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GitP HOC SINH REN LUYEN KHA NANG S A N G TAO THONG QUA DAY HDC MDT SO BAI TAP HlNH HDG KHONG GIAN Tu duy sing t?o la mdt n5ng luc can IhiSit cua mdi con ngudi trong mpi cdng vipc Trong day hpe giai lo[.]
GitP HOC SINH REN LUYEN KHA NANG S A N G TAO THONG QUA DAY HDC MDT SO BAI TAP HlNH HDG KHONG GIAN H O A N G B A THjNH - TRINH C O N G S O N ' T u sing t?o la mdt n5ng luc can IhiSit cua mdi ngudi mpi cdng vipc Trong day hpe giai loan, vipc bdi dudng nang luc l u sang tpo cho hpc sinh (HS) ddng mpt vai trd quan Irpng nhim giup cae em klidng nhirng hieu rd ban chat eua bai toan (BT) ma edn de xuat duqc nhirng y tudng mdi, BT mdi Qua dd, nang cao linh tu giac, dpe lap, sang lao vatao hdng thu hpe lap eho HS Quy trinh giai loan giao vien (GV) thudng ap dyng cho HS dd la b i t dau tu budc tim hieu, phan lieh de bai, ket thuc d budc Irinh bay Idi giai BT va bd qua budc cud'i eung eiing la mpt budc quan trpng dd la xem xet BT va sang tao them nhiing BT mdi Trong day hpe hinh hpe khdng gian dIrung hpc phd'lhdng cd nhieu "co hdi' de HS thuc hien dieu nay, bai viet dua mpt sd nhung "co hpi" dd va each thue van dung Chung vao cac hoat ddng giai loan Sang tao n h d phat hien ban chat va hien tupng cua BT Mpt BT bat ki Iudn cho ehung ta Ihay mpt hien tuong, dd la gia thiet eua BT; cd hai loai gia Ihiet, tam gpi la: gia thiet ban cha'tva gia thiet khong ban chat Blng viec lim ra,giunguyen gia thiet ban chat va thay d6l nhung gia thiet khdng ban chat, ta cdthe lam mdi BT gd'c Xet vidu sau: Vidu (Hinh hoc 11 nang cao; tr 44): Trong mp(P)ehotugiac IdiABCD;ngoaimp(P)chodiem S Hay tim giao tuyen cua haimatphlng(SAC)va(SBD) {hinh I) BT tren_cho ta tha'y hien iuffngnhusau: Thdnhat, haimalphSng (SAC) va(SBD)ed ehung mdt diem S Thdhai.lronghaimat phSng (SAC) va (SBD) lan lupt chpn dupc hai dudng thing cat la AC vaBD.DieunayladI dang thay dupe vi AC, BD cung n i m trcng mp(ABCD) Ban chat la: hai mat phing (Q) 50 Tqp chi Giao dye so 316 vajR)cd Chung mpt die'm Sya lan iuptchiia hai ductig thing c5t a, i) cung n i m mpjABOD); giii nguyen ban cheinay, ddng thdi Ihay doi hien luqng cua BT b i n g each an di dudng thing a t o ^ c b ta cd BTmdi: Vidu la: Trong mp(P)chotdgiacldi ABCD;ngoai mp(P) cho diem S E la mdl diem bat kl thudc doan thang SB va G la Irpng tam tam giac SCD Tim giao tuye'n ciia hai mat phang (SEG) va (SAC) {hinh 2} Qua p^han tich BT ta tha'y, de giai BT can tim t^ dudng thing da bi an di Sudng thang vda nim mp(SEG) vda n i m mp(ABCD), hay ndi each khac, ndiagiao tuye'n cOa haimatphlng (SEQ) va (ABCD) Theo dd, can tim giao tuyen cua hai mat phang (SEG) va (ABCD) Day chinh la djnh hudng each giai BT Keo dai SG elt CD lai M Khi dd BM la giao tuyen cue (SEG) va (ABCD) Gpi I ia giao diem cOa AC va BM thi SI se la giao tuye'n cua hai mat phang (SEG) va(SAC) Vidu 2:Ct\o tl) dien ABCD Tmng die'm cua cac dean thing AC, BC, BD, AD lan iuot la M, N, P, Q Chung minh:_AB//mp(MNPQl,CD//mp(MNPQ) Hui^giyjn.'Trong mat p h i n g (ABC)cdMN//AB, ma MN n i m mp(MNPQ) nen AB//mp(MNPQ) Tudng tu, ta chiitig minh dupc CD//mp(MNPQ) A//i^n«tTiJrgH thiet cua B T : M , N , P,Qian lupt la tmng die'm cac doan thing AC, B C B D , AD, HS cdthe'nJtra cac ke't luan can thiei: MN//AB, NP//CD.Tuynhien,de'nil raMN//AB,NP//CD khdng * TnHfat Cao l i l t « p b ^ Ngbl Aa •(ki2-8/2013) canden cac gia thiet m^nh nhudtren; ching han, de MA Chdng minh ring: neu ^ MA' Nir la du Qua dd, ed the" thiAA',BB',CC'd6ngquy Hudng din: Gpi la giao die'm cua AA', BB' Ta IhSiy gia Ihiet ban chat cua BT (bj an di) la: MN//AB, di chiing minh C , C ' , thing hang.Dieu didang NP//CD Thay dd'i gia Ihiet cda BT, ta cdBT mdi: nhan thaVvichung cung thude haimatphing (AA'P) Wdu?a.-Cho ti)dien ABCD M|t p h l n j (a) eat va(BB'N) cac canh AC, BC, BD, AD ian lupt tai cae diem M, N, Nhan xel: Vi du 3a khdng khd hon BT ban P,Q cho MNPQ la hinh binh hanh Chdng minh dau nhung b i n g each phat bieu mdi, GV cd the tao ring AB//(a), CD//(a) ^ cam giac mdi la, qua dd gay hiing thu hpc tap cho {hmh 3) HS Ddng thdi, dpng vien, khuye'n khich eae em tim iiudngdan:TtonQ ldi, soi xet kitdng BT giai deed mdt cai nhin sau BT nay, Viec chdng s i c hpn minh AB//MN khdng Vi du 4: Cho hinh don gian nhuBTtmde chdp td giac S.ABOD Be chiing minh AB// B , Gpi Mlatmng die'm cua MNIadi ehdng minh SC va N la giao diem MN//(ABD) Dieu eda SD va mat phing c6dupcnhdMN//PQ (MAB)(/?/n/)5) Sang tao n h d Chung minh SO, phat hien no! dung AM, BN dong quy va hinh thiic cua BT Hudn^ din: Gpi E Mdi BT deu chda dung mdt ndidung nha't djnh la giao diem cua SO va ^ nhung neu nhin dudi nhirng gdo dp khac nd ed AM.Ta can chung minh B,E,N thing hang Dlehiing thecd cac hinh ftifckhac Xet vi dy: minh dupc B, E, N la die'm chung cua mat phing yidu3:ChQ bdn die'm , A, B, C khdng ddng (MAB) va (SBD) =>B, N, E thing hang phing Tren eae dudng thing OA, OB, OC lan lupt Nhan xet: Do hai ket luan "SO, /4M, 5/V ddng quy" iaj; cac diem A', B', C khac cho cac dudng va "B, N, £ thing hang" la tuong dUPng nen chung thing sau day c i t cdthe thay the cho Nghien cdu BT kThon ta nhau:BCvaB'C',CA tha'y: Neu gpi P la trun^ diem BA, Q la giao diem BD vaC'A',ABvaA'B' va PC thi dudng thang S p , PM, BN ddng quy tai Chdng minh cac mpt die'm F Vi the, ta ed the de xua't BT mdi: giao diem cua cac cap Vi du 4a: di/dng thing tren Cho Id giac thing hang S.ABCD,Ola cd milAB, chi cSn ^ - ^ Hudng din: Gpi N,P,Mianiuptlagiao dilm cOa cac cpp dudng thing BC va B'CCAvaC'A'.AB va A'B' {hirih 4) Ta thay M, N, P la die'm chung cua haim|tphing (ABC) va (A'B'C) nen chung thing hang.' giao die'm dudng eheo ACvaBD.Gpi M la trung die'm SC E la giao diem AM va SO, P la trung die'm BA, Q la giao "^ , Nhanxet: Ndi dung cda BT Irong v/du3lamd'i ii§n he gida bO ba diem (A, B, C) va (A', B', C') cung die'm BD va PC, F la giao diem SQ va MP, N la giao nim Iren haim^t phIng phan biet Tuy nhien, ta cd die'm SD va mpt phing (MAB) {hinh S) Chdng minh die'm B, E, F, N thing hang IJi^phat bleu BT tren dudi d;ng sau: Vidij3a:^Cho tam giac ABC va A ' B ' C n i m tren m i t p h i n g phan biet thoa man: AB o i l A'B'tgi M;BCcalB'C'taiNvaCAeitC'A'l?iP (ki2-8/2013)- Hudng din: Theo vidu ta ed B_, E, N thing hang nen chl can chdng minh B, E, F thing hang.Ta (Xe))) tit Tqp chi Giae due so 316 51 - Dung dudng trdn tam ; - Dung dSy cung BC tren dudng trdn (0); - Dung did'm A trSn dudng trdr^ (0); - Dung tam giac j \ B C ; - Gpi H la giao die'm cua ba dudng eao; - An di eae dudng khdng c^n thiiit {hinh 6) 'Budc 2: Tim quytich:Jaove\cho did'm H, chuyen ddng die'm A, ta thu dupc v^t cua diem H cd dgng la mdt dudng trdn * Bude 3: Chung minh G V d§t CEIU hdl: Em hay chdng minh ket qua du doan quy tich cua BT trSn phan mem Cabri? ã Phan thu4n:Qgi A'\a6\Đm ddl xdng vdl C qua tam ; A"dd'i xdng vdl B qua tam Khi A chay tren cung Idn BmC t h i ^ = a, ta xet eae trudng hop sau: - Khi A chay tren eung A'mA" thi ^= a; ta cd: B H C = 180" - a khdng ddl {hinh 7) Do dd, H chay tren eung ehua gde 180° - a dung tren doan BC (cung Bm'C);-Khi A ch|yUen cung A'pB thi'X = a, S H C = akhdng dd'i, suy H chay tren cung chua gde a dyng tren doan BC (eung Bp'H') (vdi H', H" tiiude dudng trdn chda cung a dung tren doan BC va H'BIBC, H"C1BC; - Khi A chay tren eung A"qC ta cung cd: B H S = akhdng dd'i; suy H chay tren cung chua gde adiAig tren doan BC(cungCq'H"} """" Khi A ehay tren eung nhoBnC thi'S'= ° - a , B R C = a khdng dd'i Do dd, H ehay tren cung chda gde adung tren doan BC (cung H'n'H") ^ Vay, A ehay tren dudng trdn tam thi quy tieh die'm H thude dudng trdn ' (dudng trdn ' hpp nen bdihaicungchu'a gde 180°-avaavetren doan BC) Phandao: HS lu chdng minh Van dung PPDHKP day hpe giai toan tim quy tieh vdi SLf trp giup cua phan mem Cabri d phd' thdng nham gdp mot phan nhd vao edng cupc ddl mdi PPDH theo hudng tich cue hda ngudi hpc va dng dung edng nghe thdng tin day hpc G V can van dung linh hoat PPDH vao day hpe mdn Toana trudng phd'thdng ã phdp khdm phd LuĐn i n tiffn si Gifio due hpc Tnidng Dji hpc Vinh 2007 Tdi li^u t h a m khdo Nguyfin Nggc Giang K h d m phd gidi todn phd thOng bUng cdc p h i n m g p h d p todn - tin NXB Gido dvc vm Nam, H 1 As Is known, dlscoveiy learning Is an active teaching - learning method for students So to build the processor the use of Cabri dynamic geometry software In solving locus problems according with discovery learning method is an Important problem for all of us Giup tioc sinli ren luyen (Tiep theo trang 51} cd Pemp(AMB), F la giao diem SQ va MP ^ Femp(MAB): FeSQ => Femp(SBD) => F la diem chung cua mat phang (MAB) va SBD) T d d d suy B, E, F thang hang Thdng qua mdt so bai tap toan hinh hpc khdng gian dtrung hpc phd'thdng, G V cd tiie hudng dlii HS kham pharanhdngBT mdi td cae BT ban dau; t^ora ChP cae em nhung cam giac mdi la va hdng thu hpe tap Tudd, nang cao susay me nghien cdU khoa hpe, dieu ma vd'n di ludn can thiet dd'i vdi HS, • Tdi li^u t h a m k h a o G Polya S a n g tao todn hoc NXB Gido di^c, H 1978 D^o Tam (chu bi£n) Gido trinh hinh hpc soclfp NXB Dal hoc suphgm, H 2004 D o i n QuJ-nh (tfing chu bifin) - Van Nhu Cuong (chii bien) Hinh hpc 11 nfing cao NXB Gido dvc, H 2006 SUMMARY CreaUve thinkingis a necessaiycapabllifyforall of people, in every jobs In mathematic teaching, creative thinking capacity building for the pupils Is very Important for a teacher And in geometry of space teaching, there are many conditions to help the pupils training creative thinking This article mention some examples of creative thinking capacity for students training through the creation ofnewproblems (I) Le v o Bmh D