DAI HOC QUOC GIA HA NOI KHOA SU PHAM r^ # p #|» ^ p •J* ^ 0^ # ^ Thae Si BUI THI HUCING PHirONG PHAP KICH THICH NANG Ll/C TlT DUY X> CHO HOC SINH PHO THONG TRONG DAY HOC GIAI TOAN Mdso:QS.05.02 DM HOC QUOC GIA HA NOI TRUNG TAM THONG TIN THU VIEN DT / 94-^ Ha Npi, 3/2008 MUC LUC Mdddu I Noi dung Chuang 1: CO Sd KHOA HOC Vl^ KICH THICH NANG LlTC TlTDUY CHO NG\J6l HOC 1.1 M6t so net caban cua qua trinh day hpc 1.1.1 Quan niem ve hpc va day each hpc 1.1.2 Quan niem ve day hpc tich cue 1.2 Phuang phap bien doi chat luong tuduy cua ngudi hpc 1.2.1 Mot so khai niem lien quan tdi tuduy 1.2.2 Mot sophucfng thiic ton tai cua tuduy 13 1.2.3 Phuang phap bien doi chat luang tuduy cua nguoi hoc 16 Chuang : M I QUAN QUAN HE GltTA DAY HOC GIAI TOAN V&I SlT PHAT TRIEN NANG LiTC TtfDUY 2.1 Ban chat cua day hoc giai toan a nha trircmg thong 27 27 2.1.1 Tam quan trpng cua day hpc giai toan a truang thong 27 2.1.2 Quan niem ve giai toan vaday hpc giai toan 28 2.1.3 Cac budc day hpc giai toan 32 2.2 Tac dong tu-ong ho gifra boat dong giai toan voi ron luyen, boi du-ong, phat trien nang lire tuduy cua hoc sinh 32 2,2A Nang luc tu can thiet tung buoc ciia boat dong giai toan 32 2.2.2 Hinh thanh, ren luyen, boi duong pham chat tri tue toan hpc cho hpc sinh thong qua day hpc giai toan 35 Chuang : PHl/ONG PHAP KICH THICH NANG Life TlTDUY CHO HOC SINH PHO THONG TRONG DAY HOC GIAI TOAN, 3.1 De xuat phuong phap 46 46 3.1.1 Xac dinh dp kho cua cac bai toan dua phu hop voi doi tuang nguoi hpc 46 3.1.2 Nang cao long tu tin cho hpc sinh vao kha nang nhan thuc toan hpc cua hp; tung buac giup cac em tu tim lai giai cac bai toan 51 3.1.3 Bien npi day hpc giai toan (neu co the) tro cac dang tro choi vui ve , thoa mai nhung van nham vao muc tieu day 56 3.L4 Giiip hpc sinh nhan cai hay, cai dep cai thu vi cua toan hpc ciing nhung ung dung thuc tien cua n6 3.1.5 Sudung cong nghe thong tin tro tro viec day hpc giai toan 58 62 3.2 To chirc thuc nghiein va danh gia ket qua 64 Ket luan 91 Cac ky hieu viet tat Viet ddy du Viet tdt Dai hpc Quoc Gia DHQG Giao su tien sT GS.TS Nha xuat ban Nxb Trung hoc thong THPT Tien sT khoa hoc TS KH PHAN MO DAu Ly chon de tai Tu la khai dau cua moi su sang tao Nam 1986, muon doi moi toan dien dat nuac, truac tien Dang ta da dat van de doi mai tu Nha do, chung ta da dat duac tiru tang GDP hang nam tir 7% tra len, Gio day, chung ta tham du vao hpi nhap kinh te toan cau, y nghla va vai tro cua kinh te tri thirc tra cot I5i cua sir tien bp xa hpi Trong kinh ti tri thuc, ngudn nhan luc cang doi hoi duoc nang cao ve tri tue va sir nhay cam; vi the vai tro tu cua moi ca nhan tra dong lire phat trien cua dan toe va thai dai De dap img duac nhu cau d6, van de chat luang tu cua hpc sinh, sinh vien phai duac dat len hang dau Mon toan duac coi la mot nhung mon hpc quan trpng giup ma mang tri tue va phat trien tu 16 gic cho Icrp tre Trong day hpc toan a bac hpc thong, hoat dong giai toan la ca hpi tot nha't de hpc sinh duac van dung, bpc 16 va phat trien kha nang sang tao qua qua trinh dem nhimg tri thirc toan hpc da duac trang bi vao giai cac bai toan cung nhu giai quyet cac van de cupc song thuc ti6n lien quan toi toan hpc De phat huy vai tro cua viec day hpc giai toan, dieu quan trpng can chii y la phuang phap va nghe thuat dieu khien cua Thay, to chirc cho hpc sinh tham gia vao cac hoat dong giai toan mot each tich cue, thoa mai Song, hien a cac trucmg thong, viec day hpc giai toan nhi6u ba't cap Hpc sinh duang nhu bi khuon vao viec giai cac bai toan theo mot trinh tu nhat dinh, lap di lap lai nhu mot nhiem vu quen thupc dien hang nen cac em thuang hay chan nan va mat di tinh chu dong sang tao Con ve phia giao vien lai chi chu trpng den dap so, ket qua cua bai toan cu the han la day hpc sinh biet phan tich de tim each giai bai toan; biet nhan xet danh gia mot bai toan di r6i tijf sang tao each giai quyet cac bai toan khac Vdi each day do, v6 tinh da lam giam di kha nang sang tao dang tiSm an hpc sinh Tir tinh hinh cu the d6, da dat yeu cau nghien cuu de tim phuang phap moi day hpc giai toan nham kich thich nang luc tu cho hpc sinh thdng la va'n de cap thiet Muc tieu nghien curu Cong trinh nham tim phuang phap de kich thich nang luc tu cho hpc sinh thong day hpc sinh giai toan va ung dung vao day hpc m6t s6' dang toan cu the; tijf gop phan nang cao nang luc giai toan, kha nang tim toi, sang tao, gay thu hpc tap toan cho hpc sinh Doi tutfng nghien cuu Phuang phap de kich thich nang luc tu cho hpc sinh thong day hpc sinh giai toan Nhiem vu nghien cuu - Nghien curu ca sa khoa hpc ve tu duy, cac phucmg phap tu duy, ngoai luc, npi luc va nhung pham vi thupc phuang phap kich thich nang luc tu cho nguai hpc - Tim hieu moi quan he bien chung giira hoat dong giai toan voi sir phat triln nang luc tu cho hpc sinh thong, - De xuat cac phuang phap kich thich nang luc tu cho hpc sinh thong day hpc giai toan ciing cac bai giang minh hoa - T6 chuc thuc nghiem va danh gia ket qua PhuoTig phap nghien cuu - Ve phuorng phdp ludn Cong trinh dua tren ca sa ciia chu nghia vat bien chung de lam sang to phuang phap kich thich nang luc tu cho nguoi hoc noi chung va day hpc giai toan a bac hpc th6ng noi rieng - Ve phucmg phdp cu the Cong trinh da sir dung phuang phap nghien cuu tai lieu, di6u tra, quan sat, phan tich, t6ng hap, so sanh, khai quat hoa de nhan cac uu nhuac diem cua n6i dung va phuang phap day hpc giai toan a thong hien nay; tir de xua't phuang phap day mdi nham kich thich nang luc tu cho hpc sinh va trien khai thuc nghi6m de khang dinh ket qua nghien cim Ket qua nghien cuu va y nghla cong trinh - Lam sang to ca so khoa hpc cua viec kich thich nang lire tu cho nguai hpc noi chung va day hpc giai toan a thong noi rieng, - D^ xua't duac phuang phap kich thich nang luc tu cho hpc sinh thong day hpc giai toan cimg vai nhimg bai giang minh hpa - Cong trinh da duac the hien hai bai bao - Cong trinh co the lam tai lieu tham khao cho giao vien day toan a thong va cho sinh vien su pham toan 7.Cau true cua de tai Ngoai phan ma dau va ket luan cung cac danh muc tai lieu tham khao, cong trinh duac chia chuang: Chuomg CO S6 KHOA HOC VE KICH THICH NANG LlTC T U D U Y CHO NGU^ClI HOC 7.7 Mot so net ca bdn cua qud trinh day hgc 1.1.1 Quan niem ve hpc va day each hpc 1.1.2 Quan niem ve day hpc tich cue 1.2 Phuang phap bien doi chat luang tu cua nguci hpc 1.2.1 Mot so khai niem lien quan tdi tuduy 1.2.2 Mot so phuang thu'c ton tai cua tu 1.2.3 Phuang phap bien doi chat luang tu ciia nguci hpc Chuang MOI QUAN QUAN HE GIlTA DAY HOC GIAI TOAN V d l SlT PHAT TRIEN NANG LU^C TU^ DUY 2.7 Ban chdt cua day hoc gidi todn a nhd trudmg thdng ^ 2.1.1 Tam quan trpng cua day hpc giai toan a truang thong 2.1.2 Quan niem v6 giai toan va day hpc giai toan 2.1.3 Cac bu6c day hpc giai toan 2.2 Tdc dgng tirang ho giira hoat dgng gidi todn vai ren luyen, boi duong, phdt trien ndng luc tu cua hgc sinh 2.2.1 Nang lire tu can thiet timg buac cua hoat dong giai toan 2.2.2 Hinh thanh, ren luyen, boi duang pham chat tri tue toan hpc cho hpc sinh thong qua day hpc giai toan Chuang PHirONG PHAP KICH THICH NANG LU^C Tlf DUY CHO HOC SINH PHO THONG TRONG DAY HOC GIAI TOAN 3.1 De xudt phuang phdp Trong ph4n cong trinh da dua phuang phap chung va cac bien cu the de kich thich nang lire cho hpc sinh thong day hpc giai toan ciing vi du minh hpa cho timg bien phap 3.2 To chuc thuc nghiem vd ddnh gid ket qud PHAN NOI DUNG • Chuong CO SO KHOA HOC VE KICH THICH NANG LUC TUDUY CHO NGUdi HOC 1.1 Mot so net ca ban cua qua trinh day hoc 7.7.7 Quan niem ve hgc vd day cdch hgc Hgc va day each hpc la mot van de ca ban cua bat cu* nen giao due nao Mot da't nu6c duac gpi la nude co nen giao due phat trien phu thupc rat nhieu vao each hpc va day each hpc tat ca cac nha trudng, dac biet la d nha trucmg th6ng Do do, viec hieu diing ban chat cua qua trinh day hpc co y nghia quan trpng dinh hudng cho su phat trien nen giao due nude nha Chinh vi the, dieu trude tien cdng trinh muon duac diem qua cac quan niem khac ve day va hpc tir xua den Qua nghien cuu, chiing ta thay: day hpc cd tir thdi co dai Hy Lap (tiic la the ky thu* V trude cdng nguyen) Ngudi md trudng day hpc cd bai ban d^u tien la Platon {427-347 truac CN) Ong md trudng tai khu rimg gan Aten; Day la khu rimg nhan dan Hy Lap de tudng niem than Academ, nen trudng cd ten la Academi, v6 sau cac vien Ham Lam cua cac nude tren the gidi deu lay ten la Academic Trude kia, Platon cho rSng: '' Day hgc la mot cdch kich thich linh h6n'\ Quan niem xua't phat tir ca sd triet hpc coi ngudi cd hai phan : phan The xac (do tinh yeu giua cha vd me tgo ra) va phan Linh hon {do Trai phdi nhap vdo) Linh hon dau tien d vdi thuang de cho nen linh hon am hieu moi chuyen Nhung nhap vao than xac dudi gidi, linh hon quen het Nhiem vu cua cua ngudi thay la kich thich linh hon dd nhd lai nhirng dieu hieu biet sau sac tir kiep trude Vdi quan niem dd, ngudi ta sinh cung cd the gioi duac Hp khdng gidi duac la th^y giao chua biet each kich thich linh h6n hp Anh hudng cua quan niem da dan den nhi6u y kien eho rang: " Thdy nao, trd ndy ! " Cang khoa hpc cang phat trien, eon ngudi cang chii y nhieu den nang luc nhan thu'c cua ban than mdi ca nhan Khoa hpc da chung minh rang, ngoai cac yeu td sinh hpc, chi sd zen thong minh da anh hudng rat ldn den viec hpc tap cua mdi ca nhan Tijr dd, cung xua't hien nhieu quan niem khac \i day va hpc: - Quan niem truyen thdng cho rang: Day la truyen thu kien thuc cua ngudi th^y cho trd, cdn hoc la sir linh hpi kien thuc cua trd Quan niem da theo sudt qua trinh day hpc nha trudng thong d nude ta nhieu nam trude day va cang bpc 16 nhuac di6m ciia nd, Ngoai quan niem truyen thdng d tren, cdn cd rat nhieu y kien khac cua cac nha khoa hpc ve vah de Xin dan cir mot sd y kien: Y kien cua GS Nguyen Nggc Quang: - Hgc la boat dong vdi ddi tuang, dd hpc sinh la chii the, khai niem khoa hpc la ddi tuang de chiem linh Hgc la qua trinh tu giac tich cue, tu lire chiem linh khai niem khoa hpc dudi su dieu khien su pham cua giao vien - Day la dieu khien tdi uu hoa qua trinh hpc sinh chiem linh khai niem khoa hpc va bang each dd, phat trien hinh nhan each [3,93-95] Y kien cua GS.TSKH Lam Quan Thiep - Hgc la qua trinh tu bien doi minh va lam phong phii minh bang each chpn nhap va xir ly thong tin lay tir moi trudng xung quanh - Day la viec giiip cho ngudi hpc tu minh chiem linh nhung kien thirc, ky nang va hinh hoac lam bien doi tinh cam, thai dp [3,147] ngdy Ngudi thii nhdt ddnh trude ngilai thii hai ngdy va sd trang ddnh dupe gdp ldn sd trang ngudi thii hai da ddnh.Hdi tap ban thao cd bao nhieu trang?" Doi vdi hpc sinh lap 9, day Id bdi todn da cd algdrit gidi vi cdc em da dupe hpc gidi bdi bang cdch lap phuang trinh, he phuong trinh Do dd viec hudng dan hpc sinh gidi bdi todn ndy khdng cd gi Id khd khan (chi cdn liruy cdc em cdch chon dn Id so ngdy nguai thu hai ddnh) Tuy nhien, viec tim ldi giai so hpc ciia bdi todn khdng phdi Id de ddng De giiip hpc sinh tu minh tim ldi gidi sd bpc, dieu quan trpng ddu tien cua ngudi gido vien la lam cho cdc em hieu dupe y nghia cua cau " cung mot luc kit thuc mot tap bdn thdo'\ Tren ca sd dd, Gido vien sir dung cdc cau hdi phan tich di len de giiip hpe sinh nhin hudng gidi quye't cua bdi todn De tinh dupe sd trang cua tap ban thao can biet gi? (Cdn biet sd trang nguai nhdt vd ngudi thii: hai dd ddnh dugc) Mudn tinh dupe sd trang ciia ngudi thii nhdt, thii hai da danh cdn biet gi? (Biet ndng sudt vd sdngdy cua ti^g ngudi dd ddnh) Den day, hpc sinh gap khd khan vi khdng the phan tich di len dupe nua Mau chdt cua vdn de la phdi tinh dupe sd ngudi thii hai da danh Gido vien nen giup hpe sinh thao ga khd khan bang phuang phap suy luan theo gid thie't tam nhu sau: Neu gia sir sd trang ngudi thir nhat danh chi bdng sd trang ngudi thii hai ddnh thi nang sudt ldm viec cua hp nhu the nao so vdi thuc te hp da lam? (Gidm di ldn) Theo gia sir ngudi thii nhdt ddnh trude ngudi thii hai bao nhieu trang? ( X = 63 (trang) ) Liic G.V cd the minh hoa ket qua lam viec cua hai ngudi theo gia sir bdng sa dd: 82 Ngudi thu-1 j Ngudi thir \^ 63- ^ ? ^ Hudng dan hgc sinh quan sat sa dd va hdi Tai ngudi thu- hai lai dudi kip ngudi thu nhat? (Do mdi ngu&i thu hai ddnh han ngudi thii nhdt Id 30 -9 -21( trang)) Di duoi kip ngudi thur nhat, ngudi thii hai da danh bao nhieu ngay? (63: 21 =3( ngdy)) Til day, hgc sinh de dang tinh dugc sd ngudi thii nhat danh va cung dl dang tinh dugc sd trang cua tap ban thao Ddp sd: 360 trang Phirong phap quy la ve quen De' tim dugc ldi giai cho bai toan mdi, ngudi giao vien thudng hay giiip hgc sinh lien tudng de'n cac bai toan da timg giai quyet Viec lam ggi la phuang phap tu quy la ve quen Phuang phap quy la ve quen mudn co dugc hieu qua cao ddi hdi nhieu tdi nghe thuat din dat ciia ngudi thay va ca kinh nghiem da cd cua ngudi giai Ngudi giai toan phai co kha nang nhan tinh hudng mdi tinh hudng quen thugc, phat hien dugc cau true chiic nang mdi cua ddi tugng quen thugc Do ngudi giai toan cang can phai biet phan tich dac diem cua bai toan mdi, so sanh, lien tudng cac yeu td ciia bai toan da cho vdi nhirng dinh ly, tinh chat, quy tac, hoac each giai mgt bai toan nao day da lam Dudi day la mgt s6 vi du da thuc nghiem Vi du 1: Hudng din hgc sinh Idp 11 tinh dao ham bac n cua cac ham s6 - X ^ + / (;c) = sin 6x cos4x; /^(.r) = sin5xsin3x Dl hgc sinh tinh dugc dao ham bac n ciia cac ham s6 f,(x) din f5(x) bai thuc nghiem da tiln hanh nhu sau: 83 Trude tien hudmg hpc sinh dimg quy nap dk chimg minh cdng cdc cdng (") Mc: ( J _ ) = ( - ) - - ^ x-a {x-a) n+\ (sinax)f") = a"sin(ax+n|); (cosbx)'"^ = b"cos(bx+ni^) neN* Sau hgc sinh da chung minh va hilu cac cong thire tren, Giao vien chi can Sli dung v^n dap ggi md dl hgc sinh bilt quy ham s6 dang d dang la vl dang cdng thuc quen thugc Din day viec tinh dao ham cua ham s6 tren lai trd ve de dang VI du 3: Hudng dan hgc sinh tilu hgc giai cac bai toan sau: Bdi todn I: Tinh eae tdng sau a.Tinh Sn= 1+3+5+7+ b.Tinh S =0,1+0,3+0,5+ 2n+l 0,9+0,11+ 0,99 ' 1 c — + — + — + 1-2 2.3 3.4 99.100 J 1 1 d — + — + — + —-— 1.3 3.5 5.7 99.101 « 1 1 e - + - + - + 2008 De hudng dan hpc sinh gidi todn bdi todn 1, gido vien chi can day ky cho hpe sinh hieu dugc cdch giai ciia y a vd e; sau dd bang phuong phdp quy la ve quen ggi eho hpc sinh chuyen cdc y cdn lai ve each giai da biet Bdi todn 2: Mot ngudi phai di tir A den B mot thdi gian xae dinh Ngudi dd nhdn thdy rdng nSu cho xe chay vdi van toe 40km/h thi den B mud mot gid Hdi dl tdi B dung gid xe dd phai chayi vdi van toe bao nhieu Bdi todn Mdt ngudi di bp tir A den B vdi van tdc 6km/h Sau di dupe V^ quang dudng ngudi dd giam van toe cdn 4km/h, \'i vay da den B mudn hom du dinh 15' Tim quang dudng AB? 84 Qua thirc nghiem day hoc sinh tim ldi giai bai toan thu 2, cdng trinh nhan thiy ro vai trd, tac diing cua cac cau hdi ggi md tren phuang tien true quan la sa doan thing da lam cho hgc sinh chuyen dugc bai toan vl dang • quen thugc va dl dang tim dugc ldi giai Khi hgc sinh da giai dugc bai toan 2, giao vien cd thi giup hgc sinh tu tim ldi giai bai toan bSng mdt cau hdi ggi hudng sau day:" Gia sir ngudi giam van tdc tir dau thi se din B cham bao nhieu? " Vdi cau hdi cd tac dung kieh thich tu ciia hoc sinh dl cac em co sire bat dua bai toan ba ve bai toan hai da co each giai Sit dung phuang phap trirc quan, suy luan quy nap hoac dua bai toan can giai ve cac tru'dng hgp dac biet de xet hoac dua cac bai toan phu mang tinh chat ggi y cho bai toan chinh Giai toan la qua trinh ddi hdi su tu nhay ben vi bai toan that da dang va phong phii Diing trude mdt bai toan neu chua tim hudng di thi ngudi giai toan can phai thay ddi tu cua minh Gpolya da viet cuon sach " giai mdt bai toan nhu the nao" mdt cau that sau sk; " thdnh cong viec gidi bdi tap nh& vdo xdc dinh phirffng hudng chinh xdc, nh& vdo biet cdng don dung phia" De lam dugc dieu ngudi giai toan phai biet thir nghiem cac mat, cac phia Cd luc phai xet mgt vai trudng hop cu the', phai thir cac diem dac biet hoac dimg true quan h5 trg thao tac tu TTiam chi co the bien ddi bai toan da cho ve bai bai toan gan gui hon, quen thugc han nhu: - Chuyen bai toan phirc tap ve bai toan dan gian han - Chuyin tir trudng hgp chung ve trudng hgp dac biet - Chuyen tir trim tugng ve cu the - Chuyen tir toan the ve bg phan - Chuydn tir ciing ve mam bang each Id rong dieu kien ciia ba toan 85 Tit ca nhCmg digu ndi tren da dugc cdng trinh kiem nghiem qua viec day hoc sinh tim ldi giai mot s6 bai toan sau day: Bdi I: Cho tam giac ABC; Tren canh BC lay them 99 diem, ndi A vdi cac diem ' tren canh BC Hdi cd bao nhieu tam giac tao ? Bdi 2: Cho tu giac ACBD Hay tim each chia tir giac hai tur giac co dien tich bang Bdi 3: Cd hai thira rudng hinh chir nhat va hinh binh hanh nam canh Hay tim each chia hai thira rudng hai phan cd dien tich bang ma tay chi ed cuon day va hai cai egc Bdi 4: Mgt thua rudng hinh thang cd dien tich 200 m^ Day ldn gap lan day nho Ngudi ta chia thua rudng thira rugng hinh tam giac bang each cang day theo hai dudng cheo Tinh dien tich moi phan dugc chia? Ball- Cho tam giac ABC c6 dien tich 1200cm^ Tren canh AB ta ISy diem N cho BN bSng 1/3 AB Tren canh AC \ky dilm M cho AM=MC Noi BM va CN giao tai o Tim dien tich tam giac ABC Bdi 6: Cho tam giac ABC, tren canh AB va AC \iy l§n Iugt hai dilm M va N cho AM gap ddi BM, CN bang 1/3 AN Hai doan thing BN va CM cat tai Ndi AO keo dai cat BC tai P a.Tinh dien tich tam giac ABC bilt OBC bang 12 cm^ b Xac dinh ty so hai doan thang PC va PB Bdi 7: Cho cdc s6 tu din Hay diin vdo trSng tren mSr canh cua tam gidc cho tSr^g cdc s6 tren m6: canh bang nhar vd tang 86 Bdi Cho bdn dudng trdn tiep xuc tai dim Tir dilm tilp xuc ke bin dudng thang cat cac dudng trdn tai 16 diem Hay dien cac so tir 1-17 vao cac giao diem ciia dudng thang va dudng tron cho tong cac sd tren dudng tron bang 39 Bdi 9: Mdt ba ban hang that cd mgt cai can hai dia, Ba khdng tin vao can cua minh, Ba nghi: " Ne'u can thie'u cho ngudi mua la cd tgi, cdn can thiet cho minh thi Ba khdng mudn Ba nghi mgt each can nhu sau: Can sd hang cua ngudi mua lam hai ldn bang nhau: Ldn thii nha't: Hang dat ben thi qua can dat ben Lin thiic hai : Ba lam ngugc lai lan mdt Hoi ba lam the ba thiet hay lgi ? Cac bai toan d tren diu la nhimg bai toan ma hgc sinh khong phai de dang tim dugc ldi giai Song, nhd su tac dgng cac bien phap kich thich nang luc tu cho hgc sinh, cong trinh da cong bai day thuc nghiem vdi kit qua tdt Cdng trinh xin dugc neu va phan tich each day bai toan ndi tren Cdch day bdi todn 1: Viec tim hudng giai quyet cua bai toan khdng he kho khan ddi vdi hgc sinh da dugc trang bi kien thiic ve ly thuyet t6 hgp De cac em biet van dung kien thiic da hgc vao giai quyet bai toan mgt each sang tao, giao vien chi can ggi cho hgc sinh thay dugc 101 die'm tren canh BC thang 87 h^ng nen khdng th^ tao cac tam giac tir 101 diem dd Vdi ggi y hgc sinh de dang di d^n each giai 1: S = C^^^- (j^^ = 5050 (tam giac) Giao vien cung cd the' ggi cho hgc sinh thay dugc mdi lien quan giua sd * tam giac vdi sd'doan thang tren canh BC de cac em di den each giai : S = C,'o, =5050(tamgiac) Tuy nhien, hudng dan hgc sinh giai bai toan tren cac em chua dugc dugc trang bi kiln thirc vl ly thuylt td hgp la khd khan bdi cac em khdng the dem true tiep het dugc sd tam giac Dieu quan trgng each hudng dan la phai lam cho cac em nhan tha'y : - Mdi quan he giira sd diem them vao va phep toan tinh sd tam giac tao dugc tuan theo mgt quy luat t Sd diem them vao Sd tam giac tao 2+1 3+2+1 4+3+2+1 99 100+99+98+97 +2+1 - Bie't thuc hien phep tinh mgt each sang tao roi tir phat hien cong thiic: Sn = 1+2+3+4 (n + 2)(n + \) +n+l = ^ ^^ - Sau giai xong bai toan tren, giao vien cho hgc sinh giai tiep cac bai toan tir viec khai thae bai toan da lam dl tao ca hgi cho hoc sinh bgc 16 kha nang sang tao: Bai toan khai thae: Dua tren ket qua sd tam giac da tinh dugc d bai tren, yeu cau hoc sinh ndi nhanh sd tam giac, tii giac tren hinh ve 88 B A, Ag9 c Cho HS dem sd hinh chu nhat tren hinh ve (H) sau day: Cdch day bdi todn Day la mgt bai toan thuc tien vdi ngon ngir phong phu dong thdi chiia dung ham y mang tinh chat giao due Viec hudng dSn hgc sinh tu giai dugc bai toan cd mgt y giao due quan trgng No khong chi ren tu linh hoat van dung kien thiic Toan hgc vao giai quyet cac tinh hudng cugc sdng thuc tien ma cdn gay dugc cam giac thii vi, su to khoa hoc ciia hgc sinh, tir cang lam cho cac em yeu thich Toan hgc han Viec tu tim dugc ldi giai bai toan khdng phai la de dang ddi vdi hgc sinh d mgi bac hoc Song, neu ngudi giao vien biet each din dat thi chinh hgc sinh cung tu tim ldi giai mgt each nhe nhang 89 Vdi bai toan nay, giao viSn nen sii dung phuong phap giang giai minh hoa ket hgp phuong tien true quan ciing win dap ggi md de' giiip cho cac em co dugc: - Bie'u tugng ve can hai dia, each sir dung loai can - Hie'u y nghia ciia cac tir cdn thieu cho ngudi mua , can thiet cho minh - Dac biet hie'u dugc each Ba da can bai toan va cau hdi cua bai toan cung nhu chuyin dtrge bai toan thue tiln vl bai toan toan hgc Gia sir lugng hang cin mua la 2a Lan 1: a -> X Lan y ->a H • Cdn tmh x+ y > 2a Vdi sa md ta each Ba can bai toan da gpi cho hpc sinh nghi den mdi tuang quan ty le thuan : a y y= a va de dang tinh dupe X x + y = x + — > 2a (" Cung co hdt ddng thuc Cosi) X Gido vien c6 the gpi cho hpc sinh mot each giai khac dua tren mdi tuang quan ty nghich giira khdi Itrong hang dat tren dia can va dp ddi canh tay ddn: a L - = — = > X = —^ ^ =iL^y=^ y I2 Vayx+y = ^ ^: h 90 + > 2a KET LUAN Cdng trinh Kich thich nang luc tu cho hgc sinh phd thong day hgc gidi todn da giai quyet dugc eae van de sau : Da lam sang td nhimg co sd khoa hgc eua viec kich thich nang lire tu cho ngudi hgc ndi chung va cho hgc sinh d phd thdng day hgc giai toan ndi rieng De nghien cim win dh nay, cdng trinh da phai giai quylt cac van de khoa hgc quan trgng cd lien quan din de tai nhu sau : - Quan niem ve hgc va day cdch hgc Ci day, cdng trinh da nghien cim tir quan niem day hgc cua Platon, Arixtot; tir trudng phai « tieu dao », sir dung van ddp phdp cho den each day hgc truyin thing lay Thay giao lam trung tam va nay, phuang phap day hgc lay ngudi hgc lam trung tam; tir cong trinh da de xuat quan niem vl day hgc tich cue cua minh : « bdn chdt cua day hgc tich cue la mgt qud trinh ngudi thdy biet to chdc, dieu kien hgc sinh, de cdc em biet tu bien doi nhiimg kinh nghiem ben ngodi thdnh kinh nghiem ben cda chinh minh kem theo khd ndng Met van dung, sdng tao » - Cong trinh cung da giai quylt vSn dl bien phdp bien doi chdt lugng tu cho nguffi hgc Cdng trinh da di tir quan niem chung ve ban chat cua tu duy, din ddi tugng cua tu duy, nang luc cua tu duy, den cac kieu ton tai ciia tu Cdng trinh da dua vao luan dilm cua Heghen {nhd triet hoc Co dien Due md C.Mdc dd ddnh gid rdt cao) chia tu ba kieu : Tu khoa hgc, tu hinh tugng cua nghe thuat va tu bieu tugng cua tdn giao dk tap trung vao vai tro ciia tu khoa hgc va tu hinh tugng day hgc giai toan Cdng trinh cung da dk xnk dugc cac phuang phdp kich thich ndng luc tu cho hgc sinh phd thong day hoc giai toan D I de xudt phuang phap kfch thich nang lire tu duy, cdng trinh da dua cdc quan niem cua bdn thdn v6 mot sd cae vdn dk : - Quan niem v^ gidi todn vd day hpc gidi todn theo dinh hudng tich cue - Quan niem ve nang lire tu vd kieh thich nang lire tu - Ca sd tao nang lire can thiet cho hpc sinh timg budc cua day hpc giai todn Giup hpc sinh thuc hien kk hoaeh gidi todn - Giup cdc em biet nhdn dinh ddnh gid ket qua gidi todn di ndng cao long tin ve nang luc hpe todn bdn than Cdng trinh ciing da de xuat viec hinh ren luyen, bdi duong phdm chat tri tue todn hpc cho hpc sinh phd thdng thdng qua day hpc gidi todn Cdc vdn de nhu tao eho cdc em biet suy ludn tren dir kien, kha nang suy nghT theo hai chiSu; dp nhay cdm, tri tudng tupng ngoai suy tren phuong dien noi suy Id nhirng co sd de hinh thanh, ren luyen, bdi dudng pham chat tri tue thong minh (IQ) eho hpc sinh Cdng trinh da de xudt cdc budc eu th^ de kieh thich nang lue tu cho hpc sinh day hpc gidi todn dd Id : - Xdc dinh khd cua cdc bdi todn can day cho phu hap vdl ngudi • • hoc vd muc tieu dgy hgc - Ndng cao long tu tin cho hgc sinh vdo khd ndng tu todn hgc cua hg; tirng bu&c giup cdc em tu tim l&i gidi cdc bdi todn - Phdt Men nhirng thiiu hut kien thuc cua hgc sinh vd bien phdp khde phuc kiin thirc todn hgc cho hgc sinh thong qua hoat dgng giai toan - Bikn kho thdnh d'e qua each din dat hgc sinh di tim ldi giai bai toan bing cac cdu hdigffi md, cdc phuang tien true quan h6 trg thao tac tu tren v6n tri thirc da cd ciia ngudi hgc - Ndng cao hieu qud cong tdc kiim tra ddnh gid kit qua hoc tap mon toan ciing viec day hgc sinh biit tu hgc, tu kiim tra minh 92 - Bien ngi dung dgy hgc gidi todn (niu co thi) trd thdnh cdc dgng tro chon vui ve, thoa mdi nhung vdn nhdm vdo muc tiiu bdi dgy ddng thai tdng ardng cho hgc sinh gidi cdc bdi todn thuc tiin - Diing cong nghe thong tin di hd tra viec kich thich ndng luc tu cho hoc sinh de cac em them chu dgng, sang tao Cong trinh cung da tiln hanh thuc nghiem va danh gia kit qua nghien CIJU tren bon chuyen de day hgc giai toan cho hgc sinh lap 12 la: - Chuyen de cac bai toan vl hinh hgc giai tich - Chuyen de cac bai toan vl hinh hgc khong gian - Chuyen de cac bai toan vl ham s6 - Chuyen de cac bai toan vl phuang trinh, bat phuang trinh Cdng trinh cdn thuc nghiem mgt so bien phap kich thich nang tu dl giup hgc sinh tu tim each giai mgt s6 bai toan Kit qua ciia ly luan va thuc nghiem da chimg td tinh kha thi cua win dl nghien cim, dac biet la cac bien phap kich thich nang luc tu cho hgc sinh phi thong day hoc giai toan ma cdng trinh da dua Cdng trinh sd di dat dugc nhirng ket qua tren la nhd su quan tam ciia Ban Chu nhiem Khoa Su pham DHQG Ha Ngi, dac biet la Chi nhiem KhoaPGS TS Nguyen Thi My Loc da luon tao dieu kien thuan lgi cho cac hoat dong nghien ciru cua tac gia cong trinh Ben canh do, cong trinh nhan dugc sir giup dd nhiet tinh cua Phong dao tao va nghien cim Khoa hoc, to Bg mon Phuang phap, cdng nghe day hgc ciia Khoa Su pham, DHQG Ha Ngi ciing rii nhilu cac GS TS, cac Thiy co d nha trudng thong Trong dilu kien va hoan canh cho phep, cong trinh mdi chi dimg lai pham vi nghien cuu ca ban vl dac trung ciia tu va kich thich nang lire tu day hgc giai toan; ding thdi thuc nghiem chgn Igc pham vi nhat dinh, nham tudng minh nhimg win dl ly luan dat Tuy nhien, ket qua 93 nghien ciru cua cong trinh la ca sd budc ddu rat quan trpng dk nhdm tdc gia cd the ti^p tue nghien cuu, triln khai thuc nghiem viec kieh thich ndng lire tu cho cac ddi tuong hoc sinh khde tren timg dang todn, timg cap hpc cua " bac hpc phd thong Trong thdi dai hdi nhap kinh te todn cdu, khd nang iu ciia ngudi trd thdnh mot tdi sdn vd gid, Nhung mudn cd dupe tdi sdn quy bdu ndy khong phai de ddng, bdi tai nang md ngudi cd dupe chi Id 1% bam sinh, cdn 99% lao ddng sang tao Vdi ket qud nghien curu cua cdng trinh, viec tim tdi va de cao phuang phdp kich thich ndng luc tu mgi linh vuc ndi chung vd day hoc giai todn ndi rieng nhdm bi§n nang lire tu trd thdnh to chdt rieng cho ngudi hpc vd biet dat to chdt vdo boi canh cua thdi dai van minh so phdi la mgty thuc thudng true ddi mdi phuong phdp day hpe hien 94 TAI LIEU THAM KHAO Bd Giao due va dao tao, Hdi nghi tap huan Phuang phap day hgc mon Toan phd thdng, Ha Ndi -2000 Hoang Chiing (1997): Phuang phap day hgc mdn Toan d trudng THCS -Nxb Giao due Giao due hgc dai hgc, Trung tam dam bao cha't lugng va nghien ciiu phat trien phat trien giao due nam 2000 ( sach luu hanh ndi bd) Pham Minh Hac ( 1989 ): Tam ly hgc - Nxb Giao due Nguyin Phu Hy, (2000): iing dung gidi han de giai toan trung hoc th6ng Nxb Giao due Nguyen Phu Hy, (2000), Cac phuang phap giai Phuang trinh, bat phuang trinh va he phuang trinh Nguyin Ba Kim, Vu Duong Thuy (1992): Phuang phap day hgc mdn Toan - Nxb Giao due Le nin (1977) But ky triet hgc NXB sir that Nguyen My Ldc (2004) Mot s6 win de ve giao due hoc dai hoc,Nxb DHQG Ha Ndi Nguyen Hthi Luang(2002): Day va hgc hgp quy luat hoat dgng trf 6c, Nxb Van hda thdng tin 10 Nguyen Vu Luang(2007): He phuang trinh va phuang trinh chiia can thirc, Nxb DHQG Ha Ndi 11.(Mac -Angghen.Nhirng ban thao vl cac van de kinh te va triet hoc-Toan tap, tap III Nxb ST, Ha Ngi 1971) 12 Nguyen van Mau (2004) Chuyen de boi dudng hgc sinh gioi toan THPT: Mdt sd van de chon Igc ve ti'ch phan - Nxb giao due 95 13 Lam Quang Thiep ( 2000): Viec day va hgc d dai hgc va vai trd cua nha giio due dai hgc thdi dai thong tin, (Bai dang Giao due hgc dai hgc, Trung tam dam bao chat lugng va nghien ciiu phat trien phat trien giao due nam 2000) 14 Chuang trinh giao due phd thdng mdn Toan, Nxb giao due 15 De thi tuyen sinh vao cac trudng DH, CD, THCN Nxbl995 Id.Gidi thieu de thi tuyen sinh 1997-1998, 2000-2001, 2002-2006 ciia cac tac gia Doan Minh Cudng, Le Thdng Nhat, Nguyen Phii Trudng, Trin Tuah Diep, Ngd Long Hau, Nxb Ha Ndi n.Luat mdi trudng Qule hdi thdng qua 27/12/1993 Nxb Chinh trj Quic gia HNl994 18 Aendnddp, Co sd ly luan Van hoa Mac-Lenin, NxbVan hoa 1983 19.1nmanuen Kant Toan tap, Nxb Tu tudng, Matxcova, 1966, tap 4, tr366) 19.Jean- MarcDenomme' et Madeleine Roy, Pour une pedagoie interactive (Tie'n tdi mdt su pham tuang tac Ban dich tieng Viet, Nxb Thanh Nien nam 2000 20.Sue Johnston-Wilder,Peter Johnston.-Wilder, David Pimm and Johnwestwell (1999) Learning to teach Mathematics in the Secondary schoolLondon and new york 21.Nguon gdc vd nhung khia canh xd hgi triet hgc cua trdo luu gido due "hudng vdo ngU&i hgc'\hao Van nghe sd 20, 18-5-2002) 22 (Tu lieu cua An ninh the gidi 14-5-2005 sd 421, tr 28) 96 ... diing lai d tu ly tinh, qua de cao tu ly tinh giao due thi de rai vao phien dien, kieu giao due nhu the' cung de tao ngudi thieu ddng bp Trong khoa hpc giao due hien nay, ngudi ta khong chi nhdn... day: Bai Todn la gi ? The nao la giai todn? The nao la day hpc giai toan ?, Diem khac ca ban ciia hai qud trinh giai todn va day hpc giai toan la gi? Trong cac giao trinh cu ve phuang phdp day... qua trinh tu giac tich cue, tu lire chiem linh khai niem khoa hpc dudi su dieu khien su pham cua giao vien - Day la dieu khien tdi uu hoa qua trinh hpc sinh chiem linh khai niem khoa hpc va bang