JOURNAL OF SCIENCE OF HNUE Educational Sci 2011, \ b l , 5C, Xo 4, i)p, 29 37 MOT SO BIEN P H A P THIET KE CAC HOAT DONG HOC TAP TRONG DAY HOC HINH HOC KHONG GIAN 6 T R U I N G THPT THEO QUAN DIEM THI[.]
JOURNAL OF SCIENCE OF HNUE Educational Sci 2011, \ b l , 5C, Xo 4, i)p, 29-37 M O T SO B I E N P H A P THIET KE CAC HOAT D O N G HOC TAP T R O N G DAY HOC HINH HOC KHONG GIAN T R U I N G T H P T THEO Q U A N DIEM THICH NGHI TRI T U E Do Vim C~^ii5iig Tntdng Trung hoc phd thdng Hd lYiiig Ilad.n )'rn Di/nh Thimli Hda E-mail: cuonghth o gniail.com Tom t a t De tang c:Udng hoat dong (HD) nhan thiic: cnia hoc; sinh (HS) c}ua trinh hoc tap thi tam ciia vic~'c tliic'^t ke bai lupc: la thilt ke cac HD hoc ta]) Mdi HD hpc tap thudng gdm nhilu HD phan vdi muc dich rieng TluR: hien xong cac HD phan tin muc dich chung ciia HD cung dUcJc thUc hic^n Vi vay t.rong hai vic^t chiing tdi de xnki mot so bic^n phcip xay dung cac HD hoc tap cho HS day hoc IRnh hgc khdng gian trUdng pli5 thong theo quan diem thfch nghi trf tue nhim dinh hudng xay dung cac HD thich hpp, gdp phin giiip giao vien bo mon Toan CO kha nang tilp can vdi phuong phap day hpc tich circ va nang cao hieu qua day hoc Toan trudng thong hien Md dau Trong cdng cudc ddi mdi giao due d nude ta hien na}' viec ddi mdi phUdng phap day hpc ddng \'ai trd hit siic quan trpng: "Quan diem chung cua ddi mdi phuong phap da}' hpc da dupc khing dinh, la td chiic cho HS dupc hpc tap HD \'k bang HD tu giac, tich cue, chu ddng \-a sang tao ma ccjt ldi la lam cho HS hpc tap tich cue, chu ddng chong lai thdi quen hpc tap thu ddng" [3:19] Khi ndi vl moi quan he giua ndi dung clay hpc va HD, lac- gia Xguyin Ba Kim cho ring: "Mdi nOi dung da}' hpc diu lic'm he mat thilt vdi nhfrng HD n h i t dinh, Dd trudc h i t la nhfrng HD dupc tiln hanh qua trinh lich sii hinh \'a ling dung nhfrng tri thiic dupc bao ham ncji dung nay, cung chinh la nhiing HD dl ngudi hpc cd t h i kiln tao va ling dung nhung tri thiic ndi dung dd Phat hien dupc nhiing HD nhu vay mdt ndi dung la vach dudng dl ngudi hpc chilm linh ndi dung dd va dat dupc nhfrng muc tieu day hpc khac, cung dong thdi la cu t h i hda dupc muc tieu day hpc cd dat dupc hay khdng \'a dat din miic dO nao"[6;114] 29 Do Van Cudng Xhu viiy, de fang cUdng III) nhan tluic ciia IIS cpia trinh hpc t a p thi trpng lam ciia \iec thiet ke bai hpc la (liiei ke cac HD hpc (.ap Men HD hpc: tap thirdng goiii nhieu HI) phan \di muc dich rieng Thirc hicui xong cac- HD philn (hi muc dich chung (-lia \[\) cung dirpe thUc hien 2.1 N o i d u n g n g h i e n cu'u Khai niem ve thicli nghi tri t u e va quan di^m van dung vao day hoc toan d trifcfng t r u n g hoc thong Theo t;ic gia Piaget HD nhan (hiic (lia nguoi lic'u (|iian CIC'TI \'if'c- to chiic thdng lin \'a thich nghi \'(')i moi Irirdng ma ngudi hpc tri giac: no [o;ll| Id cluic thdng lin la each ma thdng lin dupc td chiic dan dc- CDU iigUdi lic'-n quan dc'-i) (-ac doi lupng ci.i the y lUdng hoac hanh dong Thich nghi la cjua trinh ngudi td chiic kiln thiic \'ao so dd nhan tlnic- ciia minh \'a ctieu chinh cac sc) na}' de "an khdp" \'di thdng lin mdi Su thfch nghi Iri tin'- bao gdm sir dong hda thong tin vao so nhan tluic da cd \'a si; dic'^u ling so dd cla cd de "an khdp vdi thdng tin mdi, tao melt so nhan tluic mdi Xdi each khac thich nghi tri tue la kha nang 'iioa giai" nhfrng tinh huong mdi cie tiep nhan (liic'Mi giai thfch van dung) tri tluic mdi Khi chii t h i tilp xuc \6\ uujt thdng tin mdi sU c-aii bang cfi se bi pha \d c-ac- so dc") da cd khdng ap dung dupc- budc- chii the phai tiln hanh cjua trinh dong hda va dieu ling, tao trang thai can b i n g mdi \'di each hir-u nay, miic dp thich nghi tri tue cua chu the"- thucx- xko tdc dp "hoa giai" nliUiig tinh hu(')ng mdi Day hpc theo quan dilm thich nghi tri tue cin t(') chiic va hudng dan cho HS thuc hien cac HD nhan thiic thdng qua cac HD chii ylu la; HD dong hoa, HD dilu ling HD biln dcii d6i tUdng va HD chu}ln hda cac lic'Mi tudng Giao vic'ui phd thdng can nhan thiic qua trinh thich nghi trf tue gin vdi su phat triln tri tue \ i vay dl day HS thich nghi tri tuc;^ cin chii trpng phat triln nang luc HD dilu liiig: HD dilu ling la HD diln vc")n tri tlnic da cd cua chii t h i chua tUdng hop vdi mdi tnrdng tri tluic mdi cin nhan thiic scJ nhan tluic da cd va tri thiic mdi khdng tUdng thich Khi dd HI) difMi ting n h i m tao lap so nhan thiic khac dC' t i l p nhan tri tluic mdi, lao sir can b i n g mdi Trong (imi trinh da}- hoc, dudi sir liudng d i n cua giao vien, HS hpc b i n g each true tiep ti("'n hanh cac HD hpc tap (trong dd chiia dung cac- npi dung kiln thiic ma ngirdi hpc c-an chilm linh) d l thdng cpia dd ma linh hdi tri thiic, ren luyen ki nang va phat trien tu duy, \'i vay, vai lid ciia gifio vien day hpc theo quan dilm thich nghi tri tiu^ t h i hien trudc hit p viec thiet kl cac HD hpc tap Th(H) chiing ldi, lien trinh hpc lap theo ciuan dilm thich nghi trf tue cua HS dupc tiln hanh nhu sau: Tinh huong mdi -+ Thuc hien HD ddng hda —> Thuc hien HD biln ddi doi lupng -^ Thuc hien HD dilu ling -^ Kiln thiic mdi, Diing trudc tinh huong mdi (mdi trudng chiia dung thdng tin) chu t h i tri giac 30 Mgt so bien phdp thiet ke cdc hoat dgng hgc tap day hgc Hinh hgc khdng gian nd (nhap thdng tin), nhung liic thdng tin dang d ben ngoai chii thi, tach biet vdi chu the; t i l p d i n chu t h i t h i y r i n g thdng tin cd t h i lien quan din minh va cd y thiic tim hilu vl nd (tilp nhan thdng tin) Khi dd, thdng tin se dupc them vao, dilu chinh hay lam thay ddi sP nhan tluic da cd trudc dd ciia chu t h i (chu thi tri giac nd) va cd t h i xay cac kha nang sau: K h a n a n g 1: Xlu thdng tin mdi khdng gin kit dupc vcii kiln tluic da cd ciia HS hoac thdng tin can hpc la melt be) phan ciia \-('')n IUC'MI bilt (lia HS thi viec hpc tap khdng xay (thdng tin khdng dupe dl)iig hda) Trudng hpp thdng tin mdi \'a von hilu bilt ciia HS rdi nhau: hpc ta]:> khdng xay Tiic la, qua trinh thich nghi cd "van de ": hoac cd \'an de d khau dong hda hoac cd \'in de d khau dieu ring Hoac thdng tin cin hpc la mot bd phan ciia v(')n hilu biet cua HS: hpc tap khdng xay Xgliia la, HS cam tha}' rhng thdng tin can hpc la mdt bd phan (tap hpp con) ciia von hilu bilt ciia minh la nhfrng dieu cac em dk bill roi, dd cac em khdng phai hpc lai K h a n a n g 2: Thdng tin mdi cd t h i g i n vdi kiln tluic da cd cua HS, dd chu t h i phai thuc hien mOt cac HD hoac thdng qua to hpp cac HD nhu: HD dong hda, HD dilu ling, HD biln ddi doi tupug hay HD chuyin hda cac lien tudng n h i m muc dich dilu chinh tri thiic hay quan niem da cd d l "an khdp'' vdi tinh hudng mdi, Xlu cdng thi viec hpc tap cai mdi xa}' ra, Sau dd, giao vien cd t h i ren luyen cho HS kha nang du doan, kha nang di xuat tao cac tinh hudng hpc tap mdi dua tren tinh huong vfra giai qu}'lt: n h i m muc dich lam cho kiln tluic cfi dupc viing chic hon \'a ren luyen dupc cac ky nang, cac thao tac cua chii t h i thao hon (thdng qua HD ddng hda), hoac ren luyen dupc chp cac em kha nang kiln tao tri thiJe mdi (thdng qua HD dilu iing), Tinh huong hpc tap mdi phai phat huy toi da kha nang su}' nghl ciia cac em, b i n g nd luc cua ban than tim hudng giai quylt vin dl Can cii vao tinh huong cu t h i giao vien mdt mat cd sir tUdng trp phu hpp: mat khac dinh hudng d l nang cap d i n kha nang du doan chinh xac, kha nang d l xuat \'a giai quylt cac tinh huong nang cao mdi cung nhu thai dp lam ^'iee ddc lap cua HS Xlu giai quylt cdng thi kiln thiic dupc sau sic hpn, ren luyen ky nang nhilu hPn Theo chiing tdi, thich nghi tri tue cd hai cap dp: thich nghi bac t h i p diln qua qua trinh HD dong hoa; thich nghi tri tue bac cao ddi hdi HD dilu ling de lam thay ddi so dd nhan thiic da cd, dilu chinh lai nhan thiic da cd cho plifi hpp vdi tinh huong cin giai quylt Vi du Cho hinh hop ABCD.A'B'CD' cd AC = BD' = B'D AB = AD = A A' = a Tinh khoang cdch giua dudng thdng BC vd CD' = a\/3, * Thuc hien HD ddng hda Von tri thiic da cd la phudng phap tinh khoang each gifia hai dudng thang 31 Dd Van Cudng eh(H) nhau, HS lliUdng linh theo melt (rong hai cpiy dinh sau: Qii}' (linh 1: \'ac dinh mat i)haiig (/') c-hiia /; \-a {D)//a Tinh khoang each (fr mo( diem M thudc- a dew {P) C^u}' trinh 2: - Xac dinh mat ])haiig {P) chiia /; va {P)//a - Xac dinh mat i)liaiig {(,)] chiia a va {(J)//!) Tinh klio;iiig each gifra hai iiia( phang {P) \'a {(J) * llu/c liini HD bien ddi dm luUlng \d\ bai loan na}', neu d l iigu}-('u khdng bilu doi gi tin IIS c-liUa the \'an di.ing true liep mot hai c|U}' trinh lien de giiii Do eld xuat hien mdi sir mat can i)aiig Tuy nhic-'n, neu giao \'ien \eu can HS bien ddi clang tluic gia thiet dc'' tim tha}- dau hien dac IrUng (iia hmh help tlii vdi \'dn kie^'u tlnic- rua minh, IIS se" bie'-ii deli dupc: l ( " - + A'C- I BD" -|- B'D' - 12cr (iremg hinh lujp ir,ng binh pliUPng tat ca e-iic- dudng CIICHJ Ijiiig tdng binh pliUdng tat ca cac canh cfia hinh hop dd) Ma AC BD' B'D - c(\/3 ne'Mi d'C = a^/ll tiic be^ju dudug cheo cua hinh hdp bing Do \CC'A' la hinh binh hanh va eo hai dudng che^o b i n g {AC = A'C) nfMi ACCA' la hinh chfr nhat, tiic la l.l' I C Tudiig tu nhu tren ta cd BB' BD \ a y A/V {ABCD), tUcmg tu \B i \DD'A') Do ABCD A'B'C'D' la hinh lap phuong Theo eiu}' trinh 1, cluing ta ed tlie'^ xac dinh mat piling {B.A'C) chiia IK" \-;i {BJ\'C')IICD' l a cd: hinh chilu cua DD' mp{A'B'C'D') la B'D' ma 13'D' nen DB' A'C Heju nfra B'H - -B'D - a, v/.3 •) BO' rs la BH X\e\\ I'C" nen B'ir' + BH' - BB" hay DB' J BO' \ a v DB' T {B.A'C) tai 77 IUMI khoang each gifra hai dudng lliaug BC" \k CU' bang dai OK OK BO', K e BO' vcii O' la tam ciia hinh vuong A'B'C'D' D K I H ' B-' • 0' D' Hinh dd: OK - ^ DU = ^ 7;7i' - - — 3 cd Dl xuat phat triln tiiih huong imng cao: Cho hinh hOp ABCD.A'B'C'D' AB = a AD ^-^- b, A A' = c va AC = BD' = B'D = Va' + 6^ + c^ Tinh theo o; b; c 32 Mgt sd bien phdp thiet ke cdc hoat dgng hgc tap day hgc Hinh hgc khdng gian khoang each gifra hai dirdng thing BC va CD' Tudng tu vi du 1, ban diu HS se chiing minh dupc hinh hop la hinh hop chfr nhat, ABCD.A'B'C'D' Tilp theo: nmu thuin, chudng ngai sinh tri thiic phUdng phap da cd ciia HS khdng tUdng thich vdi phudiig phap van dung tinh hudng tdng quat hon Man thuin lui}' sinh cac tri tluic phuPng phap van di.ing cho e-ac- trudng hpp rieng khdng thudc pham v'l ciia cai dupc khai quat Cu thi: HS tilp c:an bai toan tdng quat mi}' hp khdng thi ap dung true tilp qu}' trinh tren dl giai Xdi each khac, quy trinh tren khdng tUdug thich vdi bai loan mdi na}' la \'i: DB' khdng phai phudug vudng gdc vdi mat phing [B.A'C), dd {BA'C)//CD' Cd the khic phuc man thuin na}' dinh hudng cho HS lien tudng din thi tich hinh chdp A'.BCC di xuat hieui khoang each tfr C den mp{BA'C') Ta C('): S^^.^^, = BC.CC = -be Khi dd: V'^, ^^,^„ = -zabe Khoang each cin tim chinh bing bing dp dai dudng cao h xe tfr dilm C din mat phing {BA'C), ma theo Q, b.e Xhu va}' cac kiln thiic \'a kinh nghiem da cd ciia HS la tiln di quan trpng viec td chiic cac HD hpc tap, Cac HD hpc tap dupc giap \\en thilt ke dua tren dac dilm ndi tai cua kiln thiic chiia nd \k quan trpng hPn nfra la xuit phat tfr kiln thiic \'a kinh nghiem da cd cua HS cd lien quan din kiln thiic can day nhim gpi ddng cP, tao nhu ciu nhan thiic \'a gay nilm tin d kha nang phat hien \kn de giai quylt vin di d hp 2.2 Mot s6 kho khan thiet k^ cac HD hoc t a p Hinh hgc khdng gian theo quan diem thich nghi tri tue Hinh hoe khdng gian la ndi dung quan trpng gdp phin hpan thien tri thiic toan hpc phd thdng ciing nhu phat triln tu cho HS \'iec tang cUdng HD nhan thiic cua HS hpc ndi dung nhim giup hp nim viing tri thiic va phat triln tu la yeu ciu quan trpng Vl thuc tiln viec thilt kl cac HD hpc tap day hpc Hinh hoc khdng gian trudng phd thdng theo quan dilm thich nghi tri tue cdn gap mdt so khd khan sau day: Trudc hit, khd khan thi hien viec triln khai cac li thii}'lt day hpc hien dai vao day hpc toan d trudng phd thdng Khd khan chii }'lu la cac li thuylt day hpc hien dai dupc khai quat hda kha trfru tUpng Trong dd, viec nghien ciiu each triln khai cu thi cac phudng tluic van dung vao day hpc toan d trudng phd thdng cdn han chi Khd khan thii hai, khd khan qua trinh thu nhan va biln ddi thdng tin, thi hien b chd HS khdng bilt tich hpp nhiing thdng tin mdi nhan vao he thong thdng 33 Do van Cudng tin da tich luy, khdng bill bien ddi, dieu chinh nhiing tri thiic vk kinh nghiem da cd dl giai quyl( \aii dl nav sinh Khd khan nay bilu hie'n da phin HS phd thdng, d hp kha nang ci(')ng hda kiln (Liic trdi hdn so vdi kha nang dic'U tie:'! Klio khan, thit ba, the liicMi d klui nang (liie( ke cac HD hoc tap qua trinh van dung cac phUdng phap day hoc mdi cdn han c:h(' Kho klidn lh.it lu, la phan llvnh h.oc khdng gum d tiudng phel thdng mang tinh Irfni (irpng eao neu ddi hdi HS phai cd (ri tucjug tirpng khdng gian, cd tu logic \'a tu du}' sang tao 2.3 Mot s6 bien p h a p xay dUng H D hoc t a p cho HS day hoc Hinh hpc khdng gian d triidng ph6 t h o n g theo quan di^m thich nghi tri t u e Bien phdp 1: Ren luyen cho HS nang liic lien ividng den kien thUc cdn chiem linh thong qua viec sii dung cdc md hinh triic quan Mac- (111 muc tieu quan trpng cua vie;^c day hpc- H}.nh hoc klidng gian d trudng THPT la phat triln tri tudng tUdng khdng gian tu logic va tu sang tao cho HS, nhung khdng vi thi ma coi nhe sijf dung cac md hinh trirc quan Cac md hinh true quan nlu dupe sii dung hpp li se'^ cd vai trd quan trpng du doan cua HS Vi du De day HS phdt hien vi tri tuang doi cua hai dudng thdng khdng gian, giao vien cd the cho cdc em quan sdt mdt sd hinh dnh thitc te Chdng han quan sdt hinh: edi bim giao vien d tren ldp hoe Ta coi cac mep ban a.c va c-anh b cua chan ban la cac dudng thang a,b,e Giao vien dat nhiing cau hdi nhu sau: Dudng thang a.b cd cung nim tre"'!! mot mat hay phing khdng? Cd mat phing nao chiia hai dirdng thing a va c lioSc chiia hai dirdng thing va c hay khdng? Qua dd, HS thiy ring nhilu cap dudng thing phan biet khdng gian khdng c6 dilm chung iihung khdng song song xdi nhu trudng hpp mat phang Xhu vay, ta thiy HS gap chudng ngai va cd nhu cau cin bd sung kiln tluic cho ban than Khi dd, HS thiy dupe \'di hai dudng thing bit ki khdng gian thi dilu diu tie''!! cin phai xem xe''l chung cd dong phing hay khdng? Dinh nghia "trong mat phing nlu hai dudng thing phan biet khdng cd dilm chung thi cluing song song Hinh vdi nhau" khdng thi ap dung mdt each tdng quat cho trudng hpp bit ki khdng gian, dd xuat hien mot su mat can bing Tff dd, "dilu chinh lai tri thiic cii, di din kit luan: Khi cho hai dirdng 34 Mgt sd bien phdp thiet ke cdc hoat dgng hgc tap day hgc Hinh hgc khdng gian thang phan biet a va khdng gian thi cd thi xay hai trudng hpp: Khdng cd mat phing nao chiia ca a \k b Khi dd, ta ndi ring hai dudng thing a va b cheo Cd mat phang chiia ca a va b Khi dd, cd hai kha nang xay ra: Nlu a va b khdng cd dilm chung thi chiing song song vdi Nlu a vk b cd mOt dilm chung nhit thi chung cit Khi dd, xa}' mot sir dilu tilt thilt lap lai sU can bing P chu till Bien phdp 2: Khi thiet ke cdc HD hpc tap cdn dyi tinh tao syt phdn hoa phdn bdc giiia HD dong hoa vd HD dieu Ung Khi van dung quan diem thich nghi tri lue;^ \'ao day hpc, giao vien phai nim dupc miic dp nhan tluic cua HS dl tii}' vao tinh huong cu thi ma td chiic cac HD thich hop Deli \'di dc^i tupiig HS trung binh va kha thi giao vien thilt kl cac bai toan vdi miic del \e\\ can thirc hien HD dong hda hoac- HD dilu ling d cap dp thip la cd the giai ciuylt dupc, Ddi vdi doi tUpng la HS gidi thi giao vien cac bai toan nang cao miic dp khd \'a phai thuc hien HD dilu ling d cip dp cao mdi cd thi giai qu}'lt dupc, 17 du Cho hinh chdp S.ABCD cd ddy ABCD Id hinh binh hanh Goi I J Id hai diem thoa mdn SI = -rSA, SJ = -SB Diem P Id thudc mien cua tam gidc SCB Tim giao tuyen cua hai mat phdng {SAC) vd {SDP); {SCD) vd {PIT) \b\\ kiln thiic da cd ciia HS vl xac dinh giao tuyIn cua mat phing: giao tuyIn la dudng thing di qua hai dilm chung ciia hai mat phing dd hoac la dudng thing di qua mdt dilm chung \"a cd phuong xac dinh, Xet hai mat phing {SAC) va {SDP) la hai mat phang phan biet va cd S la dilm chung thii nhat, ta cin xac dinh dilm chung thii hai Vdi bai toan nay, nlu giii nguyen nhu gia thilt va chua biln ddi thi HS se khd khan viec tim dilm chung cua hai mat phing dd ciing nhu tim phuong ciia dudng giao tuyIn chung Do dd, xuit hien sU mat can bing, Tuy nhien, nlu giao vien yen ciu HS tim moi lien he giiia hai mat phing {SDP) va {ABCD), sau dd mdi tim moi lien he gifra hai mat phing {SDP) Hinh va {SAC), HS se biln ddi nhu sau: Trong {SBC), goi Q = SP n BC ^ Q e BC; Qe SP nen Q la dilm chung thii hai cua hai mat phing {SDP) va {ABCD) \'kx giao tuyIn cua mat phing {SDP) va {ABCD) la DQ 35 Dd Van Cudng li-ong {ABCD) gpi K = DQ H AC => K c~ AC; K € DQ nen K la dilm chung thii hai eiia mat p h i n g {SDP) va {SACJ) Vay giao tuyen ciia mat p h i n g {S.AC) va {SDP) la dudng t h i n g S'A' Ban dan, doi vdi hai mat pining {SCD) vk {PIT) (hi HS khdng cd dinh hudng de \ae- dinh elilm chung cung nliU i)hirdug eiia giao (iiye'ii dd xur'il hien sU imit e-aii bing, Tuy nhien, gia sii ta ye'"u e-au HS tim giao die''m ciia JP va SC HS se~' bien d(')i nliU sau: Trong {SBC), gpi 71* -• JPHSC > R la dic"'m cluing eiia hai mat phang {SCD) va (7^7,7) Hem mia, tfr d;'tng thiie- (1) suy L)//CD Vky giap tuyen ciia hai mat phing (.SY'/;) va (7V,7) la dirdng thang PT song song vcii CD Bien phdp 3: Khi thiet ke HD hoc tap can chu trgng viec boi dtCdng cho HS cdc ndng liic huy dgng kiin thiic cho viec dieu ling de thich nghi vd chiem linh kien thiic Khi \ae- dinh cac- nang lUc huy ddng kiln tlnic (hiing tdi thay r i n g kha nang biln ddi vin dC\ biln ddi cac bai loan ddng mdt \'ai tro rat quan trpng Xlid qua trinh biln ddi van de biln ddi c-ac- bai toan HS cd tlic' quy cac van d l mdt tinh hudng mdi, cac bai toan khd vl c-ac- vin de quen thudc, cac bai Kjan tUPng ttr giai Qua trinh biln ddi la qua trinh dilu ling de"^ HS thfch nghi chuyen den sd dd nhan thiic mdi tUdng hpp vdi tinh hudng mdi, Vi du 4- Trong khdng gian cho diem M co dinh vd khdng thudc dudng thdng d Hai diem A, B thay ddi tren d cho AB = a khdng ddi Xac dmh vi tri cua A vd B cho tdng cdc khoang cdch td M din A vd B be nhdt Vdi bai toan giao vic-'u da tao mdt tinh huong hap dan goi sir tim hi(''U cua HS sau hp da giai bai toan sau: Cho hai dn'in A B khdng thudc dudng thdng d Tim diem M tren d cho ,17,4 + MB be nhdt Mec phat hien dinh hudng giai qu}'c~'l bai toan la r i t khd khan ddi vdi HS, nlu tang tri thiic ma hp cd lai cd sir khac biet kha Idn vdi vi du da clip day dii kien da bilt la hai dilm co dinh B chi phai tim mOt dilm di dong M thudc dudng t h i n g d, cdn a vi du chi cho cd mdt dilm co dinh 47 ma phai tim tdi hai dilm di ddng thudc d Su khac bie^M trc''n da tao cho HS nhfrng khd khan, chudng ngai ma hp cin phai cd sir nd lUc sii}- nghl mdi cd t h i phat hien hudng giai quylt Giao vien cd the"' dinh hudng cho c-ac- em xem xet bai loan d hai trudng hpp: A, B c-fing phia so vdi d; A, B khdng e img phia so vdi