Tran Vi|t Cuong va Dtg Tap chl KHOA HOC & CONG NGHE 130(16) 45 50 TIEM NANG PHAT TRIEN T U DUY SANG TAG CHO HOC SINH TRUNG HOC PHO THONG QUA DAY HOC CHU DE NGUYEN HAM, TICH PHAN Tran Viet Cuong , Bui[.]
Tran Vi|t Cuong va Dtg Tap chl KHOA HOC & CONG NGHE 130(16): 45-50 T I E M NANG P H A T T R I E N T U DUY SANG TAG C H O H O C SINH TRUNG H O C PHO THONG QUA DAY H O C CHU DE NGUYEN H A M , T I C H PHAN Tran Viet Cuong , Bui Hai Linh Trif&ng Dgt lioc Sapliam - DH Tlwi Ngiiy T M TAT Chit de Nguyen ham, tich phan la mgt nhifng npi dung khd chuang trinh mdn loan d truong phd thong, nhien nd lai c6 tilm nang tdt dl cd thi khai thae nhim phat triln mot sd ylu to ciia tu sang tao (TDST) cho hgc sinh (HS) Bai bao chiing tdi phan tich tilm nang phat trien mpt sd yeu td TDST thdng qua day hpc chu dl Nguyen ham, tich phan cho HS phd thong Til' khda: nguyen ham, tich phdn lu sdng tgo, hpc sinh trung hoc thong TU DUY SANG TAO Sang tao la tao nhQ-ng gia tri mdi ve vat chat hoac tinh than, hay sang tao la tim cai mdi, each giai quyet mdi va khdng bj gd bd phu thugc vao cai da cd Tu sang tao (TDST) la nang luc tim thay nhung y nghTa mdi, nhifng mdi quan he mdi, la nang luc chii'a dyng sy kham pha, sy phat minh, sy ddi mdi, tri tudng tupng TDST bao gdm nam td: Tinh mem deo; Tinh nhuan nhuyen; Ti'nh ddc dao; Tinh hoan thien va Tinh nhay cam van de Trong cac td thi tinh mem deo, tinh nhuan nhuyen, tinh ddc dao la ba tinh chat ca ban cua TDST du, bieu thirc dudi ddu nguyen hdm cd - Tinh mem deo dugc dac trung bdi kha nang de dang chuyen tir hoat ddng tri tue sang hogt ddng tri tue khac - Tinh nhuan nhuyen dupc the hien d viec sii dung nhieu loai hinh tu da dgng viec phat hien va giai quyet van de, dai luong vi phdn xdx-—-d{9x —1) nhung HS se gap be tdc vi khdng bieu dien duac 3x theo t Trong tinh hudng dd, neu HS cd khd ndng TDST se nhanh chdng chuyen sang hogt ddng tu khdc bdng each nhgn - Tinh dgc dao dugc dac trung bdi kha nang tim kiem dugc kien thuc mdi chua biet, nhifng giai phap tdi uu TIEM NANG PHAT TRIEN M Q T SO YEU TO CUA TDST CHO HS THPT THONG QUA DAY HOC CHU DE NGUYEN HAM TICH PHAN Phat triln tinh mim deo cho HS Tinh mim deo ciia TDST duoc dac trung bdi mdt sd dgc dilm sau: Td 0978 626727 a) De dang chuyen tir hogt dong trt tue sang hogt ddng tri tue khac, van dung linh hogt cac thao tac phan tich, tdng hgp, so sanh, triru tugng hoa, khai quat boa, dac biet hoa va cac phuong phap suy luan nhu quy nap, dien dich, tuong ty Thi du 1: Tim nguyen ham cua ham so: 3x + ^J9x^-\ Nhieu HS dung trudc bdi todn ndy thudng ddt t - yj9x —\de tim nguyen hdm Mge moi quan he {3x j — 9x —\\ — \vdtu d& cd cdch giai nhic sau: Tacd ^-\-3i+V9x ck = ^x(ix-^9x^-l)(ix -1 Tacd/| = j3xVx = xVC, Tacd: Tran Viet Cudng vd Dtg Tap chi KHOA HOC & CONG NGHE I2 = jx^9x^-\dx^ ^ y 9x^-1 d{9x^-\) (9x^-1)2-hq Dat u - 2sint Ta cd du = 2costdt Khi do, ta CO , f Z cos tdt r , U^^Asin't Do dd, ta cd 1= L + L= — ( x ^ - ) -hx^ +C ' ^ 27 b) Suy nghT khdng rap khuon, khong ap dung mdt each may mdc nhung kinh nghiem, nhifng kien thiic, ky nang da cd vao hoan canh mdi dd cd nhieu yeu td da thay ddi, cd kha nang thoat khdi anh hudng kim ham ciia nhtfng kinh nghiem, nhtfng each suy nghT, nhu'ng phuong phap da cd tir trudc Thi du Tinh tich phan: , / - 130(16): 45-50 rcosx~smx \ I Q -v/3-sm2x , dx Khi gidi bdi todn ndy, nhieu HS theo kinh nghiem dd ddt / - V3 - sin 2x vd dd HS se gdp khd khdn la khdng tim duac dl Nhimg HS cd khd ndng TDST se cd cdch nhin nhdn khdc cu the a bdi ndy HS se nhgn (cosx- sin x)dx - d(s inx + cos x) vd do, suy duac u = s inx + cos x vd [ TT 12 c) Nhan nhu'ng van de mdi tKmg dieu kien quen thudc, nhin thay chiic nang mdi cita ddi tugng quen biet Thi du Tinh tfch phan: '-[ -dx sinx+ ^c v cosx Trong bdi todn nay, HS cd khd ndng TDST se de ddng nhgn dge diem eua phucmg trinh Asinx + Bcosx, tie de ddng bien doi bdi todn nhu sau Tacd ^=fsinx+ Sc c V J cosx , -dx 2> , ,1 sin(x+—) sinfxA—) -dx :f -(t\-cos^(x+-) V3 - sin 2x ^ ^4 - (1 -h sin 2x) Dat / = c o s ( j : + —) Suy ra, ta cd = 1^4 - (s mx-h cos x) Tir do, HS de ddng lim cdch gidi bdi todn ndy nhu sau: Dgt u = sinx+cosx Suy ra, ta du - (cosx - s inx) dx Tacd dt = - s i n ( j : + — ) d x cd ii:6'-\lh'^]' 3-2 sin X cosx = 4-(2 sin x cosx +1) = - ( I n | l - r | + lnll+/|) - 4-(^sinx + cosx) fl , ^ r f ^'^ Do do, ta CO y = , > / ^ 46 -ln3 Phat trien tinh nhuan nhuyen cho HS Tinh nhuIn nhuyen cCia TDST tni hien ro d hai dac trung sau day Tran Vi^t Cudng vd Dtg Tap chi KHOA HOC & CONG NGHE a) Tinh da dang ciia each xu' ly kbi giai toan, kha nang tim dupc nhilu giai phap tren nhilu gdc va tinh hudng khac Dung trudc mdt van de can giai quyet, ngudi cd kha nang TDST se nhanh chdng tim va de xuat dupc nhilu phuang an khac va tir dd tim dugc phuang an tdi uu s inxdx — sinx + cosx Thi du 4: Tinh tich phan I = Dat X = — — ? Do dd, ta CO t/x = -dt n sinx Do Do do, ta cd r sinx , "r cost dx= c ^ sin / -1- c o s / ^ sin X -I- cos X In dx • sinx-t-cosx 2/= f ^"^ cosx - sinx A+ f- ;;•"(linr-t-prRr Sin x-1-cosx ta c6 J'smx-Fcosx = [&== J cosx-sinx )dx cosx + sinx ^I I f£i(cosx-i-sinx) Vdi hudng giai bai toan tren ta cd the tinh dupc tich phan c6 dang tdng quat sau ^,Ml^ Vdi hudng giai bai toan tren ta c6 the tinh dugc tich phan co dang tdng quat sau: fA sin x-1-Bcosx , z (^x JiC sin x-hD cosx n{Csmx + Dcosxy dx C sinx-I-Z) cosx Mat khde, neu dua vdo moi quan he ciia cdc hdm so luang gidc sin vd eos vd can Idy tich phdn bdi todn ta thdy bdi todn tren lgi rai vdo dgng tich phdn dgc biet Tic do, ta co each gidi bdi todn tren nhu sau: =- r Vsin'^x nl inl m m "vsin X + \cos - —Fx - In (cos X + sin x) J /= CO S X f 2(siwc+cosx) dd, :h t = o — = sinx+cosx n Ta cd, vdi X = ta cd / = —; vdi x = — Qua quan sdt ehdng ta thdy, hdm sd du&i ddu tich phdn cd dang phdn thirc nen ta ed the bien ddi tir thirc de lim cdch viet duac qua mdu sd vd dgo hdm ciia mdu Tie dd, ta ed ldi gidi bdi todn nhu sau: Ta CO 130(16): 45-50 X Tuy nhien dimg tru&c bdi todn tieh phdn luang gidc, HS ciing cd the sir dung cdc phep bien ddi, cdc cdng thirc luang gidc de bien ddi cdc bieu thirc du&i ddu tich phdn ve cdc bieu ihicc m&i md viec tinh tich phdn duoc thudn lai Do dd, ta cd cdch gidi sau: Taco : sin x + - — : I ^ sin|x4 4 j _ i %/2sin x+- 4J ( A -cos X-H- I V2sin| x-i , 4J ^ - l-cotj? x+ A - ^l [4} 4) ( I'rr, - _ A -cot x + - Mat khdc, tic viec quan sdt bieu thue dicdi ddu lich phdn, HS di thdy biiu thuc dudi ddu tich phdn chi chira hai hdm sinx vd cosx Tir giup HS nghT din viec su dung phep dx 4j_ I ddt t = tan — de dai sd hod cdc bieu thuc cos X-I-' :^-if \dX lugng gidc Do do, la cd cdch gidi bdi todn tren nhu sau: X , 2dt Dat r = tan — Khi do, ta c6 ax = ^va \ + t^ 0J sin x + — xd sin x + ~ -l + l l ^ ^ "^ 1' sin I x+ — sinx= Ngodi ra, neu dua vdo mdi quan he giira dgng cua tir sd v&i dang eiia mdu sd eung nhu tinh chdt cua dgo hdm cua cdc hdm sd luang gidc thi se giup HS nghi den viee gidi bdi todn tren bdng each sir dung tich phdn lien kit Do dd, ta cd cdch gidi nhu sau: (3w - - ^ dx dv = -dxcos^x Mot HS thdng thuang gap bdi todn ndy se Ap dung edng thue lieh phdn timg phdn Tr§n Viet Cudng vd Dtg Tap chi KHOA HOC & CONG NGHE vd se di den mat lieh phdn phuc tgp Id r COSX—sifxc /=tanxln(sinx-i-cosx)| -Jtanx— d>c sinx + CC6X Mot HS cd khd ndng TDST se nhin nhung mdi lien he giiia cde dgi lugng COSX sinx-f-COSX Tic do, ddn tdi cdch gidi sau • cosx sinx + cosx Dat V - tanx + I ^ - I = [tanx + l)\risinK + cosx) = 2biv2 - ( x + ln|caEc|) 'COSX-Sinx dx 130(16): 45-50 KET LUAN Cac ySu to co ban ciia TDST neu tren biSu hien kha ro d HS, dac biet la d HS kha, gidi Trong hoc tSp toan ma cu thg la hoat dgng giai toan Nguyen hatn, tich phan, neu ngudi GV biet quan tam va xay dung dugc he thong cac vi du va bai tap tot thi hoan toan cd the ren luyen va phat trien mpt so dac trung ciia TDST cho HS TAI LIEU THAM KHAO 1, Nguyin Ba Kim (2005), Phuang phap day hoc mon toin, Nxb Dai hoc Su pham 2, TrSn Thuc Trinh (2003), Tap bat giang Ren tuyen lu irong dgy hoc Todn 3, G Polia (1975), Sdng tgo Todn hoc, Nxb Giao due — +-In2 SUMMARY THE POTENTIAL TO DEVELOP SOME ELEMENTS OF CREATIVE THINKING FOR HIGH SCHOOL STUDENTS THROUGH TEACHING TOPIC PRIMITIVES AND INTEGRALS Tran Viet Cuong', Bui Hai Linh College of Education - TNU Topic primitives and Integral is one of the difficult content in math programs in high school, but it has good potential to be exploited to develop some elements of creative thinking for students In this article, we analyze the potential for some elements of creative thinking through teaching topic primitives and integrals for high school students These are fexibility, fluency, originality Keywords: topic primitives, integrals, creative thinking, high school students Ngdy nhdn bdi:01/l 1/2014: Ngdy phan bien-17/11/2014: Ngay duyet ddng: 25/12/2014 Phan bien klioa hoc: TS Nguyen Danh Nam - Truang Dai hgc Supham - DHTN Tei 0978 626727 50 ... vdi X = ta cd / = —; vdi x = — Qua quan sdt ehdng ta thdy, hdm sd du&i ddu tich phdn cd dang phdn thirc nen ta ed the bien ddi tir thirc de lim cdch viet duac qua mdu sd vd dgo hdm ciia mdu Tie... tich phan, neu ngudi GV biet quan tam va xay dung dugc he thong cac vi du va bai tap tot thi hoan toan cd the ren luyen va phat trien mpt so dac trung ciia TDST cho HS TAI LIEU THAM KHAO 1, Nguyin... f ^''^ Do do, ta CO y = , > / ^ 46 -ln3 Phat trien tinh nhuan nhuyen cho HS Tinh nhuIn nhuyen cCia TDST tni hien ro d hai dac trung sau day Tran Vi^t Cudng vd Dtg Tap chi KHOA HOC & CONG NGHE