHQWH JHWWRQDWDµ GDL QRVWUL LQWHUYLVWDWL"%HKGDTXHVWRJUDILFRVLSXzIRUVHLQWXLUHPDQRQqFKLDULVVLPRTXLQGLELVRJQDULHODERUDUH XOWHULRUPHQWHLGDWLGLSDUWHQ]DLQSDUWLFRODUHSRWUHEEHHVVHUHXWLOHDJJUHJDUOLLQ FODVVLµJUXSSLGLYDORUL VLPLOLHSHUFLDVFXQDFODVVHYHGHUHTXDQWLYDORULQHIDQQRSDUWH 3HUIDUTXHVWRELVRJQDWRUQDUHDOGRFXPHQWRGLH[FHO ELFLFOHWWD DXWREXV SLHGL ELFLFOHWWD DXWREXV SLHGL ELFLFOHWWD ELFLFOHWWD SLHGL DXWREXV DXWREXV 3DUWLDPRSULPDFRQXQHVHPSLRSLVHPSOLFHXQDPLQLVWDWLVWLFDVXOPH]]RGLWUDVSRVWR XVDWRSHUYHQLUHDOH]LRQHGDLUDJD]]L8QDSLFFRODSDUWHGHOOHULVSRVWHqSUHVHQWDWD TXLDVLQLVWUDPDLGDWLVRQRPROWLGLSL'DXQDWDEHOOLQDGHOJHQHUHqGLIILFLOHIDUVL XQ LGHDSUHFLVDGHOODGLVWULEX]LRQHGHLPH]]LGLWUDVSRUWRPD([FHOIRUWXQDWDPHQWH PHWWHDGLVSRVL]LRQHXQDIXQ]LRQHFKHFLSXzYHQLUHLQDLXWRODIXQ]LRQH FRQWDVHµ FRVDIDTXHVWDIXQ]LRQH"%HKVLVSD]]RODXQDFHUWD]RQDGHOPLRIRJOLRGLH[FHOH FRQWDTXDQWHFDVHOOLQHFRUULVSRQGRQRDFHUWLFULWHULGDWLSHUHVHPSLRTXDQWHFDVHOOLQH FRQWHQJRQR SLHGLµRSSXUHTXDQWHFRQWHQJRQRXQQXPHURPDJJLRUHGLRFRVHGHO JHQHUH«&RPHVLXVDTXHVWDIXQ]LRQH"&RPHOHDOWUHIXQ]LRQL6LVHOH]LRQDHSRLVLVHJXRQROHLVWUX]LRQL 4XLQGLODSULPDFRVDGDIDUHqFUHDUHLQXQSXQWROLEHURGHOODWDEHOODO HOHQFRGHLSRVVLELOLPRGLGLDQGDUHD VFXRODVDUDQQRLQRVWULFULWHULGLVFHOWDTXLQGLLQWUHFDVHOOLQHXQDVRWWRO DOWUDSHUHVHPSLR**H* VFULYHUHPR DXWREXVµ SLHGLµH ELFLFOHWWDµ 8QDYROWDLPSRVWDWLLQRVWULFULWHULFLSRVL]LRQHUHPRDGHVWUDGHOODFDVHOOLQD DXWREXVµTXLQGLQHOODFDVHOOLQD + H SUHPHQGRLO ERWWRQH LQFROOD IXQ]LRQHµ QHOOD EDUUD LQDOWR DQGUHPR D FHUFDUH OD IXQ]LRQH FRQWDVHµQHOODFDWHJRULDGHOOHIXQ]LRQLVWDWLVWLFKH &RPSDULUjODVHJXHQWHILQHVWUDGLGLDORJRGDFRPSLODUH

46 1HOODSULPDFDVHOOLQD LQWHUYDOORµELVRJQDLQVHULUHGRYHVRQRLGDWLVXFXLIDUHODULFHUFDTXLQGLQHOQRVWUR FDVRODFRORQQDGRYHVRQRHOHQFDWHOHYDULHULVSRVWHGLRJQLLQWHUYLVWDWRGLFLDPRODFRORQQD%GDOODULJDDOOD ULJD 4XL VFULYHUHPR %%µshulqglfduh GLFHUFDUH LQTXHOO LQWHUYDOORULFRUGDUVL GL LQVHULUHLO VLPERORGHOGROODUR$OWULPHQWLFRSLDQGRODIRUPXODQHOOHFDVHOOLQHVRWWRVWDQWLO LQWHUYDOORGLYHQWHUHEEHYLD YLD %%µ %%µ«1hoodvhfrqgdfdvhoolqdlqyhfhelvrjqdlqvhuluhgluhwwdphqwhlofulwhulrglvhoh]lrqhrphjolrodfdvhoolqd GRYH TXHVWR FULWHULR q VSHFLILFDWR QHO QRVWURFDVR VSHFLILFKLDPR OD FDVHOOLQD GRYH q LPSRVWDWR LO SULPR FULWHULR DXWREXVµ TXLQGL VFULYHUHPR *µ $OOD ILQH SUHPLDPR RNµ,O ULVXOWDWR VDUj XQ QXPHUR QHOOD FDVHOOLQD+FKHVWDDLQGLFDUHTXDQWHYROWHQHOOHFDVHOOH%%qFRQWHQXWDODSDUROD DXWREXVµDGHVVR EDVWDFRSLDUHODIRUPXODDQFKHQHOOHFDVHOOHDILDQFRGL SLHGLµH ELFLFOHWWDµHLOJLRFR qidwwrdeeldprfrqwdwrohulvsrvwhlqedvhdoph]]rglwudvsruwrxvdwr,oulvxowdwrsrwujhvvhuhxqdwdehoolqdfrphtxhoodtxldghvwud (XQJUDILFRULFDYDWRGDTXHVWDSRWUjHVVHUHSHUHVHPSLRXQRGHLVHJXHQWL YHGLDPRTXLQGLFKHLQTXHVWRFDVRXQFHQWLQDLRGLGDWLGLSDUWHQ]DVRQRVWDWLULXQLWLLQFDWHJRULHHDOODILQHLQ JUDILFLPROWRVHPSOLFLHOHJJLELOL

47 6HWRUQLDPRDLQRVWULGDWLGLSDUWHQ]DTXHOOLGHLSULPLJUDILFLSRVVLDPRSURYDUHDIDUHODVWHVVDFRVD (VHUFL]LRDSSOLFDWLYR5LSHWHUHLOODYRURGLDJJUHJD]LRQHDSSHQDYLVWRVXLGDWLGHLSULPLJUDILFLSDU 'XUDQWHORVYROJLPHQWRGHOO HVHUFL]LRLUDJD]]LGDVROLGRYUHEEHURUHQGHUVLFRQWRFKHF qtxdofrvdfkhqrqyd WURSSRODYRURGDIDUHLGDWLVRQRWURSSRVSDUVLQRQKDVHQVRFRQWDUHTXDQWHYROWHqULSHWXWDXQDULVSRVWD SHUFKpOHULVSRVWHSRVVLELOLVRQRPROWLVVLPHQRQULXVFLDPRDVLQWHWL]]DUHVXIILFLHQWHPHQWHOHLQIRUPD]LRQL $TXHVWRSXQWRTXLQGLGRYUHEEHDUULYDUHLO'HXVH[0DFKLQDQHOOHYHVWLGHOGRFHQWHFKHGRYUHEEHVXJJHULUH XQDFRVDGHOWLSR HVHLQYHFHGLFRQWDUHTXDQWHYROWHqVWDWDGDWDXQDFHUWDULVSRVWDSURYDVVLPRDFRQWDUH TXDQWHYROWHqVWDWDGDWDXQD FODVVHµGLULVSRVWHSHUHVHPSLRTXDQWHYROWHLOULVXOWDWRqPLQRUHGL"2 FRPSUHVRWUDH" 6LODVFLDDTXHVWRSXQWRSHUHVHUFL]LRDLUDJD]]LLOWHPSRGLSURYDUHDPHWWHUHLQSUDWLFDFRQ([FHOTXHVWR VXJJHULPHQWR FRQVFLSHUzGHO IDWWR FKHSXUWURSSR H[FHO QRQ PHWWH D GLVSRVL]LRQHGLUHWWDPHQWHTXHVWH IXQ]LRQDOLWjYDOHDGLUHqSRVVLELOHSHULO FRQWDVHµLPSRVWDUHFRPHFULWHULR µpdqrqqsrvvlelohgduh XQFULWHULR GRSSLRµFRPHSHUHVHPSLR FRPSUHVRWUDHµ 'RSRXQSR LUDJD]]LGRYUHEEHURUHQGHUVLFRQWRGLTXHVWDOLPLWD]LRQHHSUREDELOPHQWHLSLYLVSLGRYUHEEHUR SURYDUHDSHQVDUHDXQDVROX]LRQHDOWHUQDWLYD 6HTXDOFKHUDJD]]RFLGRYHVVHDUULYDUHGDVROREHQH/RGHGLIURQWHDOODFODVVHH RQRUHµGLVSLHJDUHDJOL DOWULTXDOqODVROX]LRQHGHOSUREOHPD$OWULPHQWLVHQHVVXQRDUULYDDXQDVROX]LRQHGHOSUREOHPDLQWHPSL UDJLRQHYROLWRFFKHUjDOGRFHQWHLQGLUL]]DUOLOXQJRODVHJXHQWHVWUDGD 'DWRFKHQRQSRVVLDPRFRQWDUHOHULVSRVWHLQXQLQWHUYDOORGLYDORULPDVRORTXHOOHPDJJLRULRPLQRULGLXQD FHUWR YDORUH EDVWD FDOFRODUH SHU HVHPSLR TXHOOH PLQRUL GHOO HVWUHPR VXSHULRUH SRL TXHOOH PLQRUL GHOO HVWUHPRLQIHULRUHHIDUHODGLIIHUHQ]DIDFLOHQR" $ TXHVWR SXQWR VL ODVFLD DL UDJD]]L LO FRPSLWR GL WUDGXUUHLQ IRUPXOH TXHVWDVROX]LRQHFKH FRPXQTXH GRYUHEEH ULVXOWDUH SL R PHQR FRPHTXHOOD TXL D GHVWUD 3HUFKLDUH]]DULSRUWLDPRODVWHVVDWDEHOODYLVXDOL]]DQGRSHUzQRQLULVXOWDWLPDOHIRUPXOHGDLQVHULUH

48 GDTXHVWDWDEHOODqIDFLOHULFDYDUHXQJUDILFRFRPHTXHOORGHOODSDJLQDVXFFHVVLYDGDFXLILQDOPHQWHVLULHVFH DGDYHUHXQ LGHDXQSR SLSUHFLVDGHOODGLVWULEX]LRQHGHOOHULVSRVWH ( LPPHGLDWRGDTXHVWRJUDILFRQRWDUHFRPHHVLVWDQRGXHFDWHJRULHGHFLVDPHQWHSLJHWWRQDWHULVSHWWRDOOH DOWUHPDELVRJQDIDUHDWWHQ]LRQHDJJUHJDQGRLGDWLLQPRGRGLYHUVRO LQIRUPD]LRQHWUDVPHVVDSXzHVVHUH PROWRGLYHUVDSXUHVVHQGRHJXDOPHQWHYHULWLHUDHEDVDQGRVLVXJOLVWHVVLGDWL3HUHVHPSLRDJJUHJDQGRLGDWL LQVROHPDFURFDWHJRULHLOJUDILFRFKHVLRWWLHQHqLOVHJXHQWH

49 FKHSRWUHEEHIDULQWHQGHUHFKHOHULVSRVWHVLDQRVWDWHJURVVRPRGRXQLIRUPHPHQWHGHFUHVFHQWLGDLYDORUL SLEDVVLDLSLDOWL (VHUFL]LR WUDQVIHU LQYHQWDUH QXRYH VHULH GL GDWL FKH DJJUHJDWH LQ PRGR GLYHUVR GLDQR FRPH ULVXOWDWLJUDILFLFRPSOHWDPHQWHGLYHUVLLQIRUPD]LRQLGLYHUVHSDUWHQGRGDJOLVWHVVLGDWLLQL]LDOL (VHUFL]LR 'DWRLOVHJXHQWHJUDILFRUHODWLYRDOODGXUDWDGHLFROOHJDPHQWLLQWHUQHWGDXQFRPSXWHU ULVXOWDWRGHLGDWLULSRUWDWLQHOODWDEHOODVHJXHQWH LQGLFDUHVHOHLQIRUPD]LRQLVRQRUDSSUHVHQWDWHFRUUHWWDPHQWHVHODUDSSUHVHQWD]LRQHqLQTXDOFKHPRGR IXRUYLDQWHHLQWDOFDVRFRPHVLVDUHEEHURLQYHFHGRYXWLUDSSUHVHQWDUH