BOI DUIQNG TIf DUV THUAT GIAI CHO HOC SIHH TROHG DAY HOC GHD flt SOPME f TRDONG TODNG HOC PHO THOHG Q TS NGUYEN THANH HUNG'''' ThS TRAN NGUYEN QUANG T H A I " T }/ duy iKu^t glol {TDTG) cOa hcpc sinh (HS[.]
BOI DUIQNG TIf DUV THUAT GIAI CHO HOC SIHH TROHG DAY HOC GHDfltSOPME f TRDONG TODNG HOC PHO THOHG Q TS NGUYEN THANH HUNG' - ThS TRAN NGUYEN QUANG T H A I " }/ iKu^t glol {TDTG) cOa hcpc sinh (HS) b$t cdc thao tdc cd khdi ni^m, djnh If, cdng frong dgy hpc (DH) to6n id Ichd nOng ngudi thi}c, dtrSn hpc c6 thl tlin hdnh cdc hoqt d$ng sou: Budc 4: Hudng dSn HS nhin dgng vd ihi hiin - Thi/c hi$n cdc ihao tdc hpc t§p iheo m$t trinh ti/ thuc ihl hl^n ndng li/c xdy di/ng thu^t gldl) Budc I: Tqp luy^n cho HS thdi quen phdn tfch, Trong DH todn chO d l «Sd' phi/c" d trudng nhdn dpng bdl todn Nlu bdl todn dua ro dd c6 THPT, chOng tdl d l xud't m$t si bign phdp sou thudt gldl tht tlln hdnh tht/c hi3n theo thu$t gidl nh&n gdp ph^n bSl dudng, phdt trlln TDTG cho (T,) Nguqc Iql, to chuyin sang budc HS theo i^nh hudng: ddp ung dupe myc tlSu c6a Budc 2: R^n luyen cho HS bilt biln ddl bdl vlk: DH todn, bdm sdt chuong trinh sdch gido todn v l dqng quen thu^c GV c^n gql d^ng co, khoa hl$n hdnh, gdp phdn hinh thdnh nhdn cdch, lol cudn HS vdo hopt dpng tim tdl nhung phuong tinh ti dnuc, kT lu$t, tfnh tfch eye vd sdng tpo ^ongphdp (PP) mdl d l duo bdl todn v l dqng dd bilt Ddy Id khdu quon trpng vd khd khdn nhd't hpc tpp cua HS: Xdy difng quy trinh DH v l chil d l hoqt d$ng gldl todn GV cdn hudng dan HS cdch huy ddng kiln thue tong hpp de Hm phip blln *Si phijc' Budc 1: Ldm ndy sinh nhu c^u nhdn thOc cua d^l thfch hpp Budc 3: Sou dd blln dll, duo bdl todn v l HS hpc phdn kiln thue: «S^ phik* budc ndy, gido vl3n (GV) cd thl tlln hdnh theo m$t dpng quen thudc, HS c6n cd k l hopch gldi rll cdch: N§u vi^n d l hodc cho HS Idm m$t thi/c h l ^ Ldi gidi phdl ddm bdo m^t sd ySu du so vf dtf vd phdn vf dv, ti> dd phdt hl^n ro v^n d l nhu: khdng cd sol idm (ldl gidl khdng n3n sal sdt Budc 2: T6 ehue, hudng dfin HS tdc dpng v l kiln thiic todn hpc, v l PP suy lu^n, kr ndng Knh vdo dii tupng nhdm phdt hlSn ro dd'u hl^u bdn todn, v l kf hidu vd ngdn ngt> dlln dqt); l$p lu$n ed chd't, c^u trOc logic cOo kiln th(>c mdl GV dua cdn cu chfnh xdc (trong tung budc blln * l PT deu cdc phuong tl$n tn/c quon, vf dv vd bdl t$p, cd CO sd If lu$n); ldl gidl d ^ dO (xem xdt d ^ dO yiu edu HS quan sdt, phdn tfch, tSng hgp, so cdc khd ndng, kh&ig bd sdt trudng hpp ndo) Budc 4: Kllm tra ldl gidl, kit qud Gldl todn sdnh, trih) tupng hda, tim bdn chd't cua vd'n dl JO dd, khdl qudt hda thdnh khdl nl$m, djnh Id m$t hoqt d^ng todn hpc ting hqp, bao gdm nhllu khdu: n6m vOng kiln thue, si) dgng cdc cdng If, cdng thiJc, ^ Budc 3: Cho HS phdt bllu \q\ khdl nl$m, djnh If, cdng thOc ndu d budc dudi dqng m$t thudt *Tn«i{B9llivcTayN0i)iiB gldl GV cdn dua ro cdu hdl thfch hpp Idm n^l -;) chlo cdc Irudng hpp cy thl, dlln dqt rd rdng, thl hl|n ldl gidi dudi dpng vdn bdn, Trong qud a2x-Ay^•(ix^•2y)l = (i^•x-2y)+(2x•^y+\)i trtnh h-lnh bdy ldl gldl, HS cd thl miSc sal ldm, A2x-,ydo v^y, GV cdn ludng trudc cdc khd ndng cd thl 2x-iry-¥\ \2x-\-y = \ " [>' = -3 xdy d l hudng dfin HS trdnh nhOng sal \6m Vdy, phdn thyc cOa z Id 2; phdn cOa z Id - md cde em thudng m6c phdl, ding thdi, phdn Budc 4: HS cd thl mdc phdl sol ldm sou: tfch nguyin nhdn dfin din sol Idm dd vd d l qud trtnh blln d l l , khdng ndm vOng cdc phdp bl$n phdp kh6c phyc Budc 5; Rdn luy|n cho HS khd ndng nghldn todn cdng, tri), nhdn vd chlo hal s£f phik ndn cdc ei>u ldl gldl Khai thdc, phdn tfch vd ttm tdl ldl em thye hl|n phdp tfnh sai, xdc djnh chua di)ng gldl khoo hpc nhdt s9 glup HS budc ddu t0p dupt phdn thyc, phdn Budc 5: Trudc gldl, GV cho HS phdn tfch nghldn cuu khoa hpc, ndm dupe bdn chdt cOa vdn d l Hoqt d$ng ndy cd ^ nghTo rdt quon trpng, rd ydu edu, nhdn dpng bdl todn, blln ddl dua PT v l PT CO bdn, PT bde nhdt h | s6 phuc Tlln hdnh glOp HS lya chpn duqc thudt gidl t6i uu gldl PT thu dupe, Hm nghl|m thdo mdn ydu cdu Budc d: Hudng ddn HS Hm cdc bdl todn lidn cuo bdi todn quan, md r^ng bdl todn ban ddu ihdng quo cdc Budc d; Ydu cdu cua bdi lodn dua din vl$c thoo tde tu nhu: luong ty hda, khdl qudt hda, phdn tfch, tdng hpp vd so sdnh GV cdn tdp dupt gldl PT chua mdu myc Dqng PT ndy gdy khd khdn cho HS qud trinh gldl GV cdn glup eho HS bilt so sdnh mdt bdl todn vdl nhOng bdl todn tuong ty, Hm ro ddc dllm chung v l hinh thue, HS ndm vOng cdoi gldl PT dqng ndy Luy^n tdp cho HS gldl cdc bdl todn dd ndl dung hodc PP gldi m$t sd bdl todn don gldn, li> dd, xdy dyng thudt gldl cdc bdi todn tdng qudt bilt thudt gldi Trong chuong trinh lodn d THPT, HS dupe ghSi Vf dif )\ Cho sd' phi>c z thda mdn: (l + 0*{2-/)2=8+i + Cl + 2i)z Tim phdn thyc vd thl|u mdt sd bdl todn vd cdch gldl cdc bdl lodn dd GV cdn giOp HS ndm vOng vdn d l , nhd vd phdn cuo z? vdn dyng thdnh thqo cdc quy trinh, thudt todn c6 Budc 1: Ddy Id bdl todn Hm phdn thye, phdn sdn, cd indi quen tim cdc PP khdc vd ^pn cuo sd phuc z chua cd thupt gldl Bdn chd't PP ldl uu d l gldi quylt vd'n d l cuo bdl todn ndy Id gldl PT ttm sd phuc z, sou dd Vif c/y 2: Ttm sd phik nghjch ddo r ' cOo sl xdc djnh phdn thye vd phdn phuc z * Budc 2: Biln d l l PT v l dpng quen thu^c dd Tliudt gidl 1: Cho sd phuc z = a+b/ * , (a, b) bilt thudt gidl ER Di thyc hl$n thudt gidi gdm cde budc sou: - Cdc/j f: Ttiyc hl§n chuyin v l , d$t z ldm nhdn Budc /.-TJm mddun eua sd phuc z; |2l=i/o'+A'; tu chung, rut gpn PT, dua v l PT bde nhd't theo d'n z Gldi PT bde nhdt dd cd thu^t gidi - Cdch 2: Gid su z = x + yl Id sd' phuc cdn Budc 2: Tim sd phik lidn hpp z cOa sd f^iJc z: Hm Tlln hdnh rOt gpn theo tung v l cua PT, su z = a-bi; Budc 3: Kit ludn sd phuc nghjch ddo dyng dllu kl|n bdng nhou cua nol sd'phi>c d l Hm X vd y Budc 3: Gldl bdi todn theo cdch sou: Cdch V (1+/)'(2-0i-B + (*CI+20ro(2(K2-i>-{l + 2j> = + i VTc/v 3: Gidi PT bde hoi mdt d'n: az^ + i a + c > (a ^ 0), dd a, b, e Id sd' phi>c ô.-[4,+2-i-2yl=8.,o iii.li^ "ã ' l + 2i Thuit gidi 2: Budc 1: Xdc djnh cdc h^ sd a, b, 8-15i+2 10-15/ , , ,, , , c vd Knh bl$t thue A = t^ 4oc; Budc 2: Nlu = = — - — =2-31 Vdy, phdn thi/e cda A = 0, kit ludn PT da cho cd nghldm kdp z Id 2; phdn cua z Id - Cdc/i 2: Ddt z X + yi, dd x, y Id cdc so' thi/c To ed: Zi = ^1 = - — ; ngupc Iql, chuyin sang bude 3; (l + 0'(2-Oz = 8+i+(l+20z Budc 3: Ttm Id mdt cdn bqc hoi ci3a A; Budc 4: Tap chi SlJio due s6 (ki a ^ io/aoiai Kit ludn PT da eho cd hal nghldm phdn bl^t: Bde cao: C6 kr ndng tlln hdnh hoqt dpng TDTG Bde cao han: Cd kT xdo Hin hdnh boot ddng TDTG) Rdn luy$n Id ndng biln ddl bdt todn gidi PT sou: oj z= - 2z + (1 -21) = (Wudng dim: Budc I: Ta choHS c6:0 = 1; b = - 2; e = - 21; A' = 2/ = (1+1)^^ 0; Blln dd'l bdl todn da eho v l bdl todn dd c6 Budc 2: A' = 2/ = (1 +/)2 * 0; Budc 3: A' ed hal thu^t gldl Id vl$c rd't quan trpng Hdu hit cde cdn bde hoi Id: ±{l+l); Budc 4: Ket lu^n: PT dd bdl todn diu cho d dpng phuc tqp, gdy khd cho cd hal nghldm phdn bl^t z, = -I, Zj = 2+1) khdn cho HS qud trinh gldl Do dd, d l h) 2lz^-2{S-l)z-yl3-l = {Hudng dSn: gldl bdl lodn, ddl hdi HS phdi ed kr ndng blln dd'l bdl todn 8udcJ:Tacd:a = l ; b « ( > / - ; c = - V - / ; Vf dl/ 5: GV hudng dfin HS ndm vOng cdng A' = 0; Budc 2: A' - Kit ludn PT dd cho cd thue dqng lupng gidc cOa sd' phi>c: z = r(cosip-ism0,g>BR thdng qua ydu cdu nghi^m kdp: Z| =z,=— /—) sou: Cdc cdng ttii>c ndo dudi ddy td ddng? Si> dyng hqp If PPDH phdn hod a) = r(cos^ + isin2p),r>0,9»e^; D l vi^c Sl) dyng PPDH phdn hod theo hudng phdt trlln TDTG d$t hi$u qud cao, ddl hdl GV b) z = r(ain^ + icos0,peR; phdi xdc ^nh dupe trinh dd ciJa HS Mu^n v$y, c) r = r(cosp-/sin(!)),r > , p e / ^ ; GV cdn thyc h l ^ phdn bde hoqt dqng TDTG: d) z = r(-cx>sg)-lsia0,(peR; /; Phdn tdc rfieo btnh di$n nhin thdc: Ddc To cd: edng thue a) Id sal, cdc edng thue b), Knh cy thl hoy trOu tupng cOo ddl tupng Id mpt cQn cu de phdn bde hoqt ddng TDTG Bde ihip: c), d) ed thl blln dd'i lol nhu sou: Tlln hdnh hopt ddng t r ^ nhung doi tupng ey b) i»f(>in«' + ":oip),r>tl,peflOi=.i- codfl-pl+'iinlY-p) thl Vf dv 4: Viet cdc sd phuc sou dudi dqng c) r=i0,^eJl«>i = f-[cos(-fl>)+isin{-p)] lupng gidc: a) z = ^ / ; b ) z = ^+i;c) z=^j6-ij2: d) I - r(-cosp-*iin(i),r >0,p fRi = r[coi(;r+fl>)+,sin()F+p)] d) z=2 Bde coo: Tlln hdnh hopt ddng TDTG trdn GV ydu edu HS nil ro cdc dd'u hleu d l nhdn dll tupng tn>u tupng hon blet cdng ihuc Id: cdng thue phdi cd hal 21 Phdn bgc theo nil dung cOa hogt dgng TDTG: Cdc hopt ddng TDTG ed thl dupe phdn hdm s^ sin vd cos; cdc hdm sin vd cos eua eCing bde dyo trdn npl dung eua hopt dpng Ndi dung mdt gdc (hodc c6ng mql eung); sd mO cOa hdm cOo hoqt ddng Id nhung tri thue lidn quan tdl sin vd cos Id 1; dd'u dung lien trudc isin^ phdl hopt dqng Bic thip: Md td thudt gldl bdng ngdn Id dd'u +; r ludn duong V i ^ rdn luydn cho HS kr ndng biln doi cde ngu todn hqc Chdng hpn, sdch gido khoa da ndu thudt gldl gidl PT: oz^ + fcz + c = vd bilu thue todn hpc glup HS phdt trlln dupe ede hopt ddng cua TDTG cung nhu xdy dyng thudt az + b = vdi a, b, c vd z Id sd" phuc Bde coo: Md td thudt gldl bdng ngdn ngu so dd khd'l gidl cho cdc bdl todn chua cd thudt gldl Rdn 6dc cao hon nua: Md td thudt gidi bdng ngdn luy$n cho HS kt ndng blln dd'l bdl todn chfnh Id rdn luyln cdch nhln bdl todn dudi nhllu gdc ngCr ldp trtnh 3) Phdn bde theo sy p/iiJc hgp cua hogt ddngkhdc nhou vd phdt trlen TDTG eho cdc em d Cung dp cho HS cdc tri thue PP v l TDTG TDTG (sy phuc hqp ci3a hopt ddng cung Id mdt Qud trtnh xdy dyng mdt thudt gldl cung Id cdn cO di phdn bde cdc hopt ddng TDTG Bde rfid^; Xdy dyng mpt thudt gldl- B ^ coo; Xdy dyng qud trtnh gidl mpt bdl todn ehuo cd ihudt gldl Vt vdy, nhung tri thi>c PP v l TDTG phdl Id mqt bd thuqt gldl 1^1 uu hon) 4) Phdn bde thea chit lugng cOa hogt ddng phdn hpp thdnh Irl thi>c PP gldl bdl todn Theo (Xem tlip Irang 53) TDTG {Bde thd'p: Bilt tiln hdnh hoqt ddng TDTG "' -h-\-S ~b-S 7a ' ^^ •T^'^^6, HSdpdyngvdo Tgp Chi BIJiO due s6 tut a • io/aoia) dlim diu din ndm hgc) vdl quy Mnh g i m budc sou: Budc Blin sogn tdl llSu D l hinh thdnh ndng Igc DHTH cho G V , chung 161 dd t l ehue bidn sogn tdl ll^u hudng dfin DHTH d ede mdn Vit ll; Hod hgc; Sinh hgc; NgO vdn; Ljch su vd Dja If; Budc Ti chuc tip hud'n cho GV T l chiJc tgp hud'n v l DHTH cho GV phd thdng vd sinh NHdn trudc dl ihye t$p su phgm Trong budc ndy chO y i u Id cho GV hiiu rd nhOng n§l dung cfin TH vd edeh khol thdc cdc gid h-j TH n$i dung Tlieo hudng TH, nhllu nt;dc h-dn H i l gidi dd duo vdo hvdng hvng hgc ede mdn hgc mang tinh TH chfing hgn nhu d Aush-allo: n^l dung hgc tip cOo HS phd Hidng gdm tdm Irnh vge hge chinh thi>c {national l»y learning areas): Ngh$ thuQI; Tllng Anh; Gido dye H i l ehd'l; Ngogi ngi?; Todn; Khoo hge (U, Hod, Sinh); Nghldn euu xd h|i (Vdn, St), Djo) vd Mdl hvdng; Cdng ngh| TiehiJc nhu vfyy sd gldm duge sd mdn hgc Irong nhd hvdng DHTH d cdc trudng phi ihdng theo dung f nghTa cOa nd, ddi hdl phdl thoy d l l chucmg Irlnh, sdch gido khoa, cdch dgy, edeh hge vd Bdl duvng tir Oiuat gial (Tlip theo trang 47) cdch kilm tra thl ci) Ddy Id cdng vl^c khdng don gldn, vi hi§n cdc trudng su phgm vfin dong ddo Igo GV theo chuong Irlnh ei3a cde khoa hgc ridng rS Hi vgng Irong Hidi glan Idl cd nhi/ng thay d l l cdn bdn h-ong gido dge d l ed m i l nln gido dge hdl nh$p vdl cdc nude h-ong khu vyc vd qud'c l l Q T&lli^u tham khdo Trin Bfi Hoiinh D l i mdl p h m n g p h i p d^y b^c, chtnmg trinh vd sdch gido khoa NXB D^l h^c su phaim, H 2007 Xavier Roegiers Khoa Sirph^m tfch h hay ldm th£ Ddo d l phdt triJD cdc ndng li/c d* nhd trudng NXB Gido d\fc, H 1996 (Ngirtri djch: Ddo Trpng Quang - Nguyfin Ngpe Nhj) AJI.J^aHlijnoK Teopnti HHTerpauHH odpaso HsiWTejibCTBO Prrry 344O82 r PocTOB-Ha-floHy CaAOBax, 2000 SUMMARY Integrated teaching is one direction in order to contribute to improving the quality of teaching in schools Therefore research is needed to apply integrated perspective In teaching F^oject level of mlrdstrles 'Capacity of teaching integrated for teachers of N^t schools: ndi chung, DH chO de sd phuc ndl ridng, v l ^ rdn luy^n TDTG khdng ehi mang lgl hidu qud DH, md edn gdp phdn phdt Irlln tu cho HS • chOng tdi, m | l sd W thiic PP sou GV e i n cung d p dio HS: - Nghldn et>u bdl todn, phdl hl|n nhihig d^c ihCi, ddu hl|u ridng bl|l cua bdi todn; - Phdn Hch bdi lodn d l hllu rd phdn gid Hull vd kit ludn; • Phdn Hch bdl todn ihdnh lung b$ phdn hodc ihdnh nhihig bdl lodn don gldn hem; - Di/ dodn bdng cdch phdn ehla thdnh cdc h-udng hgp Xem xdl cdc Irudng hgp (kit hgp vdl suy ludn) bfing cdch xdt ede hvdng hgp dOe bi^l, hrong h/, khdi qudt ; - Quy Ig v l quen; • Kilm h-a vd nghldn CIHJ Idi gldl, Hm cdch gldl hgp li hon, Tdi li$u tham khdo Alexeep M - Onhisuc V - Crugliac M - Zalwtin V Vecxcle X Phdt tri^n t v hoc sinh NXB Gido rffic H.I976 Nguyfin Bd Kim HQC tfp ho^t dOng vd hiaig h09t dOng- NXB Gido ditc, H.1999 Vuong Duong Minh Rin luyfn tu thu^t gldl cUa hoc sinli d^y hoc cdc hf th6ng s6 d trudng phS thdng Lu^n dn phd ti£n si Gido dgc hpc, Trudng Djii hpc suphjim Hd NOi, 1998 SUMARRY in teaching mathematics In senior high sc^wois in general ar)d teaching the subject of complex numcD hode thay d l l cdch nhln ddl vdl bdl todn; - Si) bers In particular can perform a number ofpedagogidgng kit qud hay cdch gldi ci3a bdl todn khde; ccri measiM-es, which contributes to the dev^opment of algorithm thhidng forstudents The tralnir)g of algo- D l xufil bdl todn mdl; rithm thinldng not only brings effective teaching and learning, but also contributes to the development of Trong DH lodn d hvdng h-ung hgc phd Hidng students' thinking Mi6c phge nhi/ng dllm chua hgp li cOa ldl gldl Tap chi filao due so (ki • 10/2012) ... Ti chuc tip hud''n cho GV T l chiJc tgp hud''n v l DHTH cho GV phd thdng vd sinh NHdn trudc dl ihye t$p su phgm Trong budc ndy chO y i u Id cho GV hiiu rd nhOng n§l dung cfin TH vd edeh khol thdc... thdnh ndng Igc DHTH cho G V , chung 161 dd t l ehue bidn sogn tdl ll^u hudng dfin DHTH d ede mdn Vit ll; Hod hgc; Sinh hgc; NgO vdn; Ljch su vd Dja If; Budc Ti chuc tip hud''n cho GV T l chiJc tgp... bde hoi Id: ±{l+l); Budc 4: Ket lu^n: PT dd bdl todn diu cho d dpng phuc tqp, gdy khd cho cd hal nghldm phdn bl^t z, = -I, Zj = 2+1) khdn cho HS qud trinh gldl Do dd, d l h) 2lz^-2{S-l)z-yl3-l