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JOURNAL o r SCIHNCi; OF IINUI ; 2012, Vol 57, No, 10, pp 26 32 MOI SO DINH H U d N G TRONG VIKC DAY HOC TIM TOI , KHAM PHA KIKN THlJC GIAI ITCH CHO HOC SINH TRUNG HOC PHO THONG CHUYEN P h a m Sy N a m[.]
JOURNAL o r SCIHNCi; OF IINUI-; 2012, Vol 57, No, 10, pp 26-32 M O I SO DINH H U d N G TRONG VIKC DAY H O C T I M T O I , KHAM PHA KIKN THlJC GIAI ITCH C H O H O C SINH TRUNG H O C P H O T H O N G CHUYEN Pham Sy N a m Truifng THPT ehuyen Phan Bf)i Chdu Nghe An li-mail: pbamsynampbc@gmail.com Tom Int Vice to chflc day bpc ibco hUdng lim toi, kbiim pba kien thflc cbo hpc sinb (US) Trung hpc Phd tbdng {Tl IFI) chuyen la dicu can ibi^l - bdi ciicb lam mang muc dich kep vfla hinh ihanh cho IIS each lU bpc vfla giiip HS phat buy von kicn tbflc kinh nghiem de kidn tao, phal tnen kien tbflc cho ban than Cach lam sc giiip HS chiem linh dUdc kicn Ihflc nhieu bdn Bai viet tac gia de xual mpt so dinh hUdng viec day hoc lim ldi, kham pha kien thflc Giai U'ch cbo HS THPT chuyen nham muc dich nang can hieu qua irong day hpc Tifkhda: Day hpc kien lao, day hpc kbam pba, day hoc Giai tich Dat van de Day bpc lim tdi kham pba la mpl phfldng pbap day bpc dd boat dpng hpc dfldc cau true dc khuyen kbich ngfldi hpc hpc cho chinh minh, de hpc, dflcJc hpc va dflpc kbam pha Trong each day bpc nay, tim tdi la dfldng, la tien trinh kbam pba la diem den, la ket qua Vl vay, viec to chflc day hc>c theo hfldng tim toi, kham pba kiln thflc cho HS THPT chuyen la dilu can thiet - bdi each lam mang muc dfch kep vfla blnb cbo HS each lfl hpc, vfla giup HS pbat buy von kien tbflc, kinh ngbiem de kien tao, phat trien kicn tbflc cbo ban than 2.L Noi dung nghien cihi Cd sd ly thuyet hinh each tiep can tim toi kham pha Trfldc bet, viec bpc cua moi ca nhan HS la trung tam cua tien trinh day hpc, ma viae bpc 4y cbi Ibflc sfl diln moi HS la nhOUg thflc the boat dpng kiln tao bdn la thu dpng Ndi each khac If tbuylt kien lao la mdt nhiJng cd sd If thuyet cua each day bpc theo bfldng tim toi, kbam pba Lf tbuylt kien tao khuyen khich HS tif xay dflng kien thflc cbo ban than minb dfla trfin nbu:ng thflc nghiem ca nhan va ap dung trflc tiep vao moi trfldng hpc tap cua cac em Li thuyet kiln tao nh5n manh vai trd chu dpng ciia ngfldi hpc Mdi trUdng hpc tap vdi 26 Mt)l sd tiinh hifdng viec dgy hgc tim tdi khdm phd kiin thdc nhilu loai tien i'ch cua cdng nghe thdng tin cho phep HS dfldc kham pha va lim kiim tbdng tin, tao cac lien kel va kiln tao tri tbflc Trilt gia, nba giao due bang dau cfla My, Mortimer J Adlcr, da khang dinb sfl hoc chan chinb xuat pbat lfl sfl phat trie'n cua tam tri, chfl khdng pbai la sU hinb ky flc Su: bpc chan chinb bao gom sfl tbu nhap kien tbflc va thau bieu, chfl khdng pbai chi la chSp nban nbflng y kien dUdc quy pham san Chinh sfl thau bieu vc kiln tbflc mdi dem lai cbo ngfldi hpc nhflng y nghia kiln tbflc dd Tfl dd, nhan dfldc vai trd, nhflng flng dung cfla kiln tbflc npi bd loan hpc va thflc liln 2.2 Cac hvtdc to chiic thtfc hien 2.2.1 Birdc I: Chuan bi - GV xac djnh npi dung kiln thflc cd the to chflc cbo HS kbam pba, - GV xac djnh nhflng dinh bfldng kham pba 2.2.2 Bufdc 2: To chu-c thu'c hien - GV dfla vSn de va giao nhiem vu kham pha Hpc sinb tilp nhan nhiem vu - Hpc sinh tim kiem, kham pha (Neu HS khdng giai quyll dupc nhiem vu, GV gdi y bfldng dSn bay ndi each khac HS kbam pha dudi sfl hudng dUn va dieu khien cua GV) - Hpc sinh bao cao ket qua trfldc ldp, cd sfl cbSt van va ihao luan cua ca ldp - Phan ti'ch va danh gia kll qua (HS tfl danh gia, GV danh gia) - Kit luan ve kiln thflc mdi Cd the md la qua trinb bSng sd dd sau (Hinh 1): Xac dinh iii3i dung kien thitc CO the kham pha GV Mic dinh cdc djnh hirumg khdm pha - GV giao nhi^m vu - HS tit lim each giai quyi-t H } kilting tir i quyel diKfc O V g c r i y , hiitmg diin Hinh So qud trinh khdm phd 2.3 Mot so dinh htfdng viec tiep can day hoc tim.toi, kham pha Paul Ernest cho r^ng "Cdc kiin thdc khdch quan dupc xdc dinh ddng nhdt vdi mgt tap hgp cdc menh de (MD) vd phdt bieu, dd la phdn cot yiu cua cua kiin thdc dupc diin dgt bang ngon ngU" [3;50] Tfl dSy, de binh kien thflc mdi, chung tdi xac dinh hai bfldng tac dpng: 27 Pbam Sy Nam 2.3.1 Hirdng thiJ nhat: Tit MD diing da cd kien tao MD mdi bang each siV dung cac phep loan lao Ml) (')( Sd cua lurdng tiic ddng: Kicn tbflc dfldc xac dinh bdi tap hdp cac MD, do dc kicn iLU) kicn ibflc mdi, la co (be kicn lao cac MD mdi tfl MD da cbo De giup HS tim ldi khiim pha ibco y ifldng chiing ldi thifc hien ihco cac dinh hfldng sau: Dinb bift'fng I: Xac dinh "nghia cua kien thflc" tfl dd kiln lao phfldng phap, kien tbflc mdi Dc binh thimh "ngbTa cua kicn ihflc" Irong day hpc, dicu quan trpng nhat la phai lam cho mdi hi ihflc difdc ngifiii hoc licp ibu phai co mdl "ngbia kicn thflc" nbfl Ihl nao dii doi \iii hn Chflc nang guio due ciia day hpc dfldc tbflc bicn cbinb irong qua trinh "Ngbia kicn thflc" chi cd ibc dfldc binb tbanb irong qua irinb boat dpng cua HS, thong qua hoat ddng ciia HS, thdng qua vice nban vai trd ciia kiln thflc dd, Cung tfldng lfl nhfl doc mdl quyen sach, ciu hay ciia quyen sach dfldc cam nhan bdi ngfldi dpc va cam nhan cua mdi ngfldi vc cai hay cua quyen sdch cd the theo nhflng khia canh khac Co the md la qua irinh kicn tao kiln tbflc theo hinh Ibflc nhfl sau Kien thiic viTa hoc > "Nghia cua kicn thu'c" -¥ Van dung -> kien tao kien thu'c nidi Vidu; To chflc day hpc lim tdi, kham pha kien lao kiln Ibflc mdi, pbfldng phap mdi lfl djnh nghia dao ham tai mdl dicm Trd giiip ciia GV (neu cdn): - Cd the sfl dung cdng thflc lin M^iifHl = /'(.,,, dc gial nhiing bai toan gi? (tinh gidi han dang liin,_,^„ i^—^—/i£ol j •'' " ^ GV dat van de yen cSu HS van diing phUdng phap vira tim diJdc de tinh gi6i han ham s6 dang '-"•K !i[x} - a(.To) lira /(.r) = /(.;•„) lira 9{') = 'j(xo) thong qua viec thUc hien hoal dong, de HS phat hien kel qua liin /t'^) - /fa) = Z M " r a g{x) - g{xa) g'(xo) it 28 j'(io) M()t sd dinh hifdng irong viec dgy hgc tim ldi kluim phd kiin ihue Nlu xet trfldng bdp dac biel /(:':n)-.fy(.rn)=-n thi kll qua tren cbinb la ndi dung quy tac L'hospitalc Day la mdt quy lac khfl dang vd dinh - vki hieu qua Bang viec sfl dung dinh nghia dao ham HS cd the giai nhicu bai loan kbd ma kbdng ckn phai sfl dung nhieu ki thuat biln doi nhfl cac phfldng phap khac Chang ban: Tinh cac gidi han: /i - Hill — i->i r^ - , , -• x / n S/3.r + N - r — sin.r Xuat phat tfl quan niem "cac kicn thu'c khach quan dirpc xac djnh dong nhat vdi mot tap hpp cac menh dc va phat bieu" ta cd mot djnh hfldng mdi dc phal trien kiln tbflc Dinh hUt'fng 2: Tien banh phat trien menh de Dc phat trien menh dl chung ta sfl dung cac each lao menh d l nhfl: sfl dung cac phep keo iheo, phep bpi, phep luyen, phep tfldng dfldng, phep phu djnh, Vi du: Ngi dung lua elmn dikhdm phd: Tim tdi, kham pba kicn thflc mdi tfl djnh nghia gidi han hflu han cua bam so tai mdt diem: "Hdm sdf(x) cd gidi hgn L x ddn tt'fi i-Q neu vdi mgi ddy (.r„) tien tdi TQ thi / ( T „ ) tiin tdi L" Trp gidp cua GV (niu cdn): Neu xem menh de A la "Hdm sd ed git'fi hgn L X ddn tdi xo ", menh di B la "vdi mgi ddy (.r„) tiin ldi TQ thi f{xn) tiin tdi L", cd the diln dat djnh ngbia tren dfldi dang MD la "A =j> B" Van dung cac each tao MD mdi tfl MD tren? GV gdi y tiep neu HS khdng thflc hien dfldc yeu cau tren: Cd nban xet gi vl MD "A => B" \a" B => A "? Diln dat menh d& B dfldi dang ki hieu? Xac dinh menh d l Bl Ket qua 1: Niu tdn tgi ddy {x„) ddn tt'fi TQ md ,f{Xn)) khdng ddn tdi L tbi hdm sd f(x) khdng cd gidi hgn L Trp giiip cua GV (neu cdn): Co nhan xet gi ve gidi ban eua bam so f(x) kbi x dan ldi XQ neu liin(T„) = TQ, lim(,74) = :r,o ma lim.f{x'^) i- lvmf{x,j))l Ket qua 2: "Niu Hm./„ = T:o,lim.x' ~ Xo md lim/{.r„) ^ lim/(a;',) tbi hdm sd f(x) khdng cd git'fi hgn tgi x = xo "• Djnh hudng 3: Tim mdi lien he giua cdc kien thifc da dutfc hgc Tif mdi liin hi gida cdc kiin thdc cho phep chung la cd dupc nhu'ng su diin dgt mdi vi mpt kiin thdc, ddy Id eg sd di'kiin tgo nen kiin thdc mdi Vi du: Ngi dung lua chpn di'khdm phd: Tim moi lien h$ gifla cac khai niem dao ham, ham so liBn tuc, gidi han bam sd, gidi han day tren cd sd dd kiln tao kiln tbflc mdi Ket qua: "Ham soy = f{x) co dao bam tai J; — a 29 Ph.im ,Sy Nam -> Hiim so y = ,/'(.':) lion tuc tai x - a =!• l i l i / { ' ã ) /(ô) => moi day so i „ > it ihl Imi / (' „)) - /('.)" TO chuoi suy luan tren ta ciVHdin so v = fix) lien liic tai x = a => mpi day so x > a Ihi liiH ,/(.:ã) /(ô)" Ket quii niiy lil cd sS chuyen qua gidi han ctia cac ham so lien luc Van dung kcl qua nuii niiy giiip ta giai quyet dUrtc mpt so van de lien quan d^n hiim HO lien tuc Chiing han: Ilai loan 1; n m lal ca ciic hiim so lien luc f : It > R thoa man /(.r^) • /(r) = 1).V.7'C H Vice chuyen qua guli han ciia hiim so lien tiic lii cd sd cho nhiing phep bien doi sau: VdiO ^ X < I thi/(,) /(,(•') = ,/•(:'") do lim/( :) - lim/( •') = lim/(j:-'") = /(O) Vdi.r § Ihi /(.r) /(,rl) f{T'f' dodo lim ,/(.) = liiii/(.i-3*') = /(lim.ri'') = /{!)• Day la nhflng dicm mau chol dc cd dfldc ldi giai bai loan 2.3.2 Hu'dng thiir hai: Chuyen djch ngon ngir Cd sd Clia hUdng tdc dgng: Tbeo Paul Ernest "Phdn ctil yiu eua kien thdc dupc dien dat hdng ngdn ngu" Dilu cd nghla la viec bieu nhflng kien thflc dd phu thupc cbu yeu vao kha nang ngdn ngfl cung nbfl pbSn ldn boat dpng xa hpi va nban thflc cua ngfldi Mat kbac ngdn ngfl la mdt kien tao xa bpi VI vay de pbat trien, hieu kiln thflc cd the xuSt phal tfl ngdn ngfl, quan tam den nhflng biln doi ngon ngfl va co the kien tao kiln thflc mdi xuat phat tfl ngdn ngfl De lim tdi, kham pha mpt kiln thflc theo dinh hfldng cd the; Kham pha trflc lilp, hoac gian tiep Kham pha true tiep: dUdc liln hanh bang each: Tfl kiln thflc da bill, bang cac dicb cbuyen ngon ngfl de tbu nban kiln tbflc mdi Kham pha gian tiep: Ddi vdi cac kbai niem lien quan din ham so, gia mang kien thflc cua nd la thj bam so Hinh Vi tri tiep tuyen d tai cUc tri Vl vay, co the to chflc cho HS pbat hien cac kiln tbflc mdi lien quan den ham so tfl thj cua no Vl du: CV giao nhiem vu: Quan sat hinh anh thi va nhan xet vl vi tri tfldng doi cua dfldng ibSng d la tiep tuyin cua ihi tai diem eflc tri va dd thi ham so f{x) tren cd sd dd kbam pha nbflng kiln thflc mdi (Hinh 2) Can lflu y ring, tfl nhiing nhan djnh ma HS quan sat dfldc GV t6 chflc cbo HS thao luan, cbflng minb, nhflng kit qua kham pha dflpc la nhflng kit qua da dfldc chflng minh chat che Tra giup cua GV (niu cdn): i: 30 Mdl sd dinh hifdng irong viec dgy Iwe lim tdi khdm phd kiin thu'c Nban xet ve vj trf tfldng ddi ciia dfldng thang d va dd thj dfldng thang d va true hoanh? He s6 gdc cua dfldng thang d? Thflc hien chuyen nhflng kll qua quan sal dfldc lfl "ngdn ngii thi" sang, "ngdn ngii bdm sii" Ket qua 1: Nlu bam sd dat cifc trj tai ,r = ti va bam so cd dao ham tai / - a Ibl f'[a) = bay lilp tuyin tai dil'm eflc in cua thi ham sd sc cd phfldng trinh y = f{a.) Trfldng hdp true boanb tilp xuc dd ibj ta cd kit qua: Ket qua 2: Dilu kien dc true hoanh liep xuc vdi ihi lai dicm cd hoanh dp./ - a /(«) = ij{x) = Dieu kien cd hoanh a Ibda man cung cd ngbia he I'M = a cd ngbiem Kiem tra dieu ngfldc lai cung dung Tfl day, la cd kit qua: \/'(.T) = Ket qua 3: Dd thi bam so y im = /{,/•) tilp xuc vdi true boanb va chi kbi cd ngbiem Bang each xel h{x) qua mdi: ^ fix) • g{x) va cbu y b'{.T.) = /'(x) - g'{.r) cbung ta cd kll Ket qua 4: Hai tbi y = (fix) = 9(.T) \f'(x) = g'(.r) g{.x) tilp xuc kbi va cbi kbi be f{x).y cd nghiem GV dich chuyin dudng thdng d cbo khdng vudng gdc vdi true tung vd yiu cdu HS tiip tuc quan sdt (Hinh 3) Xel thi bam soy = /(a.) ldi tren (c; b), ta thky "tiip luyin lgi diiin cd hodnh dda & {c; b) luon ndm phia trin thj" cd nghla la xet cung boanb dp tbi "tung dp cua diem tren liip tuyin ludn ldn htfn hoac bang tung cua diem tren thi", ma tung dp cua diem tren dd tbi cbinb la f{x), tung dp cua diem tren tilp tuyen cd hoanh dp x la f'{a)[x ~a) + f[a) bay ta cd bat dang tbflc j{x) ^ f'{a){x ~a) + / ( a ) , Vx e (c; b) dau dang ±flc xay kbi x = a fj^^f^ ^ y^^-^^^ ^^^ ^ ^ x ^ ^ ' « ' ' ' ' « ' « co hodnh dp bang a Dilu kien "tiep tuyen tai diem co hoanh a luon nam phia tren thi (c; b) cung cd the tbay b§ng "do thi /{3')loi tren (c; 6) Nhfl vSy ta cd kit qua: Ket qua 5: Nlu d6 t b i / ( x ) loi tren (c; 6) t h i / ( T ) ^ / ' ( a ) ( T - a ) + / ( a ) , V.T e {c;b) Ket qua la cd s d d e H S kiln tao dfldc rat nhilu bat dang thflc mdi, chang ban, xet bam so f{x) = \n{X'\-y/x'^ + 1) tren (0; +oo) Ta co tilp tuyen eua thj bam soy = f{x) tai diem co hoanh dox ~ -Iky = -a;+ln -" ; fix) = ~ < 0, Va: > I*li;in Sy N a m (I nen thi ham so loi Iron (0; I oo) Do la co: Bai loan: Chiing minh rang l.i{,i: I- /iM~T) < -x I In ^ Vf > Bang each lint Ircn HS cci the sang lao diidc rat nhicu bat diing thiJc khac dong thdi each liim dd cung cung cap cho HS miit phiidng phap dc chiing minh bai diing thilc Ket luan Vice td chiic day hoc ihcn hadng tin toi, kham pha tao dicu kicn phat huy t6i da von kic thiic, ti'tii nghiei sii siing lao d HS, HS thu nhan diidc kicn thiic nhicu hdn dong thdi ciing hinh Ihiinh d HS each ihilc de id hoc.TOynhicn, dc thllc hicn vice day hoe thiinh cdng thi vai trd ciia ngiidi CJV cOng khdng nhd, GV phai cd sil tim toi, kham pha kien thllc dc xac dinh diidc nhiing noi dung cd the kham pha diidc, nhiing dtidng co Ihc kic-n lao kicn thilc mdi, GV cd dinh hiidng giiip HS chiing minh nhiing ket qua thu dUdc tii khiim pha la diing, hoac cd nhiing phan vi du dc giiip HS nhan diidc nhiing nhan dinh sai, ben canh dd GV cung phai la ngiidi rat hicu HS, hicu nang llic ciia HS de diia nhiing v5n d6 phu hdp, cd nhiing hiidng dan, gdi y phu hdp de kich thich sU tfch Clic hoc tap cda HS, khai thac tdi da sii sang tao cda HS TAI LIKU THAM KHAO 11 ] Doan Quynh (chii bicn), 2010 Tdi lieu gido khoa chuye'n lodn Dai so vd Ciai ti'ch II, Nxb Giao due Ha Npi |2J Doan Quynh (tdng chu bicn), 2009 Gidi tich 12 ndng cao Nxb Giao due Ha Noi [3] Paul l-rncst, i99] The Philosophy of Mathematics Education.The t'ltlmet Press ABSTRACT Enhanced teaching to enhance analysis and information acquisition among gifted high school students The manner of teaching which encourages student research and the personal discovery of information among specialized high school students is very important This approach has a double purpose in that it helps students learn on their own and encourages them to acquire more information and experience Using this approach, students can creative work and gain information by themselves Moreover, this approach will help students learn more than ever In this article the author suggests enhancing ways of teaching that could result in increased research and discovery in the area of mathematical analysis among students enrolled in gifted high schools 32 ... nhiem vu - Hpc sinh tim kiem, kham pha (Neu HS khdng giai quyll dupc nhiem vu, GV gdi y bfldng dSn bay ndi each khac HS kbam pha dudi sfl hudng dUn va dieu khien cua GV) - Hpc sinh bao cao ket... acquisition among gifted high school students The manner of teaching which encourages student research and the personal discovery of information among specialized high school students is very important... So qud trinh khdm phd 2.3 Mot so dinh htfdng viec tiep can day hoc tim.toi, kham pha Paul Ernest cho r^ng "Cdc kiin thdc khdch quan dupc xdc dinh ddng nhdt vdi mgt tap hgp cdc menh de (MD) vd phdt